[handbook of magnetic materials] volume 21 || nanocrystalline soft magnetic alloys two decades of...

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Nanocrystalline Soft Magnetic Alloys

Two Decades of Progress

Matthew A. Willard1,2 and Maria Daniil3

Contents

1. In

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troduction

Magnetic Materials, Volume 21 # 2013

2719, http://dx.doi.org/10.1016/B978-0-444-59593-5.00004-0 All rig

al Research Laboratory, Magnetic Materials and Nanostructures Section, Washingtona, USAartment of Materials Science and Engineering, Case Western Reserve University, Clev

ent of Physics, George Washington University, Washington, District of Columbia, U

Else

hts

, D

elan

SA

177

1
.1. H istorical perspective 178
1
.2. T echnical considerations 181
1
.3. A pplications 187
2. A
lloy Processing 191
2
.1. R apid solidification 192
2
.2. A nnealing procedures 197
2
.3. C ore fabrication 212
2
.4. O ther processing methods 213
3. A
lloy Design Considerations 215
3
.1. G lass forming and primary crystallization 217
3
.2. M icrostructural and microstructure evolution considerations 218
3
.3. In trinsic property considerations 225
3
.4. D omain structure considerations 228
4. P
hase Transformations, Kinetics, and Thermodynamics 229
4
.1. T hermal analysis techniques 229
4
.2. P rimary and secondary crystallization 231
4
.3. C rystallization kinetics and phase stability 237
4
.4. O rder–disorder transformations 248
5. S
tructural and Microstructural Characterization 250
5
.1. C rystal structure and phase identification 251
5
.2. M icrostructure and phase distribution 256
5
.3. M agnetic domains and characteristic magnetic lengths 259
6. M
agnetic Property Characterization 265
6
.1. M agnetic moments and saturation magnetization 266
6
.2. T emperature dependence of magnetization and Curie
temperatures
269
vier B.V.

reserved.

istrict of

d, Ohio,

173

http://dx.doi.org/10.1016/B978-0-444-59593-5.00004-0

174 Matthew A. Willard and Maria Daniil

6
.3. M agnetic anisotropy and magnetostriction 278
6
.4. E xchange interactions and interphase coupling 295
6
.5. S tatic hysteresis and AC core losses 302
6
.6. M agnetocaloric effect 304
6
.7. G iant magnetoimpedance 306
7. O
ther Physical Properties 308
7
.1. M echanical and magnetoelastic properties 308
7
.2. E lectrochemistry and oxidation 312
7
.3. R esistivity and magnetoresistance 313
8. C
onclusions 314
Ack
nowledgments 315
Refe
rences 315
Abbreviations

ac
dimensionless pre-factor for coercivity calculation ai direction cosines (where i¼1, 2, 3) am dimensionless pre-factor for permeability calculation a lattice constant (A) A angstrom (10�10 m) Acr, Aam exchange stiffnesses of crystalline and amorphous
phases (J/m)
A, Aex exchange stiffness (J/m) Aeff effective exchange stiffness (J/m) A1 Strukturbericht notation for face-centered cubic
(FCC)
A2 Strukturbericht notation for body-centered cubic
(BCC)
b critical exponent for magnetization approaching TC
b
shape factor B magnetic induction (T) B2 Strukturbericht notation for a BCC derivative phase
with prototype CsCl
BCC body-centered cubic w susceptibility (various units) C Curie constant (1/K) Cn number of contact atoms for heterogeneous nucle-
ation (atoms/m3)
dB Bloch wall width (m) dm skin depth (m) dV/V fractional change in volume of a magnetostrictive
material

Nanocrystalline Soft Magnetic Alloys 175

d‘=‘
fractional change in length of a magnetostrictivematerial
DE
change in elastic modulus with applied field (Pa) DG* nucleation activation energy barrier (J/mol) DGv driving force for nucleation (J/mol) DSM magnetic contribution to the entropy under an
applied magnetic field
DT temperature change (K) d Ribbon thickness (m) eD diffusion coefficient (m2/s) D grain diameter (m) DSC differential scanning calorimetry DTA differential thermal analysis D03 Strukturbericht notation for a BCC derivative phase
with prototype BiF3
ddw domain width (m) E elastic modulus (Pa) EA activation energy (J/mol or eV/atom) EKu
or EK
magnetocrystalline anisotropy energy density (J/m3) Es shape anisotropy energy density (J/m3) ef strain-at-fracture Emin lowest value of elastic modulus at a constant field (Pa) ETM early transition metals f heating rate (K/s) f, o switching frequency (Hz) fA,B atomic scattering factor for atoms of type A or B fn frequency factor for nucleation (1/s) F fundamental reflection Fhkl structure factor for the hkl Bragg reflection FCC face-centered cubic gs–l solid–liquid interfacial energy (J/m2) gw domain wall energy (J/m2) H magnetic field strength (A/m) Happ applied magnetic field (A/m) Hc coercivity (A/m) HCP hexagonal close packed HDC direct current bias field (A/m) Hex Heisenberg exchange Hamiltonian HK anisotropy field (A/m) HV Vickers hardness I current (A) Jij exchange energy (J) k reaction rate constant kB Boltzmann’s constant (1.38�10�23 J/K)


km
magnetomechanical coupling coefficient k0 reaction rate coefficient K1 first magnetocrystalline anisotropy constant (J/m3) Ks stress-induced anisotropy constant (J/m3) hKi effective magnetic anisotropy (J/m3) Ku1,2 first and second uniaxial magnetocrystalline anisotropy
constants (J/m3)
Ku or Kind induced anisotropy constants (J/m3) k normalized anisotropy parameter l magnetostrictive coefficient (ppm) lw Weiss mean field coefficient lsam magnetostrictive coefficient of the amorphous phase
lscr
magnetostrictive coefficient of the crystalline phase
lseff
effective magnetostrictive coefficient of the
nanocomposite material
lssurf interfacial contributions to magnetostrictive
coefficient
L intergranular amorphous phase thickness (m) Lex magnetic exchange correlation length (m) L spatial wavelength number L0 natural exchange correlation length (m) LTM late transition metals m permeability (kg m/(A2 s2)) mA atomic moment (A m2 or J/T) m0 permeability of free space (4p�10�7 kg m/(A2 s2)) mr relative permeability (unit less) ms, mt permeability for mechanically fixed and freely vibrat-
ing samples
M magnetization (A/m) Mr remanence or remanent magnetization (A/m) Ms saturation magnetization (A/m) MTM Magnetic transition metals n Avrami exponent N number of grains N nucleation rate (nuclei/m3 s) Na,b demagnetization factors Nv number of moments per unit volume (1/m3) Oi volume of the ith phase (m3) j geometric/statistical parameter j0 spin rotation angle (�) re electrical resistivity (mO cm) re0 electrical resistivity with zero applied field (mO cm) Pcv volume normalized core loss (W/m3) PTM metalloid or post-transition metal R ideal gas constant (8.3145 J/(K mol))


Rm
magnetoresistance (O) s stress (Pa) sy yield stress (Pa) sc Coble creep stress (Pa) S total spin angular momentum S1, S2 superlattice reflections y,c angles (degrees) t time (s) t0 onset time (s) T temperature (K) TTT time–temperature transformation Tann annealing temperature (K) TC Curie temperature (K) TC
am
Curie temperature of the amorphous phase (K) TC
x
Curie temperature of the crystalline phase (K) Tg glass transition temperature (K) Tmelt alloy melt temperature (K) Tp peak crystallization temperature Tx crystallization temperature (K) Tx1 primary crystallization temperature (K) Tx2 secondary crystallization temperature (K) Tx3 tertiary crystallization temperature (K) tR relaxation time (s) tq quench time (s) u frequency factor for constant heating rate kinetics
(1/Ks)
vi volume fraction of ith phase Vex exchange coupled volume (m3) X volume fraction transformed Xm magnetoreactance (O) z number of near neighbor moments Z impedance (O) Zm magnetoimpedance (O)
1. Introduction

Revolutionary steps in materials development usually accompany thediscovery of new compounds, microstructures, or processing techniquesthat provide improved properties. These types of advances allow a greaterflexibility in device design and sometimes enable completely new types ofdevices to be produced. This has been specifically true for permanentmagnet materials, which show significant jumps in energy storage whennew, high-anisotropy compounds are discovered. Similarly, this has


recently been the case in soft magnetic materials where new, nanocrystallinemicrostructures have enabled smaller, lighter, and more efficient materialsfor power generation, conversion, and conditioning applications.

This advancement in the field of soft magnetic materials has its beginningsin the development of magnetic amorphous alloys. During the 1970s, amor-phous magnets provided a new class of low loss materials with anisotropiesmuch lower than crystalline alloys due to their absence of long-range atomicorder. Crystallization of these materials resulted in large anisotropies thatdegraded the magnetic properties as the newly formed grains rapidly grewto micron-sized crystallites, leading to the notion that crystallization ofamorphous precursors should be avoided. It was for this reason that thedevelopment of a partially devitrified material with exceptional magneticsoftness has created a significant stir in the soft magnetic materials community.Since the first report of this class of nanocrystalline alloys in 1988 by Yoshizawaet al. (1988a), the field has grown rapidly with authors reporting from aroundthe world, providing intuition-building knowledge and successful new alloys.

By definition, nanocrystalline materials consist of single or multiphasepolycrystals with grain diameters less than 50 nm. Materials of this type canbe synthesized by many techniques, including but not limited to: compactednanoparticles (e.g., chemically synthesized, plasma torch synthesized,mechanically alloyed, etc.), thin film deposition techniques (e.g., sputtering,pulsed laser deposited, etc.), and devitrified metallic glasses (e.g., splat quench-ing, melt spinning, etc.) (Wilde, 2006; Willard et al., 2004). This chapterfocuses on nanocrystalline alloys produced by a combination of rapid quenchsynthesis and isothermal annealing.While there has been considerable activityin the areas of nanocrystalline soft magnetic alloy wires (Barariu and Chiriac,1999; Li et al., 2003, 2005; Neagu et al., 2001), thin films (Baraskar et al.,2007; Goscia�nska et al., 1994, 2002; Joshi et al., 2006; Li et al., 2004;Nakamura et al., 1994), and powders (Giri et al., 1996; Ji et al., 2001; Xuet al., 2000), we will limit our discussion to rapidly solidified ribbons (pleasesee cited references for select studies on these topics). It is hoped that thisreview compliments some previous reviews (Hernando et al., 2004; Lopezet al., 2005; McHenry and Laughlin, 2000) focused on specific alloys, updatesome of the more comprehensive reviews of this field (De Graef andMcHenry, 2007; Herzer, 1997; McHenry et al., 1999) and act as a educa-tional resource to compliment materials and physics textbooks (De Graef andMcHenry, 2007; OHandley, 2000).

1.1. Historical perspective

Throughout the 1980s, research efforts to improve the high-frequencyperformance of Fe-based amorphous alloys were conducted in an effort toreplace Co-based amorphous alloys in saturable core reactors, choke coils,and transformers (Kataoka et al., 1989). The Co-based alloys were betterperforming than Fe-based alloys but suffered from lower saturation


magnetizations and higher material costs. The lack of long-range periodicorder in both types of amorphous alloys reduced the magnetocrystallineanisotropy (K1) and enhanced resistivity, giving them an advantage overconventional soft magnetic materials (i.e., ferrites, Si-steels, permalloys,etc.), which relied on large grains to provide the minimum coercivity.And while Fe-based alloys solved the short-comings of Co-based alloys,they suffered from large magnetostrictive coefficients (l) (Yoshizawa andYamauchi, 1990), which increased in value with the square of their mag-netization, ultimately resulting in poor performance at high switchingfrequencies. Annealing procedures were used to reduce the residual stressin the alloys, and partial crystallization was found to increase the coercivitysubstantially. For this reason, crystallization was largely avoided.

Nanocrystalline soft magnetic alloys were first demonstrated byYoshizawa,Oguma, and Yamauchi in 1988 (Yoshizawa et al., 1988a). The Fe–Si–B–Nb–Cu alloy they described (which they namedFinemet)was truly remarkable dueto its nanocomposite microstructure (i.e., Fe–Si crystallites within a residualamorphous matrix) produced in a bulk ribbon form. The combination of largemagnetization and low magnetostrictive coefficient in a Fe-based alloyprovided an exciting advance for the field of soft magnetic alloys. And despitethe formation of crystallites in the alloy, the magnetocrystalline anisotropyremained low as exemplified by the small coercivity. It was later discoveredthat these improved properties were possible when the grains had reduceddimensions (less than �15 nm diameter) and there was sufficient exchangecoupling between grains (described by the random anisotropymodel). Balancebetween positive and negative values for the amorphous and crystalline phases,respectively, provides reduced magnetostrictive coefficients (Herzer, 1991).The two-phase, nanoscale microstructure enabled these beneficial properties,whichwere only possible due to new alloy design considerations. Since then, awide variety of compositions have been developed to achieve the samenanocomposite microstructure, providing improved soft magnetic propertiesfor various working environments.

As a demonstration of the importance of these new nanocrystallinematerials and their relationship to other magnetic materials, a timeline forthe progress in magnetic materials over the past century is shown in Fig. 4.1.The coercivity is a metric for the resistance of the magnetization to switchingin the material, having small values for so-called soft magnets and large valuesfor hard (or permanent) magnets. The distinction is important as soft and hardmagnetic materials are used in very different applications, largely due to thedifferences in coercivity. Since the beginning of the twentieth century,greater specialization of alloy compositions and processing methods haveimproved the range of available materials to cover nearly 100 millionfolddifferences between the softest and hardest magnetic materials available. Softmagnetic materials are used in applications where switching occurs easily andtherefore a low value of coercivity (less than 5 Oe (�400 A/m)) is desirable.Hard magnetic materials rely on the resistance of their magnetizations to

10 100 1000

Initial relative permeability (m0)

Sat

urat

ion

mag

netiz

atio

n (T

)

104 105 1060.10

0.5

1.5

2.5

1

2

1

FePt

Hexaferrites

AlnicosREPMs

Steels

45Permalloy

Nanocrystallinealloys

Amorphousalloys

Spinelferrite

Supermalloy78

Permalloy

FeCo alloys

1880 1900 1920 1940 1960 1980 2000

Year

Coe

rciv

ity (

A/m

)

10-1

100

101

102

103

104

105

106

107

FePt

Supermalloy

Steels

Si steels

Hexaferrites

Alnicos

Permalloys

Spinelferrite

FeCo alloys

Amorphousalloys

Nanocrystallinealloys

(Fe,Co)-based

(Fe,Si)-based

REPMs

Fe-based

Figure 4.1 (a) Timeline of progress in the improved performance for soft and hardmagnets as measured by the coercivity of different magnetic materials. (b) Diagramshowing the saturation magnetization and initial relative permeability for soft and hardmagnets.



switching in an applied magnetic field, exemplified by large coercivities(more than 125 Oe (10 kA/m)). Figure 4.1a illustrates the full range ofmodern magnetic materials, showing excellent magnetic softness for amor-phous and (Fe,Si)-based nanocrystalline alloys and superb magnetic hardnessfor rare-earth transition metal compounds. Interestingly, the (Fe,Si)-based,Fe-based (e.g., Nanoperm-type), and (Fe,Co)-based (e.g., HITPERM-type)alloys all show reduced coercivity in nanocrystalline alloys (as shown inFig. 4.1a). While the coercivity has been optimized to specialize materialsfor various applications, the saturation magnetization has been significantlyreduced (Fig. 4.1b). Saturation magnetization is an important figure of merit,and while the nanocrystalline soft magnetic alloys do not have the highestvalues, their low coercivities and moderate saturation magnetizations arepromising for many applications. Achieving the best combination of mag-netic characteristics through alloy composition and microstructure evolutionhas been areas of great scientific and technological efforts. A review ofprogress in these areas is the topic of this chapter.

1.2. Technical considerations

Magnetic materials are characterized by their reaction to applied magneticfields. Characteristics that differentiate magnetic material performance canbe determined using the hysteresis loop. A schematic loop (as shown inFig. 4.2) reveals magnetic parameters that are microstructure independent(i.e., intrinsic) and microstructure dependent (i.e., extrinsic properties).Both types of properties affect the performance of the material and deter-mine the suitability of the material for a given application. The M–H andB–H loops are related to each other through a constitutive relationship:B¼m0(MþH) (in SI units), where B is the magnetic induction (in Tesla),Mis the magnetization (in A/m), H is the magnetic field strength (in A/m),and m0 is the permeability of free space (4p�10�7 kg m/(A2 s2)).

Magnetic field strength, H (A/m)

Remanentmagnetization, Mr (A/m)

Remanent induction, Br (T)

Coercivity, Hc (A/m)

Permeability, m = B/H

Core loss, Pcv (J/m3)

(area within loop)

Magnetic induction, B (T)

Magnetic field strength, H (A/m)

Saturationmagnetization, Ms (A/m)

Coercivity, Hc (A/m)

Susceptibility, X=M/H

Magnetization, M (A/m)

m0= Permeability of free space

(4p � 10-7

kg m/A2 s

2)

Figure 4.2 Schematic diagrams of hysteresis loops using (a) M–H and (b) B–Hcoordinates.


Intrinsic magnetic properties include the saturation magnetization (Ms),magnetocrystalline anisotropy (K1), magnetostrictive coefficient (ls), andCurie temperature (TC). The saturation magnetization can be determineddirectly from the hysteresis loop at high fields. Large values of magnetizationare desirable for application since less material is required for a givenapplication as the magnetization is increased. The magnetocrystallineanisotropy and magnetostrictive coefficients indirectly influence the hyster-esis loop by their effect on the coercivity and core losses of the material.Near isotropic switching behavior is observed when these quantities arenear zero, a factor that gives increased energy efficiency. Curie temperaturesare typically determined by measurement of the thermomagnetic responseof the material under a static field and not directly from the hysteresis loop.While large values of Curie temperature are necessary for high-temperatureapplications, in most cases, the Curie temperature should be large enough toprovide adequate exchange coupling at the operation temperature.

Extrinsic magnetic properties include permeability (m), susceptibility (w),coercivity (Hc), remanence (Mr), and core losses (Pcv). These are influencednot only by the microstructure but also by the geometry of the material(through magnetostatic effects), the different forms of anisotropy found inmagnetic materials (e.g., magnetocrystalline, magnetoelastic, shape, induced,etc.), and the effect of switching frequency of the applied fields. The corelosses are technologically one of the most important properties of the materialas they are a direct measure of the heat generated by the magnetic material inapplication. The core loss is the area swept out by the hysteresis loop, whichshould be minimized to provide good energy efficiency for the core. Con-tributions to the core loss include hysteretic sources from local and uniformanisotropies and eddy currents at high frequencies. The permeability (andrelated susceptibility) can be controlled by gapping the core or by fieldannealing. For some applications, a large permeability is desirable (e.g.,chokes) for others, a low, but constant value of permeability is important(e.g., inductors). The hysteresis loop is influenced by the nanocompositemicrostructure in ways that are not commonly found in other classes ofmagnetic materials. The unusual nature of the nanostructure shows a strongmicrostructure dependence of the “effective” magnetocrystalline anisotropyof the material (typically an intrinsic property). In order to appreciate theimportance of this effect, a brief description of the nanocomposites will begiven for context followed by details in later sections of this chapter.

In general, nanocomposite soft magnetic alloys include compositions richin ferromagnetic transitionmetals with small amounts of early transitionmetals(ETMs), metalloids, and late transition metals (LTMs). The most studied typeof these alloys has nominal composition Fe73.5�xSi13.5þxNb3B9Cu1,although many other compositions have been investigated over the pasttwo decades (see Table 4.1). When optimally annealed this alloy possessesa microstructure consisting of randomly oriented grains with diameters

Table 4.1 Nanocomposite alloy systems formed by rapid solidification processingwith subsequent annealing to form the identified primary crystalline phase

Alloy composition Year Reference

Primary crystalline phase: a-(Fe,Si) or a1-Fe3Si(70–80% Fe and m0Ms�1.2–1.4 T)

Fe–Si–M–B–Cu (M¼Nb, V) 1988 Yoshizawa (1988a)

Fe–Si–M–B–Au (M¼Nb, V, Hf,

Ta, Mo, W, Cr)

1989 Kataoka (1989)

Fe–Si–M–B–Cu (M¼Ta, Mo,

W, Cr)

1991 Yoshizawa and Yamauchi (1991)

Fe–Si–Al–Nb–B–Cu 1993 Lim (1993b)/Watanabe (1993)

Fe–Si–Ga–Nb–B 1994 Tomida (1994)

Fe–Si–U–B–Cu 1995 Konc (1995)

Fe–Si–Hf–B–Cu 1995 Mattern (1995)/Yamauchi

and Yoshizawa (1995)

Fe–Si–Al–Nb–Mo–B–Cu 1999 Frost (1999)

Fe–Si–Zr–B–Cu 2001 Kwapulinski (2001)

Fe–Si–Al–Ge–Zr–B–Cu 2002 Cremaschi (2002)

Fe–Si–Nb–P–B–Cu 2003 Chau (2003)

Primary crystalline phase: a-(Fe,M,Si) or a1-(Fe,M)3Si

(70–80% Fe/M and m0Ms�0.6–1.5 T)

Fe–Co–Si–Nb–B–Cu 1992 Yu (1992)

Fe–Ni–Si–Al–Zr–B 1993 Chou (1993)

Fe–Co–Si–Mo–B–Cu 1994 Kim (1994a)

Fe–Cr–Si–Mo–B–Cu 1994 Conde (1994)

Fe–Cr–Si–Nb–B–Cu 2001 Franco (2001b)

Fe–Mn–Si–Nb–B–Cu 2001 Tamoria (2001)/Hsiao (2001)

Fe–Ni–Si–Nb–B–Cu 2001 Atalay (2001)

Fe–Co–Si–Ge–Nb–B–Cu 2004 Cremaschi (2004b)

Fe–Co–Si–Zr–B–Cu 2004 Yoshizawa (2004)

Primary crystalline phase: a-Fe(83–91% Fe and m0Ms�1.4–1.94 T)

Fe–M–B (M¼Hf, Zr) 1990 Suzuki (1990)

Fe–M–B–Cu (M¼Ti, Zr, Nb,

Hf, Ta)

1991 Suzuki (1991c)

Fe–Nb–B 1993 Suzuki (1993)

Fe–Zr–B–Si–Al 1996 Inoue (1996)

Fe–Zr–M–B–Cu (M¼Ti, V, Cr,

Mn)

1999 Bitoh (1999)

Fe–B–U–Cu 2000 Solyom (2000)

Fe–Nb–B–P 2001 Kojima (2001)

Fe–Zr–B–Ge–Cu 2002 Suzuki (2002b)

(Continued)


Table 4.1 Nanocomposite alloy systems formed by rapid solidification processingwith subsequent annealing to form the identified primary crystalline phase—cont’d

Alloy composition Year Reference

Fe–B–Si–Cu 2007 Ohta and Yoshizawa (2007)

Fe–Si–B–P–Cu 2009 Makino (2009)

(65-82% Fe and m0Ms�0.9–1.6 T)

Fe–P–C–Ge–Si–Cu 1991 Fujii (1991)

Fe–B–Nb–Cu 1995 Suzuki (1995)

Fe–B–M–Cu (M¼Zr, Hf, Nb) 1995 Kim (1995)

Fe–P–C–Mo–Si–Cu 1996 Tan (1996)

Fe–B–Zr–Cu 1998 Naohara (1998)

Fe–B–M–Cu (M¼Mo, Ti) 1999 Miglierini (1999)

Fe–P–B–Si–Al–Ga–Cu 2004 Pekala (2004)

Fe–Nb–B–P–Cu 2007 Makino (2007)

Primary crystalline phase: a-(Fe,Co) or a0-FeCo*(84–90% Fe/Co and m0Ms�1.5–1.9 T)

Fe–Co–Zr 1991 Guo (1991)

Fe–Co–Zr–B–Cu 1996 Muller (1996b)

Fe–Co–Zr–B–Cu* 1998 Willard (1998)

Fe–Co–Hf–B–Cu 1999 Iwanabe (1999)

Fe–Co–Zr–Nb–B–Cu 1999 He (1999)

Fe–Co–Zr–Hf–B–Cu 2002 Kulik (2002)

Fe–Co–Ge–Zr–B–Cu 2005 Blazquez (2005)

(62–80% Fe/Co and m0Ms�0.9–1.65 T)

Fe–Co–B–Al–Nb 1994 Cho (1994)

Fe–Co–Nb–B 1997 Kraus (1997)

Fe–Co–Nb–B–Cu 2001 Blazquez (2001)

Fe–Co–Ni–Zr–Nb–B–Cu 2001 Ausanio (2001)

Fe–Co–Zr–B–Si–Al–Cu 2004 Mitra (2004)

Fe–Co–Nb–Ta–Mo–B 2004 Um and McHenry (2004)

Fe–Co–Mo–B–C 2005 Yoshizawa and Fujii (2005)

Primary crystalline phase: g-(Fe,Co,Ni)

(80–90% Fe/Co/Ni and m0Ms�0.2–1.4 T)

Fe–Co–Ni–Zr–M–B (M¼Nb,

Ta)

1997 Koshiba (1997)

Fe–Ni–Co–Zr–B–Cu 2000 Muller (2000)

Fe–Ni–Zr–B–Cu 2001 Willard (2001b)

Co–Fe–Zr–B–Cu 2002 Willard (2002b)

Co–Ni–Zr–B–Cu 2012 Hornbuckle (2012)


less than 20 nm embedded in an amorphous matrix phase. Both the crystal-line and the amorphous phases are ferromagnetically coupled when the bestmagnetic properties are achieved. Alloys of this type have reduced magneticanisotropy (and therefore coercivity) as long as the grains are randomly


oriented and their size remains small (as first discussed by Herzer in 1989)(Herzer, 1989). To understand the origin of this “effective anisotropy”exhibited by exchanged-coupled, fine-grained alloys, a few materials prop-erties must be discussed first.

All magnetic materials possess magnetic anisotropy, which links the pre-ferred direction of the material’s local moment with the local atomic arrange-ment (usually the crystalline lattice). This quantity is referred to as themagnetocrystalline anisotropy (K1) in crystalline and amorphous materialsalike (although it is somewhat a misnomer in the latter). It is affected byrelatively short-ranged atomic arrangements (only a few atomic lengths) andpossesses the symmetry of its environment. For bulk soft magnetic materials,the K1 is typically in the range of 10

3 to 105 J/m3 (OHandley, 2000). Anotherimportant materials quantity is the magnetic exchange stiffness (A), whichdetermines how strongly magnetic moments prefer to remain in a commondirection.Most soft magnetic alloys haveA near 10�11 J/m (OHandley, 2000).

When the magnetization switches direction under the action of an appliedfield, these two quantities oppose each other. Take the case of a crystallinematerial with two magnetic domains separated by a 180� domain wall. Themagnetocrystalline anisotropy energy is lowest when themoments are alignedwith the preferred easy axis direction, so an abrupt change between domainswould be expected. The exchange energy is lowest when adjacent momentsare aligned with each other, so an infinitely wide wall would be expected.Taking both of these factors into account, K1 acts to restrict the width of thedomain wall due to its propensity to keep themagnetic moments aligned withthe crystalline lattice and A acts to widen the wall keeping adjacent momentsaligned. For the specific case here, the width of the 180� domain wall is

proportional toffiffiffiffiffiffiffiffiffiffiffiffiA=K1

p(Chen, 1986). This quantity, called the magnetic

exchange correlation length (Lex) or simply exchange length, is important toour understanding of the soft magnetic behavior in nanocrystalline alloys,showing the minimum length scale over which the magnetization can have anoticeable change in direction.

When the structural correlation lengths are near the same size as themagnetic correlation lengths (i.e., exchange length) then interesting magneticproperties are produced. Considering an amorphous alloy, the structural cor-relation is limited to the arrangement of near-neighbor and next-near-neighboratoms. In this case, the magnetocrystalline anisotropy was found to be averagedwithin the exchange length of the amorphous phase due to the local structure,as described by Alben et al. in their formulation of a random anisotropy model(Alben et al., 1978). The overall magnitude of the magnetic anisotropy islowered using the random anisotropy model, resulting in softer magneticbehavior (a much reduced “effective anisotropy” is developed).

This formulation can be applied to nanocrystalline alloys as well. Incrystalline alloys, the structural correlation length is the grain diameter(D). When the grain size is much smaller than the exchange length (Lex),


the magnetocrystalline anisotropy is averaged over the volume encompassedby Lex. The exchange energy, being longer range than the magnetocrystal-line anisotropy, dominates and forces the magnetic moments to alignregardless of grain orientation. This results in an effective magnetic anisot-ropy, hKi, of K1(D/Lex)

6 for a three-dimensional nanostructured material.Since the coercivity (and ultimately the losses) of the soft magnetic materialis strongly dependent on the magnetic anisotropy, we can clearly see theimportance of this relation (as demonstrated in Fig. 4.3). As this equationimplies, the effective anisotropy can be decreased very effectively by reduc-tion in the grain size of the alloy. For a 1-nm grain diameter, the hKi hasvalues ranging from 10�1 to 10�6 J/m3 (depending on the K1 of the crystal-lites). Using the measured magnetic correlation length from small-angleneutron scattering (SANS) measurements, Loffler et al. determined that themagnetization will only follow the anisotropy axes of individual grainswhen the grain size exceeds a critical value, approximately the size of the180� domain wall width (Loffler et al., 1999). When applied to (Fe,Si)-based nanocrystalline materials (given K1 for a-(Fe,Si) is�8–10 kJ/m3), thedomain wall width is found to be �300 nm, marking the transitionbetween these two regimes. For grains larger than the domain wall width,a 1/D dependence of coercivity is observed (see Fig.4.3).

When the losses are made small by reducing the magnetocrystallineanisotropy through grain size reduction, other loss mechanisms becomedominant. One of these remaining and important loss mechanisms is the

Grain size (nm)

D6

D−1

Coe

rciv

ity (

A/m

)

10.1

1

10

100

1000

104

10 100 1000 104 105 106

Figure 4.3 Diagram showing the variation of coercivity with grain size for softmagnetic alloys without induced anisotropy. After Herzer (1990).


magnetoelastic anisotropy, which is driven by internal or external stressfields through the magnetostrictive coefficients of the material. The simul-taneous reduction of both the magnetocrystalline and magnetoelastic ener-gies is required to achieve the maximum permeabilities (and lowest losses)in these alloys. This short description of the impact that nanocompositemicrostructure has on the hysteresis loop illustrates the importance of thisclass of materials for a variety of applications.

1.3. Applications

A wide range of devices require soft magnetic materials for energy storage,conversion, filtering, power generation, sensing, and many other uses(Willard and Daniil, 2009). Before continuing to materials processing andresultant properties, it is important to mention the potential impact of thisclass of materials. The range of applications and corresponding materialschosen for each are shown in Fig. 4.4 as a function of switching frequencyfor the magnetic component. Nanocrystalline, amorphous, and polycrystal-line alloys are limited to about 1 MHz switching frequency due to thedeleterious effects of eddy currents and their increased contribution to the

Frequency

Materials

Applications

Nanocrystalline alloys — FinemetTM

Stators and rotorsin motors and generators

Saturable reactor cores

Inductors (Filters and converters)

Switch-mode power suppliesShieldingsensors Distribution and power transformers

Microwaveapplication

Fe-based MetglasTM

Fe-Si; Fe-Ni alloys; Fe-Co Alloys

Co-based MetglasTM

MnZn-ferrites

NiZn-ferrites

HIPERM

DC

10H

z

100

Hz

1kH

z

10kH

z

100

kHz

1M

Hz

10M

Hz

100

MH

z

1000

GH

z

NanopermTM

Figure 4.4 Soft magnetic materials and potential applications with varying frequency.After Gutfleisch et al. (2011).


core loss and subsequent reduction of permeability with increasing frequency.Above 1 MHz, oxide soft magnets with the spinel crystal structure (i.e.,ferrites) are used, largely due to their high resistivity and limited eddy currentformation. However, the low saturation magnetization (less than �0.4 T) ofthese oxide materials results in an opportunity for nanocrystalline soft mag-netic alloys even at these frequencies if the eddy current components of thecore loss can be controlled (Marın and Hernando, 2000). In the design of newmaterials, two characteristics are important for applications, namely, mini-mizing losses and maximizing saturation induction.

A leading advantage of the nanocrystalline alloys over other soft mag-netic materials is their high saturation magnetization combined with theircore loss performance at frequencies up to 1 MHz. While there are manysoft magnetic thin film materials available with similar characteristics, theirthickness limits these materials to uses where lower power loads arerequired. The ribbon-shaped nanocrystalline materials produced by rapidsolidification techniques allow more flexibility in design and production ofdevices for higher power requirement applications. With the rising impor-tance of distributed architectures for power conversion (Huljak et al., 2000),the advantages of nanocrystalline soft magnetic alloys should provide anoption for smaller, lighter, and more efficient components. Reduction insize makes energy-efficient devices based on nanocrystalline alloys moreaffordable (Hasegawa, 2006).

Substantial federal and private investments have been made in an effortimprove performance by standardizing, modularizing, and miniaturizingthe packaging of power electronics components. Power electronics devicesare used to supply a specific voltage with a limited noise threshold. Theyusually consist of semiconductor-based active devices designed for highpower loads and frequencies but also require inductors and capacitors forpower conditioning. Conversion of AC line frequencies to DC, followedby DC/DC power conversion to match the different components thepower electronics support, requires high-performance soft magnetic mate-rials. In the voltage regulation circuit for instance, the soft magnetic alloyacts as a magnetic switch (sometimes referred to as a magnetic amplifier) thatrequires low and high remanent states of the magnetization to be achievedwith small applied switching fields (Hasegawa, 2004). Ideally, the softmagnetic material switches very sharply at the coercivity and the hysteresisloop has good squareness (i.e., Mr/Ms>0.9). The large squareness and lowcoercivity allow good regulation behavior, reduced dead-time, and smallreset currents. While miniaturization and high-frequency performance ofactive components have made significant progress, similar advances inmagnetic components have not been forthcoming. Efforts to provide mini-ature and modular integrated power electronics components remain aleading motivation for efforts to improve soft magnetic alloys with largermagnetization and lower core losses.


Power converters also use choke coils to reduce high-frequency harmo-nics in the current source. In this case, the inductor coil will have a largeamount of current and the inductor should not be allowed to saturate underthis condition, requiring low remanence (i.e., Mr/Ms<0.3) and high satura-tion magnetization. Large induced anisotropy and high electrical resistivityare key parameters for extending converters to higher frequencies (Yoshizawaet al., 2003). The recent use of Finemet-type alloys for a 1 MV DC powersupply illustrates the importance of nanocrystalline materials to power condi-tioning applications (Watanabe et al., 2006). Power conditioning refers toreducing the harmonic distortion in the output signal caused by fast switchingduring DC/DC conversion, for instance from a switched-mode powersupply. A common-mode choke is used in this case and requires a broadbandhigh permeability (Yoshizawa and Yamauchi, 1989).

In the field of power electronics, switched-mode power supplies havebeen replacing conventional 50 Hz power supplies due to market demandsfor higher efficiencies (Hilzinger, 1985). Higher frequency operation(above 1 kHz) provides the added benefit of size reduction for these com-ponents, which limits the choices of materials to those with high resistivity.The materials used for 50/60 Hz applications, including Si-steels, are notsuitable for these high-frequency applications due to the increased lossescaused by eddy currents. Nanocrystalline soft magnetic alloys provideexcellent performance in these applications due to their high magneticinduction and low losses at frequencies up to 1 MHz (Hilzinger, 1990).

For transformer applications, low coercivity (less than a few A/m), highsaturation magnetization (greater than 1.5 T), and large remenance ratio(more than 0.8) are desired characteristics (Hasegawa, 2006). Recent advancesin amorphous alloys have had an impact in this area; however, nanocrystallinealloys continue to have great potential in this area, too. The improvement inenergy efficiency of the core material (by reducing core losses) indirectlyreduces greenhouse gas emissions by wasting less of the generated power asJoule heating from core loss (Hasegawa, 2000), and the use of magnetic andstress field annealing allows better control of the remenance ratio of the alloys,providing improved performance of nanostructured materials.

Nanocrystalline ribbon materials have also been considered for low-frequency ground fault circuit breakers due to their combination of lowremanent magnetization and permeability adjusted by magnetic fieldannealing (Waeckerle et al., 2000). The low remanent magnetization isnecessary for this application to provide consistent working induction underhigh dynamic variations and varying waveforms. The core losses must alsobe relatively small to provide good sensitivity to low current surges.

Governmental regulations have been established to prevent the disruptionof medical devices and personal computers (susceptible to induced high-frequency noise from these devices) by the increasingly common portableelectronic devices (including cell phones and personal digital assistants) that


operate at frequencies above 1 MHz. Common-mode choke coils provideprotection of these devices by acting as a low impedance wire for the signal(e.g., differential mode currents) and high impedance inductor for high-frequency noise (e.g., common-mode currents). Chokes of this type are usedin switched-mode power supplies, uninterruptible power supplies, inverters,and frequency converters to limit electromagnetic interference (EMI). Thehigh permeability of (Fe,Si)-based ribbon materials is a favorable feature forEMI reduction in the MHz to GHz frequency range (Nakamura et al., 2004).

The high saturation magnetization and low remanence of Finemet-typeand Nanoperm-type nanocrystalline alloys provide broadband voltage atten-uation (100 kHz to 10 MHz), making these materials favorable for use incommon-mode choke coils. Reduction of the permeability in nanocrystallinesoft magnetic alloys allows them to store energy in the magnet. This isespecially important for choke coils used to prevent signal distortion in reactorelements of phase modifying devices by smoothing out the higher harmonicripples in the rectified voltage waveform. Magnetic or stress field annealingprocedures may be used to lower the permeability as well as putting an air gapin the core or using a powdered core of nanocrystalline alloy.

Core size reduction is a desired improvement, requiring simultaneousincrease in the saturation magnetization and lower core losses. The saturationmagnetization must be increased when the core is made smaller to maintain aconstant stored energy and the core loss must be reduced at the same time tocounteract the increased hysteresis loop area resulting from the increasemagnetization. A disadvantage of smaller cores is the reduced surface areaavailable for extracting the heat produced due to the core loss (Naitoh et al.,1998). For this reason, thermal management is an important considerationand reduction of core losses is emphasized as a means to produce less heatfrom the start. Nanocrystalline soft magnetic alloys with induced anisotropyare well suited for choke core applications for these reasons.

Induced anisotropy is preferred to powdered or gapped cores due to theobserved increases in core losses, resulting from these alternative means ofcontrolled reduction of permeability (Kim et al., 2003; Naitoh et al.,1997b). Finemet-type alloys are restricted to �10% changes in permeabilityduring sustained use at temperatures as high as 100 �C and limited use attemperatures between �40 and 150 �C. Due to their low values of magne-tostriction, the acoustic noise emission is also limited. These features illus-trate the importance of nanocrystalline materials over amorphous and ferritecores for use in switched-mode power supplies, frequency inverters, unin-terruptible power supplies, adjustable speed drives, and other applications,requiring robust noise suppression from rapid current changes.

Flux gate sensors have been used for ultra-sensitive magnetic fielddetection (�0.1 nT) using nanocrystalline soft magnets. The sensor ismade of two identical saturable cores with large permeability that areoppositely wound (Nielsen et al., 1994). A small AC magnetic field is


applied to each coil, and a differential voltage drop is measured when anunvarying external field is applied. These sensors are used for magneticdirection sensing applications. The near zero value of magnetostriction,high permeability, and low Barkhausen noise makes nanocrystalline softmagnetic alloys competitive for these applications. Finemet-type ribbonsannealed under a transverse magnetic field have shown 0.04 nT noise levelfor a 16 nT peak-to-peak square applied waveform (Nielsen et al., 1994).

Recent studies by Ong et al. have shown that the higher harmonicscreated in a soft magnetic amorphous ribbon can be used for accurate,remote temperature measurement (Ong et al., 2002). The high permeabilityand low coercivity found to be important for this sensor are similar to thosein nanocrystalline alloys, which might also be used in this capacity.

Nanocrystalline soft magnetic alloys have also been used for stress sensorapplications (with sensitivity up to �50 MPa) (Ahamada et al., 2002). Thetailored magnetostrictive coefficient of (Fe,Si)-based alloys along with theinduced anisotropy resulting from annealing under a stress field allowedthe development of a near linear change in magnetization with applied stress(at an applied field of 400 A/m). The so-called giant magnetoimpedanceeffect exhibited by some nanocrystalline soft magnetic alloys gives thempotential for use in magnetic field sensor applications (Naitoh et al., 1997a;Yoshizawa et al., 1988b). The magnetoelastic resonance of ribbons withtransverse anisotropy has been used in article surveillance monitoring appli-cations (Marın and Hernando, 2000).

