DEFORMATION INDUCED TRANSFORMATIONS AND

GRAIN BOUNDARY THICKNESS IN NANOCRYSTALLINE

B2 FeAl

D. NEGRI1, 2, A. R. YAVARI1{ and A. DERIU2

1Metastable and Nanocrystalline Materials (Euronano), LTPCM±CNRS, Institut NationalPolytechnique de Grenoble, B.P. 75, 38402 St-Martin-d'HeÁ res, France and 2Dipt. Fisica, Instituto

Nazionale per la Fisica della Materia, Univ. Parma, Parma, Italy

(Received 28 April 1999; accepted 26 August 1999)

AbstractÐPrecise measurement of fundamental Bragg peak shifts during milling of nanocrystalline orderedB2 Fe60Al40 has allowed for the ®rst time, the deconvolution of the 110 fundamental Bragg peak intensitiesof the b.c.c. disordered regions and of the ordered B2 regions from the start and before full disappearanceof the latter. The evolution of the lattice parameter a0 of the b.c.c. solid solution with milling time showstwo characteristics. First a jump to higher values from the initial a0 of the B2 phase, with a Da0 change ofthe order of 1% corresponding to a volume per atom DVexpansion of about 3%. Subsequently, a0 continuesto increase slowly with further milling at constant grain size D and in the absence of any B2 phase. Thiscontinuing change of a0 with further milling up to at least 180 min is attributable to a reduction of chemi-cal short-range order (CSRO) or the number of Al±Fe heteroatomic ``bonds''. The appearance of two well-de®ned maxima in the hyper®ne ®eld (HF) distributions derived from the MoÈ ssbauer spectra indicated thepresence of two ferromagnetic environments contributing to the broadened MoÈ ssbauer resonance sextet sig-nal. The evolution of the second component of this MoÈ ssbauer signal scales with the grain size. Using themean grain size D derived from X-ray peak pro®les and TEM pictures together with the grain boundarythickness dgb of 1.25 nm determined by Fultz et al. (J. appl. Phys., 1996, 7, 127) for b.c.c. Fe-based alloys,the fraction of grain boundary atoms ngb/ntotal was estimated and found to be consistent with the fractionof Fe atoms contributing to the lower HF component of the MoÈ ssbauer sextet signal. The grain boundaryatom count using both methods con®rms that grain boundaries in materials nanocrystallized by heavy de-formation are nearly as dense as in the bulk. # 1999 Acta Metallurgica Inc. Published by Elsevier ScienceLtd. All rights reserved.

Keywords: Intermetallic; Phase transformation; MoÈ ssbauer e�ect; Nano-grain boundary thickness

1. INTRODUCTION

When an ordered intermetallic undergoes heavy de-

formation, one or more of the following polymor-

phous transformations will occur [1]: (a) It will

undergo grain re®nement down to the nanocrystal-

line regime. (b) Chemical long-range order may dis-

appear as signaled by the disappearance of

superlattice re¯ections. (c) Chemical short-range

order (CSRO) may be decreased towards that of a

random solid solution [2]. (d) The basic topological

order and fundamental unit cell of the crystal may

change such as in a b.c.c.±f.c.c. transformation [3].

(e) Long-range crystalline topological order may

crumble altogether into an amorphous phase [4, 5].

Following earlier work [6], the evolution of struc-

ture and properties of B2 type FeAl intermetallics

with heavy deformation induced by ball milling or

during formation by mechanical alloying have

recently been extensively studied [7±9] and it has

been clearly established that the B2 intermetallicevolves into a disordered b.c.c. solid solution as

chemical long-range order of the B2 lattice disap-pears with multiplication of defects, especially anti-

site defects. More particularly, B2 Fe60Al40 which isparamagnetic at 300 K becomes strongly ferromag-

netic in the disordered b.c.c. state as the Fe±Fenearest neighbor population increases.

Most results of research on deformation e�ects inintermetallics reported in the literature concern de-

formation of coarse grain ordered materials.Disordering and other transformations therefore

begin for example in deformation bands as dislo-cations move, pile up and ultimately precipitate to

induce grain re®nement. During this time, measuredproperties such as lattice parameters, defect den-

sities and magnetization re¯ect average values forchemically disordered and still ordered parts of the

same grains. A clearer picture of the disorderedtransformed regions and new evidence on the trans-

formation mechanisms emerge when the startingundeformed material is fully ordered but has

Acta mater. Vol. 47, No. 18, pp. 4545±4554, 1999# 1999 Acta Metallurgica Inc.

Published by Elsevier Science Ltd. All rights reservedPrinted in Great Britain

1359-6454/99 $20.00+0.00PII: S1359-6454(99)00324-9

{To whom all correspondence should be addressed.

4545

nanoscale grain size. In this paper we follow theevolution of nanocrystalline B2 Fe60Al40 during de-

formation using high precision X-ray di�ractionanalysis and MoÈ ssbauer spectroscopy.

2. EXPERIMENTAL TECHNIQUE

Ingots of Fe60Al40 were prepared from pure com-ponents using induction melting and melt-spununder argon gas. Two to ®ve grams at a time were

then milled up to 5 days to achieve maximum grainre®nement. The powders were then sealed in quartztubes under vacuum and annealed for several hours

near 7008C, well above the ordering temperaturesas measured by DSC [7]. Energy dispersive X-raymicroanalysis (EDX) indicated that long millingtimes up to 5 days introduce contamination frag-

ments from the steel vial and from the ball. Table 1shows that about 2 at.% of Cr is thus introducedinto the initial powder. However, the subsequent ex-

periments on these powders involve short millingtimes up to 3 h with insigni®cant additional con-tamination.

One gram of annealed B2 powders with initialgrain size of 25±30 nm was then milled in vibratingmills with a single 6 cm diameter steel ball and vialunder argon gas. The powder volumes thus corre-

sponded to 10:1 cm3 [10]. The ball jump frequencywas measured to be about 20/s [11]. Structuralchanges after various thermomechanical treatments

were followed using a Siemens di�ractometer andINELCPS120-type curved detector with Fe-Ka radi-ation. Silicon powder was added onto the samples

prior to the X-ray measurements and the Si peakswere used as internal reference to correct for instru-mental aberrations. Room temperature MoÈ ssbauer

measurements were performed using a computercontrolled constant-acceleration spectrometer with a10 mCi

57Co source. The isomer shifts are referred

to that of a-iron at room temperature. The spectra

were analyzed using the NORMOS/DIST versionof the NORMOS program developed by Brand [12]with the distributions of hyper®ne magnetic ®elds

P(H) where P(H) dH is the probability for ®elds inthe range (H, H� dH) and a conventional con-strained Hesse±Rubartsch method. Fitting was

done using the expression of Billard andChamberod [13] for the asymmetry parameters.TEM observations on the as-prepared powderswere obtained on a 200 keV JEOL microscope.

3. EXPERIMENTAL RESULTS

As in other B2 structures, di�raction patterns ofordered Fe60Al