Despite the significant benefits exhibited by this class of materials, manychallenges remain for alloy developers. Some of these include developingnew materials with improved processing in air, controllable permeability,and reduction in embrittlement after crystallization. With progress in theseareas, even more widespread use of these materials is expected.

2. Alloy Processing

The optimal microstructure for soft magnetic nanocrystalline materialsconsists of grains less than 10 nm in diameter surrounded by an amorphousmatrix phase less than a few nm in thickness. Both the small grain size andthe amorphous matrix phase help to provide the excellent magnetic proper-ties found in these alloys. Substantial difficulties arise when conventionalalloy preparation techniques—such as solidified casting, forging, rolling,sintering, extrusion, etc.—are employed for preparation of nanocrystallinematerials. These techniques process materials at high temperatures wherenear-equilibrium conditions result in limited nucleation and uncontrolledgrain coarsening. These conditions are not conducive to the formation ofthe nanocrystalline microstructure.


Crystallization of a liquid occurs through a nucleation and growthprocess, where the crystalline phase forms small transformed regions withinthe liquid that subsequently grows as crystallization progresses. It is expectedthat any processing technique capable of producing a large amount ofnucleation with a limited amount of grain growth would be a requirementto achieve a nanocrystalline microstructure. For this reason, nonequilibrium(metastable) processing methods are well suited for development of thismicrostructure. Melting, evaporation, irradiation, applied pressure, and/ormechanical deformation can be employed by nonequilibrium means tocreate a fine-grain microstructure. Specific techniques that accomplish thisinclude rapid solidification, plasma processing, vapor deposition, mechani-cal alloying, and chemical synthesis. Many of these techniques provide aprecursor amorphous phase, which can be further processed to form thenanocomposite microstructure.

The most commonly used method for producing nanocrystalline softmagnetic alloys is the single-roller melt spinning technique either by planarflow casting or by nozzle injection (a.k.a. jet casting). Both techniquesproduce amorphous alloy ribbons with thicknesses less than 30 mm andwidths in the millimeter to centimeter range. Under the right processingconditions, these ribbons can be many meters long. Isothermal annealing orJoule heating is then used to produce the nanocrystalline microstructurenecessary for optimal magnetic performance. Annealing is typically carriedout in vacuum or in an inert-gas environment to prevent oxidation.

The following sections will describe progress in variations of theprocessing parameters for rapid solidification (Section 2.1), annealing(Section 2.2), and core fabrication (Section 2.3). While much of the workon nanocrystalline soft magnetic alloys has been explored by melt spinningfollowed by furnace annealing, important studies using novel techniques forboth nonequilibrium processing (e.g., wire, thin films, mechanical alloying,etc.) and crystallization (e.g., irradiation, laser processing, Joule heating,etc.) have also been studied (see Section 2.4).

2.1. Rapid solidification

Rapid solidification refers to processes where heat is extracted from a meltat rates exceeding 105 K/s. Using this extreme cooling rate, alloys withinlimited composition ranges can be kinetically arrested in a metastable,amorphous, or glassy solid state. Metastable in this case refers to a statewhere the alloy will transform to one or more crystalline phases, givenenough time (albeit extremely long times in this case). Should the coolingrate be insufficient, a crystalline or partially crystalline alloy may beproduced instead of a fully amorphous alloy. It has been found that bettermagnetic performance is possible when direct formation of crystallitesfrom the melt is avoided so rapid solidification techniques are employed


to create an amorphous precursor with subsequent postprocessing forcrystallization.

Of the many “bulk” rapid solidification techniques (including planarflow casting, roller quenching, melt extraction, atomization, etc.), the onemost commonly used for nanocrystalline soft magnetic alloy investigationsis the melt spinning technique. This technique produces ribbons or sheetsof alloy less than 30 mm thick by the expulsion of a melt onto a rapidlyrotating wheel. To ensure homogeneity, alloy ingots of the desired com-position are formed from high purity elemental constituents using an arcmelting or induction melting technique prior to melt spinning. Theresulting alloy ingots are used as stock material for rapid solidificationprocessing. During the melt spinning process, the melt is typicallycontained in a crucible with an orifice at the bottom and is heated byinduction coils (see Fig. 4.5). The surface tension of the molten alloy holdsthe melt inside the crucible until the desired melt temperature is achieved.The melt is then expelled onto the rotating wheel by a high-pressure gasfrom the top of the melt. The resulting stream impinges on the quenchwheel, providing a large quench rate.

The melt spinning technique has many independently adjustable para-meters, which can greatly affect the quality of the ribbon product. Theseinclude the speed of the quench wheel, the temperature of the melt, theorifice size and shape, the distance between the crucible and wheel, andthe ejection pressure. By controlling these parameters, the resulting ribbonscan have varied thicknesses, widths, quench rates, and degree of crystallin-ity. Ultimately, all of these factors affect the magnetic properties, stressingthe importance of understanding and controlling these parameters duringalloy processing.

Quenching wheel

Crucible

Moltenalloy

Inductioncoils

Melt-spunRibbon

Figure 4.5 Schematic diagram of a single-wheel melt spinner.


2.1.1. Melt temperature controlThe melt temperature prior to alloy ejection onto the quench wheel hasbeen studied for alloys with composition Fe73.5Si13.5B9Nb3Cu1 (Chiriacet al., 1999a; Lim et al., 1993a; Pi et al., 1993). These studies found trends inthe permeability and coercivity of alloys produced with different degrees ofexcess heating above the equilibrium melting temperature of 1473 K. Carewas taken to maintain constant ribbon thickness by adjusting the orifice sizeand wheel speed so that an accurate comparison between the resulting runscould be made. A tripling in permeability (see Fig. 4.6) and a fourfoldincrease in remanence ratio were observed when the melt temperaturewas increased from 1513 to 1653 K (Lim et al., 1993a). Further increasein melt temperature to 1723 K shows a precipitous drop in permeability.Both effects can be explained by considering the relationship of the timerequired for relaxation (tR) of the molten alloy into near-equilibriumatomic clusters and the time required to quench the alloy (tq) from themelt temperature (Tmelt) to the glass transition temperature (Tg).

An alloy with good glass-forming ability possesses a large tR, consistentwith the stability of the liquid over solid cluster formation (Pi et al., 1993).The value of tq is directly increased as Tmelt increases. In order to producean amorphous alloy, the tq must be less than the tR or solid clustering willoccur during the quench. The alloy considered here, with compositionFe73.5Si13.5B9Nb3Cu1, has a large fraction of glass-forming elements andis considered a good glass-forming alloy. Increased Tmelt in this case

Melt temperature (K)

Rel

ativ

e pe

rmea

bilit

y

1500

15 000

20 000

25 000

30 000

35 000

Chiriac (1999)

Lim (1993)

1550 1600 1650 1700 1750

Figure 4.6 Variation of permeability with melt temperature for Fe73.5Si13.5B9Nb3Cu1alloys (Chiriac et al., 1999a; Lim et al., 1993a)


(to 1650 K) is thought to increase the permeability due to its improvedhomogeneity prior to quenching. However, this effect is limited to thetemperature range where tR>tq. As the Tmelt reaches 1723 K, the largedecrease in permeability can be attributed to tq exceeding tR, resulting incluster formation during the quench (due to the larger driving force forcrystallization imposed by the higher temperature) and degraded magneticperformance (Chiriac et al., 1999a).

2.1.2. Wheel and crucible parametersFour interrelated processing parameters control the ribbon cross section bycontrolling the molten puddle on the quench wheel (both the puddle size andthe melt flow rate). These parameters are the wheel surface velocity, thecrucible orifice size, the melt ejection pressure, and the wheel-to-crucibledistance. While trends between these parameters and the ribbon thickness areknown for amorphous ribbons, (Liebermann and Graham, 1976) similartends have not been systematically studied for any of the nanocrystallinealloys. However, most studies provide some of these parameters and theyare (not surprisingly) very similar to those used in amorphous alloy processing(El Ghannami et al., 1994; GomezPolo et al., 1997; Mitra et al., 2001; Pandaet al., 2001; Tiberto et al., 1996b). Typical wheel surface velocity used inthese studies ranges from 20 to 50 m/s when a copper wheel is used forquenching. The orifice size ranges from 0.75 to 2 mm in diameter and wheel-to-crucible distances range from 0.5 to 5 mm. Ejection gases include heliumand argon with pressures between 25 and 50 kPa (about 0.25–0.5 psi).

Figure 4.7 illustrates the thickness variation with wheel surface velocityand shows the influence of orifice diameter and wheel-to-crucible spacing.Intuitively, the ribbon thickness is smaller for processing conditions thatmake both the puddle size and the melt flow rate smaller. This includesreducing the melt ejection pressure, reducing the orifice size, and increasingthe wheel surface velocity. The quench rate is improved under theseconditions, aiding in the formation of a fully amorphous ribbon. While bychanging these processing parameters the ribbon thicknesses can be varied,the resulting material may not remain fully amorphous during the quenchfor the same reasons described in Section 2.1.1 (i.e., tR must be greater thantq). At some critical ribbon thickness (dependent on composition), the alloywill begin to partially crystallize during the melt spinning process. Thegrains formed by this process typically possess preferential orientation withthe expected growth texture for the crystalline phase formed (i.e., (1 0 0) forBCC (body-centered cubic) or (1 1 1) for FCC (face-centered cubic)).

Direct crystallization from the melt of a Fe73.5Si13.5B9Nb3Cu1 alloy wasperformed by El Ghannami et al. as a function of wheel speed (from 34.5to 42.3 m/s) by quenching from very near the melting point of thealloy (1438 K) (El Ghannami et al., 1994). The resulting alloys wereonly �10% crystalline in the as-spun condition, consisting of grains about

Wheel surface velocity (m/s)

Tiberto (1996)

nozzle diameter (mm)crucible—Wheel (mm)eject pressure (kpa)

?0.625

1.40.550

1.00.550 1.4

0.550

1.90.850

1.25.050

Panda (2001)Mitra (2001)

Rib

bon

thic

knes

s (μ

m)

150

10

20

30

40

50

60

20 25 30 35 40 45

Figure 4.7 Ribbon thickness variationwithwheel surface velocity for Fe73.5Si13.5B9Nb3Cu1alloys. Other important processing parameters are provided parenthetically (nozzle diameter,crucible-to-wheel distance, andmelt ejection pressure) (Mitra et al., 2001; Panda et al., 2001;Tiberto et al., 1996b).


15 nm in diameter. Annealing resulted in the reduction of the coercivityfor all samples by a factor of 2, with the best results for the fastest wheelspeed (e.g., 0.8 A/m at 42.3 m/s). Similar alloys when quenched to a fullyamorphous phase typically have much lower coercivities (�0.5 A/m) aftersubsequent annealing (Yoshizawa et al., 1988a).

2.1.3. Atmospheric controlThe effect of chamber gas during melt spinning has been examined by Toddet al. (1999). In this study, comparisons of grain size, coercivity, and surfaceroughness were made between samples prepared at pressures between vac-uum and 1 atm. of argon, air, or helium gases. While the grain size remainedconstant at about 10 nm, a significant change in coercivity was observedwhen the chamber gas pressure exceeded about 1/3 atm. Samples preparedin 1 atm. of argon or air had similar coercivities near 1 A/m, while samplesprepared under the same pressure of helium showed only 0.65 A/m. Thisdifference was attributed to a large surface roughness difference brought aboutby gas entrapment between the melt puddle and wheel surface during meltspinning. Good surface quality was reached at 0.2, 0.4, and 0.8 atm. for Ar,air, and He gases, respectively. The variation in coercivity with ambient gaspressure and type of gas is shown in Fig. 4.8 for Fe73.5Si13.5Nb3B9Cu1 alloyswith similar post-melt spinning anneals (Todd et al., 1999).

Coe

rciv

ity (

A/m

)

Chamber pressure, Pamb (atm.)

00.5

0.6

0.7

0.8

0.9

1.0

1.1 AirArHe

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1

Figure 4.8 Effect of ambient gas pressure and type on the coercivity of Finemetannealed at 540 �C for 3600 s (circle: Ar; triangle: air; square: He). Modified fromTodd et al. (1999).


2.2. Annealing procedures

Annealing the as-spun, amorphous alloy at temperatures near glass transitionbut below the crystallization temperatures allows quenched-in stresses torelax, which in some cases can improve the magnetic performance. Thestructural relaxation effect is due to local rearrangement of atomic positionsto lower energy bonding conditions and a concomitant slight densification ofthe alloy. While the stress relief may improve the magnetic remanence andcoercivity of many amorphous alloys, the intrinsic magnetic properties (e.g.,magnetization, magnetostrictive coefficient, etc.) do not change much. Byannealing certain amorphous alloys, all of these properties can be improvedsimultaneously due to the formation of a nanocomposite microstructure.

Crystallization of amorphous Finemet alloy ribbons (Fe73.5Si13.5B9Nb3Cu1)occurs in three stages (see Fig. 4.9). During the early stages of annealing, copperclusters form throughout the material, allowing the heterogeneous nucleationof a massive number of a-(Fe,Si) nuclei necessary for the nanocrystallinemicrostructure to develop. At primary crystallization, a-(Fe,Si) grains nucleateand grow within an amorphous matrix phase. This phase has been identifiedas disordered BCC and/or atomically ordered Fe3Si (D03 structure) (Kuliket al., 1995). The primary crystallization process occurs near 510 �C (783 K),resulting in the formation of the a-(Fe,Si) phase surrounded by an amorphousmatrix phase (Herzer, 1989). During the crystallization process, the amorphousmatrix is enriched in Nb, helping to stabilize the fine-grained microstructure.The grain size of the a-(Fe,Si) crystallites tends to arrest growth at about 10 nmand increase Si content to about 20 at% regardless of annealing time for

Optimummicrostructure

Coarsening of a-(Fe,Si)& Nb/B enrichment

of residual amorphousHeterogeneous

nucleation of a-(Fe,Si) Clustering of CuAs spun

(uniform composition)

10 nm

550 °C 3600 s 550 °C 1800 s 550 °C 480 s 550 °C 120 s

Figure 4.9 Schematic diagram showing the crystallization of Fe73.5Si13.5Nb3B9Cu1alloys with annealing time at 823 K. Modified from Ayers et al. (1998) with input fromHono et al. (1999).


temperatures near primary crystallization (Varga et al., 1994b). At highertemperatures, secondary crystallization occurs resulting in crystallization ofthe remaining amorphous phase into Fe3B, Fe2Si, Fe2B, and other intermetallicphases (Duhaj et al., 1991; Yamauchi and Yoshizawa, 1995; Zhu et al., 1991).Both the primary and secondary crystallization transformations are thermallyactivated.

Clearly, the crystallization conditions are an important factor in thedevelopment of the optimal magnetic properties. In this section, the con-ditions for furnace annealing, Joule heating, and annealing under stress andmagnetic fields are discussed. The important parameters as well as advan-tages and disadvantages of each technique are presented.

2.2.1. Conventional furnace annealingWhen amorphous alloys of an appropriate composition are annealed isother-mally above the primary crystallization, but below the secondary crystallizationtemperatures, the desired nanocrystalline microstructure can be achieved. Forexample, in Fe73.5Si13.5B9Nb3Cu1 alloys, the annealing temperature shouldremain between about 500 and 600 �C. Under these conditions, a metastableequilibrium of a-(Fe,Si) crystallites surrounded by a Nb-enriched remainingamorphous phase is formed. Given sufficient time for grain growth (usuallynear 1800–3600 s), the microstructure consists of nanocrystalline grainsembedded in a 20–25 vol% amorphous matrix. This microstructure is quiteresilient to further annealing in this temperature range.

Standard annealing procedure for most studies on nanocrystalline softmagnetic alloys include annealing at temperatures near the primary crystal-lization temperature (Tx1) for at least 1800 s but usually 3600 s. The atmo-sphere is controlled by active vacuum or inert atmosphere (e.g., He, Ar, N2,H2, etc.). This is accomplished either by encapsulation of ribbon samples inan ampoule under vacuum or with inert gases or using a furnace withflowing inert gas during annealing. In either case, the heating rate is limitedby the sample insertion speed or controlled by the heating rate of the


furnace. Similar limits exist for cooling rates of the samples imposed by thequench technique or cooling rate of the furnace; however, the cooling ratesare typically not as important.

The primary crystallization reaction is thermally activated and is there-fore sensitive to both the annealing temperature and the annealing time.Many isochronal annealing studies of Fe96�zSixBz�xNb3Cu1 alloys havebeen performed to establish the relationship between these two parametersand the resulting microstructure (see Fig. 4.10) (Maslov et al., 2001; VanBouwelen et al., 1993; Varga et al., 1994b). The first important feature tonotice is the extremely slow grain growth after about 1000 s of annealingtime near the primary crystallization temperature. This arrested graingrowth allows full microstructure development after the typical annealingtime of 3600 s. The second feature of note is illustrated by the plotted line in

the graph, corresponding to theffiffiffiffiffiffieDt

pof Fe diffusing in a Fe–Si–B amor-

phous alloy, where eD is the diffusivity and t is time at temperature (Horvathet al., 1988). The calculation indicates that significant diffusion would beexpected for Fe at times as small as 3600 s, resulting in an order of magni-tude greater grain size than observed in these Fe–Si–B–Nb–Cu alloys. For

Annealing time (s)

848

K

823

K

776

K

no Nb/Cu

no Nb

Gra

in d

iam

eter

(nm

)

11

10

100

10 100 1000

Varga 773/798/823/848 K

van Bouwelen 776 K

Gupta 813 KAyers 823 K

√Dt for Fe–Si–B (am)

104 105 106

Figure 4.10 Variation of grain diameter with annealing time at various temperaturesabove the primary crystallization temperature of Fe96�zSixBz�xNb3Cu1 alloys. All have(x, z)¼ (13.5, 22.5), except van Bouwelen (12.5, 20.5) and Gupta (16.5, 22.5). Thetwo Ayers alloys are Fe76.5Si13.5B9Cu1 (no Nb) and Fe77.5Si13.5B9 (no Nb/Cu). Anneal-ing temperatures are indicated. Horvath’s diffusivity for Fe–Si–B (am) used to calculatea diffusion distance expected at 823 K (Horvath et al., 1988; Maslov et al., 2001; VanBouwelen et al., 1993; Varga et al., 1994b).


studies with short annealing times, liquid metal baths (e.g., Ga, Sn, etc.)were used with water or brine quenching.

In a study by Wang et al. (1997), improved magnetic performance andrefined grain size result from increased heating rate to an isothermal anneal-ing temperature above primary crystallization. By varying the heating ratefrom 8.3�10�3 to 4.3 K/s, the grain size was reduced from 14.6 to10.6 nm and the resulting initial permeability was tripled from 26,000 to92,000. This work and others on Fe73.5Si13.5B9Nb3Cu1 alloys emphasizethe importance of the early stages of crystallization on the nucleation andgrowth processes, the topic of Section 4.3 (Ramin and Riehemann, 1999b;Wang et al., 1997). Conventional annealing procedures under an applied pres-sure of 5 GPa resulted in the grain size reduction to about 5 nm for Fe73.5S-i13.5B9Nb3Cu1 alloys (Zhang et al., 1997).

Vazquez et al. have examined the effect of annealing at temperatureslower than the primary crystallization temperature on the permeability,coercivity, and magnetostrictive coefficient (Vazquez et al., 1994). Theseresults show a slight magnetic softening of the Finemet alloy due to relaxa-tion of the as-spun alloy (Tann�380 �C), followed by magnetic hardeningjust prior to crystallization of the alloy (400 �C�Tann�460 �C). Themagnetic hardening was attributed to Cu-cluster formation in the alloy.

Conventional annealing can, however, provide an undesirable inducedanisotropy that can limit the magnetic softness of certain alloys, especially (a)ones with low Curie temperature of the amorphous phase (e.g., Fe–Zr–Balloys) and (b) those with significant pair-ordering potential (e.g., (Fe,Co)–Zr–B). In the first case, at common annealing temperatures near primarycrystallization, the newly formed grains can remain far below their Curietemperatures, yet above the Curie temperatures of amorphous phase fromwhich they crystallize. The magnetization from the newly formed grainsinfluences the crystallization behavior, adding a uniform anisotropy on arelatively local scale to the sample, much the same as in a magnetic field-annealed samples (but with much longer range in that case) (Ito and Suzuki,2005). This can have deleterious effects due to the random orientation ofthe crystallizing grains and therefore local random-induced anisotropies.The induced anisotropy is somewhat small in these cases (<100 J/m3) butcan result in significant increases in the coercivity when the grain size hasbeen reduced to below about 15 nm in diameter (Suzuki et al., 2008a). Inthe latter case, pair ordering can lead to significant induced anisotropies asdiscussed in more detail in Section 2.2.3. One way of alleviating this effect isto perform rotating field annealing (also to be discussed in Section 2.2.3).

2.2.2. Joule annealingAn alternative method for crystallizing amorphous ribbon samples is theJoule annealing technique (also called current annealing) (Kulik et al.,1992). The technique, originally developed for relaxation of amorphous


alloys without crystallization (Allia et al., 1993b,c; Jagielinski, 1983), hasbeen successfully adapted for rapid crystallization rate using higher currentdensities (Allia et al., 1993d). This technique passes an electrical currentthrough the ribbon with densities in the range of 10–50 MA/m2 to providethe energy necessary for crystallization. The current may be pulsed (e.g.,<10A for 1 ms), applied stepwise, or continuously for times up to a fewminutes at currents between 1 and 10 A.

An advantage of the Joule annealing technique is the much largerheating rate compared to furnace annealing. In addition to potentialmodifications of the nucleation and growth for nanocrystalline alloys,this technique may provide a means to create otherwise inaccessiblemetastable crystalline phases. Heating rates in the range 102–103 K/s havebeen applied by this technique (Allia et al., 1993d). Performing Jouleannealing in a vacuum improves reproducibility by reducing tempera-ture gradients from the ribbon surfaces. Mechanical properties, includingstrain to fracture and hardness, are reported to have better performance byJoule annealing than conventional annealing (Allia et al., 1993a, 1994; Moyaet al., 2001).

During the crystallization process, the resistivity of the sample measuredas a function of the time of applied current has two distinct features withthermal origins (Mitrovic et al., 2000). When a large enough current isapplied, the sample crystallizes generating heat from the exothermic crystal-lization reaction; this results in a peak in the resistivity due to the increasedtemperature of the sample. After 10–20 s, the resistivity equilibrates as theheat generation from the applied current and structural changes in thesample are balanced with dissipation from the sample environment (radia-tion, convection, and conduction).

The temporal effect of current density on amorphous ribbons andresulting phases formed in Fe73.5Si13.5Nb3B9Cu1 alloys is presented inFig. 4.11. Analogous to the time–temperature transformation diagram inconventional annealing, a time–current density transformation diagramshows the phase relations for crystallization. At low current densities andshort times, the ribbons consist of amorphous phase. At intermediate timesand current densities, the sample partially crystallizes into a-(Fe,Si) or a0-Fe3Si phases, indicated by þ and �, respectively. At high current densityand long times, secondary crystalline phases are observed (indicated bycircles).

A drawback of this technique is the large temperature variations (�30 K)found as a function of position along the length of the ribbon (Allia et al.,1993b). For the class of nanocomposite magnetic alloys, the optimal perfor-mance can vary with isothermal annealing temperature changes of 5 K, sothermal control is critically important in these materials. Upscaling of thistechnique to the toroid fabrication level is another factor that has not beenfully examined.

Time (s)

Fe2B/Fe3B

Amorphous

α-FeSi/α¢-Fe3Si

Cur

rent

den

sity

(A

/m2 )

1010 × 106

60 × 106

20

30

40

50

100

Figure 4.11 Time–current density transformation (TJT) diagram showing the crystal-lization transformation with varying exposure time to a given current density inFe73.5Si13.5Nb3B9Cu1 alloys (Allia et al., 1993a; Allia et al., 1993d; Baricco et al.,1994; Gorrıa et al., 1993; Murillo and Gonzalez, 2000; Tiberto et al., 1996a). Dotindicates amorphous phase; þ, a-(Fe,Si); �, a0-Fe3Si; and o, Fe2B/Fe3B.


2.2.3. Magnetic field annealingWhen properly applied, induced anisotropies can be a transformative tool fortuning hysteresis loop shapes. From early studies by Yoshizawa and Yamauchi,the shape of the hysteresis loopwas shown to be influenced greatly by annealingsamples in a magnetic field (Yoshizawa and Yamauchi, 1989). An appliedmagnetic field during crystallization creates an induced uniaxial anisotropywith easy axis along the applied field direction for (Fe,Si)-based alloys. Themagnitude of the induced anisotropy is in the order of 5–50 J/m3.

During the magnetic field annealing process, two typical orientations areused to create an induced anisotropy (Ku) that dominates over otheranisotropies present in the material. Longitudinal field annealing creates asquare hysteresis loop in Fe–Si–Nb–B–Cu-type alloys, where switching isdominated by 180� wall motion (Yoshizawa and Yamauchi, 1989). Trans-verse field annealing shears the hysteresis loop, providing a lower perme-ability that is directly related toKu

�1. In this case, switching occurs largely byrotation of the magnetization into the applied field direction. Alloy compo-sition, annealing time and temperature, and magnetic field strength are allfactors that affect the anisotropy. Typically, the longitudinal field appliedduring annealing is limited to 1 kA/m due to field/furnace geometry con-straints. Transverse field annealing is performed in the 50–250 kA/m fieldrange. Examples of the differences in loops formed during the magnetic fieldannealing process for Fe73.5Si13.5Nb3B9Cu1 alloys annealed at 813 K for3600 s are shown in Fig. 4.12 (Herzer, 1996).

Magnetic field, H (A/m)

Ma

gnet

ic in

duct

ion,

B (

T)

−10

Fe73.5Si13.5B9Nb3Cu1

−1

0

1

0

Z

RF1

F2

10

Figure 4.12 DC hysteresis loops of nanocrystalline Fe73.5Si13.5Nb3B9Cu1 annealed at540 �C for 3600 s: (R) without applied magnetic field; (Z) with longitudinal appliedmagnetic field; (F2) with transverse applied magnetic field; (F1) first crystallizedwithout magnetic field and then transverse field annealed at 350 �C. Modified fromHerzer (1996).


In general, induced anisotropies shear the hysteresis loop in a way thatreduces the permeability and gives greater magnetic energy storage capacityto the material. Assuming that the hysteresis is small and that the loop islinear, the induced anisotropy (Kind) is related to the alloy’s saturationmagnetization (Ms) and anisotropy field (HK) through the equation:Kind¼m0MsHK/2. A maximum permeability can be estimated through theslope of the B–H hysteresis loop with the material saturating at the anisot-ropy field. By this consideration, the following equation can be used todetermine the permeability: mr¼m/m0¼Ms

2/2Kind. Using this expression,the permeability is 40,000, 600, and 75 for induced anisotropy values of15, 1000, and 8000 J/m3, respectively (for m0Ms¼1.23 T, a typical value for(Fe,Si)-based nanocrystalline alloys).

Magnetic field annealing can be performed either during or after primarycrystallizations; however, themagnitude ofKind is greatly reducedwhen a two-step annealing process is used. Single-step annealing of a Fe73.5Si13.5B9Nb3Cu1alloy at 530 �C in a 192 kA/m transverse field gives an induced anisotropy of30–50 J/m3 (Lovas et al., 1998). In contrast, an alloy of the same compositionannealed without a magnetic field at 530 �C to create the nanocrystallinemicrostructure and subsequently annealed in a 192 kA/m transverse field attemperatures up to 450 �C has an induced anisotropy limited to 7 J/m3. Thepermeability and remanence ratio were controlled independently when aFe73.5Si15.5B7Nb3Cu1 alloy was annealed with a magnetic field for part ofthe crystallization process immediately followed by a field free annealing period(Waeckerle et al., 2000). A range of anisotropies induced using magnetic

Field-annealing temperature (K)

Mag

netic

fiel

d-in

duce

d an

isot

ropy

(J/

m3 )

5000

10

20

30

40

50

550 600 650 700 750 800

803 K

813 K

843 K

850


tann= 3600 sHann> 185 kA/m

Figure 4.13 Magnetic field-induced anisotropy against magnetic field-annealing tem-perature for Fe73.5Si13.5Nb3B9Cu1 alloys annealed for 3600 s with applied magneticfield exceeding 185 kA/m. Circles: Herzer (1994a); squares: Yoshizawa and Yamauchi(1989) and Yoshizawa and Yamauchi (1990); triangle: Ferrara et al. (2000); downwardtriangle: Lovas et al. (1998). Closed symbols: field crystallized (no preanneal); opensymbols: conventional anneal (no field, temperature specified) with subsequent fieldannealing.


field annealing are shown in Fig. 4.13 for a Fe73.5Si13.5B9Nb3Cu1 alloy.Samples were annealed at temperatures above primary crystallization for3600 s with fields above 185 kA/m applied during annealing (closed symbols).We follow the terminology of Ohodnicki et al. and call these field-crystallizedsamples (Ohodnicki et al., 2008c). The open symbols indicate samples thatwere crystallized without magnetic field (as indicated), followed by magneticfield annealing after crystallization to provide induced anisotropy. The effect ofmagnetic field annealing on induced anisotropy for samples without priorcrystallization was found to be somewhat larger for most samples.

Considerably larger anisotropies are induced by magnetic field annealingin the (Fe,Co)-based alloys. Figure 4.14 demonstrates this effect on mag-netic field-annealed and magnetic field-crystallized alloys. The magneticfield-annealed samples were found to have a maximum in the inducedanisotropy for 50:50 ratio of Fe:Co, as might be expected for a pair-ordering model (see Chikazumi and Graham, 1997). On the other hand, asharp increase in induced anisotropy is observed at Co-rich compositions inthe field-crystallized (Fe,Co)78.8Nb2.6B9Si9Cu0.6 and (Fe,Co)88Zr7B4Cu1alloys (Ohodnicki et al., 2008d; Yoshizawa et al., 2004). This has beenattributed to a strong dependence of the amorphous phase Curie tempera-ture on the composition of the alloy (Ohodnicki et al., 2008d).

0.10

500

1000

1500

2000

2500

0

500

1000

1500

2000

2500

0.2 0.3 0.4 0.5

Co fraction

(a)

(b)

Co fraction

Mag

netic

fiel

d-in

duce

d an

isot

ropy

(J/

m3 )

Mag

netic

fiel

d-in

duce

d an

isot

ropy

(J/

m3 )

0.6 0.7 0.8 0.9 1.0

0.10 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

FA (Co,Fe)89Zr7B4/(Co,Fe)88Zr7B4Cu1FA (Co,Fe)90Zr10

FC (Co,Fe)89Zr7B4/(Co,Fe)88Zr7B4Cu1FC (Fe,Co)81Nb7B12FC (Fe,Co)90Zr7B3FC (Fe,Co)78.8Nb2.6Si9B9Cu0.6

Field annealed

Field crystallized

Figure 4.14 Induced magnetic anisotropy for (a) magnetic field-annealed samplesof (Fe,Co)89Zr7B4, (Fe,Co)88Zr7B4Cu1, and (Fe,Co)90Zr10 alloys (Fukunaga andNarita, 1982; Ohodnicki et al., 2008d) and (b) magnetic field-crystallized samplesof (Fe,Co)89Zr7B4, (Fe,Co)90Zr7B3, (Fe,Co)88Zr7B4Cu1, (Fe,Co)81Nb7B12, and(Fe, Co)78.8Nb2.6B9Si9Cu0.6 alloys (Ohodnicki et al., 2008d; Skorvanek et al., 2006;Suzuki et al., 2006; Yoshizawa et al., 2003).



Annealing-induced anisotropies are controlled by application of a staticmagnetic field during annealing, resulting in a coherent uniaxial anisotropy.However, magnetic-induced anisotropies are not exclusively found in mate-rials which have been magnetic field processed. Even in samples that havebeen annealed without applied magnetic fields, induced anisotropieshave been identified in samples where the annealing temperature exceedsthe Curie temperature of the amorphous matrix. The effect results from thelocal magnetic fields of the ferromagnetic grains as they form in the paramag-netic matrix, creating localized regions of induced anisotropy (not coherentacross the sample as in magnetic field annealing). This case is exemplifiedin Fe84Nb7B9 alloys, where the coercivity was lowered using a rotatingapplied field to remove annealing induced uniaxial magnetic anisotropies(Ito and Suzuki, 2005). In this case, the induced anisotropy is randomlydistributed, but on a larger scale than the magnetic exchange length.

2.2.4. Stress annealingStress annealing is a technique for creating induced anisotropy in nano-crystalline ribbons by applying a stress to the material during stress relaxa-tion, crystallization, or post-crystallization anneals. The anisotropyinduced in this way is proportional to the applied tensile stress and canbe used to create an easy axis that is parallel or perpendicular to theapplied stress direction (depending on the magnetoelastic effects of thealloy which are composition dependent). The effects are not directlyrelated to the magnetostriction of the alloy, rather the local atomicenvironment contributions to magnetostriction (anelastic polarization ofamorphous matrix) have been suggested to give rise to the inducedanisotropy due to stress annealing. A normalized anisotropy parameter(k) can be used to describe the stress-induced anisotropy (Ks) in a similarform to anisotropy from magnetostrictive sources, namely, Ks¼�2ks/3(Herzer, 1994b). Comparison of the magnetostrictive coefficient andnormalized anisotropy parameter for a series of Fe96�zSixBz�xNb3Cu1alloys annealed under different conditions is presented in Fig. 4.15. Thevolume fraction transformed seems to be the correlating factor between kand ls, leading to the conclusion that a magnetoelastic anisotropy isresponsible for the induced anisotropy, and it is mediated bycrystallization-induced stresses in the sample and an elastic polarizationof the amorphous matrix (Herzer, 1994b).

This anisotropy induced in samples by annealing in a stress field (some-times referred to as creep-induced anisotropy) tends to have orders ofmagnitude larger values than those samples annealed in a magnetic field.A linear dependence of the stress-induced anisotropy on the applied stressduring crystallization has been observed in Fe73.5Si13.5B9Nb3Cu1 alloysusing standard annealing temperatures and times (see Fig. 4.16). The highestvalues of induced anisotropy, near 8 kJ/m3, can reduce the permeability to a

Si content (at%)

k = -2/3 K/s

z = 18.5 lsz = 20.5 lsz = 22.5 lsz = 23.5 ls

z = 18.5 kz = 20.5 kz = 22.5 kz = 23.5 k

k an

d l s

(pp

m)

ls

0

-5

0

5

10

2 4 6 8 10 12 14 16 18 20

Figure 4.15 Comparison of a creep-induced anisotropy parameter and magnetostric-tive coefficient with variation of Si content in Fe96�zSixBz�xNb3Cu1 alloys. FromHerzer (1994b).

Stress (MPa)

Approxim

ate rela

tive permeability, m

r

Str

ess

indu

ced

anis

otro

py (

J/m

3 )

00

1000

2000

3000

4000

5000

6000

7000

8000

200 400 600 800 1000

1200600

300

150

100

75

Herzer 813 KHofmann 813 KFukunaga 803 K

Figure 4.16 Variation in stress-induced anisotropy with applied stress for Fe73.5Si13.5-Nb3B9Cu1 alloys annealed for 3600 s (at 803 (Fukunaga et al., 2000) or 813 K (Herzer,1994b; Hofmann and Kronm€uller, 1996)).


great extent (Hofmann and Kronmuller, 1996). Such materials have advan-tages over the commonly used gapped ferrite cores as they produce atunable permeability (by stress applied during crystallization) over a widefrequency range, with larger saturation magnetization and without thedetrimental leakage flux issues.

Annealing temperature (K)

Annealing time (s)

Str

ess-

indu

ced

anis

otro

py(J

/m3 )

Str

ess-

indu

ced

anis

otro

py (

J/m

3 )

7600

1000

2000

100

788 K139 MPa

778 K139 MPa

768 K

808 K/139 MPa

813 K/450 MPa

139 MPa

103 104 105

1000


tann = 3600 s

3000

4000

5000

6000

7000

8000845 MPa

718

630600

520527450

213353

272

236

15190

145139

82

780 800 820 840 860 880 900 920

Figure 4.17 (a) Stress-induced anisotropy variation with annealing temperature forFe73.5Si13.5Nb3B9Cu1 alloys annealed for 3600 s (circles: Hofmann and Kronm€uller(1996); squares: Alves et al. (2000); triangle: Lachowicz et al. (1997); downwardtriangle: Nielsen et al. (1994)) and with applied stress (MPa) marked for reference.(b) Effect of annealing time on stress-induced anisotropy for Fe73.5Si13.5Nb3B9Cu1alloys annealed at 768 (closed symbols), 778 (open symbols), 788 (right-filled symbols),808 (left-filled symbols), and 813 K (diamonds) and with applied stress 82 (circles), 139(squares), 145 (triangles), and 450 MPa (diamonds) (Alves et al., 2000; Hofmann andKronm€uller, 1996).


When crystallization is not allowed to fully progress, the induced anisot-ropy has a commensurately lower value. In Fig. 4.17, the stress-inducedanisotropy variation with annealing time and temperature is shown forFe73.5Si13.5B9Nb3Cu1 alloys. When the annealing temperature is variedfor samples annealed for 3600 s, the induced anisotropy is found to increasewith applied stress at all temperatures, but the stress only gives its fullest


effect when the temperature allows a large volume fraction of crystallites toform (near the primary crystallization temperature, see Fig. 4.17a). Thiseffect can be more clearly seen in Fig. 4.17b, where the dependence ofstress-induced anisotropy on annealing time is shown. With reference toFig. 4.10, the stress-induced anisotropy begins to saturate at annealing timesthat are consistent with the slowing of grain coarsening (indicating that themicrostructure is fully developed).

Typical domain structures for as-quenched ribbons consist of a “stresspattern,” resulting from the quenched-in stresses from the rapid solidifica-tion process (Schafer, 2000). Field-annealed specimens show wide stripedomains with magnetization perpendicular to the applied stress direction(and in the plane of the ribbon). A stripe domain width repeated with periodof �250 mm was observed by Kraus et al. for a sample with compositionFe73.5Si13.5B9Nb3Cu1 and annealed at 540 �C for 1 h and under a stress of150 MPa (Kraus et al., 1992). Similar transverse domain formation has beenobserved by others with stripe widths ranging from 25 to 150 mm, depend-ing on the annealing conditions (Alves and Barrue, 2003; Fukunaga et al.,2000; Hofmann and Kronmuller, 1996). Annealing at temperatures as lowas 330 �C for 4 h is enough to destroy the stress-induced anisotropy.

Stress-induced anisotropy in Fe–Si-based alloys has been interpreted tooriginate from magnetoelastic effects, atomic short-range pair ordering, andanelastic polarization of the residual amorphous phase. While the interpre-tations vary, a few facts about the structural aspects of stress-annealedsamples have been reported in common. Stress-annealed samples do notexhibit crystallographic texture or grain elongation (Hofmann andKronmuller, 1996; Kraus et al., 1992). The stress-induced anisotropy isdestroyed at temperatures where only short-range diffusion or relaxationeffects are possible (Herzer, 1994b; Hofmann and Kronmuller, 1996; Krauset al., 1992), and a stress-induced uniaxial anisotropy can be achieved inpreviously crystallized ribbons, although the kinetics for creating theinduced anisotropy is slower (Herzer, 1994b; Hofmann and Kronmuller,1996; Kraus et al., 1992).

Based on these observations, Kraus suggested the polarization of inter-atomic bonds due to anelastic strains formed in the intergranular amorphousphase during annealing resulted in the stress-induced anisotropy (Krauset al., 1992). Similar reasoning was used to describe the induced anisotropyfrom sputtered SiO2 coatings on Fe–Si-based nanocrystalline alloy ribbons(Delreal et al., 1994). Herzer found a strong correlation between both themagnetostriction of the nanocrystallites and the induced anisotropy as afunction of Si content in alloys composition Fe96�zSixNb3Bz�xCu1(Herzer, 1994b). From this observation, the induced anisotropy was attrib-uted to the magnetoelastic effect from the crystalline phase caused by ananelastic polarization of bonding in the amorphous matrix, which occurredduring stress annealing. Hofmann and Kronmuller suggested use of the Neel


pair order model to describe the effect (although they do not rule out eitherof the preceding opinions) (Hofmann and Kronmuller, 1996).

The recent work of Ohnuma et al. has shown the anisotropy in an X-raydiffracted beam from the (6 2 0) planes of the Fe3Si phase in stress-annealedFe73.5Si15.5Nb3B7Cu1 alloys, when the sample is rotated parallel and perpen-dicular to the applied stress direction (Ohnuma et al., 2003a, 2005). As theapplied stress during annealing was increased from 10 to 621 MPa, so toowerethe deviations between the d-spacings in the parallel and perpendicular orien-tations (see Fig. 4.18). This study provides physical evidence for plastic flow ofthe residual amorphous phase during the strain-annealing process, resulting inan induced anisotropy with magnetoelastic origin (Ohnuma et al., 2005).

2q (degree)

H (A/m)

B (

T)

(a)

Inte

nsity

(ar

b. u

nits

)

(b)

45.5

621 MPa

-4000

-1.0

-0.5

0.0

0.5

1.0

-2000 0 2000

621 MPa

334 MPa

103 MPa

10 MPa

4000

334 MPa

103 MPa

10 MPa

46.0 46.5 47.0 47.5

Figure 4.18 (a) Magnetization curves and (b) XRD profiles of Fe73.5Si15.5Nb3B7Cu1ribbons annealed under different tensile stresses. All curves in sad were measured alongthe RD (parallel to the tensile stress). In (b), the circles indicate a diffraction vectorparallel to the RD, while the lines mark a vector perpendicular to the RD.Reprinted withpermission from M. Ohnuma, et al. Applied Physics Letters 86, 152513, (2005). Copyright2005, American Institute of Physics.


Stress annealing has also been reported in conjunction with Jouleannealing. An induced anisotropy as high as 1000 J/m3 was reported foran alloy with composition Fe73.5Si13.5Ta3B9Cu1 (Gonzalez et al., 1994).The maximum induced anisotropy was observed for short annealing times(less than 30 s) at a large enough current density (30–35 A/mm2) to pro-mote primary crystallization (Miguel et al., 2000). However, the hysteresisloops do not exhibit the same constant permeability over a wide field rangeas the conventionally stress-annealed samples. This may be an indication of aswitching mechanism different than the coherent rotation typicallyobserved in conventionally stress-annealed samples.

Alves et al. have used flash annealing under an applied stress to achieveinduced anisotropy in an alloy with composition Fe74.3Si15.5Nb2.7B6.5Cu1(Alves and Barrue, 2003; Alves et al., 2000). Using the activation energy of4.5 eV/atom, the temperature necessary to achieve the optimal microstruc-ture was estimated in a short annealing time, in this case 660 �C and 15 s.The resulting anisotropy of 2340 J/m3 was obtained with an applied stress of270 MPa (Alves and Barrue, 2003). A transverse stripe domain structure wasobserved with domain widths of 150 mm, resulting in permeabilities aslow as 300.

Even though stress annealing has clear benefits for applications where thepermeability must be low, there are some difficulties to overcome forcommercial application. The common industrial technique used for stressannealing of amorphous alloys involves applying a tensile stress to the alloyas the ribbon is passed through a furnace. Using this process for nanocrystal-line alloys results in alloy embrittlement as the amorphous precursor crystal-lizes, limiting this technique’s general use. Yanai et al. have used acontinuous stress-annealing furnace with tensile stresses limited to150 MPa to demonstrate induced anisotropy in a rapid, consistent mannerover lengths of ribbon up to 50 cm (Yanai et al., 2005). While ribbonbrittleness was not discussed, cores with 3 mm ID were produced from thestraight, annealed ribbons.

Recent efforts to address this problem have shown some success bywrapping a pair of ribbons with similar compositions into a toroidal shapeprior to devitrification (Gunther, 2005). The ribbon pair is selected to havecrystallization temperatures separated by 20 K so that the density reductionthat accompanies crystallization (typically �1%) can be used to create thenecessary tensile stress on the sample. A resulting permeability of 8000 wasachieved by this technique. A drawback of this technique is the necessity ofone ribbon being magnetostrictive to get the induced stress effect, resulting inhigher losses than a magnetostriction-free alloy. Fukanaga et al. used a tech-nique to constrain the ribbon samples at different toroid radii (between 1 and3.2 cm ID) to control the stress within the sample and ultimately optimize thestress state of the core simply by geometry (Fukunaga et al., 2002a). Thisresulted in constant, relative permeabilities between 260 and 300 for frequen-cies up to 1 MHz. While this technique showed lower losses compared to a


gapped ferrite core, the flexibility in controlling sample inductance is limitedby the fixed core geometry (Fukunaga et al., 2002a; Yanai et al., 2005).

2.3. Core fabrication

Most cores consist of ribbon windings around a mandrel to create a laminatedstructure referred to as a tape-wound core. Due to ribbon embrittlement afterannealing, amorphous ribbons are typically wrapped prior to primary crystal-lization. When long, continuous ribbons are wound in this manner, theresulting core has low losses and high permeability into the hundreds of ofkHz frequency range (Yoshizawa et al., 1988a). This fabrication techniquehas limitations in the geometry and size of the resulting core.

Other methods have been investigated for core fabrication to allowmore flexibility in the geometry of the core shape and size. Powder coreshave been produced from melt spun ribbon materials with subsequentmilling, annealing, and consolidation. Various milling techniques havebeen employed to achieve both ribbon flakes (e.g., 1–3 mm length) andpowders (e.g., 1–1000 mm). Two different types of annealing procedureshave been reported: crystallization annealing above primary crystallizationand stress relaxation annealing (usually at lower temperatures). Sometimesboth annealing steps are done simultaneously after core fabrication. Hot andcold pressing have been used, typically with a binder to ensure isolation ofthe particles and a high degree of densification.

Some general characteristics have been observed for nanocrystalline softmagnetic alloy powder cores, which are described in the following para-graphs. First, regardless of themillingmethod, the coercivity of the cores tendsto increase as smaller sized particles are used tomake the core (Kim et al., 2003;Leger et al., 1999). As an example, cores made from 56- to 90-mm-sizedparticles were found to have more than 3.5 times the coercivity of coresmade from 1- to 1.4-mm flake cores (Nuetzel et al., 1999). This effect islikely due the larger amounts of deformation imposed on the ribbons tocreate the smaller particles. Stress relaxation by annealing has been per-formed; however, the coercivity is never recovered to a level equal towound ribbon cores (Heczko and Ruuskanen, 1993; Muller et al., 1999;Nuetzel et al., 1999).

Next, cold-pressed powder cores tend to have lower permeability thanhot-pressed powder cores; however, their switching frequency limit tendsto be higher for the cold-pressed than for hot-pressed cores. The reducedvalue of permeability for cold-pressed cores is due to the high internaldemagnetization fields from the smaller isolated particles that make up thecore. Since the particles are well isolated, the eddy current effects remainsmall until frequencies near 1 MHz (Kim et al., 2003; Leger et al., 1999).Hot pressing improves the magnetic performance at lower frequencies byproviding higher density compacts and higher permeability; however, the


particles do not remain isolated resulting in higher eddy current losses athigher frequencies (Iqbal et al., 2002; Nuetzel et al., 1999). Iqbal et al.report a high packing density and good uniformity for a puck milled powdercore annealed at 540 �C and possessing an initial permeability of 1100 butwith a relaxation frequency of 10 kHz (Iqbal et al., 2002).

Finally, coatings have been used to aid in separation of individualparticles prior to consolidation. Jang et al. showed a factor of 2 improvementin core loss at 10 kHz by applying a Zn-phosphate coating to powders withsize less than 45 mm over powders without the coating (Jang et al., 2006;Kim et al., 2003).

While the hysteretic and core losses tend to be larger for powder cores,the low, constant permeability is beneficial to some applications (e.g.,reactors and choke coils). With the proper binder, powder cores may besuitable for machining, allowing better flexibility in the fabrication ofcomplex core geometries.

2.4. Other processing methods

2.4.1. Thin film processingVarious nanocrystalline soft magnetic thin film materials have been pro-duced by either devitrification of amorphous films or direct formation ofnanostructures via heated substrates. Early work in this area was accom-plished by inhibiting grain growth in Fe–M–C alloys (M¼Zr, Hf, Ta, etc.)by formation of an MC phase at the triple points during crystallization ofsputtered amorphous films (Hasegawa et al., 1993). Due to the reduced sizeof the carbide phase (<3 nm diameter), the material maintained goodintergranular coupling and exhibited strong soft magnetic performancewith saturation induction of �1.6 T and 1 MHz permeability of 6000.

Thin film materials were found to exhibit coercivity proportional to thegrain size squared (Hc�D2) for Fe–Si–B–M–Cu alloys (where M¼Nb, Ta,W, Mo, Zr, V) (Yamauchi and Yoshizawa, 1995). This result differs from theD6 dependence for coercivity observed in ribbon materials and is due to thetwo-dimensional geometry of the thin film sample (compared to the three-dimensional geometry of the ribbon). A similar correspondence betweengrain size and coercivity was observed recently in nanocrystalline Fe66Ni11-Co11Zr7B4Cu1 alloys with low ferromagnetic resonance line widths pro-duced by a one-step physical laser deposition onto a heated substrate (Yoonet al., 2008). The origin of the reduction in grain size dependence withnanostructure dimensionality is discussed in more detail in Section 6.3.

2.4.2. Mechanical alloying and powder processingHigh-energy ball milling can be used to mechanically alloy powders ofnanocrystalline soft magnetic alloys, where the repeated process of weldingand fracturing of the alloy imparts enough energy for significant grain


refinement or vitrification. This is different from the milling of rapidlysolidified ribbons, where the starting materials are already amorphous.The breakingup of ribbons by ball milling has been discussed in Section 2.3.

Several studies of Fe73.5Si13.5B9Nb3Cu1 alloys have investigated mechan-ical milling effects on magnetic properties. When elemental powders of thedesired composition are mechanically alloyed, the resulting powders tend tohave high coercivity which increases linearly with milling time upto �3.6�106 s, to a maximum value between 7 and 25 kA/m (Chiriacet al., 1999b; Kovac et al., 2002; Raja et al., 2000). Milling of amorphousor partially crystalline ribbons of the same composition tends to have anincreased coercivity for milling up to 2.5�106 s and decreasing coercivityfor longer milling times (Fechova et al., 2004). The peak value of coercivitywas around 10 kA/m and was attributed to a change in the magnetizationswitching mechanism to coherent rotation as the critical single domainparticle size was produced. Further milling was consistent with the formationof superparamagnetic particles and a commensurate reduction in coercivity.

Mechanically milled nanocrystalline Fe66Ni11Co11Zr7B4Cu1 alloyswere prepared from melt spun ribbons with subsequent anneal for crystalli-zation and then screen printed on Mylar to produce thick film cores(Baraskar et al., 2008). The sample milled for 10 h was found to have asaturation magnetization of 1.3 T and a coercivity of about 5.8 kA/m withan average particle size of about 5 mm. The screen-printed samples showedan ferromagnetic resonance (FMR) linewidth of about 80 kA/m.

Powder cores provide a sheared hysteresis loop that can be advantageousfor applications where low, constant permeability is required over a largefield range. Near net-shaped cores have been examined for DC–DC con-verter applications at frequencies around 100 kHz (Vincent and Sangha,1996). Oxide-coated coarse flakes (0.5–2 mm diameter) were hot-pressed at550 �C to produce the desired permeability (above 1000). Insulation layerswere produced by a Mn-doped phosphoric acid solution, resulting inimproved high-frequency performance over uninsulated pressed cores. Inanother study, samples of Fe73.5Si13.5B9Nb3Cu1 were shock-compacted toform dense cores from powdered amorphous ribbons (Ruuskanen et al.,1998). Annealing was required to provide the desired nanocrystallinemicrostructure and reduce stress-induced anisotropies. The preparation ofcores made from powder inert-gas condensation, high-energy ball milled,and cryogenic melted powders has been recently reviewed by Mazaleyratand Varga (2000).

2.4.3. Surface treatments and laser processingAs-spun ribbons have large-scale undulations, in the order of tens ofmicrons, on their wheel-side surfaces resulting from the rapid quenchingof the alloy. The free side of the as-spun ribbons tends to have a smoothersurface than the wheel side with much larger scale fluctuations observable


without microscopes. This surface morphology has been observed by scan-ning tunneling microscopy (STM) and atomic force microscopy (AFM) tobe slightly changed by primary crystallization of Fe73.5Si13.5B9Nb3Cu1ribbon samples (Gorrıa et al., 2003; Nogues et al., 1994). However, AFMand STM studies have shown that crystallization of Fe86Zr7B6Cu1 andFe44Co44Zr7B4Cu1 alloys results in an increased surface roughness, consist-ing of elliptically shaped bumps a few hundred nanometers in diameter(Hawley et al., 1999; Nogues et al., 1994). This observation has beenattributed to the presence of stress effects from the crystallization processwhich are more limited in the (Fe,Si)-based alloys due to the redistributionof Si or the influence of higher diffusivity on the surface of the ribbonduring crystallization.

Kollar et al. have used a XeCl-excimer laser to melt pits into the ribbonsurface a few microns deep (Kollar et al., 1999). The pits were found toincrease the local surface coercivity by �300% compared to the regionswithout laser treatment. The sample coercivity increased as the pits werespaced more closely. As observed by Kerr microscopy, the transversecomponent of the magnetization switched at the laser surface treated area(although longitudinal components of magnetization did not see to beaffected) (Zelenakova et al., 2001). Small core loss benefits were reportedfor close line spacing of laser-treated samples at frequencies above 20 kHz(Ramin and Riehemann, 1999a).

Laser processing has been used to crystallize amorphous ribbons in recentstudies. An advantage of this technique is the laser’s ability to achieve rapidheating and cooling rates and uniformly crystallize the sample in a shortperiod of time. Lanotte and Iannotti used a CO2 laser irradiation techniqueto crystallize amorphous Fe73.5Si13.5B9Nb3Cu1 ribbon samples by translat-ing the laser beam over the sample at a rate of 3 cm/s and under incidentlaser power between 20 and 50 W (Lanotte and Iannotti, 1995). While thistechnique showed the capability of laser annealing to establish the nano-crystalline microstructure, the grain sizes were not as fine as those producedby conventional furnace annealing. Due to the larger grain sizes, the result-ing permeability was lower for the laser-processed ribbons than for theconventionally annealed samples.

3. Alloy Design Considerations

A wide variety of nanocrystalline soft magnetic alloy compositionshave been explored, necessitating a short taxonomy to distinguish a fewimportant varieties. As a matter of classification, the alloys can be arrangedinto groups that are distinguished by the phases formed during primarycrystallization, their compositions, and ultimately their properties. In

Table 4.2 Elemental makeup of typical nanocomposite soft magnetic alloys with fourmajor components (grouped parenthetically): magnetic transition metals (MTM), earlytransition metal (ETM), metalloid/post-transition metals (PTM), and late transitionmetal (LTM)

Fe Cr

Co MnNi

!66�91

Ti V

Zr Nb Mo

Hf Ta W

0@ 1A2�8

B C

Al Si P

Ga Ge

0@ 1A2�31

Cu

Au

� �0�1

Atomic percentages of common ranges for each major component are shown in subscript. Specific alloydesignations are shown in Table 4.1.


general terms, a nanocrystalline soft magnetic alloy consists of elements fromat least two, but typically three or four of the following groups: magnetictransition metal (MTM), ETM, metalloid or post-transition metals (PTM),and LTM (Table 4.2).

Ferromagnetic transition metals are obviously a necessary componentof these alloys, with larger quantity increasing the magnetization of thealloy. Cr and Mn are part of this designated group since they typicallycombine substitutionally with the ferromagnetic elements in a nanocom-posite alloy (although they are clearly not ferromagnetic elements) (Sobczaket al., 2001; Tamoria et al., 2001). A less obvious, but equally essential,component is the ETM (esp. Nb, Zr, Hf, Ta, Mo), which preventsexcessive grain growth during annealing due to its ability to decrease thediffusivity of the MTM. Ti and V are less effective in preventing graingrowth in these materials. The ETM elements have been found to inhibitthe formation of borides and impede grain coarsening. While not all ofthese alloys possess metalloids (e.g., B, Si, Ge, etc.) or post-transition metals(e.g., Al, Ga, etc.), most alloys include at least one of these elements to aid inglass formation and provide thermal stability for the amorphous phase.Finally, in some alloys, the LTM elements (e.g., Cu, Au) have been foundto aid in the nucleation of the primary crystallites, but not all alloys benefitfrom this alloying addition.

Specific classes of nanocrystalline soft magnetic alloys have been identi-fied largely by the primary crystalline phase. The first class of alloys, withtrade names Finemet or Vitroperm, has either the solid solution a-(Fe,Si) oratomically ordered Fe3Si phase as the primary crystallite and typically has acomposition of Fe–Si–Nb–B–Cu (Herzer, 1996; Yoshizawa et al., 1988a).The Fe content in these alloys typically falls in the range of 67–79 at% withat least 5 at% Si. Both Nb and Cu are essential for the microstructuredevelopment in these alloys. These alloys are presently the only nanocrystal-line soft magnetic alloys available commercially (via Hitachi Metals (Japan),Vacuumschmelze (Germany), Imphy (France), etc.). The second class ofalloys, with trade name Nanoperm (via Alps Electric Co. (Japan)), is made


up of a-Fe primary crystallites and typical composition Fe–Zr–B–Cu(Makino et al., 1997; Suzuki et al., 1991a). These alloys typically have80–90 at% Fe which provides a larger saturation magnetization comparedto the (Fe,Si)-based alloys. The third class, HITPERM alloys, has a0-(Fe,Co) or a-(Fe,Co) as the primary crystalline phase and typical compositionsof Fe–Co–Zr–B–(Cu) (Willard et al., 1998). Other alloys that do not fitthese categories include Co–(Fe)–Zr–B–(Cu) and Ni–(Fe,Co)–Zr–B–(Cu)alloys where either the e-Co or g-(Fe,Co,Ni) phases form during primarycrystallization (Pascual et al., 1999; Willard et al., 2001a; Willard et al.,2002a). The alloy composition in each class requires amorphous phaseformation using rapid quenching and a fine-grained, equiaxed microstruc-ture within a residual amorphous matrix phase after an annealing process.

The following sections discuss the processing, structure, and propertyconsiderations, which put limits on the potential compositions of nanocrys-talline materials with exceptional magnetic performance. These criticalfactors for good alloy design include (1) glass-forming ability of an amor-phous precursor; (2) primary crystallization of a desirable magnetic phase;(3) alloying additions to form and/or maintain an optimal microstructure;(4) optimization of intrinsic magnetic properties; and (5) control of themagnetic domain structure.

3.1. Glass forming and primary crystallization

The desired microstructure, with limited grain size and large nucleationdensity, has been most easily achieved by first forming an alloy consisting ofa single, amorphous phase followed by an isothermal annealing step forcrystallization (as described in Section 2.2). The amorphous precursor tothe nanocrystalline alloy puts limitations on the amount of MTM in thealloy due to the necessary introduction of alloying elements used to stabilizethe liquid. As the liquid is most stable for alloy compositions at the eutecticpoint (i.e., liquid in equilibrium at the lowest temperature), the addition ofalloying elements having deep eutectics with MTMs is most desirable. Thedeep eutectics ensure that the maximum amount of magnetic transition metalcan be incorporated into the alloy. In Fe–Si–Nb–B–Cu alloys, a wide rangeof good glass-forming compositions are available due to the large amounts ofSi, Nb, and B, which have deep eutectics with Fe. In Fe–M–B and (Fe,Co)–M–B alloys (where M¼Zr, Nb, Hf), the glass-forming region is smaller andthe best performance (with highest magnetization) is near the Fe/Co-richcompositions. In both cases, increasing the glass-forming elements (e.g., B,M, and/or Si) aids in the formation of the amorphous precursor phase—anessential starting point for optimal microstructure development. However,consideration of Curie temperature of the residual amorphous phase and thesaturation magnetization of the alloy requires as much MTM as possible,requiring sensitivity to all issues in the alloy design process.

ETM atomic radius (Å)

Fe89 – xMxZr4B6Cu1

Crystalline (BCC)

Amorphous

Cr V Ti/Mo/W Nb/Ta Zr/Hf

1.800

1

2

3

4

5

1.85 1.90 1.95 2.00 2.05 2.10 2.15 2.20

ET

M c

onte

nt (

at%

)

Figure 4.19 Glass-forming limits for as-spun Fe89�xZr4MxB6Cu1 alloys with varyingearly transition metal radius (Suzuki et al., 1991c). Dots indicate amorphous phase andopen circles indicate BCC phase.


Most nanocrystalline soft magnetic alloys have boron as an alloying ele-ment. The reasons for this include its stabilizing effect on the amorphous phase(and increase inTx1); its near zero solubility in the nanocrystallites of a-Fe, a0-(Fe,Co), anda-(Fe,Si); and its strengthening of the intergranular coupling aftercrystallization (via the increased Curie temperature of the residual amorphousphase (Suzuki et al., 1996)). The addition of small amounts of Cu to Fe–Si–Nb–B alloys has been shown to increase the number of nucleation sites duringprimary crystallization (Noh et al., 1990). After annealing,Cu-rich precipitateshave been observed due to coarsening of these elements which are not solublein the MTM-rich matrix (Hono et al., 1992; Zhang et al., 1996b).

In Fe89�xZr4B6Cu1Mx alloys, the ETM type and amount are very impor-tant for glass formability. As illustrated in Fig. 4.19, ETMs with large atomicradii tend to have greater glass formability and larger content of these elementsaids in glass formation (Suzuki et al., 1991c). The use of Hf and Zr is mostcommon in these alloys due to their easy of vitrification with minimal Bcontent; however, the glass-forming ability can be improved with otherETMs when concurrent substitutions with B are made (Suzuki et al., 1993).

3.2. Microstructural and microstructure evolutionconsiderations

The unusual microstructure, consisting of nanocrystalline grains surroundedby an amorphous phase, facilitates the low core losses found in thesealloys. Control of the microstructure necessitates an understanding of


compositional effects on the resulting microstructure and the processingthat allows the best grain refinement. Achievement of the desired microstruc-ture necessitates a large nucleation density at the early stages of crystallizationcombined with slow crystallite growth rate to maintain the fine-grain size.Conventional amorphous alloys relied on metalloids to aid in glass forma-tion while maintaining a large atomic fraction of MTMs. However,the magnetic properties are found to degrade rapidly with prolongedexposure at 300 �C due to the dendritic a-Fe formation once nucleationhad occurred (Naohara, 1996a). Crystallization occurs more quickly inFe–Si–B alloys at higher temperatures, with smallest achievable grainssizes limited to�40 nm (Tong et al., 1992). In nanocrystalline soft magneticalloys, the use of ETM alloying elements has been found to both aid in glassformability of the amorphous precursor alloy (by raising Tx1) and retard graingrowth during the isothermal annealing step (Naohara, 1996b; Yoshizawaand Yamauchi, 1990). Furthermore, the addition of an element without solidsolubility in Fe (e.g., Cu or Au) has been found to increase the nucleationdensity (Kataoka et al., 1989; Yoshizawa and Yamauchi, 1990). The bestrefinement of the microstructure by crystallization of an amorphous precursorvia annealing has been found to correlate with the smallest value of the freeenergy barrier to nucleation (Shi et al., 1995).

A widely accepted model for the crystallization of (Fe,Si)–Nb–B–Cualloys is shown in Fig. 4.9. In 1990, Yoshizawa and Yamauchi discussed thebasis of this model in the most general terms, being largely refined withspecific details by Ayers et al. and Hono et al. (Ayers et al., 1994; Honoet al., 1992; Yoshizawa and Yamauchi, 1990). The four-stage microstruc-ture evolution process begins with the rapidly quenched alloy consisting of acompositionally homogeneous amorphous phase (Ayers et al., 1997, 1998;Hono et al., 1999). After the alloy has been rapidly solidified in the first stageof microstructure evolution, the resulting amorphous alloy is isothermallyannealed. The development of a uniform nanocrystalline microstructurethroughout the full volume of the material is only possible if crystallization isavoided during the rapid solidification process.

Due to the significant separation of primary and secondary crystallizationtemperatures for Fe96�zSixBz�xNb3Cu1 alloys (with 18.5<z<23.5 and15<x<16.5), a wide range of annealing temperatures will result in thedesired nanocrystalline microstructure. Typical annealing conditions consistof isothermal temperatures (spanning the range from crystallization onsetto �100 �C above onset) and times near 3600 s. The second stage is identi-fied by the formation of fine-grained Cu-rich regions within the amorphousmatrix phase. The positive heats of mixing of Cu with Fe and Nb andnear zero value for Cu with B are thought to be largely responsible forthe Cu-clustering effect. This stage has been observed during short annealingexperiments by 3D atom probe field ion microscopy (APFIM) (Honoet al., 1991, 1993) and extended X-ray absorption fine structure (EXAFS)


(Ayers et al., 1993, 1994; Kim et al., 1993). It is expected to also occur in theearly part (first hundreds of seconds) of the conventional annealing process,although Cu clustering has been observed even below the primary crystalli-zation temperature (Kim et al., 1993). These Cu clusters are limited in sizeduring the second stage to less than a few atomic planes in size making themdifficult to observe by electron microscopy (Ayers et al., 1993). The Cuclusters have atomic coordination consistent with the FCC phase as deter-mined by EXAFS (Ayers et al., 1993; Kim et al., 1993). A 3D APFIM studyshowed the Cu-cluster density in the alloy was about 1024/m3, a value highenough to be consistent with the number density of nanocrystalline grains inthe final microstructure and consistent with values from the electron micros-copy studies (Hono et al., 1999; Tonejc et al., 1999a). When the Cu contentof the alloy was less than 1 at%, the resulting microstructure suffered frominhomogeneous grain size with resulting deterioration of magnetic properties(Yoshizawa and Yamauchi, 1990).

Heterogeneous nucleation of a-(Fe,Si) crystallites on the preexisting Cuclusters occurs during the third stage of microstructural evolution (Ayerset al., 1993). Samples annealed for 600 s at the optimal annealing temperatureshow direct contact of the Cu-rich clusters with each a-(Fe,Si) nanocrystal-line grain, as observed by APFIM (Hono et al., 1999). The Cu clusters remainat the interphase interface as the crystallites grow and the remaining amor-phous phase becomes enriched in Nb and B due to their low solubility in thecrystalline phase (Hono et al., 1999). During this early stage of crystallization,the a-(Fe,Si) crystallites tend to have larger amounts of Si than the overallcomposition, near 16 at%, by Mossbauer spectroscopy (Knobel et al., 1992).The well-known Nishiyama–Wasserman or Kurdjumov–Sachs orientationrelationships between the FCC and BCC close-packed planes/directions mayprovide the low-energy interface, enabling an easier nucleation by the intro-duction of Cu in these alloys. This may be a reason for the greater stability ofthe a-(Fe,Si) phase over the intermetallic phases which tend to form whenslow cooling is used instead of rapid solidification.

The fourth stage is characterized by the coarsening of the (Fe,Si)-richcrystallites and stabilization of a diffusion-inhibiting, residual amorphousphase, enriched in Nb, B, and Cu. This stage ultimately results in theoptimum microstructure consisting of 70–80 vol% crystalline phase withgrain diameters near 10 nm. The remaining amorphous phase surrounds theequiaxed crystallites forming a 1- to 2-nm-wide region between grains. Thecrystallites formed by this process are enriched in Fe and Si compared tothe remaining amorphous phase, which has higher Nb and B contents(Hono et al., 1991, 1993). The Si content of the crystalline phase was progres-sively increased from stage 2, reaching 18–20 at% in the optimally crystallizedsample (Herzer, 1990; Knobel et al., 1992). As crystallization progressesduring the fourth stage, atomic ordering in the crystalline phase having theD03 structure and Fe3Si composition is found (as discussed in Section 4.4)


(Ayers et al., 1998; Herzer and Warlimont, 1992). Annealing at tempera-tures above 600 �C has shown increased crystallite Curie temperatures, anindication of reduced Si content by this thermal treatment (Herzer, 1990).The arresting of the grain growth for extended annealing times in theseFe96�zSixBz�xNb3Cu1 alloys is due to the residual amorphous matrix phase,which prevents both the contact of adjacent nanocrystallites and the result-ing grain boundary diffusion. Since the grains do not share a boundary, thesurface area-driven coarsening of the grains does not occur. With sufficientannealing time at the optimum annealing temperature, the Cu clusterscoarsen by Ostwald ripening and are commonly seen by XRD (Zhanget al., 1996a). It is also important for good magnetic properties that inter-metallic phases, such as Fe2B and Fe3B, are avoided at primary crystalliza-tion. Typically, these phases are observed if the annealing temperatureexceeds about 600 �C, resulting in relatively large intermetallic boride phasesto form (50–100 nm diameters) at the expense of the intergranular amorphousmatrix.

The role of Nb and Cu on microstructure refinement in theFe96�zSixBz�xNb3Cu1 alloys is illustrated in Fig. 4.20, where a schematicmicrostructure is shown for four (Fe,Si)-based materials. The combinationof both Nb and Cu in the Fe–Si–B base alloy is necessary to provide theoptimized microstructure (Noh et al., 1990; Yoshizawa and Yamauchi,1990). Less than 3 at% Nb results in increased grain sizes (above 15 nmdiameter), which significantly reduced the magnetic performance ofthe alloys (Ayers et al., 1994; Yoshizawa and Yamauchi, 1991). The additionof a few at% of ETM elements improves the stability of the nanocrystallinemicrostructure; however, too much of these elements result in a considerable

Equiaxed grains ofa-(Fe,Si) with Nb/B-rich

residual amorphous matrix(8–10 nm)

10 nm100 nm 100 nm 100 nm

Fe73.5

Si13.5

B9Nb

3Cu

1550 °C 1800 s

Fe74.5

Si13.5

B9Nb

3550 °C 1800 s

Fe76.5

Si13.5

B9Cu

1550 °C 1800 s

Fe77.5

Si13.5

B9

550 °C 1800 s

no CuEquiaxed grains of

a-(Fe,Si) and Fe23B6(30–50 nm)

no NbSpheroidal

a-(Fe,Si) grains(50–100 nm)

no Nb/CuLarge dendritic grains

(1–2 mm)

(a) (b) (c) (d)

Figure 4.20 Schematic diagram of the evolved microstructures for amorphous alloysannealed at 550 �C for 1800 s: (a) Fe73.5Si13.5B9Nb3Cu1, (b) Fe74.5Si13.5B9Nb3,(c) Fe76.5Si13.5B9Cu1, and (d) Fe77.5Si13.5B9.


decrease in the Curie temperature of the amorphous phase and degradedmagnetic performance. The absence of Cu in the alloys showed a muchsmaller nucleation rate and consequently larger grain sizes (Yoshizawa et al.,1988a). Amounts of Cu as small as 1 at% provide a substantial increase in theseparation of primary and secondary crystallization temperatures, allowing themicrostructure to evolve without intermetallic borides (Noh et al., 1990).

Similar stages in microstructure evolution are found in Fe–Zr–B and(Fe,Co)–Zr–B alloys; however, the fine-grained microstructure does notalways require Cu in these alloys (which removes stage 2 of the process). Forinstance, in the (Fe0.5Co0.5)88Zr7B4Cu1 alloy, Cu was not found to clusterduring the early stages of annealing and was partitioned to the intergranularamorphous phase as the nanocomposite microstructure evolved duringannealing (Ping et al., 2001). The lessened glass-forming ability of thesealloys and compositional fluctuations in the rapid solidification process maybe reasons for the large number of nucleation sites in the as-cast ribbonswithout Cu (Goswami and Willard, 2008; Suzuki et al., 1994). AlthoughCu is not necessary for producing the nanocomposite microstructure, insome cases, it has been shown to improve the soft magnetic properties.

Replacement of the Cu as a nucleation aid has been investigated in severalstudies. The substitution of the noble metals Pt and Pd for Cu in theFe73.5Si13.5B9Nb3Cu1 alloy resulted in a significant increase in the crystalliza-tion onset temperature; however, the primary crystallization products wereFe3B and a-(Fe,Si), with 20 nm grain diameters (Conde et al., 1998). Thepresence of the Fe3B phase and the larger than desired grain size indicate thatPt and Pd do not share the same role in the crystallization process with Cu.Substitution of Ag for Cu resulted in larger grain sizes (above 30 nm) andcommensurate higher coercivity (�10 A/m) (Chau et al., 2005). On theother hand, substitution of Au for Cu has been demonstrated to providesimilar microstructure evolution (Kataoka et al., 1989).

The microstructure evolution is critically dependent on the amount andtype of ETMs. Many studies have examined the role of ETMs in theFe73.5�xSi13.5þxB9M3Cu1 alloys where Ti, V, Cr, Mn, Zr, Mo, Hf, Ta,and W have replaced Nb. A summary of the grain size variation withannealing temperature for different ETM substitutions is provided inFig. 4.21. A clear trend in the grain size can be observed, with smallerETM elements (e.g., Mn, V, Cr, Ti) acting as a less effective deterrent tograin growth and large ETMs (esp. Mo, Hf, Ta, and Nb) are good diffusioninhibitors (Mattern et al., 1995; Yamauchi and Yoshizawa, 1995;Yoshizawa and Yamauchi, 1991). As long as the temperature remainssignificantly below the secondary crystallization temperature, only slightvariations in the grain size are found for all samples that were annealed fortimes between 1200 and 3600 s, regardless of ETM type. The effect ofexceeding the secondary crystallization temperatures for samples with Moand Nb can clearly be seen by the increased grain size with annealing


Gra

in d

iam

eter

(nm

)

7000

20

40

Mn

Fe73.5Si13.5B9M3Cu1

Cr

V

Ti

MoTa

60

80

100

750 800 850 900 950 1000

Figure 4.21 The effect of annealing temperature on the grain diameter forFe73.5�xSi13.5þxB9M3Cu1 alloys annealed for 1200–3600 s (where M¼Ti (open circle),V (open square), Cr (open triangle), Mn (open downward triangle), Zr (half-closedcircle),Mo (closed downward triangle),Hf (closed circles), Ta (closed square),W (closedtriangle), Nb (closed diamonds), and x�2) (Cziraki et al., 2002; Frost et al., 1999; Hakimand Hoque, 2004; Hernando and Kulik, 1994; Kulik and Hernando, 1994; Liu et al.,1997b;Mattern et al., 1995;Mazaleyrat and Varga, 2001; Noh et al., 1993; Yamauchi andYoshizawa, 1995; Yoshizawa and Yamauchi, 1991; Zhang et al., 1998a).


temperature. Taking average grain sizes for samples annealed at low tem-peratures (nearly constant values in Fig. 4.21), a correlation is found whenplotted against the ETM atomic radius (see Fig. 4.22) (Muller et al., 1996a).ETMs with large atomic radii tend to provide the smaller grain sizes thatlead to desirable magnetic properties.

While the Nb and Cu have been found critically important to the devel-opment of the nanostructured microstructure, the grain size itself is stronglydependent on the B content of the alloy and the type of ETMused in the alloy(see Fig. 4.23). This is not only true for (Fe,Si)–Nb–B–Cu alloys (Herzer,1997) but also for Fe–Zr–B–(Cu) alloys. This indicates that B may also beinvolved in the grain growth inhibition; however, its effect is insufficient tocreate the nanocrystalline microstructure unless it is assisted byNb (or anotherETM). The ETMs tend to suppress the formation of boron-containing inter-metallics, making the combined use of B and ETMs necessary.

The processing–composition relationship described above is extremelyimportant in the context of providing the essential microstructure thatdrives the low coercivity observed in these materials. Limiting the grainsize to less than about 15 nm explains the ultra-low coercivities using therandom anisotropy model in Section 6.3. Establishing the desired primarycrystalline phase allows an increase in the magnetization, resulting in

Atomic radius (Å)

Ave

rage

gra

in d

iam

eter

(nm

)

1.750

10

20

30

40

50Mn

Cr

V

Ti

MoW

Nb

Ta

Zr

Hf

1.80 1.85 1.90 1.95 2.00 2.05 2.10 2.15 2.20

Fe73.5Si13.5B9M3Cu1

Tann ~ 823 K

Figure 4.22 Variation of grain diameter with early transition metal radius in optimallyannealed Fe73.5Si13.5B9M3Cu1 alloys (where M¼Mn, Cr, V, Ti, Mo, W, Ta, Zr, Hf)(Cziraki et al., 2002; Frost et al., 1999; Hakim and Hoque, 2004; Hernando and Kulik,1994; Kulik and Hernando, 1994; Liu et al., 1997b; Mattern et al., 1995; Mazaleyratand Varga, 2001; Noh et al., 1993; Yamauchi and Yoshizawa, 1995; Yoshizawa andYamauchi, 1991; Zhang et al., 1998a).

B content (at%)

Gra

in d

iam

eter

(nm

)

Fe–Si–Nb–B–Cu

Fe–Zr–B–(Cu)

04

6

8

10

12

14

16

18

2 4 6 8 10 12 14 16 18 20 22 24

Figure 4.23 Grain size dependence on the boron content of (Fe,Si)–Nb–B–Cu(Herzer, 1997) and Fe–Zr–B–(Cu) alloys. Grain sizes for the Fe–Zr–B–(Cu) alloysare plotted as an average from the following studies (Arcas et al., 2000; Garitaonandiaet al., 1998; Gomez-Polo et al., 1996; Kaptas et al., 1999; Kim et al., 1994b; Kopcewiczet al., 1997; Slawska-Waniewska et al., 1994; Suzuki et al., 1991b; Suzuki et al., 1996;Zhou and He, 1996).



improved miniaturization of components, further discussed in Section 6.1.In addition, maintaining a residual amorphous phase provides a robustresistivity, allowing increased operation frequencies for these materials, tobe discussed in Section 6.5.

3.3. Intrinsic property considerations

The success in reducing the losses in Fe–Si–Nb–B–Cu alloys has as much todo with the microstructure as it does with the composition of the phasesformed during optimal annealing. The Si-rich crystallites approach thecomposition where bulk Fe–Si has a low magnetocrystalline anisotropy(�20 at%) (Herzer, 1995). The Nb/B-rich residual amorphous phase hasbeen found to possess a positive magnetostriction coefficient which balancesthat of the Si-rich crystallites (which have a negative value), giving anoverall near zero value. Both of these circumstances aid the reduced lossesobserved in these alloys. Based on these findings, it is not surprising thatvaried amount and type of alloying have a strong effect on both themagnetic properties, the crystallization behavior of the alloy, and the opti-mal annealing conditions.

For most soft magnetic applications, the saturation magnetization is afigure of merit with larger values being more desirable. In Fe–Si–Nb–B–Cualloys, the saturation magnetization is somewhat low with m0Ms�1.25–1.35 T. The saturation magnetization is larger for Fe–Zr–B with valuesabove 1.5 T; however, the coercivity is increased. Substitution of differenttypes of Co for Fe in Fe–Co–Zr–B alloys has been found to vary thesaturation magnetization in a way similar to the well-known Slater–Paulingcurve (Fig. 4.24) (Pauling, 1938; Slater, 1937). Using the average number ofcombined 4s and 3d electrons per atom (e�/atom) as a composition vari-able, the saturation magnetization shows a pronounced peak near 8.35 e�/atom for alloys with small amounts of Si added (<5 at%). When the Sicontent is increased to 10 at% or more, the peak in saturation magnetizationis shifted to compositions consisting of a greater fraction of Fe (near 8.1–8.2e�/atom). As shown in Fig. 4.24a, the peak can be completely eliminatedwhen Si content is increased beyond about 13 at%. While MTMs can beused to improve the saturation magnetization of the alloy, the coercivitytends to increase by these same composition variations (see Fig. 4.24b).Again, the balance of alloy design parameters requires a good understandingof the application needs.

The addition of Cr as an alloying element has been studied widely due toits extreme effect on the Curie temperature of the amorphous phase (espe-cially after partial crystallization) (Chau et al., 2006; Conde et al., 1994;Hajko et al., 1997; Marın et al., 2002). Replacing 4.5 at% Fe with Cr hasbeen found to reduce the Curie temperature of the amorphous phase by110–470 K (Hajko et al., 1997). The Curie temperature of the amorphous

Co content, x (Co/(Fe+Co))

(a)

(b)

Co content, x (Co/(Fe + Co))

(Fe1 - xCox)73.5Si15.5B7Nb3Cu1

(Fe1–xCox)73.5Si15.5B7Nb3Cu1

(Fe1–xCox)86B6Zr7Cu1

(Fe1 - xCox)86B6Zr7Cu1S

atu

ratio

n m

agn

etiz

atio

n (T

)

Coe

rciv

ity (

A/m

)

0

0.4

1

10

100

1000

10,000

0.6

0.8

1.0

1.2

1.4

1.6

1.8

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1

Figure 4.24 Variation of (a) saturation magnetization and (b) coercivity with mag-netic transition metal content in (Fe,Co)73.5Si15.5Nb3B7Cu1 and (Fe,Co)86Zr7B6Cu1alloys. After M€uller et al. (1996b).


phase is an important parameter, as it is the temperature limit for exchangecoupling between the crystallites of the nanocrystalline soft magnetic alloy.When the Curie temperature of the amorphous phase is exceeded, thecoercivity increases at an accelerating rate with increased over-temperature.While the details of this effect will be discussed in the section on thetemperature dependence of magnetic properties, it is clear that the magneticcharacter of the alloy can be substantially modified by minor compositionmodifications.

The most important parameter for the reduction of losses in soft mag-netic materials is a near zero value of magnetocrystalline anisotropy (K1).


It has been shown in Section 1.2 that the effective magnetocrystallineanisotropy can be strongly influenced by the microstructure as describedby the random anisotropy model (more details are found in Section 6.3).When applied to nanostructure soft magnets, aD6 reduction in coercivity isfound when the grain size is reduced below �100 nm. At the same time,the effective anisotropy (and therefore coercivity) also depends strongly onthe crystalline phase magnetocrystalline anisotropy, K1

4. For this reason, thesize, composition, and distribution of the primary crystalline phase areimportant as together they contribute to the losses in the material. In thecase of Fe–Si–B–Nb–Cu alloys, the magnetocrystalline anisotropy ofthe crystallites is dependent on the composition of the alloy, especiallyevident with variation of Si (Chikazumi and Graham, 1997). When theeffective magnetocrystalline anisotropy has been reduced enough, the mag-netoelastic anisotropy becomes a dominant factor.

The magnetostrictive coefficient (ls) for nanocrystalline alloys is sensi-tive to both the nominal composition of the alloy and the annealingconditions for crystallization. An as-spun ribbon with Fe73.5Si13.5B9Nb3Cu1composition has a large, positive value of ls¼20�10�6 (ppm), which israpidly reduced when annealed above the primary crystallization tempera-ture to values below 5 ppm (Herzer, 1991). This reduction in ls is due tothe volume fraction-weighted average of positive coefficient from theamorphous phase (ls

am�20ppm) and the negative value of the nanocrystal-line phase (ls

cr��5ppm). When the alloy is about 70–80 vol% crystallized,the equation ls¼Xls

crþ (1�X)lsam describes the trend in ls with Si con-

tent. It has been noted that the near zero value of ls is found at highernominal Si contents in nanocrystalline alloys than expected from polycrys-talline a-(Fe,Si) alloys (at �12 at% Si) due to the preferential segregation ofthis element to the crystalline phase (Herzer, 1991).

Magnetostrictive coefficients for the alloy series Fe96�zSixBz�xNb3Cu1(where 18.5�z�23.5 and x�17.5) show a near constant value for the as-spun alloys at �22 ppm, independent of the alloy composition (Herzer,1996). However, samples crystallized at 540 �C for 1 h show a composi-tional dependence of ls with a broad maximum at x�5 and a near zerovalue at x¼16–17. This is important, as the internal stresses can be 1–2 MParesulting in magnetoelastic anisotropy near 50–100 J/m3 for amorphousalloys. In comparison to the 2–3 J/m3 resulting from the exchange averagedmagnetocrystalline anisotropy in the nanocomposite alloys, this would be asignificant and dominating factor if the magnetostriction were not reducedby nanostructuring. For instance, the relatively large value of coercivityobserved in (Fe,Co)–Zr–B–Cu alloys (see Fig. 4.24b) is a result of thecomposition naturally having a large magnetoelastic anisotropy. In thiscase, the benefits of very high Curie temperature of the residual amorphousphase and large saturation magnetization outweigh the increased coercivity,allowing these materials to be used for high-temperature applications.


3.4. Domain structure considerations

As soft magnetic materials are typically used in applications where ease ofswitching is a necessity, the magnetic domain structure is an importantdesign factor for these materials. Magnetic domains in soft magnetic materi-als form readily when no magnetic field is applied due to the large reductionin magnetostatic energy when the free magnetic poles are removed from thesurface. In the process, domain walls are formed between the domains.Switching between large positive and negative magnetic fields results indomain wall motion, yielding a net change in the magnetization. Nonuni-form arrangement of domains within a material can result in larger losses ifimpediments to domain wall motion are present in the material (i.e.,domain wall-pinning sites). These can include nonmagnetic inclusions,regions of large anisotropy, grain boundaries, or surface effects.

Nanocrystalline soft magnetic alloys possess domain structures indistin-guishable from amorphous alloys by optical microscopy techniques,including features such as stripe domain patterns and stress patterns ifthe magnetostriction is nonzero (Schafer et al., 1991). Sharp domain wallsare observed by Lorentz microscopy for an amorphous (i.e., as-spun)Fe73.5Si13.5B9Nb3Cu1 alloy (Shindo et al., 2002). After optimal annealingthe domain walls broaden and remain straight, consistent with the magneticsoftening of the alloy. Annealing the material at temperatures exceedingsecondary crystallization (e.g., 923 K and above) results in domains follow-ing the grain boundaries of the enlarged grain (<50 nm). Measuring thedomain structure of the optimally annealed sample at temperatures abovethe Curie temperature of the intergranular amorphous phase results in adecoupled domain structure (Hubert and Schafer, 2000).

When contributions from magnetocrystalline anisotropy and magneto-striction have been minimized through proper processing and choice ofcomposition, induced anisotropies dominate. These anisotropies can beused to control the domain structure of the material, allowing some amountof tuning of the hysteresis loop. This type of loop shape adjustment allowsone material to be used for various applications. Annealing the material in afield (either stress or magnetic) can create an induced magnetic anisotropy asdescribed in the previous sections. The resulting domain structure in thebest-performing alloys shows a stripe domain configuration. A coherentrotation switching mechanism can be achieved when the vector normal tothe domain walls of these stripe domains is parallel to the applied switchingfield. This reduces the permeability of the material without the necessity ofcreating an air gap, a benefit for inductor applications. Transverse magneticfield annealing of a Co60Fe18.8Si9Nb2.6B9Cu0.6 alloy annealed at 803 Kshowed regular domains with 180� domain walls along the direction ofthe induced anisotropy (Saito et al., 2006).


Unfortunately, not all alloy compositions are well suited for field anneal-ing to control the magnetic domain structure. The embrittlement of manyalloys during the crystallization process limits the stress-annealing techni-que’s general use. Magnetic field annealing has strong compositional depen-dences, resulting in small values of induced anisotropy for many Fe-richcompositions (with significant improvements found in Co-rich alloys)(Ohodnicki et al., 2008b; Ohodnicki et al., 2008c; Suzuki et al., 2008a).The induced anisotropies formed by magnetic field annealing have alsobeen found to change the effective anisotropy as described by Suzuki et al.(1998). The typical D6 dependence of the coercivity with grain diameter isreduced to a D3 dependence when a long-range, uniaxial anisotropy (asfound in field annealing) is induced.

4. Phase Transformations, Kinetics,

and Thermodynamics

The rapid solidification and annealing processes that results in an alloywith nanocomposite microstructure and desirable magnetic properties are theresult of careful consideration of factors that affect the thermodynamics andkinetics of the transformations in these materials. Important factors to con-sider include the kinetics of the nucleation and growth processes, the ther-modynamics of the crystallization process, and other phase transformations,resulting in optimized magnetic performance. Understanding crystallizationand other phase transformations can improve our ability to choose the bestannealing temperatures and times to achieve the desired microstructure.

In Section 4.2, phase diagrams for crystallization of the as-spun ribbonswill be discussed for various nanocrystalline alloy systems. Using time–temperature transformation (TTT) diagrams, Section 4.3 will describe thecrystallization kinetics to show the necessary critical cooling rates for amor-phous alloy formation and the crystallization process at different tempera-tures. Order–disorder transformations that are important in several alloysystems will be discussed in Section 4.4.

4.1. Thermal analysis techniques

Differential thermal analysis (DTA) and differential scanning calorimetry(DSC) are standard techniques that have been successfully used to identifycrystallization temperatures for amorphous ribbon samples. In some cases,the glass transition and Curie temperatures are also observed by thesetechniques. The DTAmeasurement uses a differential temperature betweenan unknown sample and reference material to determine when heat is


generated or absorbed by the samples. The reference is chosen to have asimilar heat capacity to the unknown, and both materials are contained inthe same furnace so that they are both subjected to the same thermalenvironment. Typical measurements by DTA are performed with a con-stant heating rate (between 1 and 100 K/min) with minimal amounts ofsample, less than 10 mg. The sample should be large enough to provideadequate signal during heating, which depends on heating rate due to thethermal activation of the crystallization process. However, it must also besmall enough to avoid temperature gradients through the sample. Typicaltemperature ranges are from 300 to 1000 K with a sensitivity of 10–100 mJ/s.DSC is a similar technique where the power difference required to maintainthe two cups at the same temperature is measured, giving a more accuratedetermination of the enthalpy of reactions.

These techniques are used widely because they are a quick and easy wayto identify critical parameters for annealing procedures. By heating thesample at a constant heating rate, the glass transition and Curie temperaturescan be identified if they are much smaller than the primary crystallizationtemperature. Each can be identified by a slope change in the DTA or DSCsignal. Primary and secondary crystallization peaks (labeled Tx1 and Tx2) areobserved as exothermic reactions where the high entropy amorphous phaseis transformed into the low entropy crystalline phase (see Fig. 4.25). Anassociated enthalpy change occurs at each crystallization temperature. Stud-ies typically report two different crystallization temperatures for each

Measurement temperature (K)

2 K/min

5 K/min

10 K/min

DHx1

onset onset Tx2pp

Tem

pera

ture

diff

eren

ce (

K)

4002.8

3.0

3.2

3.4

3.6

3.8

4.0

4.2

4.4

4.6

4.8

420 440 460 480 500 520 540 560 580 600 620 640 660 680 700

Tx2Tx1Tx1

Figure 4.25 Variation of peak temperature with heating rate in differential thermalanalysismeasurements for a Fe4.45Co84.55Zr7B4 as-cast alloy, heated at 2, 5, and 10 K/min.


crystallization event, the temperature of crystallization onset and the tem-perature of peak signal. These temperatures can be separated from eachother by as much as 30–40 K. Since the crystallization process is thermallyactivated, the onset and peak temperatures and the enthalpy of reaction arevariable with the heating rate used during the measurement. Slower heatingrates tend to have smaller peaks at lower temperatures than faster heatingrates. Measuring several samples with varying heating rates can provideinformation about the activation energy of crystallization (described inmore detail in Section 4.3).

4.2. Primary and secondary crystallization

While it is possible to produce nanocrystalline microstructures by othertransformations (e.g., eutectic or polymorphous) (Lu, 1996), the mostcommon method for ribbons is by primary crystallization of an amorphousprecursor. In order to achieve a nanocrystalline microstructure with aspecific crystalline phase, we must consider the thermodynamics and kinet-ics of primary crystallization, which depend on the composition of the alloyand the processing conditions of the rapidly solidified alloy. Understandingthe thermodynamics can help identify compositions that are favorable foramorphous alloy formation as well as favorable for primary crystalline phasesthat might form during subsequent annealing. Understanding the kinetics ofprimary crystallization allows us to identify compositions that are likely toproduce the desired fine-grained microstructure. Properly designed alloyswill allow the formation of beneficial primary crystalline phases, highnucleation rates, and slow growth of grains, resulting in improved magneticproperties. This is achievable when crystallization occurs in a multistageprocess, with large separation of crystallization temperatures for desirableprimary crystalline phases and unwanted secondary phases. The microstruc-ture obtained by annealing above the primary, but below the secondarycrystallization temperature, consists of nanocrystalline grains embedded in aresidual amorphous matrix phase. Full crystallization of the sample does notoccur at primary crystallization due to elemental partitioning between theforming crystalline phase and the remaining amorphous phase. The amor-phous alloys that successfully form nanocrystalline microstructures typicallypossess a large temperature difference between the primary (Tx1) andsecondary crystallization (at Tx2). The larger the range between thesetemperatures, the more opportunity exists for optimization of the micro-structure by varying annealing conditions.

Table 4.1 shows many classes of nanocrystalline soft magnetic alloysseparated by the primary crystalline phase and observed saturation magneti-zation. In general, the most suitable phases during primary crystallizationinclude a-(Fe,Si), a-(Fe,Co,Ni), and g-(Co,Ni,Fe), due to their largemagnetizations and cubic symmetry. For the purpose of this discussion,


we will refer to these phases as simple MTM phases. Limited solubility ofthe glass-forming elements in these phases is an important factor since ETMand metalloid elements tend to substantially reduce the magnetization of theMTM. In some cases, the atomically ordered, cubic, a0-Fe3Si or a0-FeCointermetallic phases are observed at primary crystallization. If the primarycrystallites are not simple MTM phases (or MTM intermetallics), but insteadare intermetallics of MTM and either ETM and/or metalloid elements, theperformance of the materials is significantly impaired due to the increasedmagnetocrystalline anisotropy of these noncubic phases and the deteriora-tion of the desired microstructure.

At temperatures exceeding secondary crystallization, the residual amor-phous phase also crystallizes into intermetallic phases and borides, includingFe2B, Fe3B, Fe23B6, Fe23Zr6, Fe2Zr, and/or Fe3Zr. The secondary crystalli-zation products for a given alloy depend strongly on the composition of thealloy; however, the microstructure coarsens dramatically for all compositions.Secondary crystallization degrades the magnetic performance considerablyand in many cases poses the upper temperature limit for potential application(Willard et al., 2012b). It is essential to avoid secondary crystallization whenannealing the samples during devitrification. Even small volume fractions ofFe2B crystallites can have a detrimental effect on the magnetic performance.Two factors are responsible for the degradation. First, the grain sizes tend tobe larger than the primary crystallites, in the range of 50–100 nm, which islarge enough to provide significant domain wall pinning. Second, the mag-netocrystalline anisotropy is quite large for Fe2B, K1¼�4.3 MJ/m3 at roomtemperature. Both of these effects together result in coercivities in excess of100 A/m. Structure and characteristics of primary and secondary phases arediscussed in more detail in Section 5.

Early observations of these alloys identified the necessity of both ETMsand copper as alloying elements to achieve a nanocomposite microstructure(Kataoka et al., 1989; Noh et al., 1990; Yoshizawa and Yamauchi, 1991). Themost generally accepted microstructure evolution model to achieve nano-composite microstructure in Fe96�zSixBz�xNb3Cu1 alloys was refined overabout 10 years (Ayers et al., 1993, 1994, 1997; Hono et al., 1992, 1999). Themodel uses nucleation and growth principles to describe the roles of both Nband Cu and has been discussed in more detail in the earlier sections.

Due to the complex nature of the roles of each element in the crystalli-zation process, strong variations in crystallization temperature are observedas the composition is varied. For instance, in Fe96�zSixBz�xNb3Cu1 alloyswhen the total amount of SiþB is 18.5, the primary and secondary crystal-lization temperatures tend to increase with increased Si content and a thirdcrystallization temperature is observed (see Fig. 4.26) (Herzer, 1997). In thiscase, primary crystallization forms a-FeSi, secondary crystallization addsFe2B and Fe3B, and only at tertiary crystallization is all of the amorphousphase completely crystallized as a FeNbB phase is formed. At higher SiþB,

Si content, x (at%)

Cry

stal

liza

tion

tem

pera

ture

(K

)

0600

700

800

900

1000

1100

2 4 6 8 10

z = 18.5

Fe96 - zSixNb3Bz - xCu1

Tx3

Tx2

Tx1

z = 20.5 z = 22.5

12 14 16 18

Figure 4.26 Crystallization temperature variations with Si content in Fe96�z-

SixBz�xNb3Cu1 alloys. After Herzer (1997).


the primary crystallization temperature is relatively stable with changes in Sicontent, and merged secondary/tertiary crystallization increases with Sicontent for SiþB¼22.5. An important factor for proper microstructureevolution is the large temperature difference between crystallization ofprimary and secondary phases, which is observed for the whole compositionrange. Another factor is the formation of a desirable phase at primarycrystallization, which is also found.

Since the magnetic properties are dependent on both the microstructureand the composition of the crystallized phases, many studies of modified tothe Fe–Si–Nb–B–Cu alloys have been made. As an alloying element, Ga hasbeen shown to form an a-(Fe,Si,Ga) solid solution (Matsuura et al., 1996).Similarly, Al additions to Finemet act as substitutional elements for Si in thecrystalline phase (Frost et al., 1999; Lim et al., 1993b). While small additionsof Al have been shown to reduce the coercivity (through reduction in K1),the magnetization drops rapidly with Al additions. However, improvedperformance has been observed in the (Fe,Si,Al)-based alloys at cryogenictemperatures, an effect attributed to lower magnetocrystalline anisotropyand magnetostriction (Daniil et al., 2010a). The replacement of Nb by Gd,examined by Crisan et al., resulted in the formation of RE–Fe–B phases atsecondary crystallization (among other phases) and increased growth kinet-ics of the primary crystallites (Crisan et al., 2003). Replacement of Si withGe showed a significant increase in TC

am (Cremaschi et al., 2004a).The substitution of noble metals, Pt and Pd, for Cu in a Fe–Si–B–Nb–M

alloy results in a substantial decrease in he crystallization onset temperature;however, the primary crystallization products are Fe3B and a-FeSi withgrain diameters of 20 nm and larger (Conde et al., 1998). The absence of a


single a-FeSi phase and the larger grain size indicate that Pt and Pd do notshare the same role as Cu in the crystallization process. The use of M¼Agshowed larger grain sizes (<30 nm) and correspondingly larger coercivities(�20 A/m) than alloys using Cu (Chau et al., 2005). On the other hand, Auhas been shown to provide good grain refinement and comparable coerciv-ities to Cu-containing alloys (Kataoka et al., 1989). The role of Cu as aheterogeneous nucleation site and the optimization of the amount of Cunecessary to maximize magnetic softness have been examined by meticulousDSC and small-angle neutron scattering experiments (Ohnuma et al.,2000). These results indicate that the Cu-clustering phenomena are ther-mally activated and that optimal Cu content is found when the numberdensity of Cu clusters is maximized at the start of primary crystallization. Forthis reason, the optimal Cu content is closely related to the Fe–Si content ofthe alloy and heating rate to primary crystallization.

Although Cu or Au is an indispensible element for grain refinement dueto its ability to enable a large number of heterogeneous nucleation sites inmany nanocomposite alloy compositions, the grain growth must also becontrolled to yield the desired microstructure. In the (Fe,Si)–Nb–B–Cualloys, this has been accomplished by the use of Nb; however, several otherelements are also good grain growth inhibitors. The ETMs (or refractorymetals) have been shown to provide similar grain growth inhibition(Kataoka et al., 1989; Yoshizawa and Yamauchi, 1991). In Fe73.5-Si13.5B9Nb3�xMxCu1 alloys, the variation of the primary crystallizationtemperature shows a 50 K increase between ETMs with small atomic radius(e.g., V or VþNb) and those with large atomic radius (e.g., Ta, Zr), asshown in Fig. 4.27. The atomic radii of these atoms are larger than those ofthe MTMs. The effectiveness of these elements in providing nanocrystallinemicrostructures is related to the atomic radii, with best results for the largestatoms, Nb and Ta (Muller and Mattern, 1994). An increased primarycrystallization temperature indicates an increased stability of the amorphousphase compared to the primary crystalline phase.

MTMvariations in an alloy are used to tune the saturation magnetizations,Curie temperatures, and losses in nanocomposite soft magnets. Varyingthe MTM composition can significantly change the primary crystallizationtemperatures as illustrated in Fig. 4.28 for Fe73.5�xMTMxSi13.5B9Nb3Cu1alloys. Substitution of Cr for Fe has the strongest effect, with a near linearincrease in Tx1 to�910 K at 10 at% Cr (Hajko, 1997). This trend in primarycrystallization is shared with the trend in activation energy for primarycrystallization observed in Cr-substituted alloys (to 5 at% Cr at least) (Chauet al., 2006). Slight increases are observed for Ni substitution for Fe; however,the secondary crystallization temperature is significantly lowered withincreasing Ni content (Agudo and Vazquez, 2005). Alloying with Co tendsto keep a steady primary crystallization temperature between 780 and 800 K

Average atomic radius ETM (Å)

Prim

ary

crys

talli

zatio

n te

mpe

ratu

re (

K)

1.90

740

750

760

770

780

790

800

810

1.95 2.00 2.05

M = V, V + Nb

Fe73.5Si13.5B9Nb3 − xMxCu1

M = ZrM = Mo, Mo + NbM = TaM = WM = Nb

2.10 2.15

Figure 4.27 Effect of early transition metal type and content on the primary crystalli-zation temperatures in Fe73.5Si13.5B9Nb3�xMxCu1 alloys (where M¼V, Mo, W, Nb,Ta, Zr) (Borrego and Conde, 1997; Degro et al., 1994; Hernando and Kulik, 1994;Herzer, 1989; Kulik, 1992; Lim et al., 1993b; Liu et al., 1997b; Mitra et al., 1998;Rodrıguez et al., 1999; Yoshizawa and Yamauchi, 1991; Yoshizawa et al., 1988a;Zhang et al., 1998a; Zorkovska et al., 2000).

MTM substitution for Fe (at%)

MTM = Cr

MTM = Ni

MTM = Co

Fe73.5 - xMTMxSi13.5B9Nb3Cu1

Cry

stal

liza

tion

tem

pera

ture

(K

)

0

700

750

800

850

900

10 20 30 40 50 60 70 80

Figure 4.28 Variation of primary crystallization with magnetic transition metal substi-tution in Fe73.5�xMTMxSi13.5B9Nb3Cu1 alloys, where MTM¼Cr (Atalay et al., 2001;Chau et al., 2006; Conde et al., 1994; Franco et al., 2001b; Gonzalez et al., 1995; Hajkoet al., 1997), Ni (Agudo and Vazquez, 2005; Atalay et al., 2001), Co (Atalay et al., 2001;Borrego et al., 2001a; Chau et al., 2004; Gercsi et al., 2006; Gomez-Polo et al., 2001;Kolano et al., 2004; Mazaleyrat et al., 2004; Yu et al., 1992).



until �50% of the Fe has been substituted with Co (Mazaleyrat et al., 2004).At higher Co contents, the Tx1 drops to below 750 K.

Fe–Zr–B-type nanocomposite alloys do not have the same alloy designrequirements as those containing Si. While Cu has been found to help refinethe microstructure and improve coercivity in some alloys (e.g., Fe–Si–Nb–B–Cu), it is not a necessary element to achieve the nanocomposite micro-structure in others (e.g., Fe–Zr–B or Fe–Co–Zr–B) (Suzuki et al., 1991c).The effect is attributed to two factors, the lowering of Tx1 (extension of thea-Fe phase stability) and the refinement of the grain size. The addition of atleast 1 at% Cu has been found to expand the composition range of Fe–Zr–Balloys that exhibit large permeability (above 104). Microstructure evolutionof these alloys shows a nearly complete rejection of Zr from the crystallizinga-Fe phase during the crystallization process of Fe–Zr–B alloys (Zhanget al., 1996c). A trend in Tx1 with ETM radii is observed in Fe–ETM–Zr–B alloys, having higher crystallization temperatures as the atomic radii isincreased (similar to Fig. 4.27) (Bitoh et al., 1999; Muller et al., 1997). Thestability of the amorphous phase against primary crystallization is alsostrengthened by substituting B for Fe in Fe–B–M–Cu and Fe–Nb–B alloys(Kuhrt and Herzer, 1996; Lee et al., 1994).

When the MTM composition is varied in the Si-free (Fe,Co,Ni)88Zr7B4Cu1 and (Fe,Co)86Zr7B6Cu1 alloys, the variation in primarycrystallization temperature with MTM substitution is more gradual acrossthe whole composition range than in Fe73.5�xMTMxSi13.5B9Nb3Cu1alloys. As shown in Fig. 4.29, Tx1 for Fe (8 e�/atom) is about 80 K higher

Valence electrons per atom

(Fe,Co)86Zr7B6Cu1

(Fe,Co,Ni)88Zr7B4Cu1

(Co,Ni)88Zr7B4Cu1

Cry

stal

liza

tion

tem

pera

ture

(K

)

8.0

700

800

900

1000

8.2 8.4 8.6 8.8 9.0 9.2 9.4 9.6 9.8 10.0

Figure 4.29 Variation of primary and secondary crystallization with magnetic transi-tion metal substitution in (Fe,Co,Ni)88Zr7B4Cu1 and (Fe,Co)86Zr7B6Cu1 alloys(Caballero-Flores et al., 2010; Hornbuckle et al., 2012; M€uller et al., 1996b; Willardet al., 1999a, 2000, 2007).


than for Co (9 e�/atom) in (Fe,Co)86Zr7B6Cu1 alloys (Muller et al.,1996b). Further decreases in Tx1 are observed when Co is substituted forNi (10 e�/atom) to values below 700 K, indicating a deterioration of thestability of the amorphous phase against crystallization similar to that foundin the Si-containing alloys (Hornbuckle et al., 2012).

4.3. Crystallization kinetics and phase stability

Above the primary crystallization temperature, the amorphous precursoralloy crystallizes by an exothermic reaction, resulting in the evolution of ananocomposite microstructure. To achieve the best magnetic properties, thisprimary crystallization product phase of the supersaturated amorphous solidsolution should be a low anisotropy, high magnetization phase. In most cases,this restricts the best alloy compositions to MTM-rich alloys (hypoeutectic)where primary crystallites are cubic phases (e.g., A2, D03, and/or A1 struc-tures). Lower symmetry phases, such as Fe2B, Fe3B, Fe3Zr, etc., tend to havelarger magnetocrystalline anisotropies and smaller saturation magnetizations,making them undesirable. These phases can be avoided by choosing compo-sitions where the high-symmetry phases form at significantly lower tempera-tures than the low symmetry phases. Methods of lowering the Tx1 and raisingTx2 extend the processing window exemplifying the importance of under-standing reaction kinetics. In this section, the thermodynamic and kineticfactors for the crystallization reaction will be discussed.

The majority of nanocrystalline soft magnetic alloys are produced by themelt spinning technique. At the end of this rapid solidification step, thedesired product is typically a compositionally uniform, metastable amor-phous alloy. Standard post-quench processing would promote partial crys-tallization of the alloy by two thermally activated processes, nucleation andgrowth. While this simplistic view captures the main aspects of microstruc-ture evolution of nanocrystalline soft magnetic alloys, the details of heatflow, thermodynamics, and the nucleation and growth process provide thenecessary guidance to aid in alloy design and performance optimization.The rate at which heat can be extracted from the liquid limits the range ofpossible compositions to produce an amorphous precursor alloy. The pri-mary crystallization product is determined by the thermodynamics of thealloy system, and the nucleation and growth kinetics shape the ultimatemicrostructure evolution. In the end, achieving a fine-grained microstruc-ture requires high nucleation rate (given by large supersaturation or hetero-geneous nucleation sites) and low growth rate (given by slow diffusion).

The nucleation of competing crystalline phases from the amorphousprecursor is largely determined by the lowest value of activation energybarrier to nucleation, DG* (Boettinger and Perepezko, 1985). The influ-ence of heterogeneous nucleation sites and undercooling for each compet-ing phase are prime factors for establishing the value of DG*. The


nucleation rate ( eN ) has an abrupt increase with the magnitude of under-cooling (DT) which can be described by the classical nucleation theory:

eN ¼ fnCn exp�DG�

kBT

� �ð1Þ

with preexponential factors for frequency of stable nuclei formation (fn) andnumber of atoms in contact with the heterogeneous nucleation site per unitvolume (Cn) (Porter and Easterling, 1992). The exponential dependence ofthe nucleation rate with the undercooling temperature is captured in theactivation energy barrier term (DG*). This term in the classical formulationdepends on the solid–liquid interfacial energy (gs�l), the driving force fornucleation (DGv/DT), and a shape factor (b� (16p/3) S(y), where S�1)in the following relation:

DG� ¼ bgs�l3

DG2v

ð2Þ

This relationship infers that either lowering gs–l or raising DGv canreduce the activation energy barrier. The reduction of the solid–liquidinterfacial energy (gs–l) is largely influenced by the introduction of suitableheterogeneous nucleation sites. An example of successful alloy design takingadvantage of gs–l to improve the nucleation rate is the addition on Cu to Fe–Si–B–Nb and Fe–Zr–B alloys, resulting in increased number of nuclei andnucleation rate (Ayers et al., 1994; Hono et al., 1992; Zhang et al., 1996b).The maximum driving force for nucleation (DGv) can be used for thedetermination of the nucleus composition so long as the solid–liquid inter-facial energy and shape factors are not a strong function of composition.This technique was used to analyze the observation that BCC crystallites ina Co-rich HITPERM alloy were forming due to the Fe enrichment of theinitial nuclei (Goswami and Willard, 2008; Willard et al., 2007). Thedensity of nuclei has been observed by HRTEM and STM to be 1�1023

to 1�1024 nuclei/m3 after primary crystallization (Goswami and Willard,2008; Tonejc et al., 1999a). In some cases, the nuclei are present in the as-quenched alloys (e.g., Co-rich HITPERM), and other cases, some nucleiare present in the as-quenched state but further nucleation is required toaccount for all of the grains in the coarsened microstructure (e.g., Fe–Si-based alloys) (Goswami and Willard, 2008; Hirotsu et al., 2004).

During the rapid solidification process, surface nucleation can occur ifthe solidification rate is too slow. Typically found on the glossy side of theribbon (i.e., farthest from the quench wheel, often referred to as the “free”side of the ribbon), the grains formed by surface nucleation typically growwith either (1 1 0) or (1 1 1) fiber texture for BCC or FCC grains,respectively. This effect becomes more pronounced in alloys with greater


MTM contents where the amorphous phase is more difficult to form.Surface crystallization has been found to greatly influence the magneticperformance of partially crystallized metallic glasses through the magne-tostrictive induced anisotropy produced by the stress field from the crystal-lites (Herzer and Hilzinger, 1986).

Achieving the desired nanocrystalline microstructure requires eitherpreexisting nuclei or very rapid nucleation rate in the early stages ofcrystallization followed by a slow growth rate. The large initial nucleationrate has been influenced by control of composition (e.g., adding Cu to Fe–Si–Nb–B), by two-stage annealing (e.g., annealing near but below Tx1

where the driving force for nucleation is highest), and by control of theheating rate (e.g., Joule heating). The slow growth rate, required in thelatter stages of crystallization, has been accomplished by adding alloyingelements that retard the diffusion of FTMs (e.g., incorporation of ETMs).

The elimination of Cu from Fe–Si–Nb–B–Cu and Fe–Zr–B–Cu alloysresults in a less refined grain size and an over all inferior magnetic perfor-mance to Cu-containing compositions. However, Cu is not the onlyelement found to provide heterogeneous nucleation sites in Fe–Si-basedalloys. Common characteristics of alloying elements that enhance thenucleation site density (and rate) include elements which have low solubilityin BCC Fe (having positive heats of mixing with Fe) and weak bondinginteractions in the amorphous phase (allowing large mobility at low anneal-ing temperatures). These elements include Cu and Au. Two-stage anneal-ing effects have been studied as a method of improving the grain refinementof the nanocrystallites (He et al., 2000; Noh et al., 1993). The first stage,designed to aid nucleation rate with little growth, is performed at tempera-tures below primary crystallization. The second stage, designed for graingrowth, is similar to the standard (e.g., one-stage) annealing temperaturenear or above the primary crystallization.

The growth rate is also a temperature-dependent process, although notas critically determined by the undercooling of the alloy as the nucleationrate. In nanocrystalline soft magnetic alloys, the growth rate is largelydetermined by the diffusivity of Fe through the intergranular amorphousphase. The incorporation of ETM elements to Fe–B–Si-based alloys wasfound to reduce the growth rate substantially (Kulik, 1992). An increase inthe stability of the remaining amorphous phase was also observed, leadingwider separation of the primary and secondary crystallization temperaturesfrom 36 K without ETMs to 150 K with 3 at% Nb or Ta. Crystallizationkinetics and tracer diffusion studies show that trap-retarded diffusion of thelarger Nb (or other ETM) atoms in the amorphous matrix phase is the rate-limiting factor for grain growth in Fe–Si–Nb–B–Cu alloys (Damson andWurschum, 1996).

The composition evolution during grain growth shows marked differ-ences in Fe–Si–Nb–B–Cu- and Fe–Zr–B–Cu-type alloys (Lovas et al.,


1998). In the former case, nanocrystalline grains tend to increase theirsolubility of Si as the annealing time progresses. In contrast, the Fe–Zr–B–Cu alloy shows reduction of Zr in the crystalline phase with increasingannealing time. In both cases, the remaining amorphous phase has increasedstability as indicated by the increased secondary crystallization temperature.

The kinetics of crystallization for nanocrystalline soft magnetic alloyshave been widely studied through controlled isothermal annealing studiesand through constant heating rate studies (McHenry et al., 2003; Yavari andNegri, 1997). The resulting view of this thermally activated process hasbeen analyzed by two major methods depending upon the type of datacollected, the Johnson–Mehl–Avrami (JMA) technique for isothermalkinetics and the Kissinger method for constant heating rate kinetics(Avrami, 1939, 1940; Johnson and Mehl, 1939; Kissinger, 1956, 1957).This section describes both of these techniques, the parameters resultingfrom these analyses, and a unifying analysis of both techniques.

The isothermal crystallization kinetics has been described by the JMAequation:

X ¼ 1� exp �k t� t0ð Þn½ ð3Þ

where X is the volume fraction transformed in time t, n is the Avramiexponent, and t0 is the transformation onset time (Burke, 1965). Thereaction constant, k, is described by the Arrhenius equation:

k¼ k0 exp�EA

kBT

� �ð4Þ

which provides the temperature dependence to the crystallization process.In this equation, EA is the activation energy for crystallization and k0 is thereaction rate coefficient. From isothermal crystallization theory, the Avramiexponent (n) has contributions from the nucleation conditions (p) and thegrowth conditions (q). The value of p is 0 when all of the nuclei are presentat the transformation onset and 1 when nucleation occurs throughout thetransformation process. The value of q ranges from 1/2 to 3 dependent ontwo factors: (1) the dimensionality of the crystallite growth (values of 1, 2, 3,respectively, for rod, plate, and sphere morphologies) and (2) the growth-limiting factor (1/2 for diffusion-controlled growth and 1 for interface-controlled growth). These two factors are combined, resulting in n¼pþqvalues ranging from 1/2 (preexisting nuclei and diffusion-controlled,rod-like growth) to 4 (continuous nucleation and interface-controlledsphere-like growth).

The use of the JMA model for kinetics in nanocrystalline soft magneticalloys violates two of the simplifying assumptions of the model. First,in the strictest sense, the model applies to compositionally invariant


transformations (e.g., polymorphic reactions). This does not strictly apply tothe nanocrystalline soft magnetic alloys due to the multiphase nature of thealloys and the preferential segregation of certain elements to each phase. Asan example, during the crystallization of Fe–Si–B–Nb–Cu alloys, crystallitesare enriched in Fe and Si, while the remaining amorphous phase is enrichedin Nb and B. Second, in the later stages of crystallization the modelconsiders the overlap of diffusion fields between grains that arrest thetransformation. Again, this does not apply to this type of nanocompositemicrostructure, where each grain tends to be isolated from others by theintergranular amorphous matrix. That being said, the analysis of nanocrys-talline soft magnetic alloys by JMA kinetics has been widely used to discussprimary crystallization with reasonable values of activation energies andAvrami exponents (in most cases).

A study of the isothermal crystallization kinetics of an alloy withcomposition Fe73.5Si15.5B7Nb3Cu1 reported Avrami exponents for a seriesof annealing temperatures and annealing times, using DSC and XRD todetermine crystalline volume fractions transformed (X) (Yavari and Negri,1997). The Avrami exponents were found to change with annealingtime from n¼2.5–3 at early stages of annealing to n¼0.75–1.1 for latestages. The latter values were too low to be explained by the JMAkinetics model and were attributed to the inexactness of the DSC estimatesfor X and composition gradients formed during the devitrification process(a point that opposes the assumptions of the JMA model). Nucleationsite saturation effects may also play a role in the observed reduction in n(Christian, 2002).

Constant heating rate experiments for crystallization of amorphousalloys have been described by the Kissinger equation:

fT2p

¼#exp�EA

RTp

� �ð5Þ

with the peak transformation temperature at Tp, constant heating rate of f,a frequency factor #, and ideal gas constant, R (8.314 J/(K mol)). Theactivation energy for crystallization can be determined by measuring theexothermic crystallization peak temperature (Tp) at various heating rates andplotting the resulting values as log[Tp

2/f] versus Tp�1. This approach

requires limited time for collecting enough data for analysis of activationenergy, giving it an advantage over the isothermal technique. Kissingeranalysis should only be applied to systems where the peak transformationtemperature is coincident with a constant value of fraction transformed(which may or may not be true for the nanocomposite alloys). Notwith-standing, the measurements seem to give reasonable values of activationenergy and have been widely applied to nanocomposite alloys. Quantitativecomparison between the JMA and Kissinger kinetics models is possible by

Table 4.3 Activation energies for primary crystallization (Ea1) and secondarycrystallization (Ea2) for Fe–Si–B–(Nb,Cu) alloys

Ea1 (kJ/mol) Ea1 (eV/at) Ea2 (kJ/mol) Ea2 (eV/at)

Fe77.5Si13.5B9 395.8�101.0 4.10�1.05 350.3�59.2 3.63�0.61

Fe76.5Si13.5B9Cu1 247.8�14.2 2.57�0.15 259.3�8.74 2.69�0.10

Fe74.5Si13.5B9Nb3 409.3�43.4 4.24�0.45 – –

Fe73.5Si13.5B9Nb3Cu1 378.3�66.8 3.92�0.69 443.9�59.6 4.60�0.62

Averages and standard deviations are provided based on values from both Johnson–Mehl–Avrami andKissinger analyses (Bigot et al., 1994; Blazquez et al., 2003; Borrego and Conde, 1997; Chau et al., 2004;Chen and Ryder, 1995; Duhaj et al., 1991; Illekova, 2002; Kane et al., 2000; Kulik, 1992; Leu and Chin,1997; Panda et al., 2000; Surinach et al., 1995; Varga et al., 1994a; Zhang and Ramanujan, 2005; Zhanget al., 1998a; Zhou et al., 1994).


taking the time derivative of the JMA isothermal kinetics equation (Damsonand Wurschum, 1996):

f¼ @X

@t¼ nk 1�Xð Þ �Ln 1�Xð Þ½ n�1ð Þ=n ð6Þ

For this reason, the two techniques should give similar activation energyresults. The average activation energies for Fe–Si–B–(Nb,Cu) alloys areshown in Table 4.3, with values averaged from both JMA and Kissingertechniques.

Several studies have examined the activation energy for substitution ofETMs in Fe73.5Si13.5Nb3�xMxB9Cu1 alloys. With the small amount of Cugiving heterogeneous nucleation sites in the early stages of primary crystal-lization, the strongest contributor to the activation energy is the growth ofthe crystallites. For this reason, variation of the ETM content has a substan-tial effect on the activation energy. A reduction in activation energy hasbeen observed as Ta and V are substituted for Nb (Borrego and Conde,1997; Conde and Conde, 1994; Kulik, 1992). Mo substitution has beenfound to slightly decrease the activation energy and partial Zr substitutiontends to raise the activation energy (Borrego and Conde, 1997). Theseresults are consistent with variation of crystallization temperature in Fe73.5-Si13.5M3B9Au1 alloys, where M¼Ti, V, Cr, Zr, Nb, Mo, Hf, Ta, W(Duhaj et al., 1991; Kataoka et al., 1989). Figure 4.30 shows the phasesformed in the Fe73.5Si13.5M3B9Au1 alloy series under different isothermalannealing conditions (3600 s). While Cu was used in the activation energystudies and Au in Fig. 4.30, the very similar role these elements play in thekinetics validates comparison. The greatest stability of the amorphous phaseis observed in the Nb-containing alloy, with Mo, Hf, W, and V, providingan as-spun amorphous phase and primary crystallites with amorphous matrixafter annealing above 700 K for 3600 s. On the other hand, substitution of

Early transition metals

Ann

ealin

g te

mpe

ratu

re (

K)

Ti200

400

600

800

1000

1200

1400

Fe73.5

Si13.5

ETM3B

9Au

1

tann= 3600 s

Amorphousa-(Fe,Si) (A2)

Fe23B6

V Cr Zr Nb Mo Hf Ta W

Figure 4.30 Schematic diagram showing phases formed after annealing for 3600 s atvarious temperatures for Fe73.5Si13.5M3B9Au1 alloys, whereM¼Ti, V, Cr, Zr, Nb,Mo,Hf, Ta, W (Duhaj et al., 1991; Kataoka et al., 1989).


Ti and Zr is found to have poor glass formability, with crystallites in the as-spun state. The reduced secondary crystallization observed when Cr sub-stitutes for Nb is consistent with the smaller atomic radius of Cr giving it arole in alloying in the a-(Fe,Si) crystallites rather than partitioning to theremaining amorphous phase. Limited substitution of Mo for Nb in Fe73.5-Si13.5M3B9Cu1 alloys is shown in Fig. 4.31 (Borrego and Conde, 1997;Borrego et al., 1998; Liu et al., 1996a; Zhang et al., 1996a). The results areconsistent with the Au-containing alloys in Fig. 4.30.

In alloys that do not contain Si, the activation energy for primarycrystallization has been examined as a function of the MTM content.Figure 4.32 shows slightly decreased activation energy when Co is substi-tuted for Fe in (Fe,Co,Mn)–M–B–Cu alloys (M¼Zr or Nb). Alloys higherin B content (14–15 at%) showed moderately higher activation energy (near350 kJ/mol) than alloys with lower B content (4–5 at%) near 290 kJ/mol(Blazquez et al., 2001, 2005; Conde et al., 2004b; Johnson et al., 2001;Majumdar et al., 2007). Alloys with composition (Fe,Co,Ni)88Zr7B4Cu1had intermediate values near 325 kJ/mol, with a drop to near 200 kJ/mol asthe compositions become rich in Ni (>9.2 e�/atom) (Hornbuckle et al.,2012; Willard and Daniil, 2009; Willard et al., 2012c).

Any technique that possesses sensitivity to the crystallization process maybe exploited to examine the crystallization kinetics, including measure-ments of resistivity, magnetization, heat evolved, and density. Kinetics ofcrystallization can be tracked in many ways. Resistivity and magnetizationwill be discussed in later sections. The density of an amorphous Fe73.5-Si13.5Nb3B9Cu1 alloy was found to be 7150 kg/m3 (El Ghannami et al.,

4d early transition metals

Ann

ealin

g te

mpe

ratu

re (

K)

Zr200

400

600

800

1000

1200

1400

Amorphous

Fe3Si (D03)Fe2BFe23B6

Fe3B (D011)

a-(Fe,Si) (A2)

Nb Mo

Fe73.5

Si13.5

ETM3B

9Cu

1

tann= 3600 s

Figure 4.31 Schematic diagram showing phases formed after annealing for 3600 s atvarious temperatures for Fe73.5Si13.5M3B9Cu1 alloys, where M¼Nb, Mo, NbþMo(Borrego and Conde, 1997; Borrego et al., 1998; Liu et al., 1996b; Zhang et al., 1996a).


(Fe,Co)88Zr7B4Cu1

(Fe,Co)83Zr6B5Ge5Cu1

(Fe,Co)83Zr6B10Cu1

(Fe,Co,Mn)78Nb6B15Cu1

(Fe,Co,Mn)78Nb6B16

(Fe,Co,Ni)88Zr7B4Cu1Act

iva

tion

ener

gy fo

r P

rimar

y cr

ysta

lliza

tion

(kJ/

mol

)

7.80

100

200

300

400

8.0 8.2 8.4 8.6 8.8 9.0 9.2 9.4 9.6 9.8 10.0

Figure 4.32 Activation energy for primary crystallization for (Fe,Co)88Zr7B4Cu1(open circle: Johnson et al., 2001; Majumdar et al., 2007), (Fe,Co)83Zr6B5Ge5Cu1(closed circle: Blazquez et al., 2005), (Fe,Co)83Zr6B10Cu1 (half-closed circle:Blazquez et al., 2005), (Fe,Co,Mn)78Nb6B15Cu1 (opened square: Blazquez et al.,2001; Conde et al., 2004a), (Fe,Co,Mn)78Nb6B16 (closed square: Blazquez et al.,2001; Conde et al., 2004a), and (Fe,Ni,Co)88Zr7B4Cu1 (diamonds: Hornbuckleet al., 2012; Willard et al., 2012c) alloys with variation in valence electrons per atom.



1994). Upon crystallization, the density was found to increase by 1–2% ashigher density crystalline phases replace the lower density amorphous phase.Added usefulness is found when the technique yields information propor-tional to the fraction of the sample transformed with time or temperature.For this reason, differential thermal techniques (DTA, DSC), thermomag-netic techniques, resistivity (T/t dependent), in situ X-ray diffraction (T/t-dependent), and in situ transmission electron microscopy (T/t dependent) canprovide greater information about the transformations.

In combination, these techniques can provide information about thetime necessary for a transformation to occur and the resulting phases that areformed. The time-temperature transformation (TTT) diagrams are usefulconstructs for examining the crystallization kinetics of amorphous alloys. Inaddition to providing information about the time–temperature relationshipfor achieving primary crystallization and avoiding secondary crystallization,such a diagram can also estimate the critical cooling rate necessary foramorphous alloy formation. An extensive discussion of isothermal andconstant heating rate crystallization kinetics as well as their use for describingTTT diagrams is found in a recent review (Clavaguera-Mora et al., 2002).

The TTT diagrams for Fe77.5Si13.5B9 and Fe76.5Si13.5B9Cu1 alloys indi-cate that even relatively low annealing temperatures (below 700 K) result inpartial crystallization of the alloys (Fig. 4.33). The primary crystallizationtemperatures cannot be identified since all annealed samples show some signof crystallization; an indication that the amorphous phase has little stabilityin these alloys (especially true for Fe77.5Si13.5B9). The secondary crystalliza-tion temperature is clearly identified for both alloy compositions, exhibitingshorter times to transformation in the Fe76.5Si13.5B9Cu1 alloys at tempera-tures above 800 K. However, the secondary crystallization occurs at lowertemperatures for the Fe77.5Si13.5B9 alloy when annealed for 1800 s. This isconsistent with the role of Cu as an aid for crystallite nucleation.

The Fe73.5Si13.5B9Nb3Cu1 alloy has been extensively studied, allowing agreater degree of detail for its TTT diagram. Figure 4.34 shows the TTTdiagram with clear indication of both primary and secondary crystallization.It should be noted that the a-(Fe,Si) phase is typically identified at shortertimes and lower temperatures than the ordered a1-Fe3Si phase. This may bean incidental effect due to an inability to identify the atomic ordering in thealloy due to Bragg intensity broadening with the small grain size. It may alsobe a direct effect related to the lack of ordering that occurs at short times andlow temperatures. It is not clear from experiments whether either of these(or both) is true. Separation between primary and secondary crystallizationseems to be nearly constant from 102 to 105 s with a value of �150 K. Atthe secondary crystallization temperature boundary, the amorphous phase isidentified concurrently with some Fe2B, Fe23B6, or Fe3B phases; however,at higher temperatures and longer times, the phase is no longer found. Thehighest annealing temperatures and longest annealing times tend to show allof these secondary phases with coarsened a-(Fe,Si) or a1-Fe3Si.

Time (s)

Fe77.5Si13.5B9

Fe76.5Si13.5B9Cu1

Amorphous

Fe3Si (D0

3)

Fe2B

Fe23

B6

Fe3B (D0

11)

a-(Fe,Si) (A2)

Amorphous

Fe3Si (D0

3)

Fe2B

Fe23

B6

a-(Fe,Si) (A2)

Tem

pera

ture

(K

)Te

mpe

ratu

re (

K)

1500

600

700

800

900

1000

500

600

700

800

900

1000

10 100 1000 104 105 106

Time (s)

1 10 100 1000 104 105 106

Figure 4.33 Time–temperature transformation (TTT) diagrams for Fe77.5Si13.5B9

(Kataoka et al., 1989; M€uller et al., 1992; Noh et al., 1990; Zhang and Ramanujan,2005, 2006; Zhou et al., 1994) and Fe76.5Si13.5B9Cu1 alloys (Ayers et al., 1998;Noh et al., 1990; Yoshizawa and Yamauchi, 1990; Zhang and Ramanujan, 2006;Zhou et al., 1994).


Similar results are found for the Fe73.5Si16.5B6Nb3Cu1 alloy; however,both primary and secondary crystallization temperatures seem to be shiftedto longer times and higher temperatures. As shown in Fig. 4.35, an addi-tional secondary phase loosely identified as FeNbSi is shown (unknowncrystal structure).

There are noticeable differences between the TTT diagrams of theFe73.5Si13.5B9Nb3Cu1 and the Fe91Zr7B2 alloys (see Figs. 4.34 and 4.36).First, the primary crystallization temperature is much lower than in the Si-containing alloy. Second, the separation of primary and secondary crystalli-zation is substantially larger. The lower primary crystallization temperatureindicates a stabilization of a-Fe over the amorphous precursor. In the case ofFe91Zr7B2 alloys, the secondary crystalline phase was identified as Fe3Zr(possibly with Fe23Zr6 structure). The activation energy for primary

Tem

pera

ture

(K

)

Time (s)

1400

600

800

1000

1200

1400Fe

73.5Si

13.5B

9Nb

3Cu

1

Amorphousa-(Fe,Si) (A2)Fe3Si (D03)Fe2BFe23B6

Fe3B (D011)

10 100 1000 104 105 106

Figure 4.34 Time–temperature transformation (TTT) diagrams for Fe73.5Si13.5B9Nb3Cu1alloy (Alvarez et al., 2001; Ayers et al., 1998; Chen andRyder, 1995;Cremaschi et al., 2002;Crisan et al., 1997;Duhaj et al., 1995; Gorrıa et al., 1996;Hampel et al., 1995;Herzer, 1993;Hono et al., 1999; Kataoka et al., 1989; Matta et al., 1995; M€uller et al., 1992; Noh et al.,1990; Pascual et al., 1999; Rixecker et al., 1992; Saad et al., 2002; Vazquez et al., 1994;Wang et al., 1991).

Time (s)

Fe73.5

Si16.5

B6Nb

3Cu

1

Tem

pera

ture

(K

)

1400

600

800

1000

1200

1400

10 100 1000 104 105 106

Amorphousa-(Fe,Si) (A2)Fe3Si (D03)Fe2BFe23B6

Fe3B (D011)FeNbSi

Figure 4.35 Time–temperature transformation (TTT) diagrams for Fe73.5Si16.5B6Nb3Cu1alloy (Bie�nkowski et al., 2004a; Blasing and Schramm, 1994; Gorrıa et al., 1996; Gupta et al.,1994; Herzer, 1993; Kulik et al., 1997; Matta et al., 1995; M€uller et al., 1991; Yoshizawaand Yamauchi, 1990; Zemcik et al., 1991).


Time (s)

Amorphous

Fe3Zr

a-Fe

Fe91

Zr7B

2

Tem

pera

ture

(K

)

10400

600

800

1000

1200

1400

100 1000 104 105 106 107

Figure 4.36 Time–temperature transformation (TTT) diagrams for Fe91Zr7B2 alloy(Suzuki et al., 1990; Suzuki et al., 1994; Suzuki et al., 1996).


crystallization in similar alloys was in the range of 320–370 kJ/mol, consis-tent with grain growth of the a-Fe phase and also consistent with theobserved primary crystallization observed in the TTT diagram (Al-Hajand Barry, 1998; Duhaj et al., 1996; Hsiao et al., 2002).

Chen Chen and Ryder have examined the crystallization process ofFinemet on preannealed samples by differential scanning calorimetry(Chen and Ryder, 1995). They then determined the activation energy forcrystallization as a function of preannealing temperature using a Kissingeranalysis. Their results show a rapid increase in activation energy from 401 to494 kJ/mol as the preannealing temperature was varied from 400 to 500 �C.The crystallization temperature at 10 K/min was reported as 522 �C, butX-ray diffraction of the samples annealed as low as 480 �C shows signs ofcrystallization. These results indicate slowing diffusion as the crystallizationprocess proceeds, consistent with Nb enrichment of the remaining amor-phous matrix and the retarded growth of the nanocrystalline grains atextended annealing times.

4.4. Order–disorder transformations

Long-range atomic ordering has been observed in (Fe,Si)–Nb–B–Cu and(Fe,Co)–Zr–B–Cu alloys. In the former, the BCC solid solution of Fe withSi is found to order as the Si content is increased, first by losing the bodycentering to form an a2-FeSi phase (B2 structure) and then to a slightly

Table 4.4 Two types of superlattice reflections and fundamental reflectionsidentified for atomic ordering in (Fe,Si) alloys

Structure factors (D03) D03Fm�3m

B2

Pm�3mA2

Im�3m

S2 Fhkl¼4(fA� fB) (1 1 1) – –

S1 Fhkl¼4(fB� fA) (2 0 0) (1 0 0) –

F Fhkl¼4(3 fAþ fB) (2 2 0) (1 1 0) (1 1 0)

S2 Fhkl¼4(fA� fB) (3 1 1) – –

S1 Fhkl¼4(fB� fA) (2 2 2) (1 1 1) –

F indicates a fundamental reflection, S1 is a superlattice reflection found by B2 ordering, and S2 is anadditional superlattice reflection from D03 ordering.


more complicated a0-Fe3Si phase with D03 structure. The ordering can beevident in the saturation magnetization, magnetocrystalline anisotropy,resistivity, and lattice parameters, so atomic ordering is quite important inmany of the studied alloys (e.g., see Hall, 1959) (Table 4.4).

In (Fe,Si)–Nb–B–Cu alloys, the ordered Fe3Si phase is frequentlyreported after primary crystallization. Two types of superlattice reflectionsare found with D03 ordering, one set comes when the BCC solid solutionloses its body-centered ordering (A2 transforms to B2) and the second whenfurther ordering of the Si occurs to form the D03 structure (described inmore detail in Section 5.1). Both sets of superlattice reflections are observedin D03-ordered samples; however, the size of the diffraction peaks is smallerthan the fundamental peaks and broader due to their nanocrystalline size,making them difficult to identify in many cases. If only the S1-type super-lattice peaks are observed, the FeSi (B2) phase is present (although this is nottypically observed, it may be possible for high Si-content alloys). It is likelythat some diffraction patterns do not have sufficient intensity to show theatomic ordering (or partial ordering) in the samples even when it is present.

Primary crystallized alloys with composition Fe75.5Si12.5B8Nb3Cu1show enrichment of remaining amorphous phase in Nb and B as thecrystallites grow in diameter (Van Bouwelen et al., 1993). Slight differenceswere observed for the Si content of the remaining amorphous phase and thecrystallized a-(Fe,Si) in this alloy annealed at 776 K for 105 s. The degree ofordering is both a function of the Si content of the alloy and the annealingconditions. For a Fe73.5Si13.5B9Nb3Cu1 alloy, the degree of atomic orderingwas determined for various annealing conditions by tracking the ratio ofsuperlattice to fundamental peaks (of both S1- and S2-types) from X-raydiffraction experiments (see Fig. 4.37) (Zhang et al., 1998b; Zhu et al.,1991). A common trend was found in both sets of superlattice reflections,indicating that B2 ordering and antisite disorder are not likely. Higher Sicontent in the crystalline phase (as determined by lattice parameter

Annealing temperature (°C)

Long

-ran

ge o

rder

par

amet

er

480

(111) S2

(200) S1

(311) S2

0.50

0.55

0.60

0.65

0.70

0.75

0.80

490 500 510 520 530 540 550 560 570 580 590 600

Figure 4.37 Long-range order parameter for D03 ordering in Finemet-type withannealing temperature. After Zhang et al. (1998b).


measurements) accompanied the stronger ordering observed at higherannealing temperatures.

In (Fe,Co)–Zr–B–Cu alloys, the B2-type atomic ordering has beenobserved; however, the superlattice reflections are very difficult to deter-mine due to the similar atomic scattering factors of Fe and Co, with thestructure factor being proportional to the difference between the two. Forthis reason, special X-ray diffraction techniques must be used to observe thesuperlattice reflections (see Willard et al., 1998, 1999b for example).

5. Structural and Microstructural

Characterization

The phases formed during primary crystallization and the compositionof each phase in the nanocomposite microstructure have a strong effect onthe magnetic properties. As an illustration of the importance of crystalstructure and composition of phases on the properties, the coercivities of aseries of Fe73.5�xMxSi13.5B9Nb3Cu1 alloys (with M¼Cr, Co, Ni) are plot-ted against composition in Fig. 4.38. Significant increases in coercivity areobserved for (Fe,Cr)-containing alloys occur near 10 at% substitution. In thiscase, Cr efficiently reduces the Curie temperature of the intergranularamorphous phase causing decoupling between grains, which leads to therising coercivity. Amount and distribution of Cr are important in this case.A significant rise in coercivity is also observed for (Fe,Co)-containing alloys

M content (at%)

Fe73.5 – xMxSi13.5B9Nb3Cu1

M = NiM = CoM = Cr

Coe

rciv

ity (

A/m

)

10.1

1

10

100

1000

10,000

10 100

Figure 4.38 Coercivity variation with magnetic transition metal content inFe73.5�xMxSi13.5B9Nb3Cu1 alloys where M¼Cr (Atalay et al., 2001; Chau et al.,2006; Franco et al., 2001b; Marın et al., 2002), Ni (Atalay et al., 2001; Agudo andVazquez, 2005), and Co (Atalay et al., 2001; Chau et al., 2004; Gomez-Polo et al.,2001; Kolano-Burian et al., 2004b; Marın et al., 2006; Mazaleyrat et al., 2004).


above 50 at% substitution. In this case, the structure change of the primarycrystalline phase to FCC and/or HCP results in the observed increase incoercivity (Gomez-Polo et al., 2001). This section discusses typicallyobserved phases, compositional effects, and the microstructures and domainstructures that are important for understanding extrinsicmagnetic properties.

5.1. Crystal structure and phase identification

The nanocomposite microstructure developed during primary crystalliza-tion can be formed of several types of crystallites—a feature that largelydetermines how we classify the alloy. The structure of the crystalline phasecan have a significant impact on the magnetic properties. Cubic crystallitesthat are rich in MTMs are most desirable for primary crystallization due totheir large magnetization and their typically small magnetocrystalline aniso-tropies. When alloys are rich in Fe (without significant Si content, e.g.,Fe–Zr–B–(Cu)), they typically form the BCC phase, upon primary crystal-lization. Substitution of Co for Fe in these alloys can result in the long-rangeordering within the crystallites, producing an a0-FeCo phase with CsCl(B2)-type ordering. Ni-rich alloys tend to form an FCC phase, and Co-richalloys have been found to have both FCC and hexagonal close-packed(HCP) structures during primary crystallization. Due to the metastablenature of the processing, the phase-field boundaries between BCC, FCC,and HCP phases are typically different from equilibrium.

(a) (b) (c)

z

y

Figure 4.39 Relationship between crystal structures of common primary crystallinephases (a) a-Fe (A2), (b) a0-FeCo (B2), and (c) a0-Fe3Si (D03).


When Si is substituted for Fe (instead of Co), the ordered phase a0-Fe3Siand/or disordered phase a-(Fe,Si) are observed. The disordered phase has theBCC structure where Fe and Si form a solid solution. While intermediateordering between the a0-Fe3Si and a-(Fe,Si) phases is possible (e.g., thea2-FeSi phase with B2 structure), it is not commonly reported. The orderedFe3Si phase has a D03 crystal structure Fm�3mð Þ with a lattice parameter abouttwice the size of the disordered BCC phase (near 5.667 A). In the binaryFe–Si phase diagram, the Fe3Si phase has substantial solubility for Si extendingto mainly Fe-rich compositions from 25 at% Si in Fe (Massalski, 1990). Twoinequivalent Fe sites are positioned at (1/4, 1/4, 1/4) and (1/2, 1/2, 1/2)(Wyckoff 8c and 4b) and Si at the (0, 0, 0) sites (Wyckoff 4a). The (1 1 1) and(2 0 0) superlattice reflections are indicative of the D03 ordering, differentiat-ing it from BCC and B2 crystal structures (see Fig. 4.39). Partial substitutionof Co for Fe in Fe73.5�xCoxSi13.5B9Cu1 nanocrystalline alloys showed pref-erential population of Co on the 8c site by neutron diffraction (resulting inadditional ordering forming an L12 phase) (Gomez-Polo et al., 2002).

Due to the deleterious effect of secondary crystallization on the stabilityof the nanocrystalline microstructure, recent studies have focused on under-standing these phases. In (Fe,Si)-based alloys, the most common secondaryphases include the tetragonal Fe2B phase, the orthorhombic Fe3B phase,and the cubic Fe23B6 phase. The former two structures are shown inFig. 4.40. The Fe2B phase is an equilibrium phase forming by peritecticreaction at�1660 K. Its structure (Strukturbericht, C16) consists of stackedFe and B layers in a body-centered configuration with B atoms having 10near neighbors (i.e., 8 Fe in a square anti-prism in a–b plane and 2 B atomsforming caps along the c-axis—see Fig. 4.40a). The Fe atoms are topologi-cally close packed with a coordination number of 15 in a Frank–Kasper-type configuration.

Both Fe3B and Fe23B6 are metastable phases. While several Fe3B phaseshave been reported, the most commonly identified crystal structure duringsecondary crystallization is the well-known Fe3C (cementite) prototype(Strukturbericht, D011). The B atoms in this orthorhombic structure haveeight close Fe near neighbors and one more at about 20% greater distance,

(a) (b)y

z

y

x

x

Figure 4.40 Crystal structures for two common secondary phases in (Fe,Si)-basedalloys: (a) Fe2B (C16) viewed along [0 0 1]; (b) Fe3B (D011) viewed along [11 0 4]direction. Large spheres represent Fe atoms and small spheres represent B atoms.

(a)

z

yx

z

yx

(b)

Figure 4.41 Crystal structures for two common secondary phases in Fe-based alloys:(a) Fe23B6 (D84) (large spheres—Fe; small spheres—B), (b) Fe23Zr6 (D8a) (largespheres—Zr; small spheres—Fe). Lower left shows the arrangement of atoms thatpopulate the FCC sites for each structure (see text).


forming a tri-capped trigonal prism (illustrated in Fig. 4.40b). The Fe atomshave a nearly close-packed structure (with B in distorted interstitial sites).All B atoms are closely networked with Fe in the structure but share closeproximity with other B atoms. In contrast, the Fe23B6 phase (with cubicCr23C6 structure (Strukturbericht, D84)) exhibits well-separated B atomsand a high degree of symmetry (see Fig. 4.41a). In this structure, the FCCsites are populated with a central Fe atom surrounded by 12 other Fe atomsin a cuboctahedron and 6 B atoms in an octahedron. All tetrahedral sitesbetween these clusters are filled with Fe, and all octahedral interstices arefilled with eight Fe atoms in cube formation. This results in B atoms havinga square anti-prism coordination of eight Fe atoms and no near-neighbor Batoms. The Fe atoms have four inequivalent sites, with three of these sites


having Frank–Kasper-like coordination and the final site being the high-symmetry FCC site.

Another secondary phase commonly found in Fe–Zr–B–(Cu) alloys isthe Fe23Zr6 phase (along with Fe23B6). Although Fe23B6 and Fe23Zr6 areboth FCC phases with 116 atoms per unit cell, they are structurally quitedifferent. The FCC sites in Fe23Zr6 are occupied by a central Fe atomsurrounded by a cube of 8 Fe atoms, an octahedron of 6 Zr atoms, and acuboctahedron of 12 more Fe atoms (which share vertices with clusters onadjacent FCC sites) (see Fig. 4.41b). All octahedral interstices are filled withfour Fe atom tetrahedra. The Zr atoms are arranged with a seven-cappedpentagonal prism configuration with a coordination number of 17 (13 Feand 4 Zr atoms). The Fe atoms have four inequivalent sites, two areicosahedral, one is Frank–Kasper-like, and the final site has the high-symmetry FCC placement. Table 4.5 provides information regarding com-monly observed primary and secondary crystalline phases.

The soft a-(Fe,Si) phase is retained after secondary crystallization, but itcoarsens due to the absence of the intergranular amorphous phase at thesetemperatures. In an alloy with composition Fe73.5Si13.5B9Nb3Cu1, second-ary crystallization resulted in heavily twinned Fe2B at temperatures as low as580 �C (Wang et al., 1991; Zhu et al., 1991). The Fe3B phase was observedby others after annealing at 600 �C for 3.6 ks, and the (Fe,Nb,Si)23B6 phasewas found after annealing at 700 �C (Chen and Ryder, 1997).

The nominal composition of the primary crystalline phases is rich inMTMs, whereas the glass-forming elements, Nb, Zr, B, etc., have beenchosen not only for their aid in rapid solidification to a fully amorphousalloy but also for their limited solubility in the primary crystalline phase.However, due to the nonequilibrium processing, some solubility of theseelements is found in the primary crystalline phase. For instance, a latticeparameter 4% larger than a-Fe is observed in Fe91Zr7B2 alloys after crystal-lization above the primary crystallization temperature (Suzuki et al., 1991c).As the annealing temperature is increased, the lattice parameter decreasestoward the a-Fe phase value. Detailed analysis of the composition profilesthrough crystallizing grains using APFIM on the similar Fe90Zr7B3 alloyshows near complete rejection of Zr from the crystallites and retention ofsome B, leading to the increased lattice parameter (Zhang et al., 1996c).A similar effect is observed in other Fe- and (Fe,Co)-based alloys which donot contain Si (Makino et al., 1995; Willard et al., 2002c, 2007).

In the Fe73.5Si13.5B9Nb3Cu1 alloy, the lattice parameter of the primarycrystalline phase also tends to change with annealing time and temperature.In this case, Si is enriched in the crystalline phase as annealing progressesuntil the lattice parameter of a-(Fe,Si) is near that of 20–23% Si in Fe (whichwas also found to be consistent with the observed Curie temperature(Herzer, 1991)). Thermal expansion coefficients for the a-(Fe,Si), Fe3B,and Fe2B phases were determined from in situ neutron diffraction studies,

Table 4.5 Primary and secondary crystalline phases identified for typical nanocomposite soft magnetic alloys

Phase Prototype and

(Strukturbericht)

Space

group

Lattice parameter

(A)

Pearson

symbol

Atom type and

(Wyckoff notation)

Special

positions

a-Fe W, BCC (A2) Im�3m a¼2.8664 cI2 Fe (2a)

g-(Fe,Ni) Cu, FCC (A1) Fm�3m a¼3.5240 (Ni) cF4 Fe (4a)

a0-FeCo CsCl (B2) Pm�3m a¼2.8508 cP2 Fe (1a)

Co (1b)

a0-Fe3Si BiF3 (D03) Fm�3m a¼5.6554 cF16 Si (4a)

FeI (4b)

FeII (8c)

Fe2B Al2Cu (C16) I4/mcm a¼5.110

c¼4.183

tI12 B (4a)

Fe (8h)

xFe¼0.334

Fe3B Fe3C (D011) Pnma a¼4.439

b¼5.428

c¼6.699

oP16 B (4c)

FeI (4c)

FeII (8d)

xB¼0.3764

zB¼0.4426

xFeI¼0.0388

zFeI¼0.6578

xFeII¼0.1834

yFeII¼0.0689

zFeII¼0.1656

Fe23B6 Cr23C6 (D84) Fm�3m a¼10.595 cF116 FeI (4a)

FeII (8c)

B (24e)

FeIII (32f) FeIV (48h)

xB¼0.276

xFeIII¼0.381

yFeIV¼0.171

Fe23Zr6 Mn23Th6(D8a) Fm�3m a¼11.578 cF116 FeI (4a)

FeII (24d)

Zr (24e)

FeIII (32f1) FeIV (32f2)

xZr¼0.203

xFeIII¼0.321

xFeIV¼0.178

Lattice parameters and special positions are identified for bulk crystalline samples. Primary phases are identified in bold face (Buschow et al., 1983; Ellis and Greiner, 1941;Khan et al., 1982; Ohodnicki et al., 2008a).


with da/a values of 1.78�10�5, 1.34�10�5, and 1.15�10�5 K�1, respec-tively (Barquın et al., 1998). The result for a-(Fe,Si) was somewhat largerthan expected.

5.2. Microstructure and phase distribution

The average grain size is the most important aspect of improving the losscharacteristics of nanocomposite soft magnetic alloys. However, the typicalmicrostructure for these nanocomposite soft magnetic materials consists ofmultiple phases, so the grain size alone does not describe the microstructure.For example, the high-resolution transmission electron micrograph inFig. 4.42 shows several important features not described by the graindiameter. First, the grains are largely equiaxed, but some are more elongatedthan others. Second, the material is not fully crystalline, with an intergran-ular amorphous phase up to 3 nm in width surrounding the grains. Theseare common features of most of the successful alloys of this type, but thesecharacteristics are not the only ones that are important for refining themagnetic properties.

The phase and grain size distributions, the compositions of each phaseand their crystal structures, and the fraction of each phase in the optimizedmicrostructure are terms that should not be ignored due to their importancein the magnetic performance of the alloys. For example, the partitioningof elements during crystallization can have a great effect on the microstruc-ture, the Curie temperature of the remaining amorphous phase, andthe magnetization of the alloy. Also, the fraction transformed to the crystal-line phase affects the magnetostriction and thermomagnetic properties of

5 nm

Figure 4.42 High-resolution transmission electron micrograph for a(Fe0.05Co0.95)89Zr7B4 alloy showing 8–12 nm nanocrystalline grains embedded in1–2 nm-wide amorphous matrix (Goswami and Willard, 2008).


the nanocomposite. With more specificity, in Fe–Si–B–Nb–Cu alloys, thedesired grain refinement is not achieved unless both Nb and Cu are added insmall amounts. If Nb is not included, grain growth is not inhibited andcoarsening occurs rapidly (see Fig. 4.43). After the first stage of crystalliza-tion of a Fe76.5Si13.5B9Cu1 alloy, the grain size and its standard deviationwere found to be 71 and 22 nm, respectively (Kulik, 1992). When both Nband Cu are eliminated from the composition, the average grain size isfurther degraded to near 300 nm. Refinement is possible by the substitutionof 3 at% Nb and 1 at% Cu for Fe, resulting in 11 nm grain diameters with4.5 nm standard deviation. Figure 4.43 shows transmission electron micro-graphs of Fe73.5Si13.5Nb3B9Cu1 and related alloys, which have been

Fe77.5Si13.5B9


Fe76.5Si13.5B9Cu1

Fe77.5Si13.5B9

Fe74.5Si13.5B9Nb3200

100

50

20

101 102 103 104

Fe76.5Si13.5B9Cu1

Gra

in d

iam

eter

(nm

)

Annealing time (s)

8 s at 550 °C

3600 s at 550 °C

3600 s at 550 °C

50 nm

50 nm50 nm

7200 s at 550 °C8 s at 550 °C

Fe77.5Si13.5B9

Fe76.5Si13.5B9Cu1


Figure 4.43 Diagram showing the average grain size as annealing time at 550 �C isvaried for Fe73.5Si13.5Nb3B9Cu1, Fe76.5Si13.5B9Cu1, and Fe77.5Si13.5B9 with supportingtransmission electron micrographs for selected samples (Ayers et al., 1998; Willard andHarris, 2002).


annealed for various times at 823 K. The absence of Cu has a far smallereffect on the grain size than the absence of Nb.

The partitioning of elements in the alloy during the crystallizationprocess has a significant effect on the resulting microstructure and magneticproperties. Cu clustering during the early stages of crystallization has beenspatially correlated with a-(Fe,Si) crystallites in Fe73.5Si13.5B9Nb3Cu1 alloysusing APFIM (Hono et al., 1999). The clusters were determined to be FCCin structure (by EXAFS), enabling them to provide low-energy heteroge-neous nucleation sites for the a-(Fe,Si) (Ayers et al., 1998; Sakurai et al.,1994). As crystallization progresses, Nb has been determined to segregate tothe remaining amorphous phase while Si partitions to the a-(Fe,Si) crystal-lites. The Nb-enriched intergranular amorphous phase inhibits further graingrowth and the Si-enriched crystallites have lower magnetocrystallineanisotropy; both aid the performance of the material. The final composi-tions of each phase, volume fractions transformed, and grain size depend onthe nominal composition of the Fe–Si–Nb–B–Cu alloy and the annealingconditions (temperature and time) (Herzer, 1993). Annealing for 1 h abovethe primary crystallization temperature is generally long enough to allownearly all of the available Si to partition to the crystalline phase, leaving theremaining amorphous phase near an (Fe,Nb)2B composition. The Cu-richclusters that form during the early stages of annealing tend to slowly coarsenover time and are typically found in the intergranular region.

Due to the stability of the ETMs enriched intergranular phase, nano-composite alloys never reach 100% primary crystalline phase. The fractiontransformed to the crystalline phase has a strong influence on the magneticproperties of the nanocomposite, especially when the Curie temperature ofthe intergranular amorphous phase is near the operation temperature. In theFe73.5Si13.5B9Nb3Cu1 alloy, the crystalline fraction transformed and mag-netostrictive coefficient of the alloy are intimately linked. This effect iscomplex and related to the changing composition of the crystalline andamorphous phases during crystallization, as well as the individual magne-tostrictive coefficients of each phase (Herzer, 1995). Figure 4.44 illustratesthe variation of the magnetostrictive coefficient with crystalline fraction fora Fe73.5Si13.5B9Nb3Cu1 alloy (Twarowski et al., 1995a). In Fe89Zr7B4

alloys, the volume fraction transformed has been tracked using electronmicroscopy for various annealing temperatures for 3600 s (see Fig. 4.45a)(Malki�nski and Slawska-Waniewska, 1997). The coercivity is directlyaffected by the fraction transformed through the intergranular exchangeinteractions which are only weakly ferromagnetic in the amorphous phase(TC

am�293 K). The result is a lower coercivity with crystalline fractiontransformed attributed to the compositional changes in the intergranularamorphous phase that raises the TC

am (Fig. 4.45b).The structural correlation length chosen to describe nanocomposite

materials is typically the average grain diameter. In most cases, the standard

Crystalline fraction (%)


Mag

neto

stric

tive

coef

ficie

nt (

ppm

)

0

0

5

10

15

20

10 20 30 40 50 60 70 80 90

Figure 4.44 Magnetostrictive coefficient variation with crystalline fraction trans-formed in a Fe73.5Si13.5B9Nb3Cu1 alloy (Twarowski et al., 1995a).


deviation is less than�0.5 giving, close agreement between the median andmean grain sizes (da Silva et al., 2000; Willard et al., 2000). However, thedependence of the coercivity on grain size having a strong D6 dependencemeans that large grains will have a greater influence on the coercivity thansmaller grains. This is especially true for samples with bimodal grain sizedistributions, where a small volume fraction of significantly larger grains hasbeen shown to increase the coercivity by �50% in Fe–Nb–B alloys (Bitohet al., 2004). Simulations of nanocomposite Fe86Zr7B6Cu1 alloys show thatbreadth in grain size distribution tends to lower the magnetic exchangelength (Lex), resulting in the necessity for smaller average grain sizes toachieve the same effective magnetocrystalline anisotropy (through the ran-dom anisotropy model) (da Silva et al., 2000). The effect is quite significantwith a reduction in Lex by a factor of 3 when the grain diameter standarddeviation is raised from 0.01 to 0.4.

5.3. Magnetic domains and characteristic magnetic lengths

Soft magnetic materials easily form multiple magnetic domains when anapplied magnetic field is removed from the material due to their smallmagnetic anisotropy and large magnetization. The reduction in magneto-static energy is responsible for the formation of domains, which is favorabledespite the added energy cost of the domain walls between the fullysaturated domain regions. In nanostructured magnetic materials, the mag-netic exchange length provides a fundamental length scale over whichnanocrystalline grains are coupled. So the magnetic domain does not

Annealing temperature (°C)

Cry

stal

line

frac

tion

(%)

Crystalline fraction (%)

(a)

(b)

Coe

rciv

ity (

A/m

)

4000

20

40

60

80

420 440 460 480 500 520 540 560 580 600 620 640

Fe89Zr7B4

Fe89Zr7B4

tann= 3600 s

660

3510

100

1000

40 45 50 55 60 65 70 75 80 85 90

Figure 4.45 (a) Variation of volume fraction transformed with annealing temperature(3600 s) for Fe89Zr7B4 alloys; (b) effect of volume fraction transformed on the coerciv-ity (Malki�nski and Slawska-Waniewska, 1997).


necessarily possess a precise direction for the magnetization, rather themagnetization may slightly vary in orientation across a macroscopic domainin these materials. This section describes processing steps to control domainsstructure, domain configurations and sizes, domain wall motion, and thefundamental nature of the exchange correlation length.

The configuration of magnetic domains can have a significant impacton the magnetic performance in soft magnetic materials. As mentionedin earlier sections, the use of stress or magnetic fields during alloy processingcan greatly influence the domain structure changing the switching modefrom domain wall motion to coherent rotation. The former switching


mode gives a square loop with a large remanent magnetization, and the lattergives a sheared loopwith constant permeability over a wide range of fields.Withsuch a dominant effect on the magnetic behavior, knowledge of the domainstructure is an important factor in nanocrystalline alloy characterization.

The domain structure of nanocrystalline materials is in most ways indis-tinguishable from metallic glasses with regular, wide domains and wide, well-defined domain walls (Schafer, 2000). Two distinct domain configurationsare typically found in the as-quenched ribbons of Fe–Si–Nb–B–Cu alloys dueto variations in the stress state of the sample and their large magnetoelasticanisotropy (Guo et al., 1998, 2001; Schafer et al., 1991). Regions with largelytensile stresses show wide domains (from 50 to 100 s mm wide) with anundulating character to the domain boundaries. In regions with local com-pressive stress, the domains consist of narrow laminar patterns (�10 mmwide)arranged in a maze-like pattern. The domain structure of as-cast alloys withcomposition Fe73.5Si16.5Nb3B6Cu1 showed regions with both of these char-acteristics within the same micrograph (Grossinger et al., 1990). Thesecharacteristics are also observed in amorphous magnets when the magne-tostrictive coefficient is not exactly zero.

After annealing at the optimal annealing temperature, the domains arelargely 180� in character with wide domains at the center of the ribbon (up toa few mm in width) and narrower closure domains near the ribbon’s edge(Grossinger et al., 1990). Stress annealing of a Fe73.5Si13.5Nb3B9Cu1 alloy (at540 �C and 150 Mpa for 3.6 ks) was found to produce stripe domains withspacing of about 100–150 mm in a direction transverse to the ribbon length (seeFig. 4.46) (Alves and Barrue, 2003; Fukunaga et al., 2002b; Kraus et al., 1992).Similar results for transverse domains on stress-annealed Fe–Si–Nb–B–Cualloys have been reported elsewhere (Fukunaga et al., 2002b; Hofmannand Kronmuller, 1996; Lachowicz et al., 1997). Transverse domains werealso formed by magnetic field annealing in a saturating field when a Fe73-Si16Nb3B7Cu1 alloy was crystallized at 843 K for 1.8 ks (Flohrer et al., 2005).

Longitudinal Transverse

Ribbon axis

Figure 4.46 Schematic diagram showing the effects of induced anisotropy on mag-netic domains (a) longitudinal and (b) transverse domains.


The stripe domains in this casewere 125–150 mminwidth. Stress annealing in aFe84Zr3.5Nb3.5B8Cu1 alloy produced the opposite domain configuration fromthe Fe–Si–Nb–B–Cu alloys, with wide domains (several hundred micronswide) parallel to the ribbon length (and therefore the applied stress) (Alvesand Barrue, 2003). In Fe78.8�xCoxSi9B9Nb2.6Cu0.6 alloys, a correlationbetween the induced anisotropy (Ku) and the domainwidth (ddw)was observedwith ddw/ ffiffiffiffiffiffiffiffiffiffi

1=Ku4p

(Saito et al., 2006).The domain structure of a Fe73.5Si13.5Nb3B9Cu1 alloy annealed at 550

�C,observed using Lorentz microscopy, showed circularly magnetized domainswith 5 mm radius, an expected domain configuration for low anisotropymaterials (Kohmoto et al., 1990). At this annealing condition, the grain sizeis about 10 nm insinuating that each domain contains 2.5�105 grains in alocally uniform anisotropy region. An electron holography study showedsomewhat smaller domain size for an alloy with similar processing; however,in this case, the magnetic softness of the alloy was demonstrated by tilting thesample within the remanent magnetic field from the inactive objective lens(�160 A/m) (Shindo et al., 2004). A small in-plane component of themagnetic field (10–15 A/m) was enough to saturate the sample.

When the sample is annealed above the secondary crystallization tem-perature (1073 K), the domains are clearly pinned on the coarsened grains,which are a few hundred nanometers in diameter (Kohmoto et al., 1990).Shindo et al. who used electron holography on a sample annealed at 973 Kfor 3.6 ks found that the domain sizes were smaller than the optimallyannealed condition and the domain walls were immobile due to the forma-tion of Fe–B compounds (see Fig. 4.47e and f) (Shindo et al., 2004). Theseresults are consistent with the random anisotropy model at small grain sizeswhere domain walls are not impeded by the fine grains (Hc/D6). Micro-structures consisting of larger grains show domain walls pinned on the grainboundaries, which is partially due to the formation of secondary crystalliza-tion, and illustrate the magnetic hardening of the alloy and the transitioninto the Hc/1/D regime.

Dynamic domain wall motion has been observed for a section of a toroidalcore using differential imaging of magneto-optical Kerr effect microscopy(Zaveta et al., 1995). The Fe73.5Si16.5B6Nb3Cu1 core was optimally annealedand measured using an alternating current magnetic measurement system at1 kHz, while simultaneously observing the domain walls move under differ-ent applied field amplitudes. Some regions of the sample were found to havebetter domain wall mobility than others with large jumps in wall positionobserved as the applied field amplitude was increased.

Further dynamic domain observations were observed using stroboscopicKerr microscopy imaging with a time resolution of up to 1.5 ns (Flohreret al., 2005, 2006). Magnetic field annealing was used to prepare theFe73.5Si16B7Nb3Cu1 cores to different levels of induced anisotropy (near5, 10, and 29 J/m). Weak induced anisotropy resulted in irregular domain

H perpendicular to foil

(a) (b)

(d)(c)

(e) (f)

Some in-plane H

500 nm

500 nm

500 nm

As-

spun

823

K 3

.6 k

s97

3 K

3.6

ks

Har

dly

chan

ged

Eas

ily s

witc

hed

Figure 4.47 Reconstructed phase images from electron holography measurements ofFe73.5Si13.5Nb3B9Cu1 thin foils (a,b) as-spun; (c,d) annealed at 823 K; (e,f) annealed at973 K with (a,c,e) no tilt (b,d,f) 3�, 4�, 6� tilt (�160, A/m field). Modified from Shindoet al. (2004).


patterns and more active switching regions than the stronger inducedanisotropy samples due to high domain nucleation rates (see Fig. 4.48)(Flohrer et al., 2006). The core losses were noticeably larger for sampleswith greater degrees of induced anisotropy which was linked to the widerdomains and smaller amount of domain nucleation at high frequency (andtherefore lower number of switching regions near the domain walls). Theswitching behavior of the domains, in this case, was observed to be largelyby coherent rotation of the magnetization (Flohrer et al., 2005). Domainwall velocities tended to increase with measurement frequency and withdegree of induced anisotropy, with values of �0.75 and 1.4 m/s for mod-erate and strong Ku, respectively.

Magnetic correlations in the two-phase nanocomposite alloys have beendirectly investigated by SANS. These experiments use an external magneticfield applied perpendicular to the incident neutrons to image a two-dimensional scattering profile for the material. The profile is then separatedinto two parts, one related to the square of the angle between the scatteringvector and the applied field and the other independent of angle(Wiedenmann, 1997). The angular-dependent part of the scattering profilecan be directly correlated to the magnetic correlation length of the sample,while the angular-independent part is related to the structural correlation(nuclear scattering).

50 Hz

6

5

4

3

2

1

00 2 4 6

Magnetic field,easy axis,magneto-opticalsensitivity axis

Specific classical eddy current loss per cycle

Frequency [kHz]

Strong Ku

Moderate Ku

Weak Ku

Sp

ecif

ic p

ow

er

loss p

er

cycle

(mW

s/k

g)

8 10

Strong

Ku

Moderate

Ku

Weak

Ku

200 mm

1kHz 5 kHz 10 kHz

Specific hysteresis loss per cycle

Figure 4.48 Specific power loss per cycle versus frequency and corresponding domainimages of nanocrystalline Fe73Si16B7Nb3Cu1cores with different strengths of theinduced anisotropy Ku. The domain images are taken around the point of zero magneticinduction. Domain refinement is distinctive with increasing frequency. Modified fromFlohrer et al. (2006).


Kohlbrecher, Wiedenmann, and Wollenberger found that an optimallyannealed Fe73.5Si15.5B7Nb3Cu1 alloy had strong temperature sensitivity in theanisotropic scattering intensity as the temperature was varied from 404 to720 K (Kohlbrecher et al., 1997). This effect was correlated with the differ-ence in magnetization between the crystallites and amorphous matrix phaseswhich increase as the Curie temperature of the amorphous phase is exceeded(at 650 K). The presence of a paramagnetic amorphous phase which decou-ples the ferromagnetic grains, starting slightly below the Curie temperature ofthe amorphous phase and increasing in magnitude as the temperature isincreased, has been observed in a less direct manner in the increased coercivity(Herzer, 1991). This decoupling was also observed by magneto-optic Kerreffect microscopy measured at 623 K, where domains were observed to be farmore localized and less laminar in shape (Schafer et al., 1991).


Variation in the SANS differential scattering cross section with appliedfield revealed a nonuniformity in the spin orientation on the scale of 100 nmfor a Fe73Si16B7Nb3Cu1 alloy with 17 nm grain size (Michels et al., 2005).These field-annealed samples showed sheared hysteresis loops that saturateat fields above 10 mT and are made up of domains about 100 mm in size.For this reason, the nonuniform spin orientation, manifesting itself as amagnetization ripple, is more closely related to the magnetic exchangelength rather than individual domain configurations (Hasegawa et al.,1996; Hoffmann, 1969). In Fe89Zr7B3Cu1 alloys with smaller volumefractions transformed (�40%), the dipolar interactions between high mag-netization a-Fe grains were observed by SANS (Vecchini et al., 2005). Theeffect was not observed in an alloy with same composition but largercrystalline fraction (near 70%) and was attributed to the large change inmagnetization across the interphase interface. The lower Curie temperatureof the amorphous phase has in Fe–Zr–B alloys also been suggested to giverise to larger dipolar contributions to the domain ripple in these materials(Hasegawa et al., 1996).

The random anisotropy model used to describe the magnetic softness innanocrystalline materials works on the premise that the grains are not strongdomain wall-pinning centers, since the grains are smaller than the exchangecorrelation length. It has been shown (indirectly using SANS) that theexchange length is much larger than the grain size, but smaller than thedomain size. Using Lorentz microscopy, the magnetic domains in aFe44Co44Zr7B4Cu1 alloy have been shown to be much larger than thegrain size without discernible pinning of the domain walls at the grainboundaries (De Graef et al., 2001). The domain wall width was estimatedto be less than�2 mm using a magnetic force microscope for the Fe91Zr7B2

alloy, giving a exchange correlation length of�500 nm (or equivalently 104

grains) (Suzuki et al., 1997). This value is consistent with the observedcoercivity, but not the calculated exchange length of 50 nm (assumingK1Fe�47 kJ/m3). It is surmised that the discrepancy may be due to the slight

dissolution of Zr and B in the a-Fe grains (as determined by atom probe)(Hono et al., 1995).

6. Magnetic Property Characterization

The constitutive relationship between magnetic induction (B in Tesla),magnetization (M in A/m), and magnetic field (H in A/m) is given byB¼m0(HþM). An attempt to use SI units under the Sommerfeld conven-tion will be made throughout this section. This equation describes themagnetic behavior of a material and magnetic fields both above and belowthe Curie temperature. However, a spontaneous magnetization is only found


for the magnetically ordered phase below the Curie temperature, where theexchange interaction is strong enough to align magnetic moments on adja-cent atoms. The saturation magnetization (Ms) is an intrinsic material quantitydependent on the composition of the phases, comprising the alloy andestablished when a large magnetic field is applied to the alloy causing thealignment of all of the magnetic moments in the material. When smallmagnetic fields are applied, a good soft magnetic material possesses largepermeability (m¼B/H) and susceptibility (w¼M/H). Since soft magneticmaterials require very little H to create large changes in magnetization, the BandM are sometimes used interchangeably (referring toM erroneously inTeslafor instance). Due to the nonlinear behavior of a material’s response to anapplied magnetic field, a range of permeabilities are observed as a material istaken from zero applied field to saturation. Much of this behavior is linked tochanges in the magnetic domain structure that can be greatly affected by themicrostructure.

Soft magnetic materials have been continually improved, most recentlyby the development of the materials described in this review. Theseimprovements include higher saturation magnetization, higher permeabil-ity, lower coercivity, and ultimately lower hysteretic and core losses. Theeffects of processing and composition on these characteristics will be thefocus of the following sections.

6.1. Magnetic moments and saturation magnetization

The saturation magnetization (Ms) is the maximum magnetic moment perunit volume for a magnetic material. This intrinsic property is an importantfactor for soft magnetic applications, since large values allow miniaturization.In nanocrystalline soft magnetic alloys, the composition of the alloy, structureof the crystalline phase, and fraction of crystalline and amorphous phases havea significant impact on the saturation magnetization of the alloy. Mostprominent among these is the influence of MTM on the saturation magneti-zation of the alloy. In polycrystalline alloys, this variation was famouslydescribed separately by Slater (1937) and Pauling (1938), with the observationthat a maximum value of saturation magnetization of 1.95�106 A/m(2.43 T) is found for a Fe65Co35 alloy with BCC structure (Pfeifer andRadeloff, 1980). A steady decline of magnetization becomes linear with Coenrichment for contents greater than about 60% Co, which is especiallyevident for compositions with FCC crystal structure. The Fe–Co alloysshow a break in their magnetization upon transition from the BCC phase(left) and the FCC phase (right) in Fig. 4.49. The Fe–Ni alloys show a similartrend with composition, with peak at slightly higher Fe contents and steadylinear decline of magnetization for Ni contents exceeding about 45% Ni.Rigid band and virtual bound state models have been used to describe the

FeCo (BCC)

FeNi

FeCo (FCC)

(Fe,Co)

(Fe,Ni)

Si ³ 10 at%

Si £ 9 at%

Si £ 1 at%

(Fe,Cr)

2.5

2.0

1.5

1.0

0.5

07.6 7.8 8.0 8.2 8.4


(a)

(b)(Fe,Co)86B6Zr7Cu1

(Fe,Co)84B9Nb7

(Fe,Co)83Si1B8Nb7Cu1

(Fe,Co)79.4Si9B9Nb2.6

(Fe,Co)78.8Si9B9Nb2.6Cu0.6

(Fe,Co)71.5Si10Nb4B13.5Cu1(Fe,Co)73.5Si13.5B9Nb3Cu1 (1)

(Fe,Co)73.5Si13.5B7Nb3Cu1 (2)(Fe,Co)73.5Si13.5B7Nb3Cu1 (3)(Fe,Co)73.5Si15.5B7Nb3Cu1(Fe,Ni)78.8Si9B9Nb2.6Cu0.6

(Fe,Cr)73.5Si13.5B9Nb3Cu1

Sa

tura

tion

mag

netiz

atio

n (T

)

8.6 8.8 9.0 9.2 9.4 9.6 9.8 10.210.0

2.5

2.0

1.5

1.0

0.5

07.8 8.0 8.2 8.4 8.6


(Fe,Co,Ni)86Zr7B6Cu1S

atu

ratio

n m

agne

tiza

tion

(T)

8.8 9.0 9.2 9.4 9.6 9.8 10.0 10.2

Figure 4.49 Variation of saturation magnetization with magnetic transition metalcontent for (a) (Fe,Co,Ni)86Zr7B6Cu1 alloys (� BCC, þ FCC) (M€uller et al., 2000)and (b) (Fe,Co)79.4�xSi9B9Nb2.6Cux (x¼0, 0.6) (Ohnuma et al., 2003b; Yoshizawaet al., 2003, 2004) (square, diamond), (Fe,Co)73.5Si13.5Nb3B9Cu1 (circles), (Fe,Co)73.5Si15.5Nb3B7Cu1 (rt pointing triangles (Chau et al., 2004, 2006; Kolano-Burianet al., 2004a; Mazaleyrat et al., 2004; M€uller et al., 1996b)), (Fe,Co)86Zr7B6Cu1(downward triangles (M€uller et al., 2000)), (Fe,Co)83Si1B8Nb7Cu1 (triangle(Yoshizawa and Ogawa, 2005)), and (Fe,Co)71.5Si10Nb4B13.5Cu1 (lt pointing triangles(Inoue and Shen, 2003)), (Fe,Ni)78.8Si9B9Nb2.6Cu0.6 (� (Ohnuma et al., 2003b;Yoshizawa et al., 2003, 2004)) alloys.



filling of electronic bands during the alloying process and its effect on thesaturation magnetization of the material (OHandley, 2000).

The variation of the saturation magnetization of nanocrystalline alloyswith MTM content is compared to the Slater–Pauling curve for polycrys-talline alloys in Fig. 4.49a. Interestingly, the alloys without the substitutionalelement, Si, show a very similar behavior, exhibiting a peak in the saturationmagnetization at about 40% Co substituted for Fe. The transition fromBCC to FCC with composition is shifted to higher Co content with greaterstabilization of the BCC phase as exhibited by the shift in observed BCCphase to higher Co content compared with polycrystalline alloys (seediscussion of BCC stabilization in Ohodnicki et al., 2009). The saturationmagnetization remains lower than the crystalline alloys of the same MTMcontent, which is expected as the composition is made up in part ofnonmagnetic elements, which dilute the magnetization. As the materialhas a nanocomposite microstructure, each phase contributes to the magne-tization weighed by the respective phase fraction and their individualmagnetizations. In most cases, the saturation magnetization is increasedupon crystallization due to the relatively small values of magnetizationobserved in most amorphous alloys.

In (Fe,Co,Ni)–Si–B–Nb–Cu alloys, the saturation magnetization doesnot show the same peak behavior as observed in the alloys without Si (seeFig. 4.49b) (Yoshizawa et al., 2003). Rather than slightly increasing withincreased Co or Ni content, the saturation magnetization shows a flatsaturation magnetization with Co alloying and reduced magnetizationwith Ni alloying. The strong drop in magnetization for Fe–Ni alloys atabout 3:1 ratio of Fe:Ni is similar to the trend observed in polycrystallinealloys, resulting from the magnetic phase instability at the transitionbetween BCC and FCC compositions (termed Invar effect for the resultinginvariance in thermal expansion coefficient for these alloys) (Chikazumi andGraham, 1997). Similar invariance in thermal expansion coefficient has notbeen discussed with regard to these alloys. Substitution of transition metalsin Fe–M–Si–Nb–B–Cu-type alloys results in the substitution of the Fe(4b)sites for MTMs (M¼Co and Ni) and Fe(8c) sites for ETMs (M¼Ti, V, Cr,and Mn) in the D03 nanocrystallites (Gomez-Polo et al., 2003). Neutrondiffraction experiments were conducted to establish this connection, whichhas a direct effect on the magnetization as a function of composition.

Much of the work done in nanocrystalline alloy design has focused onincreasing magnetization while simultaneously decreasing coercivity.Reduced coercivity has been demonstrated by the substitution of Al inFe–Si–Nb–B–Cu and Fe–Zr–B–(Cu) alloys (Lim et al., 1993b; Moya et al.,1998). However, this substitution results in reduced magnetization, a trendalso observed in crystalline alloys with similar substitutions (Fig. 4.50)(Bozorth, 1959). Higher contents of Al and Si result in greater reduction ofmagnetization, especially evident in the Al/Si-rich Fe87�zAlxSiz�xNb3B9Cu1

x, Al/Si content (at.%)

Sa

tura

tion

mag

netiz

atio

n (T

)

00

0.5

1.0

1.5

2.0

2 4

Fe87 – zAlxSiz - xNb3B9Cu1 Tann= 823 K Tann= 873 K

Tann= 823 K

Tann= 777–819 K

Tann= 793 K

Fe87Zr7B3Al2Cu1

Fe90 – xZr7B3SixFe90 – xZr7B3Alx

Fe73.5 – xAlxSi13.5Nb3B9Cu1

Fe73.5 – xAlxSi13.5Nb3B9Cu1

Fe88 – xZr7B5Alx

6 8 10 12 14 16

Figure 4.50 Effect of Al content on the saturation magnetization for (Fe,Al,Si)87M3B9Cu1 alloys where M¼Nb or Mo (Borrego et al., 2001b; Daniil et al.,2010a; Szumiata et al., 2005; Tate et al., 1998; Todd et al., 2000; Zorkovska et al.,2002) and (Fe,Al,Si)90Zr7B3(Cu) alloys with 0<Al<15 at% (Hison et al., 2006; Inoueet al., 1996; Kovac et al., 2002).


and Fe73.5�xAlxSi13.5Nb3B9Cu1 alloys (Borrego et al., 2001b; Daniilet al., 2010a; Szumiata et al., 2005; Tate et al., 1998; Todd et al., 2000;Zorkovska et al., 2000). Despite the reduced magnetization, a nanocrystallineFe63Si17.5Al6Nb3B9Cu1 alloy was recently shown to provide lower coercivityand higher magnetization than the commercially available Cryoperm-10 alloyfor cryogenic applications (Daniil et al., 2010a).

Although the type of ETM does not seem to have a strong impact on thesaturation magnetization, the saturation magnetization tends to decreasesteadily with the amount of ETM in the alloy. This effect is shown inFig. 4.51, where several combinations of Nb, Mo, V, and U are shown toreduce the magnetization from the ETM-free value of �1.5 T by a factorthat greatly exceeds a dilution effect. The Curie temperature of the amor-phous phase continually decreases with increasing ETM content (seeFig. 4.54); however, it remains large enough to have little impact on thesaturation magnetization at room temperature.

6.2. Temperature dependence of magnetization and Curietemperatures

Ferromagnetic order relies on positive exchange interactions between mag-netic moments in the material to promote parallel alignment of thosemoments. At sufficiently high temperatures, all ferromagnetic materials

M content, x (at.%)

Sa

tura

tion

mag

netiz

atio

n (T

)

Fe76.5 - xMxSi13.5B9Cu1

00

0.5

1.0

1.5

1 2 3 4

no ETM

M = Nb + Mo

M = Nb + V

M = Nb

M = U

5 6 7 8 9

Figure 4.51 Effect of early transition metal content on saturation magnetization forFe76.5�xMxSi13.5B9Cu1 alloys (where M¼Nb, NbþMo, NbþV, U) (Conde et al.,1997; Konc et al., 1995; Wang et al., 1997; Yoshizawa and Yamauchi, 1990).


become paramagnetic due to the thermal disruption of the coupling betweenmagnetic moments. The temperature at which the magnetic order is lost inthe material is called the Curie temperature. Below the Curie temperature,the spontaneous magnetization acts as the order parameter for ferromagnetism(a higher-order phase transformation). At the Curie temperature, the magne-tization is reduced to zero as thermal switching of the magnetization occurs.The Curie temperature is higher in materials where the exchange coupling isstronger and when the atomic moments are larger; however, the variation ofCurie temperature with composition is dependent on many complicatingfactors, including the types of magnetic atoms, their coordination and sym-metry in their local environment, and their bonding characteristics (especiallylocalized bonding and bond lengths). Due to natural variations in thesecharacteristics, amorphous alloys tend to have lower Curie temperaturesthan crystalline alloys with similar MTM ratios.

Measurement of the saturation magnetization with temperature givesimportant information about magnetic ordering and limitations of a givenmaterial for environments other than near room temperature. Obviously,the magnetization must remain large at the operation temperature forany soft magnetic material, with no exception for nanocomposites. InFig. 4.52, the saturation magnetization alone limits some alloys to near roomtemperature applications (e.g., (Fe,Si)-based alloys), while the saturationmagnetization is quite large to high temperatures for others (e.g., especially(Fe,Co)-based alloys). Thermomagnetic experiments are especially impor-tant for nanocomposite materials due to the requirement of good exchange


Ma

gnet

iza

tion

(A m

2 /kg

)

2000

50

100

150

300 400

Fe44.5Co44.5Zr7B4

Fe77Co5.5Ni5.5Zr7B4Cu1

Co83.6Fe4.4Zr3.5Hf3.5B4Cu1

Fe88Zr7B4Cu1

Fe73.5Si13.5Nb3B9Cu1

500 600 700 800 900 1000 1100

Figure 4.52 Saturation magnetization variation with measurement temperature forFe-based, (Fe,Si)-based, and (Fe,Co)-based alloys.


coupling between grains to maintain the exchange softening conditionthroughout the alloy. The details of this will be discussed in the next section;however, the fact that the Curie temperature of the amorphous matrix is thelimiting factor for their high-temperature operation is the motivation forour detailed discussion of TC

am and the following discussion of theoreticalmodels.

Two theories help us to understand the interaction of atomic moments—the Weiss mean field theory and the Heisenberg exchange theory. By theWeiss mean field theory, the moments are brought to alignment by an(nonphysical) internal magnetic field (i.e., mean field) that acts to align themoments in the absence of an applied field. The mean field is used toapproximate the interaction of the surrounding widespread environment onindividual moments in the material. This leads to the spontaneous magneti-zation observed in ferromagnetic materials. The Heisenberg exchange theory,on the other hand, considers the alignment of the magnetic moments due toquantum mechanical exchange interactions between near-neighbor atoms(local environment). Heisenberg exchange can be used to describe ferro-magnets, ferrimagnets, and antiferromagnets by consideration of size ofmagnetic moments and sign of the exchange interaction. Combined use ofthese models gives us insight into themagnitude of the Curie temperature andits composition dependence.

Using the Weiss mean field theory to describe the internal magnetiza-tion, the Langevin function (or Brillouin function) can be applied tocalculate the reduced magnetization as a function of temperature. Althoughthis method results in a transcendental equation, it can be solved numeri-cally to estimate the Curie temperature:


m0Ms Tð Þm0Ms 0Kð Þ¼ tanh

mAHapp

kBTþmAlWm0Ms Tð Þ

kBT

� �ð7Þ

In this equation, the atomic moment mΑ experiences an applied mag-netic field Happ and mean field lWm0Ms(T), where lW is the Weiss meanfield constant. An extension of this model has been used to estimate thedependence of magnetization with temperature for amorphous alloys, usinga modified Brillouin function to reflect the distributions of exchange inter-action that occur due to the varied interatomic distances found in amor-phous alloys (Gallagher et al., 1999; Handrich, 1969; Kobe and Handrich,1970). This method has been used to estimate Curie temperatures for theamorphous phase when the TC

am exceeds the crystallization temperatures(see Hornbuckle et al., 2012; Willard, 2000).

TheHeisenberg exchangemodel provides aHamiltonian (Hex) to describe

the exchange energy in the system as Hex¼�2Xi<j

Jij S!i� S

!j, where Si are

total spin angular momenta and Jij is the exchange energy between the ith andjth atomicmoments.When Jij is positive or negative, the spins prefer parallel orantiparallel configurations, respectively. Strictly speaking, the HeisenbergHamiltonian applies to materials with localized magnetic moments only(e.g., oxide magnets). However, when combined with the Weiss mean fieldmodel, it can be extended for macroscopic calculations of the exchangeenergy, specifically theWeiss mean field can be clarified in terms of exchangeinteractions by lWm0Ms Tð Þ¼ 2zJij

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiS Sþ1ð Þp

=m0Nvm2A, where Nv is thenumber of moments per volume (�1028–1029 m�3) and z is the number ofnear-neighbor moments. An extension of the Curie law results inMs(T)¼C(HappþlWm0Ms(T))/T, where C¼m0NvmA

2/3kB and kB is Boltzmann’s con-stant. Using these expressions, the Curie temperature can be estimated using

TC ¼ 2zJijS Sþ1ð Þ3kB

ð8Þ

While the estimated values of Curie temperatures using this equationtend to be much higher than experimentally observed, the proportionalityof the exchange energy with the Curie temperature can be used to explaincompositional trends in amorphous and crystalline alloys. The empiricalrelationship of the exchange energy with the ratio of atomic separation to3d atomic orbital diameter, or Bethe–Slater curve, has its foundation in theband theory of solids. The Curie temperature dependence on compositionis therefore dependent on the interatomic effects (via Jij) and the size of thelocal atomic moments (via S(Sþ1)), which ultimately are affected by thecoordination number of magnetic atoms, the distance between these atoms,and the localized bonding. The exchange stiffness (Aex) used in the defini-tion of the exchange correlation length, a defining length scale for the


exchange softening which is critically important to nanocrystalline softmagnet performance, can also be described using the Heisenberg exchangetheory with Aex¼zJijS

2/2a, where a is the lattice constant.For ferromagnetic alloys at temperatures far below the Curie tempera-

ture (T/TC<0.5), the magnetization drops more quickly with temperaturethan expected by the mean field model described above. This has beenexplained by the decay of magnons (spin waves) in the alloy and is betterdescribed by the Bloch T3/2 law:

Ms 0Kð Þ�Ms Tð ÞMs 0Kð Þ ¼ 1�C3=2

T

TC

� �3=2

ð9Þ

where C3/2 is a proportionality constant. The nanocrystalline alloy Fe73.5Si13.5B9Nb3Cu1 has been observed to follow the Bloch T3/2 law between80 and 230 K (Zbroszczyk, 1994). The addition of a (T/TC)

5/2 term wasfound to extend the Law’s applicability to the temperature range 1.5–300 K(Guo et al., 1993; Holzer et al., 1999). Spin wave stiffnesses were deter-mined from this analysis to have values between 100 and 161 meV A2 withtendency to increase in value for samples annealed at higher temperatures(Guo et al., 1993; Kiss et al., 2003; Zbroszczyk, 1994). The resultingexchange stiffness (Aex) was determined to be near 5.7–7.2�10�12 J/mfor nanocrystalline Fe73.5Si13.5B9Nb3Cu1 samples (Holzer et al., 1999; Koncet al., 1995).

Being a two-phase material, nanocrystalline soft magnetic alloys possess amore complex temperature dependence of magnetization, which is depen-dent on the processing conditions (e.g., microstructure and phase evolution)and composition of each phase. At low temperatures, both amorphous matrixand nanocrystalline phases are fully exchange coupled. The Curie tempera-ture of the amorphous matrix phase is lower than that of the crystalline phasedue to alloying with nonmagnetic elements, local coordination of magneticatoms (OHandley, 2000), and distributed exchange that varies the exchangeinteraction (Gallagher et al., 1999). Dependent on the distribution andseparation distance between crystallites, partial or total decoupling of thecrystalline phase has been observed as the temperature has been raised throughthe Curie temperature of the amorphous phase. Hardening of the nanocom-posite alloy is typically observed above this temperature. However, forsufficiently small grains and high temperatures, superparamagnetic behaviorcan be observed. These topics will be discussed in this section and Section 6.4in the context of standard thermomagnetic analyses.

Improvements in the Curie temperature of the amorphous phase resultfrom substituting some Co for Fe in nanocomposite soft magnetic alloys.Substitution of Co for Fe in a (Fe1�xCox)73.5Si13.5B9Nb3Cu1 alloy results inincreased TC

am to from 593 K for x¼0 to about 720 K for x¼60 (seeFig. 4.53a) (Fernandez et al., 2000; Gercsi et al., 2006). Further increase


Cur

ie te

mpe

ratu

re (

K)

7.5

200

400

600

800

1000

7.6 7.7 7.8 7.9 8.0

(Fe,M)3Si

M = Co (Fe,Co)3Si(Fe,Cr)3Si(Fe,Mn)3Si(Fe,V)3Si

M = CrM = MnM = Ni

(Fe1 - xMx)73.5Si13.5B9Nb3Cu1

(Fe,Co)82Nb3Ta1Mo1B13

(Fe,Co)84Zr3.5Nb3.5B8Cu1

(Fe,Co)86Zr7B6Cu1

(Fe,Co)86Hf7B6Cu1

(Fe,Co)88Zr7B4Cu1

(Fe,Co)89Zr7B3Cu1

(Fe,Co)90Zr10

(Fe,Co,Ni)88Zr7B4Cu1

(Co,Ni)88Zr7B4Cu1

8.1 8.2 8.3 8.4 8.5 8.6 8.7 8.8 8.9 9.0


(a)

(b)

Cur

ie te

mpe

ratu

re (

K)

8.0

200

400

600

800

1400

1000

1200

8.2 8.4 8.6 8.8 9.0 9.2 9.4 9.6 9.8 10.0

Figure 4.53 Effect of magnetic transition metal on amorphous phase Curie tempera-ture in (a) Fe73.5�xMxSi13.5Nb3B9Cu1 alloys (where M¼Cr (Chau et al., 2006; Condeet al., 1994; Hajko et al., 1997; Malki�nski and Slawska-Waniewska, 1996; Marın et al.,2002; Randrianantoandro et al., 1997), Mn (Kolat et al., 2002), Co (Borrego et al.,2001a; Chau et al., 2004; Gomez-Polo et al., 2001; Mazaleyrat et al., 2004) and Ni(Agudo and Vazquez, 2005)) and (b) (Fe,Co)90Zr10, (Fe,Co,Ni)88Zr7B4Cu1, (Fe,Co)86(Hf,Zr)7B6Cu1, (Fe,Co)89Zr7B3Cu1,(Fe,Co)84(Nb,Zr)7B8Cu1, and (Fe,Co)82(Nb,Ta,Mo)5B13 (Caballero-Flores et al., 2010; Hornbuckle et al., 2012;M€uller et al., 1996b; Suzuki et al., 2002b; Willard et al., 1999a; Willard et al., 2000;Willard et al., 2007). Curie temperatures above secondary crystallization temperaturesare approximate. For comparison, the Curie temperatures of (Fe,M)3Si (M¼Co, Cr,Mn, V) intermetallic phases are shown in (a) (Chakravarti et al., 1991; Mahmood et al.,2004; Niculescu et al., 1979; Nishino et al., 1993; Waliszewski et al., 1994).



in Co substitution did not result in further increases in TCam. When Ni was

substituted instead of Co, the TCam only showed a small improvement with

small amounts of Ni substitution and then a slow reduction for furtheradditions. Reductions in TC

am accompany the substitution of Cr or Mn forFe in (Fe1�xMx)73.5Si13.5B9Nb3Cu1 alloys, with a more rapid decrease inmagnetic ordering temperature for Mn substitution. Both of these alloyingelements couple antiferromagnetically with the Fe, resulting in the destabi-lization of the ferromagnetic order. Similar results have been reported for(Fe,M)3Si alloys where M¼Co, Cr, Mn, and V (see Fig. 4.53a)(Chakravarti et al., 1991; Mahmood et al., 2004; Niculescu et al., 1979;Nishino et al., 1993; Waliszewski et al., 1994).

The ETMs are essential to formation of the nanocrystalline microstruc-ture in (Fe,Si)-based alloys. For this reason, some amount of ETM must beadded to the alloy to keep the coercivity low; however, the magnetizationand Curie temperatures are both reduced as the amount of ETM isincreased. In Fig. 4.54, the Curie temperature of the amorphous phase isplotted for many Fe76.5�x(Si,B)22.5ETMx(Cu,Au)1 alloys with varying

ETM content (at.%)

0

450

500

550

600

650

700

750

1 2 3

Fe76.5 - x(Si,B)22.5ETMx(Cu,Au)1

4 5

no ETMNb

V + NbZr + NbMo + Nb

Hf + NbTa + NbW + Nb

6 7 8 9

Am

orph

ous

phas

e C

urie

tem

pera

ture

(K

)

Figure 4.54 Effect of early transition metals on the Curie temperature of the amor-phous phase in Fe76.5�x(Si,B)22.5ETMx(Cu,Au)1 alloys (Agudo and Vazquez, 2005;Barandiaran et al., 1993; Chau et al., 2004; Conde and Conde, 1995a; Degro et al.,1994; Franco et al., 2001a; GomezPolo et al., 1997; Hakim and Hoque, 2004; Hampelet al., 1992; Hernando and Kulik, 1994; Herzer, 1989, 1991; Kataoka et al., 1989; Kuliket al., 1994; Lovas et al., 1998; Mattern et al., 1994; Mitra et al., 2002; M€uller et al.,1991, 1992; Noh et al., 1991; Panda et al., 2003; Pekala et al., 1995b; Ponpandian et al.,2003; Rodrıguez et al., 1999; Surinach et al., 1995; Tonejc et al., 1999b; Yoshizawaand Yamauchi, 1990, 1991).


Sa

tura

tion

ma

gnet

iza

tion

(T)

2500

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

300 350 400 450 500 550

Fe89Zr7B4 813 K

Fe86Zr7B6Cu1 573 K

Fe86Zr7B6Cu1 773 K

Fe86Zr7B6Cu1 823 K

Fe86Zr7B6Cu1 873 K

600 650 700 750 800

Figure 4.55 Saturation magnetization variation with measurement temperature forFe89Zr7B4 and Fe86Zr7B6Cu1 alloys (Slawska-Waniewska et al., 1994; Suzuki et al.,1991c).


ETM type. A reduction in TCam is observed at a nearly constant rate of 30 K

per at% ETM substitution for Fe, regardless of the type of ETM used.Many Fe-based samples tend to have Curie temperatures for the as-

spun amorphous phase near room temperature (see Fig. 4.55). As theFe86Zr7B6Cu1 alloy is annealed above the primary crystallization tempera-ture, partitioning of the Zr and B to the remaining amorphous phasechanges the composition of that phase, resulting in an increased TC

am.The unusual behavior of increasing TC

am with reduced Fe content hasbeen observed in Fe–B amorphous alloys and has been attributed to thelocal coordination of glass-forming elements in the alloy (see Bhattacharyaet al., 2012 for details). However, even in the partially crystallized alloys, thecrystallites do not always exhibit the Curie temperature of a-Fe of 1043 K.This is due to the nonequilibrium compositions found in the crystallinephase, with greater amounts of B and Zr that tend to reduce the Curietemperature. Due to the low Curie temperature of the amorphous phase inFe–M–B alloys, thermomagnetic measurements of the as-spun alloys havebeen used as sensitive probes of the crystallization kinetics for primarycrystallization. Both isothermal and constant heating rate experimentshave been performed and activation energies for primary crystallizationhave been determined using JMAK and Kissinger kinetics, respectively(Hsiao et al., 1999; Hsiao et al., 2002).

In contrast, TCam in the HITPERM-type alloys tends to increase well

above 800 K with increasing Co content resulting in estimated peak valuesabove 1000 K (see Fig. 4.53b). This increase in Curie temperature can be

Co content (at.%)

Sa

tura

tion

ma

gnet

iza

tion

(T)

00

0.5

1.0

1.5

10 20 30 40 50

Above Tx2

60

Fe86-xCoxHf7B6Cu1

70 80

298 K373 K473 K573 K673 K773 K873 K948 K

90

Figure 4.56 Saturation magnetization as a function of Co content and measurementtemperature for (Fe,Co)88Hf6B6Cu1 alloys (Liang et al., 2007).


linked to both the increased magnetic moments and the generally largerexchange interaction expected for Fe–Co compositions. These values donot follow trends observed in crystalline (Fe,Co)-based alloys, due to thegenerally lower values of TC

am found in Co-free compositions. In general,the very high TC

am for (Fe,Co)-based alloys allows high operation tempera-tures, only limited by the breakdown of the nanocrystalline microstructureat the secondary crystallization temperature (Willard et al., 2012a).

Similar to the (Fe,Co)–Zr–B–Cu alloys reported in Section 6.1, thesaturation magnetization shows a peak value at about 35% substitution ofCo for Fe in (Fe,Co)86Hf7B6Cu1 alloys. As the measurement temperature isincreased, a shift in the peak magnetization value to higher Co contents isobserved (see Fig. 4.56). Considering the operation temperature should notexceed secondary crystallization, the peak value at the maximum operationtemperature of 773 K is found for the alloy with even amounts of Co and Fe(Liang et al., 2007). The magnetization does not show strong degradationfor alloys measured above Tx2; however, the coercivity of these alloys wassubstantially degraded for these samples.

Several types of nanocomposite soft magnetic alloys have been found topossess only short-range magnetic order at cryogenic temperatures (i.e.,spin-glass behavior). For example, in Fe91�xZr8RuxCu1 alloys, the spin-glass phenomenon was observed in the as-spun amorphous alloy and spin-dependent magnetoresistance was found in the nanocomposite alloy withx¼10 (Suzuki et al., 2002a). This result was attributed to the reduction ofamorphous phase Curie temperature by alloying with Ru which contrib-uted to the spin-dependent scattering in the nanocomposite alloy.


6.3. Magnetic anisotropy and magnetostriction

Magnetic anisotropy is found in all magnetic materials to varying extentswith origins from atomic arrangements, shape of the magnet, magnetoelas-tic, or induced during processing (e.g., stress or magnetic field annealing).Each contributes to the overall loss of the material as the magnetization isswitched from one saturated direction to another, which means that reduc-tion of all sources of magnetic anisotropy is desirable for optimal soft magnetperformance.

In crystalline materials, the magnetocrystalline anisotropy, due to thecoupling of the atomic magnetic moments with the crystal lattice, is adominant factor. The behavior is described by a series of magnetocrystallineanisotropy constants (i.e., K1, K2, etc.) with angular dependence describedby the symmetry of the crystalline lattice. For materials with tetragonal orhexagonal crystal lattices, the energy density is described by

EKu¼Ku1 sin

2yþKu2 sin4y ð10Þ

where y is the angle between the uniaxial direction and the magnetizationvector. Similarly for cubic crystal structures:

EK ¼K1 a21a22þa22a

23þa23a

21

� �þK2 a21a22a

23

� � ð11Þ

where ai are the direction cosines between the magnetization vector and theprincipal axes of the crystalline lattice. The magnetocrystalline anisotropyconstants are dependent on temperature and composition and tend to havereduced values as the order of the angular dependence is increased. In manycases, the first magnetocrystalline anisotropy term is the largest and mostimportant.

As the magnetization of the alloy changes directions, the shape of thesample changes (d‘=‘), resulting in amagnetoelastic contribution to the overallanisotropy of the material. The saturation magnetostrictive coefficient (ls)creates an additional anisotropy term (Ks) with form:Ks¼3/2 lss, where s isthe stress in the sample (tensile). For a uniaxial stress state,Ks replacesKu1 andy is the angle between the stress direction and the magnetization vector.

The magnetostatic energy is a result of the formation of a magnetic fieldexternal to the magnetized material produced by the magnetization of thematerial. A demagnetizing field within the material results from the forma-tion of the external field and the need to preserve the constitutive relation-ships between the field B, H, and M (via Faraday’s law). The shapeanisotropy energy density (Es) results from the demagnetizing effect andhas the form:

Es ¼ m0M2s

2Na cos

2cþNa sin2c

� � ð12Þ


for a prolate spheroid with major equatorial axis a and minor axis b, c is theangle between the polar axis and the magnetization direction, and Na is thedemagnetizing factor for the equatorial axis. In ribbon-shaped samples (e.g.,suitable for measurement in a vibrating sample magnetometer), the shapeanisotropy is dominant due to the small contributions from exchangeaveraged magnetocrystalline anisotropy and relatively random orientationof local stresses (lowering the magnetoelastic contribution). The macro-scopic shape anisotropy is not a material property (being dependent onsample geometry) and can be largely eliminated by creating a wound ribboncore. Powder cores use the shape anisotropy to lower the overall perme-ability of the composite material, important for use in inductor applications.

Nanocrystalline soft magnetic alloys possess magnetic anisotropy valuesfar lower than expected from polycrystalline materials, resulting inextremely small values of coercivity. Herzer performed a systematic studyof the grain size dependence on coercivity, where he employed a randomanisotropy model to describe the results (Herzer, 1990). The randomanisotropy model was first developed to describe the large anisotropyfound in rare earth iron amorphous alloys (Harris et al., 1973) and wasfurther refined by describing the effects in terms of magnetic correlation andstructural correlation lengths (Alben et al., 1978). By this model, thecoercivity of perfectly random amorphous materials was found to be pro-portional to the sixth power of the structural correlation length to magneticcorrelation length ratio. Noting the fact that the grains were exchangecoupled through the residual amorphous matrix, a random anisotropymodel was applied to show that the coercivity was proportional to thegrain size to the sixth power (Herzer, 1992).

In general, the magnetic energy of a nanostructured material is the sumof the exchange and anisotropy energies (E¼EexþEa):

Eex ¼�AX

i;a

ðVi

d3x rmai

� �2�Xi;jh iIij

d

ðSij

d2xmimj ð13Þ

wheremi(x) is the space-dependent magnetization unit vector within graini of volume Vi and A is the intragranular exchange constant (Loffler et al.,1999). The first term represents the exchange energy within a single phaseand the second term refers to the exchange between neighboring grainsthrough the interface Sij of width d and intergranular exchange Iij. Theanisotropy energy has the form:

Ea ¼�KX

i

ðVi

d3x minið Þ2 ð14Þ

where ni is the direction of the easy anisotropy axis (varying with randomorientation for each grain) (Loffler et al., 1999). In small grains, the


exchange energy dominates, and in large grains, the anisotropy energydominates. The dividing line between these sizes is the magnetic domainwall width, which is intimately related to the magnetic exchange correlationlength (L0).

The random anisotropy model applies when the following threerequirements are met: (a) the magnetic correlation length is greater thanthe structural correlation length, (b) the grains have random orientation, and(c) the grains are exchange coupled. The use of the random anisotropymodel for nanocomposite materials relies on scaling arguments and statisticalconsiderations (Suzuki and Cadogan, 1998), which are naturally met whenthese three conditions are satisfied. The magnetic exchange correlationlength (L0) indicates the minimum size scale over which the atomicmoments must remain aligned due to exchange forces. The magnitude ofthis fundamental magnetic material parameter can be found by

L0 ¼ffiffiffiffiffiffiffiffiffiffiffiffiA=K1

pð15Þ

where A is the exchange stiffness and K1 is the first magnetocrystallineanisotropy constant. For perspective, the 180� Bloch wall has a valuedB¼pL0. A resulting L0 of 35 nm was calculated for Fe–Si-based alloysand a dB of nearly 100 nm.

When the structural correlation length of the material (i.e., grain size) ismuch smaller than the exchange correlation length, the magnetic momentsin each individual grain cannot relax into the local easy direction dictated bythe grain orientation. This results in an averaging of the local magnetocrys-talline anisotropy over the exchange correlation volume. In this case, theeasiest magnetization direction is not determined by the magnetocrystallineanisotropy, as it is in micron-sized polycrystalline materials, rather it isdetermined by statistical fluctuations of the grains within the exchangecorrelation length. Using a random walk type, random anisotropy model,an effective magnetocrystalline anisotropy (hK1i), representing the material

response can be determined as K1h i¼K1=ffiffiffiffiffiN

pwithN being the number of

grains within the exchange correlation length. The natural reduction in themagnetocrystalline anisotropy reflected in hKi results in an increasedexchange length for the nanocrystalline material defined as

Lex¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiA= K1h ip

, which can have values of hundreds of nm when D isreduced below 10 nm. The value of N in a cubic volume with sides Lex canbe estimated by the relation: N¼ (Lex/D)3.

Using the definitions of hK1i, Lex, andN, the effective anisotropy can bedetermined in terms of the crystalline materials parameters, K1, A, and D:

K1h i¼K41D

6

A3ð16Þ


The more general equation for n-dimensional system has the form:

K1h i¼K1

DffiffiffiffiffiffiffiffiffiffiffiffiA=K1

p !2n= 4�nð Þð17Þ

yielding D2/3, D2, and D6 dependences for n¼1, 2, and 3, respectively(Herzer, 1991). Interestingly, due to dimensional constraints alone, a nano-wire will have a reduced exchange softening (D2/3) compared to thin films(D2) and bulk materials (D6). These dependencies are shown in Fig. 4.57a,which follows this equation for an (Fe,Si)-based alloy with parameter valuesfor Fe80Si20 found in Table 4.6. In each of the three cases (n¼1, 2, 3), the

Grain size, D (nm)

Grain size, D (nm)

(a)

(b)

Exc

hang

e le

ngth

, Lex

(nm

)E

ffec

tive

K1,

áK1ñ

(J

m-3

)

1 10

3-D

3D

2D

1D

2-D

1-D

10-4

10-2

100

102

10

102

103

104

105

106

104

106

100

1 10 100

Figure 4.57 Schematic diagrams of (a) the exchange averaged magnetocrystallineanisotropy and (b) the exchange length as a function of grain size for 3D, 2D, and 1Dsolutions of the random anisotropy model below the natural exchange length (red dot)and the 3D solution for large grain sizes. Parameter values for these calculations arefound in Table 4.6 for the Fe80Si20 phase.

Table 4.6 Calculations using the multiphase, 3D random anisotropy model forseveral different samples

Fe80Si20 Fe Fe50Co50 Fe70Co30

K1 (J/m3) Crystalline phase

magnetocrystalline

anisotropy

8.2�103 47�103 5.9�103 1.1�104

L0 (nm) Natural exchange

length

35 15 41 30

ls (ppm) Magnetostrictive

coefficient

�6 �4.4 �80 �45

hKi (J/m3) Effective anisotropy 2.3 2600 0.7 8.1

Lex (nm) Effective exchange

length

2085 62 3780 1120

Hc (A/m) Coercivity 1.21 832 0.18 2.10

mi Permeability 260�103 612 3.5�106 297�103

m0Ms (T) Saturation

magnetization

1.23 2.0 2.4 2.45

Assuming D¼10nm, (1�Vam)¼0.75, and A¼10�11 J/m. Where Hc¼pchKi/m0Ms and mi¼pmMs2/

m0hKi and pc¼0.64 and pm¼0.5 (Herzer, 1995; Pfeifer and Radeloff, 1980; Suzuki et al., 2008b).


definitions of Lex and hK1i are the same; however, the exchange coupledvolume is reduced to N¼ (Lex/D)2 for 2D and N¼Lex/D for 1D. For thisexample, the natural exchange length (L0) was found to be 32 nm and thenanocrystalline exchange length (Lex) varied as shown in Fig. 4.57b.

The total magnetocrystalline anisotropy energy is unchanged by the aver-aging; however, the fluctuations are diminished leading to lower coercivity andhigher permeability for the nanocomposite alloy. Since the fluctuations of theanisotropy are the important factors in considering magnetization switching,the coercivity and initial permeability can be calculated using these equations(and a coherent magnetization rotation model (Stoner and Wohlfarth, 1948))with good accuracy for grain sizes less than 40 nm using the relations:

HC ¼ aCKh i

m0Ms

� aCK4

1D6

m0MsA3and mi ¼ am

m0M2s

Kh i � amm0M

2s A

3

K41D

6ð18Þ

when the dimensionless parameters aC and am have values of 0.13 and 0.5,respectively (Herzer, 1990). The 3D solution for the effective anisotropywas used in the coercivity and permeability equations above; however, the2D, 1D, and equations using uniform anisotropies can also be used (asdemonstrated in Fig. 4.58). When these grains with cubic anisotropy arerandomly oriented, the squareness of the hysteresis loop is enhanced,reflecting the strong exchange coupling and the dominance of exchangeenergy over anisotropy energy in the alloy (resulting in remanence ratios

Grain size, D

3D

2D

1D

Coe

rciv

ity, H

c (A

/m)

1 nm10-1

100

101

102

103

100 nm 10 mm 1 mm

Figure 4.58 Calculated coercivity as a function of grain size for 3D, 2D, and 1Dsolutions of the random anisotropy model below the natural exchange length (apex)and the 3D solution for large grain sizes. Using equations from Table 4.7 with Vam¼0,j¼1, no Ku, and parameter values from Table 4.6 (Fe80Si20).


(Mr/Ms) exceeding 0.83) (Herzer et al., 2005). A large degree of scatter isexperimentally observed in the coercivity even for a single grain size(Herzer, 2005). This is due in part to the intimate relationship betweenalloy composition and processing. Producing the nanocomposite micro-structure inevitably requires changes in composition of the phases in thealloy, with variations in the annealing temperatures, annealing times, andalloy compositions resulting in varied volume fractions transformed andcompositions of the crystallites and residual amorphous phases.

Reduction in coercivity by exchange softening has also been modeledusing a domain wall-pinning formalism (Chikazumi and Graham, 1997).Due to spatial fluctuations in the local domain wall energy (gw), themagnetization sees different amounts of resistance to motion by an appliedfield, resulting in a coercivity determined by the maximum value of spatialfluctuation (with wavelength, L) (Herzer, 1990):

HC ¼ 1

2m0Ms

@gw@x

� �max

�ffiffiffiffiffiffiffiffiffiAK1

pm0MsL

ð19Þ

For small grains, the spatial wavelength parameter, L, is equal to theexchange length, Lex, and the magnetocrystalline anisotropy, K1, is replacedby the exchange averaged hKi. Grains exceeding the domain wall width (orabout pLex) tend to follow a 1/D relationship describing a well-knowndomain wall pinning on grain boundaries (Mager, 1952). The experimentalcomparison of coercivity and initial permeability against grain size forD>150 nm shows good agreement using the following relations:


HC ¼ aC

ffiffiffiffiffiffiffiffiffiAK1

pm0MsD

and mi ¼ amm0M

2s Dffiffiffiffiffiffiffiffiffi

AK1

p ð20Þ

when the dimensionless parameters aC and am have values of 2.6 and 0.05,respectively (Herzer, 1990). A similar argument is given considering thecoherent rotation previously considered for nanocrystalline grains. Whenthe grain size and exchange length are approximately the same, the magne-tocrystalline anisotropy is not averaged over the exchange length and thecoercivity and initial permeability are commensurately deteriorated:

HC ¼ aCK1

m0Ms

and mi ¼ amm0M

2s

K1

ð21Þ

resulting in a maximum value of coercivity and minimum value ofpermeability (Herzer, 1990).

To this point, the random anisotropy model has been applied to nano-crystalline materials without consideration of the multiphase nature of thesematerials. Multiphase solutions of the random anisotropy model are neces-sary to describe (1) magnetic hardening at elevated temperatures (near theCurie temperature of the amorphous phase where grains start to decouple)and (2) magnetic hardening during the initial stages of crystallization (smallvolume fractions of crystallites in large amorphous matrix) (Suzuki andCadogan, 1998). An extension of the random anisotropy model to multi-phase materials was provided by Herzer, considering the problem from theperspective of the spatial fluctuations of the mean square amplitude ofthe anisotropy energy (hEa

2i) and its effect on the effective magnetocrystal-line anisotropy (hK1i) (Herzer, 1995). In this case, the volume of the ithphase (Oi) determines the structural correlation length which is compared tothe exchange coupled volume (Vex) to determine its affect on hEa

2i. Thefollowing expression gives the general mean square amplitude of the anisot-ropy energy:

E2a

¼XOi<Vex

Ni OiKið Þ2þX

Oi�Vex

Ni VexKið Þ2 ð22Þ

where Ki is the magnetocrystalline anisotropy of the ith phase, Oi¼aDi3,

and Vex¼aLex3 (a is a geometric factor between 0.5 and 1) (Herzer, 1995).

Using the relation K1h i¼ffiffiffiffiffiffiffiffiffiffiE2a

q=Vex and the definition Ni¼viVex/Oi

(where Ni is the frequency with which the anisotropy changes within theexchange coupled volume), we find

K1h i¼X

Di<Lex

viD3i K

2i

A3=2þX

Di�Lex

viK2i A

3=2

D3i K1h i3

" #2ð23Þ


This expression reduces to the aforementioned effective magnetocrystal-line anisotropy when a crystalline phase with Ki¼K1 and amorphous phasewith Ki¼0 are the only two phases in the material and the dimensions ofeach phase never exceed Lex. Not only does this formulation allow us toconsider multiple magnetic materials, but it also allows consideration ofgrain size distributions. Solutions for three important cases using the multi-phase solution of the random anisotropy model are (A) when all grains areless than the magnetic exchange length; (B) when all grains are exactly thesame size as the exchange length; and (C) when all grains are larger than theexchange length. The solutions for each are shown here:

⟨ ⟩: ∑

BA

: ∑C ∑

ð24Þ

When largest grains are less than the exchange length, the usual D6

dependence from the random anisotropy model is observed. When thegrains are all the size of the exchange length, the maximum coercivity isobserved, with the effective K equaling the root mean square of the types ofgrains in the material. For samples with minimum grain size larger than theexchange length, a D�6/7 power law is observed. The two regimes areobserved in the (Fe,Si)–(Nb,Mo)–B–Cu samples shown in Fig. 4.59a, withthe transition between D6 and D�6/7 at about 55 nm. As previously men-tioned, the reduced dimensionality of thin films results in the observed D2

dependence as shown in Fig. 4.59b. Deviations from the D6 dependence(e.g., Fe–Zr–B–Cu in Fig. 4.59a) due to uniform anisotropies will bediscussed later in this section.

The situation is more complicated when grain size distributions areconsidered. For narrow distributions (with standard deviations s near0.01), the result is identical to those cases just described. For wider grainsize distributions (s�0.4), the transition between power law regions isbroadened significantly (da Silva et al., 2000). In this case, a gradation ofthe power laws between D6 and D�6/7 is found even when the mean grainsize is half of the natural exchange length, resulting in accelerated deterio-ration of the coercivity as the standard deviation is increased. For thisreason, the distribution of grain size can be extremely important. This isespecially evident when a bimodal distribution of grain sizes is observed, andcan have a significant impact on the coercivity of the material. Fiftypercentage larger coercivity values were reported when a small volumefraction of relatively large grains (�40 nm) was taken into considerationfor its effect on coercivity, despite the vast majority of the grains being lessthan 20 nm (Bitoh et al., 2004).

Grain diameter (nm)

(a)

(b)

Grain diameter (nm)

Fe–Zr–B–Cu

Fe91Zr7B2

Fe90Zr7B2Cu1

Fe73.5Si13.5B9Nb3Cu1Fe66Ni11Co11Zr7B4Cu1Fe67Ni11Co11Zr7B4

(Fe,Si)–(Nb,Mo)–B–Cu

Coe

rciv

ity (

A/m

)

D3

D2

D3

D6

10

10-1

1

104

103

102

10

Coe

rciv

ity (

A/m

)

10-1

1

104

105

103

102

10

10 1000

10 100

Fe78PxC18 – xGe3Si0.5Cu0.5

Figure 4.59 (a) Variation of coercivity with grain diameter for ribbon samples of(Fe,Si)–(Nb,Mo)–B–Cu (D6)and Fe–Zr–B–Cu (D3) alloys (del Muro et al., 1994;Gomez-Polo et al., 1996; He et al., 1994; Herzer, 1990, 1993; Kulik and Hernando,1996; Kulik et al., 1994, 1997; Liu et al., 1997a; Majumdar and Akhtar, 2005; Matternet al., 1995; Mazaleyrat and Varga, 2001; M€uller et al., 1991, 1992; Panda et al., 2003;Suzuki and Cadogan, 1999; Suzuki et al., 1996; Todd et al., 1999, 2000; Xiong et al.,2001; Zhou et al., 1996). (b) Variation of coercivity with grain diameter in thin filmsamples of Fe73.5Si13.5Nb3B9Cu1 and Fe66�xNi11Co11Zr7B4Cux alloys (D2) (Baraskaret al., 2007; Yamauchi and Yoshizawa, 1995) and ribbon samples with uniaxial anisot-ropy of Fe78PxC18�xGe3Si0.5Cu0.5, Fe91Zr7B2, and Fe90Zr7B2Cu1 alloys (D

3) (Suzukiet al., 1998).



Another benefit of this formulation is the extension of the randomanisotropy model to describe magnetic hardening at elevated temperaturesand during the initial stages of crystallization. In the first case, the magnetichardening results from decoupling of the grains as the Curie temperature ofthe intergranular amorphous matrix is exceeded. In the latter case, the smallvolume fraction of isolated grains in a large amorphous matrix is addressed.In these cases, the exchange coupling between the grains has been phenom-enologically adjusted to simulate elevated temperatures using various rela-tions for exchange stiffnesses, including Aam¼gAcr by Hernando et al.(1998a,b), a relation of the exchange stiffnesses defined through a definitionof the spin rotation angle between crystalline and amorphous coupling pairs

j0¼D=ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiAcr= Kh ip þL=

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiAam= Kh ip

by Suzuki and Cadogan (1998), andan effective exchange stiffness Aeff¼ (1�Vam)

1/3/Acrþ (Vam)1/3/Aam by

Loffler et al. (1999). The results give surprisingly similar values of effectiveanisotropy:

Kh i¼ 1�Vamð Þ4j6

K41D

6 1ffiffiffiffiffiffiffiAcr

p þ 1�Vamð Þ�1=3�1ffiffiffiffiffiffiffiffiAam

p" #6

ð25Þ

where Acr and Aam are the exchange stiffness of the crystalline and amor-phous phases, respectively, j is a geometric/statistical parameter with valuenear 1, and Vam is the volume fraction of the amorphous matrix phase.These considerations are extremely important when discussing the high-temperature performance of nanocomposite materials (see Section 6.4).

Consideration of localized random anisotropy with long-range inducedanisotropy was first discussed by Alben et al. (1978) resulting in coercivitywith a grain size to the third power dependence (as opposed to grain size tothe sixth without induced anisotropy). Reduced power-law dependence ongrain size is also found in lower dimensional systems as first discussed byHoffmann for magnetization ripple in thin films (Hoffmann, 1968).Uniform anisotropies (induced or magnetoelastic in origin) tend to domi-nate in nanocomposite alloys in a similar way to amorphous alloys due totheir small local anisotropies. The remanance ratio (Mr/Ms) has beenobserved to change from �0.5 for samples with strong induced anisotropy(indicative of uniaxial anisotropy dominance) to above 0.83 for sampleswith random anisotropy dominance in Fe-based nanocrystalline alloys(Suzuki and Cadogan, 1998). For this reason, uniform anisotropies can bean important tool to modify the magnetic behavior from sharp magneticswitching to energy storage behaviors.

Many electronic devices use inductor core to store magnetic energy(e.g., choke coils, reactors, etc.). For these applications, large saturationmagnetization, low core losses, and consistent, low permeabilities over awide frequency range are important factors. Gapped ferrite cores have been


used for these applications; however, continued miniaturization of mag-netic components using ferrites has become problematic due to the largeleakage fluxes at the gap (Fukunaga et al., 2000). For these reasons, inducedanisotropy has become an important field of study.

The generalization of the random anisotropy model to consider uniformuniaxial anisotropy (Ku) in addition to exchange averaged local anisotropieswas approximated in the large Ku limit by Suzuki and Cadogan (Suzukiet al., 1998). Later, an exact solution to the quartic equation describing thecombined anisotropy contributions was shown by Ito (2007). The solutionshows that power-law scaling for grain size dependence of effective anisot-ropy (hKi) is strongly dependent on the ratio of the uniform anisotropy (Ku)to random anisotropy (hK1i) contributions. When Ku/hK1i>2, theuniform anisotropy dominates and the power law is reduced from D6 toD3 dependence (Suzuki et al., 2008b). Such a change has been observed inFe-based nanocrystalline alloys and is thought to be responsible for theirreduced sensitivity to exchange softening. This results in theD3 dependenceof coercivity observed in the Fe–Zr–B–Cu alloys shown in Fig. 4.59a and b.The formulae for the use of the multiphase random anisotropy modelconsidering cases with and without a uniform uniaxial anisotropy areprovided in Table 4.7.

A uniaxial induced anisotropy results in sheared hysteresis loops, effec-tively lowering the permeability of the alloy without the necessity of an airgap. The anisotropy energy is typically determined from these sheared loopsas the area between the upper branches of the flattened hysteresis loops (firstquadrant) for the field-annealed and non-field-annealed samples (Lovaset al., 1998). The origin of the magnetic field annealing induced anisotropyhas been attributed to the directional ordering of the magnetic and non-magnetic elements in the Fe–Si–Nb–B–Cu alloys (Yoshizawa andYamauchi, 1989). Induced anisotropies tend to have an effect when theiranisotropy values exceed the averaged magnetocrystalline anisotropy hKi(e.g., �5 J/m3 for 10 nm a-(Fe,Si) grains). As a result, slightly lowercoercivities were observed for field-annealed samples; an effect attributedto the reduction in spatial fluctuations for domain wall pinning and thesimplified domain wall configuration (Herzer, 1992).

The lower bound for coercivity reduction solely by grain size refine-ment is near 0.5 A/m and is determined by anisotropies with origin otherthan magnetocrystalline, including surface roughness, magnetoelastic cou-pling, induced anisotropies, etc. (Herzer, 1991). For this reason, successiverefinement of grain size does not result in continued lowering of theanisotropy unless all forms of anisotropy can be reduced simultaneously.In nanocrystalline soft magnetic alloys, where the magnetocrystallineanisotropy energy has been exchange averaged, the magnetization process islargely determined from the contributions of magnetoelastic energy anddemagnetization effects (magnetostatic energy).

Table 4.7 Effective magnetic anisotropy for 1D, 2D, and 3D exchange coupled volumes, without and with consideration of uniformanisotropies (Ku)

Two phases: hKi ( J/m3)

3D (no Ku) 1�Vamð Þ4j6

K41D



p" #6

2D (no Ku) 1�Vamð Þ2j2

K21D



p" #2

1D (no Ku) 1�Vamð Þ4=3j2=3

K4=31 D2=3 1ffiffiffiffiffiffiffi

Acr

p þ 1�Vamð Þ�1�1ffiffiffiffiffiffiffiffiAam

p" #2=3

3D (w/Ku)

Kh i¼ 1�Vamð Þ2D6K41

4j6A3þ1

2

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffif 1=3

3ffiffiffi23

pA3

þ4K2u

3þ16

ffiffiffi23

pA3K4

u

3f 1=3þ 1�Vamð Þ4D12K8

1

4j12A6

vuutþ1

2

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi�f 1=3

3ffiffiffi23

pA3

þ8K2u

3�16

ffiffiffi23

pA3K4

u


1

2j12A6þ h

4ffiffig

pvuut

g¼ f 1=3

3ffiffiffi23

pA3

þ4K2u

3þ16

ffiffiffi23

pA3K4

u


1

4A6

f ¼ 128K6uA

9þ27 1�Vamð Þ4K4uK

81D

12A12=j12

þ ffiffiffiffiffi27

p ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi256 1�Vamð Þ4K10

u K81D

12A12=j12þ27 1�Vamð Þ8K8uK

161 D24A6=j24

q(Continued)

Table 4.7 Effective magnetic anisotropy for 1D, 2D, and 3D exchange coupled volumes, without and with consideration of uniformanisotropies (Ku)—cont’d

Two phases: hKi ( J/m3)

h¼ 8 1�Vamð Þ2j12D6A6K2u

41 þ 1�Vamð Þ6D18K12

1

j18 9

2D (w/Ku)

Kh i¼ 1

2

1�Vamð ÞD2K21

j2Aþ

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi4K2

u þ1�Vamð Þ2D4K4

1

j4A2

24 351D (w/Ku)

Kh i¼ 1

2

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffif1=31

3ffiffiffi23

pA3

þ4K2u

3þ1

ffiffiffi23

pA3K4

u

3f1=31

vuut þ1

2

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi�f

1=31

3ffiffiffi23

pA3

þ8K2u

3�16

ffiffiffi23

pA3K4

u

3f1=31

þ h1ffiffiffiffig1

p

vuut

g1 ¼ f1=31

3ffiffiffi23

pA3

þ4K2u

3þ16

ffiffiffi23

pA K4

u

3f11

f1 ¼ 128K6uA

9þ27 1�Vamð K81D

4A7=j4

þ ffiffiffiffiffi27

p ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi256 1�Vamð Þ 6

uK81D

4A16=j4þ27 1�Vamð Þ8K161 D8A14=j8

q

h1 ¼ 2 1�Vamð Þ2D2K41

j2A

Reduces to single-phase models by selecting Vam¼0. F is a geometric and statistical parameter ith value near 1.

K

Asffiffiffiffi6

3

=3

Þ4ffiffiffi4K

w


A major contributor is the magnetoelastic energy, which is proportionalto the magnetostrictive coefficient and the internal stress in the alloy.While internal stresses (evaluated by an impedanciometry technique) werefound to be significantly reduced during the crystallization process inFe73.5Si16.5Nb3B6Cu1 alloys, from 15 MPa in the as-cast sample to0.2 MPa in a sample annealed at 580 �C (Carara et al., 2002). However,achieving the lowest core losses requires near zero values of magnetoelasticanisotropy not merely reduced stress fields. Fortunately, the nanocompositenature of the microstructure provides a way of tuning the magnetostrictionin a way that is not possible in single-phase soft magnetic alloys. The localcompositions of the nanocrystalline and residual amorphous phases in thealloy can be adjusted by small variations in the nominal composition of thealloy and by adjustments of the annealing conditions. In this way, the largepositive value of magnetostrictive coefficient observed in most amorphousalloys can be reduced, as the alloy is partially devitrified.

As the magnetization of the alloy changes (in direction or magnitude),the shape of the sample changes (d‘=‘ and/or dV/V ), resulting in amagnetoelastic contribution to the overall anisotropy of the material. Wecall this stress dependence of the magnetocrystalline anisotropy, “magneto-striction.” Due to the polycrystalline nature of the microstructure and thelow magnetocrystalline anisotropy of nanocrystalline soft magnetic alloys,the linear magnetostrictive coefficient (ls) can be obtained using a straingage to measure the d‘=‘ as a saturating magnetic field is rotated within thesample (Claassen et al., 2002). The relationship between the ls and thechange in shape d‘=‘ is simply:

d‘‘¼ 3

2ls cos2y�1

3

� �ð26Þ

where y is the angle between the magnetization direction and the straingage direction (Datta et al., 1984). Capacitance, dilatometers, and transversesusceptibility methods are also used to determine magnetostrictive coeffi-cients for this class of materials (Kaczkowski et al., 1996; Vlasak et al., 2003).

The saturation magnetostriction coefficient has been found to vary widelywith Si content in Fe–Si–Nb–B–Cu alloys, with values ls¼þ1.4 ppm forFe73.5Si13.5Nb3B9Cu1 (Tann¼580 �C) and ls¼�0.3 ppm for Fe73.5Si16.5Nb3B6Cu1 (Tann¼550 �C) (Herzer, 1995; Polak et al., 1992). Theeffect has been attributed to a balancing of the negative magnetostrictioncoefficient for the crystalline phase (ls

cr��3ppm) and a positive magneto-striction coefficient for the amorphous matrix phase (ls

am�12�17ppm),yielding an effective magnetostrictive coefficient (ls

eff) with near zero valuefor the nanocomposite alloy (Herzer, 1992; Twarowski et al., 1995b). Thelseff is found as the weighted average of the ls and the volume fraction of each

phase: lseff¼ (1�x)ls

amþxlscr, where x is the volume fraction transformed


(a) (b) (c)Fe73.5Si15.5B7Nb3Cu1

tann= 3600 s


tann= 3600 sFe73.5Si16.5B6Nb3Cu1

tann= 3600 s

Mag

neto

stric

tive

coef

ficie

nt (

ppm

)

700-5

0

5

10

15

20

25

30

800 900 1000 750 800 850 900 650 700 750 800 850 900

Figure 4.60 Magnetostrictive coefficients plotted against annealing temperature for(a) Fe73.5Si13.5Nb3B9Cu1 (Agudo and Vazquez, 2005; Herzer, 1993; Kulik et al., 1994,1995; Lim et al., 1993b; Todd et al., 2000; Vazquez et al., 1994; Yoshizawa andYamauchi, 1990; Zbroszczyk et al., 1995), (b) Fe73.5Si15.5Nb3B7Cu1 (Herzer, 1992;M€uller et al., 1991; Nielsen et al., 1994; Twarowski et al., 1995a; Yoshizawa et al.,1994), and (c) Fe73.5Si16.5Nb3B6Cu1 alloys (Carara et al., 2002; Herzer, 1994b; Kuliket al., 1997; M€uller et al., 1991; Nielsen et al., 1994; Tejedor et al., 1998). Differentsymbols are used per reference except in (a) where average results are used (error barsindicate standard deviations).


(Hernando et al., 1997; Herzer, 1991). An additional parameter (6xlssurf/D,

where D is the grain diameter) for interfacial contributions was found to benecessary in some cases to achieve an accurate ls

eff (Murillo et al., 2004;Slawska-Waniewska et al., 1997; Szymczak et al., 1999). The ls

surf in thesecases was found to be quite small (in the range 0.1–0.7 ppm). The annealingconditions and composition of the alloy have a profound effect on theeffective magnetostrictive coefficient for the nanocomposite. In Fig. 4.60,the change in magnetostrictive coefficients with annealing temperature isplotted for several very similar Fe73.5(Si,B)22.5Nb3Cu1compositions. Whenthe sample is amorphous, the magnetostrictive coefficient is large. As thealloys are annealed at temperatures near the primary crystallization tempera-ture for 3600 s, the magnetostrictive coefficient reaches near zero values,which vary depending on the nominal composition of the alloy.

In general, a near zero value of magnetostrictive coefficient can beachieved when the Si to SiþB ratio is near 0.7 and when the sample isannealed at temperatures that allow a large volume fraction crystallized. Theseresults for Fe73.5(Si,B)22.5Nb3Cu1 are summarized in Fig. 4.61, which showslsam (filled circles) with large values across the composition range and a

lowering trend with increased Si content. It also shows reduced lseff as the

annealing temperature is increased to the primary crystallization temperature.

Si/(Si + B)

Mag

neto

stric

tive

coe

ffic

ient

(pp

m)

0.20

0

5

10

15

20

0.25

Fe73.5Si22.5B22.5 – xNb3Cu1

763–773 K783–793 K798–803 K813 K823 K

838–843 K853–863 K873–883 K>893 K

tann= 3600 s

0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 0.70 0.75 0.80 0.85

Figure 4.61 Magnetostrictive coefficient plotted against Si/(SiþB) for a series ofFe73.5(Si,B)22.5Nb3Cu1 alloys annealed at various temperatures for 3600 s (Agudo andVazquez, 2005; Carara et al., 2002; Herzer, 1992, 1993; Herzer, 1994b; Kulik, 1995;Kulik et al., 1994, 1997; Lim et al., 1993b; M€uller et al., 1991; Nielsen et al., 1994; Nohet al., 1991; Tejedor et al., 1998; Todd et al., 2000; Twarowski et al., 1995b; Vazquezet al., 1994; Yoshizawa and Yamauchi, 1990; Yoshizawa et al., 1988a, 1994;Zbroszczyk et al., 1995).


While, in most magnetic amorphous alloys, the magnetostrictive coeffi-cient is proportional to the square of the magnetization, nanocrystalline softmagnetic alloys provide a class of materials where the magnetostrictivecoefficient can be near zero up to m0Ms above 1.5 T (Makino et al.,1995). This is an advantage of nanocomposite alloys over amorphous alloys,broadening the potential composition ranges for optimal magnetic perfor-mance. However, many substitutions that enhance the saturation magneti-zation possess commensurately large magnetostrictive coefficient, includingthe obvious substitution of Co for Fe in these alloys.

A sharp rise in magnetostrictive coefficient with Co substitution for Fe isobserved in nanocrystalline (Fe,Co)86–88Zr7B4-6Cu1 and (Fe,Co)73.5Si13.5–15.5Nb3B7-9Cu1 alloys (see Fig. 4.62). The peak value was near 18 ppm for (Fe,Co)73.5Si13.5–15.5Nb3B7-9Cu1 alloys with nearly 50% substitution of Co forFe (Kolano-Burian et al., 2004b; Muller et al., 1996b). In (Fe,Co)86–88Zr7B4–6Cu1 alloys, the peak value was �40 ppm near 70% substitutionof Co for Fe (Muller et al., 2000; Willard et al., 2002b). Substitution of Nifor Fe in Fe73.5�xNixSi13.5Nb3B9Cu1 results in increased magnetostrictivecoefficients (above 13 ppm) for 10�x�40 when the alloys have beenannealed to promote partial crystallization (Vlasak et al., 2003). Adjustmentof the magnetostrictive coefficient has also been achieved by varying theETM content in Fe-based alloys. Figure 4.63 shows the near zero


(a)

(b)

Co content, x (at.%)

Mag

neto

stric

tive

coef

ficie

nt (

ppm

)

0-5

0

5

10

15

20

10 20 30 40 50 60 70 80

Large symbol: MTM86Zr7B6Cu1Small symbol: MTM88Zr7B4Cu1

Mag

neto

stric

tive

coef

ficie

nt (

ppm

)

7.8

0

10

20

30

40

8.0 8.2 8.4 8.6 8.8 9.0 9.2 9.4 9.6 9.8 10.0

(Fe1 – xCox)73.5Si15.5B7Nb3Cu1

(Fe1 – xCox)73.5Si13.5B9Nb3Cu1

(Fe,Co) BCC(Fe,Co) FCC(Fe,Ni) BCC(Fe,Ni) FCC(Fe,Co,Ni) BCC(Fe,Co,Ni) FCC(Co,Ni) FCC

Figure 4.62 Effect of magnetic transition metal on magnetostrictive coefficient in (Fe,Co,Ni)86Zr7B6Cu1 (M€uller et al., 2000) and (Fe,Co,Ni)88Zr7B4Cu1 (Willard et al.,2002a) alloys.


magnetostrictive coefficient can be produced in samples with 50–75% Nbsubstituted for Zr and concomitant increase in B to maintain glass formabil-ity. Similar alloy design ideas have been used in (Fe,Co,Ni)-based alloys(Knipling et al., 2012).

The sign of the magnetostrictive coefficient (l) is an important indicatorof the magnetic material’s response to a stress field. When l>0, an appliedtensile stress field results in an increase in the magnetization along theapplied stress direction and under the application of an applied field.Reversing the sign of l (or applying a compressive stress field) results in a

x, Nb/Hf substitution for Zr

Ma

gnet

ostr

ictiv

e co

effic

ient

(pp

m)

0

-1.0

-0.5

0

0.5

1.0

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1

(Fe89Zr7B3Cu1)1 – x(Fe

83Nb

7B

9Cu

1)x

(Fe90

Zr7B

3)1 – x(Fe

84Nb

7B

9)x

Fe85

Nb3.5

Hf3.5

B7Cu

1

Fe89

Hf7B

4

Figure 4.63 Variation of magnetostrictive coefficient with Nb or Hf substitution forZr in Fe–M–B–(Cu) alloys (Makino et al., 1995; Makino et al., 2000; Wu et al., 2001).


lowering of the magnetization magnitude. These phenomena are calledVillari effects (or piezomagnetic effects) and result in induced anisotropy,especially when applied during annealing (see Section 2.2).

6.4. Exchange interactions and interphase coupling

The previous discussion of the reduction in coercivity by microstructurerefinement is predicated on the assumption that the randomly oriented grainsare sufficiently exchange coupled through the intergranular amorphousmatrix phase. In Section 6.2, the Curie temperature of the amorphous matrix(TC

am) was shown to be�593 K for a Fe73.5Si13.5Nb3B9Cu1 alloy annealed at793 K for 1 h. For operation temperatures exceeding TC

am, the coercivity ofthe nanocomposite material rises quickly from less than 1 A/m at 473 K to80 A/m at 673 K (see Fig. 4.64B) (Herzer, 1991). The increased coercivitywith measurement temperature reflects a reduced exchange couplingbetween grains, through the amorphous intergranular region, reducing theeffectiveness of the exchange interaction to create a lowered average anisot-ropy, hKi. The domain structure changes from broad stripe domains to anirregular domain pattern as the temperature passes from below to above TC

am

(Schafer et al., 1991). So long as the temperature is not increased to thesecondary crystallization temperature (i.e., no allowance for change in micro-structure or phases), the increase in coercivity is fully reversible when thematerial’s temperature is reduced (Willard et al., 2012a).

In general, the magnetic behavior of the nanocomposite is dominated bythe intergranular amorphous phase when TC

am is exceeded, due to reducedexchange interactions between grains. The coercivity shows a significant peak


(a)

(b)

Coe

rciv

ity (

A/m

)C

oerc

ivity

(A

/m)


4000

100

200

300

400m

793 K Fe72Si13.5Nb4.5B9Cu1


tann= 3600 s @ Tann

793 K773 K813 K848 K873 K

803 K Fe72Si13.5Nb4.5B9Cu1813 K Fe72Si13.5Nb4.5B9Cu1793 K Fe73.5Si13.5Ta3B9Cu1

753 K Fe73.5Si13.5Ta3B9Cu1

773 K Fe73.5Si13.5Ta3B9Cu1

m

Tac (Ta 793 K)m

450 500 550 600 650 700 750 800

2500.1

1

10

100

1000

10000

300 350 400 450 500 550 600 650 700 750 800 850 900

Tac (Ta 753 K)

Tac (Ta 773 K)m

Tac (Nb 793 K)m

Tac (appro)

Figure 4.64 Coercivity against measurement temperature for (a) Fe72Si13.5Nb4.5B9Cu1 (squares) and Fe73.5Si13.5Ta3B9Cu1 (triangles). Annealing conditions areshown in parenthesis and amorphous phase Curie temperatures (with ETM and Tann

indicated) are also shown. (b) Fe73.5Si13.5Nb3B9Cu1 (Herzer, 1991, 1993; Kim et al.,1996; Kulik and Hernando, 1994; Mazaleyrat and Varga, 2001).


as the measurement temperature is increased (see Fig. 4.64a). The rise incoercivity occurs when anisotropy and magnetostatic energies become dom-inant over exchange energy. The temperature at which peak coercivity isobserved is slightly higher than the TC

am determined from thermomagneticexperiments. The differences in the Curie temperatures for the two alloysshown in Fig. 4.64a are consistent with the variation in TC

am with ETMcontent (see Fig. 4.54). When temperatures are sufficiently high, the grainscompletely decouple, resulting in superparamagnetic behavior and a resultingdecrease in the coercivity. Samples prepared with low enough annealing


temperatures tend to have greater amounts of intergranular amorphous phase,resulting in more complete decoupling at lower operation temperatures withcommensurately lower temperatures for the onset of superparamagnetism (seeFe72Si13.5Nb4.5B9Cu1 (793/803 K) and Fe73.5Si13.5Ta3B9Cu1 (753 K) data inFig. 4.64a). There are several proposed reasons for the observed peak incoercivity and its temperature dependence, including exchange penetrationthrough the intergranular amorphous phase, superferromagnetism, and dipo-lar interactions (Hernando and Kulik, 1994; Herzer, 1995; Skorvanek andO’Handley, 1995).

From a practical standpoint, the increase in coercivity is quite small overa wide temperature range in (Fe,Si)-based alloys (see Fig. 4.60b) and islimited by the Curie temperature of the residual amorphous phase for allcompositions (Willard et al., 2012a). While the increase in coercivity basedon these thermal effects is reversible, it can be a limitation for high-temperature use of the alloys. The main limiting factor for the alloysshown in Fig. 4.64b, however, is not the coercivity rise. Rather, thesaturation magnetization decreases sufficiently with temperature to makeit the limiting factor (see Fig. 4.52).

This effect can be explained using the critical exponent equation for thethermomagnetic response of the nanocomposite material with the exchangeaveraged anisotropy equation for hKi. Realizing that the exchange stiffness (A)weakens most rapidly as the operation temperature is increased and that itdepends on (m0Ms(T ))2, the following proportionality is found (Herzer, 1989):

Kh i/ m0Ms Tð Þð Þ�6 / T amC �T

T amC

� �6b

ð27Þ

When this holds true, Eq. (25) can be used to describe the full multiphasedependency of the effective anisotropy with operation temperature(through the weakening of the exchange stiffness of the amorphous matrix(Aam)). Figure 4.65a shows the effective anisotropy with three levels ofdecoupling: fully coupled (5�10�12 J/m), partially coupled (10�12 J/m),and decoupled grains (5�10�13 J/m). As the grains lose exchange coupling,the anisotropy energy dominates magnetic switching. Magnetostatic andmagnetocrystalline sources of anisotropy raise the coercivity in a reversibleway, leading to deteriorated performance of the magnetic material atoperation temperatures near TC

am. Similar results are observed if thin filmor nanowire forms of the effective anisotropy are considered.

Examination of the critical exponent (b) for the saturation magnetizationas a sample is heated to the Curie temperature (TC) helps to determine thevalue of TC. Such an analysis finds proportionality between the reducedmagnetization (i.e., saturation magnetization (Ms (T )) at a given tempera-ture divided by the saturation magnetization at absolute zero (Ms (0 K))) andthe reduced temperature to a fractional exponent:

Fraction amorphous phase, Vam

(a)

(b)

áK1ñ

(J/

m3 )

áK1ñ (

J/m

3 )Aam= 5 ´ 10–13

Aam= 1 ´ 10-12

Aam= 5 ´ 10-12

Exchange stiffness (10-12 J/m2)

0.20

1090%transformed

80%

75%

70%

20

30

40

50

60

70

80

90

100

110

0.3 0.4 1 2 3 4 5 10

0.2

20

40

60

80

0.4 0.6 0.8 1.0

Figure 4.65 (a) Calculated effective anisotropy variation (Eq. 25) with fraction amor-phous phase for 3D exchange coupled nanocomposites. (b) Variation of effectiveanisotropy with exchange stiffness for several volume fractions of crystalline phase(K1¼104 J/m3, Acr¼10�11 J/m2, j¼1, and D¼10 nm).


m0Ms Tð Þ¼ m0Ms 0Kð Þ TC�T

TC

� �b

ð28Þ

The critical exponent is found to be b¼1/2 using the mean field model.Analysis of thermomagnetic data collected for an as-spun Fe73.5S-i13.5B9Nb3Cu1 alloy, showed a critical exponent, b¼0.36, and a Curietemperature of the amorphous phase (TC

am) of 593 K (Herzer, 1991). Sam-ples of the same compositions, annealed at 520 �C for 1 h to partiallycrystallize the ribbon, show two Curie temperatures, TC

am remains at593 K and the Curie temperature of the a-(Fe,Si) phase (TC

x ) at about873 K. The value of TC

x is lower than the 1043 K expected for a-Fe and


is consistent with 20–23 at% Si in a a-(Fe,Si) phase. The alloy Fe66Cr8-Si13B9Cu1 shows that Cr reduces TC

am to 490 K but does not significantlychange the critical exponent (b¼0.364) (Slawska-Waniewska et al., 1992).Similar substitution of Mn (up to �5 at%) for Fe in (Fe,Si)-based nanocrys-talline alloys results in lower TC

am and subsequently reduced exchangecoupling through the residual amorphous phase (Gomez-Polo et al.,2005; Hsiao et al., 2001).

The variation of hK1i with Aam is shown in Fig. 4.65b for Vcr from 0.7to 0.9. Smaller Aam is equivalent to higher temperature of the nanocompo-site, with Aam<10�12 J/m2, indicating decoupling of the grains, so highertemperatures trend to the left in Fig. 4.65b. By this method, we see thatsignificant increases in hK1i are observed in the typical range of crystallitevolume fractions 0.7�Vcr�0.8 for this class of nanocomposite alloys.Larger volume fractions transformed result in smaller hK1i as the grainsare decoupled, indicating a potential benefit for high-temperature use.However, mean intergranular amorphous phase thickness (L) also decreaseswith increasing Vcr, resulting in L<0.4 nm for Vcr¼0.9, which may beinadequate to prevent significant grain coarsening, ultimately limiting thepracticality of this approach for improving high-temperature performance.

The most effective way to improve the high-temperature performanceof nanocomposite soft magnetic materials has been MTM substitutions,especially Co for Fe. In nanocrystalline (Fe1�xCox)84Zr3.5Nb3.5B8Cu1alloys, a coercivity of less than 60 A/m is observed for operation tempera-tures up to 773 K when x is near 0.4–0.5 (Gercsi et al., 2006). The x¼0.3alloy had the lowest coercivity over the temperature range from 573 to773 K, with a value between 40 and 45 A/m. Similar results are reported in(Fe1�xCox)86Hf7B6Cu1 alloys, which show increased coercivity as the Cocontent is increased, from less than 20 A/m at x¼0.2 to near 50 A/m forx¼0.9 (see Fig. 4.66) (Liang et al., 2005). The Fe-based alloy showedsignificant persistent increase in coercivity across the whole temperaturerange. Each Co-containing alloy showed a slight increase in coercivity asthe temperature increased up to the secondary crystallization temperature(�875 K) where the coercivity experienced a large irreversible increase dueto deterioration of the intergranular amorphous matrix (quite evident inFig. 4.66 for alloys with closed symbols).

Compared with (Fe,Si)-based alloys, the rate of coercivity increase withtemperature is quite small for (Fe,Co)-based alloys; however, the overallcoercivity is much larger due to the increased magnetostrictive effects as Cocontent is increased. Similar Co substitution into (Fe,Si)-based alloysresulted in large increases in coercivity at about 600 K due to the partialdecoupling of nanocrystalline grains at TC

am (i.e., superferromagnetic behav-ior). For temperatures exceeding 600 K, the coercivity of (Fe,Co)-basedalloys is lower than (Fe,Si)-based alloys (comparing Figs. 4.66 and 4.64a).Additionally, the (Fe,Co)-based alloys maintain a strong saturation


(Fe1 – xCox)86Hf7B6Cu1

Tann = 823 Ktann = 3600 s

x = 0x = 0.2x = 0.4x = 0.5

x = 0.6x = 0.8x = 0.85x = 0.9

Coe

rciv

ity (

A/m

)

250

10

100

300 350 400 450 500 550 600 650 700 750 800 850 900 950

Figure 4.66 Effect of measurement temperature on coercivity of (Fe1�xCox)86Hf7B6Cu1 alloys annealed at 823 K for 3600 s (Liang et al., 2005).

Co content, x

Tmeas = 298 K

Tmeas = 723 K

(Fe1 – xCox)86Hf7B6Cu1

Fe77Co5.5Ni5.5Zr7B4Cu1

Co

erc

ivity

(A

/m)

00

10

20

30

40

50

60

70

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Figure 4.67 Comparison of coercivities measured at 298 and 723 K for a series of(Fe1�xCox)86Hf7B6Cu1 alloys (Liang et al., 2005). A Fe77Co5.5Ni5.5Zr7B4Cu1 alloy isshown for comparison (Knipling et al., 2009).


magnetization as the temperature is increased, making them more suitablefor high-temperature applications.

At room temperature, the coercivity tends to increase with increasingCo content in (Fe1�xCox)86Hf7B6Cu1 alloys (see Fig. 4.67). The increase islikely related to the increased magnetostrictive coefficient, similar to poly-crystalline Fe–Co and (Fe,Co)-based amorphous alloys (see OHandley,1977). For alloys measured at 723 K, the coercivity is increased at allcompositions, with the largest increase observed for the Co-free alloy.

Switching frequency (Hz)

Finemet (FT-1M)Finemet (FT-1L)Finemet (stress ann.)

Finemet (400m powder) 60% packedCo-based amorphous alloyFe-based amorphous alloyMn–Zn ferriteNi–Zn ferrite

Fe powder core4–79 Mo permalloyFit of Snoek’s limit

Rel

ativ

e pe

rmea

bilit

y

103

102

103

104

105

106

1

10

104 105 106 107 108 109

Figure 4.68 Comparison of relative permeability with varied switching frequenciesfor several soft magnetic materials (Chikazumi and Graham, 1997; Mazaleyrat andVarga, 2000; Thornley and Kehr, 1971; Yoshizawa et al., 1988b).


This is due to the low Curie temperature of the intergranular amorphousmatrix and decoupling effects. Alloying additions that raise TC

am conse-quently improve the soft magnetic performance at elevated temperatures.The substitution of equal amounts of Ni and Co for Fe has recently shownimproved high-temperature performance for a low-Co alloy composition,where the magnetostriction can be more easily controlled giving betterenergy efficiency.

The high-temperature magnetic performance of Fe73.5�xCox-Si13.5B9Nb3Cu1 alloys showed improved permeability above 573 K forx¼30 over no substitution (Gomez-Polo et al., 2002). The observedimprovements were observed at temperatures exceeding the Curie temper-ature of the amorphous phase (TC

am) and were attributed to exchangepenetration from the ferromagnetic crystalline phase through the thin,paramagnetic intergranular amorphous phase. The room temperature valuesof coercivity were found to increase with Co substitution from 3.6 A/m(x¼0) to 14.8 A/m (x¼45) at 1 kHz and magnetic field amplitude of48 A/m. Low coercivity values (below 15 A/m) were observed for x¼30at an applied magnetic induction value of 0.5 T at low frequency andoperation temperatures up to 773 K (Mazaleyrat et al., 2004). Highercoercivity values deteriorated the soft magnetic performance of alloyswith x�30, which was attributed to the increasing positive values ofmagnetostrictive coefficients which tend to dominate the losses in thesealloys. When these alloys are annealed at temperatures exceeding thesecondary crystallization temperature, boride phases form resulting in


much larger coercivities. For example, the Fe2B phase, which is a secondarycrystallite for (Fe,Si)- and Fe-based nanocrystalline alloys, hasK1�430 kJ/m3

(with Lex�5 nm) (Herzer, 1996).The thermomagnetic phenomenon, superparamagnetism, results from

the thermal activation of exchange coupled moments in particles (Bean andLivingston, 1959). The unique magnetic behavior observed includes lack ofhysteresis (i.e., zero coercivity) and universal curve behavior for magnetiza-tion plotted against Ms H/T. Samples of Fe66Cr8Si13B9Cu1 annealed attemperatures between 803 K for 1.2 ks were found to possess superpara-magnetic behavior when measured at temperatures between 523 and 773 K,but not at 423 K (Slawska-Waniewska et al., 1992). The Curie temperatureof the amorphous phase was determined to be 490 K by thermomagneticanalysis, indicating that at the lowest measurement temperature, the samplewas fully ferromagnetic (both phases). At higher temperatures, TC

am isexceeded and the grains fully decouple due to the low volume fractiontransformed (�18 vol%) and resulting large distance between adjacentgrains (Lachowicz et al., 2002). The mean field approximation describedabove can be used to describe superparamagnetism in this case, replacing theatomic moment with a super-moment consisting of all of the exchangecoupled moments in the grain. A spherical grain with diameter �10 nm (asobserved in this alloy) has a volume of �525 nm3, which compares favor-ably to the volume of each superparamagnetic moment from the best fit tothe experimental data (548 nm3). Superparamagnetism was not observed inFe73.5Si13.5B9Nb3Cu1 until temperatures much higher than TC

am, rathersuperferromagnetism was observed due to the stronger interactions betweenparticles (Slawska-Waniewska et al., 1993). At sufficiently high tempera-tures (exceeding 600 K), superparamagnetic behavior was observed in aFe72Si13.5B9Nb4.5Cu1 annealed at 803 K for 3.6 ks (Kim et al., 1996).

At temperatures below 50 K, spin-glass and spin-freezing effects havebeen observed in Fe73.5Cr5B10Nb4.5Cu1 alloys (Skorvanek and Wagner,2004). This has been characterized by strong irreversibility between zerofield cooled and field cooled conditions.

6.5. Static hysteresis and AC core losses

High permeability is desirable for applications where the core materialswitches under low-field conditions, such as common-mode chokes orground fault interrupts. Low permeability is necessary for high-frequencypower transformers in power electronics applications or interface transfor-mers for telecommunications. In both instances, common characteristicsthat improve performance include low losses, high resistivity, and goodthermal stability. Control of permeability and reduction of core loss are twoengineering aspects of these materials that are important for application andwill be discussed in this section.


Magnetostatic effects (e.g., powders) and induced magnetic anisotropy (viastress or magnetic field annealing) can be used to tune the permeability duringalloy processing. In both cases, themagnetic domains can play an important rolein the switching.Magnetic domains are easily formed in soft magneticmaterialsdue to their large magnetizations and small values of magnetic anisotropy,which aid in reduction of magnetostatic energy. To saturate the material, amagnetic field must be applied to sweep the unfavorably oriented domains outof the material and then rotate the remaining favorably oriented domain intothe magnetic field direction. From the demagnetized state, small, appliedmagnetic fields cause reversible domain wall motion until the domain wallsreach pinning centers in the material. Additional field is required to move thedomain walls away from the pinning centers, which results in irreversibledomain wall motion (a large contributor to the coercivity). When all of thedomain walls are swept from the material, the magnetization then rotates intothe applied field direction as the field is further increased. Amagnetic hysteresisloop results from cycling the magnetic field between large positive and largenegative fields. When this is done slowly, the area swept out by the loop isminimized and it is referred to as the static hysteretic loss. High-frequencyswitching results in larger losses due to the formation of eddy currents, whichscreens out the applied field and confines the switching to thematerial’s surface.

The total core losses of a material switched at high frequencies aredependent on the amplitude of the applied field, the hysteresis loss, theexcitation frequency, and geometry of the sample, in addition to eddycurrents. In Fig. 4.68, the permeability of various state-of-the-art softmagnetic materials is shown for low-field switching at various frequencies.Transverse field annealing has been found to lower the permeability (e.g.,shearing the hysteresis loop) in Fe73.5Si13.5Nb3B9Cu1 alloys, while longitu-dinal field annealing gives better squareness to the loop and increases themaximum permeability (Herzer, 1995). For powder cores, the distributedair gap causes a reduced permeability due to the effect of the demagnetizingfield. At high enough frequencies, the magnetic resonance of the materialreduces the permeability at the Snoek limit (marked in Fig. 4.68).

The core losses are well described by their contributions from frequency-insensitive sources (e.g., hysteretic losses) and frequency-sensitive sources(e.g., classical and excess or anomalous eddy current losses). To this point,the discussion of coercivity has largely referred to frequency-insensitive mea-surements carried out by vibrating sample magnetometry. The area of ahysteresis loop is the hysteretic loss, and it is closely related to the width ofthe loop (i.e., coercivity). The nanocrystalline alloys presented here generallyhave low hysteretic losses due to their fine-grained microstructure in combi-nationwith their lowmagnetoelastic anisotropy. The eddy current losses in thisclass of materials begin to show their significance at frequencies approachingtens to hundreds of kilohertz. The eddy currents tend to increase when theskin depth of the material (i.e., dm� ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

re=pf m0mp

) is smaller than half the


ribbon thickness. While some work has been done on amorphous alloys toreduce the ribbon thickness in attempts to increase the operation frequency,little work has been done on nanocrystalline materials (Beatrice et al., 2008).

As a general principle, the eddy current losses can be described by

Pcv / d2f 2B2

re

where d is the ribbon thickness, f is the switching frequency, B is themagnetic induction amplitude, and re is the electrical resistivity. Fromthis equation, it is clear that the rapidly solidified nanocomposite ribbonshave advantageous thicknesses (d�18–25 mm) and modest resistivities(100–130 mO cm), which help to limit the eddy current losses. An addi-tional eddy current term is dominant at frequencies in the tens kHz which isdue to the fast magnetization switching near domain walls (called excesseddy current losses) (Ferrara et al., 2000; Willard et al., 2005).

Figure 4.69 shows the core losses for several state-of-the-art soft mag-netic materials. The core losses naturally increase as the magnetic inductionamplitude is increased (or commensurately the magnetic field strength), dueto the progressively increased area swept out by larger minor hysteresis loops(Fig. 4.69a). As the material starts to saturate, the magnetization of thematerial provides less of the increase to induction (and the magnetic fieldprovides more). This requires significantly more energy resulting in a sharprise in the core losses near saturation. The core losses also increase as thefrequency is increased due to dynamic domain wall motion and eddycurrent losses (Fig. 4.69b). In both parts of Fig. 4.69, the (Fe,Si)-basednanocrystalline alloys have the lowest losses for a given magnetic inductionamplitude (in A) or switching frequency (in B). This is due to the exchangesoftening of the magnetocrystalline anisotropy due to the refined micro-structure, the near zero magnetostrictive coefficients due to the balancedcomponents from the phases in the nanocomposite, and the high resistivityof the residual amorphous phase allowing reduced eddy currents.

The coercivity (Hc), saturation magnetization (Ms), and initial suscepti-bility (w0) have been used to determine the switching behavior of Fe73.5Si13.5B9Nb3Cu1 alloys in the as-cast and annealed conditions using the ratiow0 Hc/Ms (Zbroszczyk, 1994). Coherent rotation was calculated to have avalue of 0.21 and domain wall motion a value of 0.008 (Herzer, 1990;Hofmann et al., 1992), the latter comparing favorably with experimentaldata for optimally annealed samples (0.0079) (Zbroszczyk, 1994).

6.6. Magnetocaloric effect

The magnetocaloric effect is an adiabatic temperature change in a materialdue to a change in applied magnetic field (Pecharsky and Gschneidner, 1999).It can be used to perform solid-state cooling in adiabatic demagnetization

Maximum induction amplitude (T)

(a)

(b)

f = 50 Hz (sine)

Bm= 0.2 T (sine)

Supermendur

80 Permalloy

Fe–3.5 at% Si

Fe–3.5 at% Si

Mn–Zn ferrite

Fe78Si9B13

Fe78Si9B13

Fe44.5Co44.5Zr7B4

Fe86Zr7B6Cu1

Fe86Zr7B6Cu1



Cor

e lo

ss (

W/k

g)C

ore

loss

(W

/kg)

Switching frequency (kHz)

0.2 0.5 1 2

11

0.001

0.01

0.1

1

10

10

102

103

104

105

10 100 1000

Figure 4.69 (a) Comparison of core losses with applied induction amplitude forseveral soft magnetic materials using sinusoidal waveforms and a switching frequencyof 50/60 Hz (Gutfleisch et al., 2011; Suzuki et al., 1991a) and (b) with frequency forseveral soft magnetic materials using sinusoidal waveforms and an applied inductionamplitude of 0.2 T (Suzuki et al., 1991a; Willard and Daniil, 2009; Yoshizawa andYamauchi, 1989).


refrigerators, exhibiting maximum efficiency when the magnetic refrigerantmaterials possess small coercivity, strong temperature dependence of magne-tization near the operation temperature, and (especially) large magneticcontribution to the entropy (under an isothermal magnetic field, DSM). Inconventional magnetocaloric materials, materials containing elementswith large atomic moments are used to maximize the DSM; rare earth-containing compounds are typically used (e.g., diluted paramagnetic salts(near 0 K); elemental Gd, magnetic garnets, and Gd5(Ge,Si)4; (Pecharskyand Gschneidner, 1997); etc.). Although these materials have large intrinsic


magnetic entropy, they are also quite expensive and in high demand for manyother energy applications.

The use of nanostructured materials for magnetocaloric applications wasposed by McMichael et al. (1992) and specifically to (Fe,Si)-based alloys byKalva (1992). In principle, the advantage of nanocrystalline materials lies intheir small grain size that can act as superparamagnetic (or superferromag-netic) clusters when thermally activated. The large moments from theseclusters provide large magnetic entropy as the blocking temperature isapproached (near the Curie temperature of the amorphous phase). Animprovement in magnetocaloric entropy change was observed in aCo66Si12Nb9B12Cu1 alloy annealed at 843 K, exhibiting a maximum�DSM of 0.035 emu/(g K) for a field change of 0.1 T and at a temperatureof �125 K (Didukh and Slawska-Waniewska, 2003). Under these proces-sing conditions, the alloy consisted of 7.4 nm grains embedded in anamorphous matrix with a volume fraction of crystallites �5–7%. Thepeak in DSM was consistent with the amorphous phase Curie temperature,which decoupled the well-separated grains in the material resulting insuperparamagnetic behavior. The maximum DSM shifted to lower tem-peratures for higher volume fraction transformed.

However, in most nanocrystalline soft magnetic alloys, the magnetoca-loric effect is reduced when samples are partially crystallized. For example, aFe68.5Mo5Si13.5B9Nb3Cu1 alloy showed deterioration of the DSM afterpartial crystallization (Franco et al., 2006b). In amorphous alloys, substitu-tion of 5 at% Co for Fe in a Fe83Zr6B10Cu1 alloy resulted in increasedmagnetocaloric entropy (from 1.4 to 1.6 J/kg K); however, the Curietemperature of the amorphous phase was also increased (from 400 to485 K) (Franco et al., 2006a). Recent studies of dual substitution of Coand Ni for Fe in a Fe88Zr7B4Cu1 amorphous alloy show a similar trend withalloying, but with larger values of magnetic entropy change (Caballero-Flores et al., 2010). In the relaxed amorphous state, the magnetocaloricproperties of this material were favorable when compared to Gd5(Ge,Si)4materials due to their lower coercivity (and much lower materials cost).

6.7. Giant magnetoimpedance

The giant magnetoimpedance (GMI) effect was first reported by Panina andMohri in a Fe4.3Co68.2Si12.5B15 alloy when they observed a change in ACimpedance (Z¼Rþ ioL) as high as 60% by the application of an ACcurrent (I¼ I0 exp(�iot)) to an electrically conducing magnetic materialunder an applied DC bias field (HDC) (Panina andMohri, 1994). The strongfield sensitivity of this effect makes it suitable for sensor applications. Theeffect itself was attributed to a combination of skin depth and sensitive fielddependence of circumferential or transverse permeability. Such effects havesince been observed to depend strongly on the magnetostrictive coefficient


and the subsequent domain structure formed in materials with wire andribbon morphologies (Barandiaran and Hernando, 2004; Guo et al., 2001).The frequency (o¼2pf) dependence is highly influenced by the electricalresistivity (re) through the skin depth (dm¼ (re/pfm)

1/2) and the permeabil-ity (m), especially for f greater than a few MHz. This is due to the formationof eddy currents in the center of the ribbon cross section, causing the ACcurrents to flow closer to the ribbon surface and resultant switching bymagnetization rotation. For f less than a fewMHz and low applied fields, theGMI effect is dominated by domain wall displacements.

The total impedance (Z) has been found to decreases rapidly with appliedmagnetic field when the magnetic material possesses a small, negative value ofmagnetostrictive coefficient (ls��10�7) (Phan and Peng, 2008). Thedomain structure for a material with this characteristic has a core with axialmagnetization surrounded by a shell of circumferential domains with a stripedomain pattern. At low fields, the core saturates along the applied fielddirection. With increasing field, the circumferential domains align with thefield direction by a coherent rotation process, thereby reducing the imped-ance. The inductive component of an AC wire voltage can be decreased by50% for an applied field as low as a few hundred A/m by this method. Thisprocess is dependent on both magnetic field amplitude and frequency. Setupfor making this type of measurement is described by Knobel et al. (1997).

Nanocrystalline Fe73.5Si13.5B9Nb3Cu1 alloys with near zero magne-tostrictive coefficient showed similar, large total magnetoimpedance (Zm)with contributions from magnetoresistance (Rm) and from magnetoreac-tance (Xm), where Zm(f,H)¼Rm(f,H)þ i Xm(f,H) (Chen et al., 1996). Thecomposition series Fe74SixB22�xCu1Nb3 (x¼4–18) and annealing temper-ature dependence of GMI showed that peaks in the permeability and MIratio coincide, with highest field sensitivity of 23%/Oe and 67% MR ratiofor an x¼16 alloy after annealing at 570 �C (Ueda et al., 1997). The peak inGMI ratio for nanocrystalline Fe73.5Si13.5B9Nb3Cu1, Fe90Hf7B3, andFe90Zr7B3 alloys peaked between 100 and 500 kHz with values of �10%,25%, and 27%, respectively (Knobel et al., 1997). The difference wasattributed to the influence on the transverse permeability (implied throughthe negative magnetostrictive coefficients) for the Fe-based alloys and thenear zero value for the (Fe,Si)-based alloy. Higher frequency measurements,to 5 MHz, resulted in an increase of both field sensitivity (40%/Oe) andmaximum GMI ratio (640%) for nanocrystalline Fe71Al2Si14B8.5Nb3.5Cu1alloys (Phan et al., 2006). This effect was also reported for Fe88Zr7B4Cu1nanocrystalline alloys, with GMI ratio of 409% at 10 MHz (Chen et al.,1997). No reports have been made on the GMI of HITPERM-type alloys,likely due to their lower permeability.

The application of similar amorphous materials as current and fieldsensors has been investigated (Valenzuela et al., 1996, 1997). MaximumGMI sensitivity was found for the frequency range 50–500 kHz and AC


current amplitudes of 8–15 mA. Sensors made from (Fe,Si)-based nano-crystalline alloys sandwiched around a copper lead showed optimal perfor-mance for small values of ribbon length-to-width ratio and relativepermeability (controlled by stress annealing) (Bensalah et al., 2006).Frequency-modulated GMI sensors with 15%/Oe sensitivity over thefield range �2 Oe have been demonstrated using a nanocrystalline ribboncore (Wu et al., 2005).

7. Other Physical Properties

7.1. Mechanical and magnetoelastic properties

Few studies have focused on the mechanical properties of nanocrystallinesoft magnetic alloys. Typical alloys of this type are thin and narrow and quitebrittle after annealing, making standard techniques for measuring bulkmechanical properties difficult. Despite these limitations, some studies ofalloy microhardness, nanohardness, and relative strain at fracture have beeninvestigated. A recent study of the amorphous precursor ribbons of Fe73.5Si13.5Nb3B9Cu1 alloys shows tensile strengths of 2000 MPa and a highnotch toughness of 89 MPam1/2 (El-Shabasy et al., 2012).

Many connections betweenmagnetization and strain behavior inmagneticalloys have been observed under the application of varying combinations ofmagnetic or stress fields or applied torques. Most important among theseinclude magnetostrictive effects (i.e., shape change due to changing magneti-zation), DE effect (i.e., mechanical softening due to changing stress), andVillari effect (i.e., magnetization changing due to applied stress field). Thefollowing sectionwill describe some of the experimental results of these effectsin nanocrystalline soft magnetic alloys. More detailed descriptions of theseeffects (and others) can be found elsewhere (Kaczkowski, 1997; OHandley,2000). Magnetostrictive effects are a major source of hysteretic losses innanocomposite alloys, so these properties have been discussed in Section 6.3.

The magnetomechanical coupling coefficient (km) provides informationabout the suitability of a given magnetostrictive material for transducerapplications by defining the amount of magnetic energy that is convertedto mechanical energy. This may be accomplished by measuring the perme-ability under an oscillating magnetic field for (1) a freely vibrating sample(mt) and (2) a mechanically fixed sample (ms), resulting in: km

2 ¼ (1�ms)/mt.Experimentally, this value may be determined using a resonant/antiresonantmagnetoimpedance technique (Kaczkowski, 1997). The low magnetocrys-talline anisotropy, high saturation magnetization, and high electrical resis-tivity found in nanocrystalline soft magnetic alloys make them goodcandidates for transducer applications. However, the magnetostrictive coef-ficient must be increased substantially (to above 15 ppm) to provide the

Annealing temperature, T (°C)

Cou

plin

g co

effic

ient

, km

(%) M

agnetostriction, l

s (ppm)

010

15

20

25

30

35

40

45

50

55

60

65

70

50 100 150 200 250 300 350 400 450 500 550 6000

5

10

15

20

25

Figure 4.70 Maximum values of the magnetomechanical coupling coefficient (km) ofthe Fe73.5Si15.5B7Nb3Cu1 samples annealed in vacuum and saturation magnetostriction(ls) of the Fe73.5Si13.5B9Nb3Cu1 samples annealed in air versus annealing temperature(Tann) for 3600 s. Modified from Kaczkowski et al. (1995) and M€uller et al. (1992).


necessary large values of km. For this reason, different processing conditionswill be optimal for transducer applications than for power conditioning andconversion applications, where nearly zero magnetostriction is desired.Magnetomechanical coupling coefficients as high as km¼0.62 were foundfor Fe73.5Si13.5Nb3B9Cu1 samples annealed below the primary crystalliza-tion temperature and dropped quickly as the nanocrystalline microstructuredeveloped due to reduced magnetostrictive coefficients (see Fig. 4.70)(Kaczkowski et al., 1995).

TheDE effect was measured using a vibrating reedmethod by Bonetti andDel Bianco on a Fe73.5Si13.5Nb3B9Cu1 alloy as a function of both annealingand measurement temperatures (Bonetti and Del Bianco, 1997). The changein elastic modulus (DE) was evaluated by DE/E¼ (E�Emin)/Emin, where Eis the elastic modulus when a saturating magnetic field is applied and Emin isthe lowest value of elastic modulus measured at a constant magnetic field. TheEmin value was observed to coincide with the anisotropy field of the magnetichysteresis (Gutierrez et al., 2003). By this method, amorphous samples hadtypical values of DE/E between 0.05 and 0.08. Annealed samples(Tann>700 K) showed improved magnetoelastic coupling with DE/E valuesin excess of 1.1, which quickly dropped as the temperature was increased to800 K (e.g., crystallization of the sample). Similarly, by comparing conven-tionally annealed and Joule annealed samples, the maximum in DE/E wasfound in relaxed amorphous samples (e.g., low internal stresses and largepositive magnetostriction) (Bonetti et al., 1996). The elastic (Young’s)


modulus of a Fe73.5Si13.5Nb3B9Cu1 alloy was found to not vary appreciablyunder the application of a magnetic field for an as-cast sample, exhibiting avalue of between 150 and 160 GPa (Kaczkowski et al., 1997). After annealingabove the primary crystallization temperature, the elastic modulus at magneticsaturation was found to vary between 160 and 180 GPa (slightly less thanBCC-Fe�210 GPa).The elastic modulus of Fe64Ni10Si13Nb3B9Cu1 at mag-netic saturation was found to be between 177 and 186 GPa for the amor-phous phase depending on the relaxation annealing conditions and between184 and 209 GPa after partial crystallization, resulting in improved km(Gutierrez et al., 2003). The largest coupling coefficients (km�0.85) coin-cided with the largest values of DE/E (0.61), for this alloy compositionannealed just prior to crystallization (at 460 �C).

The magnitude of elastic softening due to the DE effect can be correlatedwith the magnetostrictive coefficient by the relation:

DEE

¼ l2sEs

KF

whereK is the anisotropy constant, and F is a factor that depends on the easyaxis distribution and applied field (Hogsdon et al., 1995). The shape of DEversus applied field plots is directly related to the anisotropy, domainstructure, and saturation magnetostriction (through the above relation)and therefore can help interpret switching in these alloys (Atalay et al.,2001). From the shape and magnitude of the DE versus magnetization plots,the motion of 180� domain walls was found to dominate as Fe73.5Si16.5Nb3B6Cu1 samples were annealed at temperatures to 620 �C.

Magnetoelastic effects were examined on a Fe73.5Si16.5Nb3B6Cu1 toroi-dal core which was subjected to varying applied compressive stresses duringhysteresis measurement (Bie�nkowski et al., 2004b). A Villari point (where(dB/ds)Η¼0) was observed for samples with low crystalline volume frac-tions, inferring a change in the sign of the magnetostrictive coefficient. Forthe sample with optimal soft magnetic performance (Tann¼580 �C for 1 h),the magnetic induction was reduced as the compressive stress was increasedto 10 MPa for all applied fields.

The class of nanocrystalline soft magnetic alloys, as a whole, exhibitssignificant embrittlement after crystallization, requiring that toroidal coresbe wound to their final shape prior to crystallization. The use of Jouleannealing to partially devitrify a Fe73.5Si13.5Nb3B9Cu1 alloy has been attrib-uted with improved ductility after crystallization. A comparative studybetween the strain-at-fracture (ef) values of conventionally annealed andJoule annealed samples resulted in about a factor of 2 increase (from �0.05to �0.13) (Allia et al., 1994). Both of these values are much lower than the0.18 value for the as-cast ribbon, which has significant flexibility (butlimited ductility). Skorvanek and Gerling found that ef was reduced for a

D-0.5 (1/nm0.5)

FeMoSiBFeMoSiB/FeCuSiB

Mic

roha

rdne

ss, H

v (G

Pa)

Hall–Petch Coble creep

0.056.0

6.5

7.0

7.5

8.0

8.5

9.0

9.5

10.0

10.5

0.10 0.15 0.20 0.25 0.30 0.35

Figure 4.71 Variation in microhardness with D�1/2 for (Fe0.99 M0.01)78Si9B13 alloyswhere M¼Mo, Cu (Liu et al., 1993a; Liu et al., 1993b).


Fe73.5Si13.5Nb3B9Cu1 alloy annealed at temperatures below the onset ofprimary crystallization, which was attributed to an increase in the density ofthe amorphous phase (reduction in free volume) (Skorvanek and Gerling,1992). They further studied a partially crystallized sample (545 �C for 1 h)under neutron irradiation and found little change in ef with neutron fluence(remaining at �0.04 over the range 1017 to 1019 nth/cm

2). Similar studieson the embrittled amorphous alloys showed a restoration of the high degreeof ef (to near 1) for alloys annealed at 300 and 400 �C. The author’sconclusion from these findings was that the residual amorphous phase wasnot solely responsible for the brittle behavior in the nanocrystalline alloys.Large relative strain at fracture (above 0.35) was observed in Co-rich(Co1�xFex)89Zr7B4 alloys after primary crystallization (Daniil et al.,2010b; Heil et al., 2007). Analysis of the fracture surfaces showed increasedmicrovoid coalescence dimple size with enrichment in Co. Materials withthis large ef are capable of processing after annealing, giving a greaterflexibility in the processing route for cores; however, the improvedmechanical performance seems to be limited to x>0.1 (Fig. 4.71).

A linear dependence of the microhardness values with 1=ffiffiffiffiD

pwas

observed for Fe77.22Mo0.78Si9B13 and Fe77.22Cu0.78Si9B13 samples withvaried grain diameters (D) between 30 and 200 nm, and an inverse depen-dence was found for grains smaller than 30 nm (Liu et al., 1993a,c). Thisresult shows behavior consistent with the Hall–Petch relationship for grains

with diameter greater than �45 nm, namely, sy¼ sy0þ fffiffiffiffiD

p� ��1, where


sy is the yield stress (proportional to the hardness, Hv), sy0 is the stressnecessary to make dislocations mobile (lattice friction stress), and f is aconstant. For grains with diameter less than 45 nm, Coble creep may bethe dominant deformation mechanism where sc¼A/DþBD3 (where sc isthe creep stress (again proportional to the hardness, Hv) and A and B areconstants) (Chokski et al., 1989; Lu et al., 1991; Masumura et al., 1998).While these relationships are consistent with other nanocrystalline materials,a thorough investigation of the mechanical property variation with grainsize has not been performed on this class of materials.

7.2. Electrochemistry and oxidation

Experiments have been conducted by annealing in an oxygen atmosphereand by immersion in acid solutions to establish the oxidation and corrosionproperties of nanocrystalline soft magnetic alloys. Conventional methods forannealing to promote crystallization are conducted in an inert atmosphere toavoid the deleterious effects of oxidation on the saturation magnetization.Marino et al. found that annealing nanocrystalline samples of Fe73.5Si13.5NbxB10.5�xCu1 (x¼0, 3, 5) in an oxygen atmosphere at 400 �C resultedin the formation of a passivating oxide layer (Mariano et al., 2003). High Nbcontent samples showed faster oxidation; however, slower weight gain duringoxidation was observed for lower Nb content samples, indicating that thepassivating layer was more efficient at preventing further oxidation.

A Fe74Si13.5Nb3B8.5Cu1 alloy was investigated by immersion in a 0.1 MH2SO4 solution for evaluation of the corrosion resistance of the alloy. Thecorrosion rate (evaluated as weight loss over a fixed immersion time) wasfound to be larger for the as-spun (1.1–1.2�10�4 g/(cm2 h)) than for thenanocrystalline alloy (0.1–0.3�10�4 g/(cm2 h)) (Souza et al., 1999). Simi-lar studies of a Fe80Zr3.5Nb3.5B12Cu1 alloy showed a much higher corrosionrate than for the (Fe,Si)-based alloy in both the as-spun alloy (2.1�10�4 g/(cm2 h)) and the nanocrystalline sample (5.8�10�4 g/(cm2 h)) (Souzaet al., 2002). The improvement in corrosion resistance in the (Fe,Si)-based alloy was attributed to the SiO2-passivating oxide which was foundto form on the surface of the ribbon; the Fe-based alloy did not possess thischaracteristic. The substitution of Co for Fe in (Fe,Si)-based and Fe-basedalloys resulted in an improvement of corrosion resistance to H2SO4, but to asmaller extent than the substitution of Si (May et al., 2005). In Fe73.5�xCrx-Si13.5Nb3B9Cu1 (x¼0, 2, 4, 6) alloys, increased Cr substitution (i.e., x¼4, 6)was found to substantially improve the oxidation resistance during immersionin a 0.1 M Na2SO4 solution (Pardo et al., 2001).

The potentiodynamic method was used to examine the corrosionbehavior of Fe73.5AlxSi13.5�xNb3B9Cu1 (x¼0, 1, 2) alloys using 1 MNaCl with a pH of 9.0 (Alvarez et al., 2001). Two anodic peaks—corresponding to dissolution of Fe2þ from the a-(Fe,Si) grains and residual


amorphous phases, respectively—were observed for all three compositionsprior to the creation of a passivating silica layer. No significant effect of Alon the corrosion resistance of the alloy was observed. In Fe64�xCo21NbxB15

alloys, short etching with dilute HNO3 was found to dissolve a-Fe pre-cipitates, which formed during rapid solidification processing, giving asensitive method for evaluating surface crystallization (Kraus et al., 1997).While the glass-forming ability of Fe–M–B alloys is improved for M¼Zr orHf over Nb, the latter has better resistance to oxidation. For this reason, theFe–Zr–B and Fe–Hf–B alloys require inert atmosphere during meltprocessing.

Transmission electron microscopy and atom probe microscopy requirethinning of the ribbon samples to dimensions less than a few hundrednanometers. One technique for reducing the sample thickness is the useof electrochemical polishing. In some studies, a 90% glacial acetic acid and10% perchloric acid (HClO4) solution at room temperature has been used asan electrolyte during electropolishing or jet polishing for TEM samplepreparation (Millan et al., 1995). Other studies have used a perchloric acidand methanol solution (at �35 �C) for electrochemically thinning TEMspecimens (Chen and Ryder, 1997; Moon and Kim, 1994). Twin jetelectrochemical polishing 5–10% perchloric acid-acetic acid solution hasalso be used for thinning (Conde and Conde, 1995b; Houssa et al., 1999).However, in most cases, TEM foils can be prepared by direct ion milling ofthe ribbons for plan view samples due to their �25 mm thickness (Makinoet al., 2003; Miglierini et al., 1999; Wu et al., 2001).

7.3. Resistivity and magnetoresistance

The resistivity of soft magnetic materials is an important parameter due to itsdirect influence on the core losses via eddy current mechanisms, which areespecially important at high switching frequencies. The resistivity can besubstantially larger than conventional soft magnetic alloys due to the amor-phous intergranular phase surrounding the nanocrystalline grains. This isone reason for the reduced losses compared with 3% Si steel (seeSection 6.5). It is important to note that the resistivity is sensitive tocomposition and processing conditions that effect the amorphous matrix.

The resistivity of a Fe73.5Si13.5Nb3B9Cu1 alloy was found to increaseabout 5% upon primary crystallization at a constant heating rate due to theformation of (Fe,Si) crystallites (Barandiaran et al., 1993). In alloys wherethe Nb content was reduced below 2 at%, the resistivity was found todecrease upon crystallization, an effect that is amplified as the Nb contentapproaches zero (Pekala et al., 1995a). With increasing grain size from 30 to90 nm in Fe77.22Si9B13Cu0.78 alloys, the resistivity was found to decrease bya factor of 3 from 126 to 44 mO cm (Liu et al., 1993c). In contrast,crystallization of the Fe86Zr7B6Cu1 alloy caused a reduction of the resistivity


by about 10% when the sample was heated through the crystallizationtemperature (Barandiaran et al., 1993). Typical values of room temperatureelectrical resistivity for Fe–Si–B–Nb–Cu and Fe–Zr–B–Cu alloys withoptimal magnetic performance are 115–125 mO cm and 50–60 mO cm,respectively (Herzer, 1996; Knobel et al., 1997). Prior to crystallization,the resistivity is typically higher with values of 160�8 and 145�7 mO cmfor Fe73.5Si13.5Nb3B9Cu1 and Fe86Zr7B6Cu1, respectively (Barandiaranet al., 1993).

The magnetoresistive effect is defined as (Dre/re0)¼ (rek�re?)/re0,where rejj and re? are the resistivities in the longitudinal and transversesaturating fields and re0 is the resistivity in zero applied field. When thevolume fraction of crystallites in Fe73.5Si15.5Nb3B7Cu1 exceeds 50%, anegative ferromagnetic anisotropy of resistivity is observed (Kuzmi�nski et al.,1994). Similar results were earlier reported for a Fe–Cr–Si–Nb–B–Cualloy (Slawska-Waniewska et al., 1993). Small spin-dependent magne-totransport was observed in Fe81Zr8Cu1Ru10 alloys with nanocrystallinemicrostructure (Suzuki et al., 2002a). These alloys have an ordinary magneto-resistance in the as-cast state and show anisotropic magnetoresistance (mostprominent at 130 K) only after the nanocrystallinemicrostructure is formed byannealing (indicating strong ferromagnetic coupling through the amorphousmatrix).

8. Conclusions

Over the past 20 years, nanocrystalline soft magnetic alloys haveproven an important test bed for nanoscience and nanotechnology. Therapid commercialization of this class of materials is a testament to theirtechnologically interesting characteristics. The breadth and depth of thebody of research presented in this chapter illustrate continued interest andprogress in the development of new materials for future generations of highefficiency magnetic materials. With the growing interest in sustainableenergy, magnetic materials innovations will surely play an important role,with nanocomposite materials at the forefront.

Materials with widely varying compositions have been shown to possessimproved magnetic performance when formed with nanocomposite micro-structures. For high-frequency applications, Fe–Si–Nb–B–Cu alloys haveshown lower losses and higher magnetization than ferrites and amorphousalloys. Their magnetizations (near 1.2–1.35 T) are higher than otherextremely low loss materials, such as permalloy and Co-based amorphousalloys, allowing components using them to be reduced in size. In applica-tions where higher magnetizations are required, the Fe–Zr–B alloys areadvantageous, exhibiting lower losses than permalloys and Fe-based


amorphous alloys. The Fe-based compositions and processing into thinribbon morphologies provides an ease of manufacture for these materialswill low raw materials cost. For high temperatures, the use of (Fe,Co)–Zr–Bor (Fe,Co,Ni)–Zr–B alloys shows improved performance against FeCoalloys due to their nanocomposite microstructures.

Future research in this area will likely address issues in mechanicalperformance of the alloys, processability of ribbons in air, and furtherimprovements in high magnetization/low core loss alloys. The richness ofthe scientific phenomena found in these alloys, along with the large degreeof tunable magnetic properties, will drive new innovations in this class ofsoft magnetic alloys for years to come.

ACKNOWLEDGMENTS

The authors would like to thank the Office of Naval Research for support of this work.M. A. W. would also like to thank the many collaborators and colleagues who throughconversations over the years have greatly influenced his thoughts about nanocrystallineexchange coupled alloys.

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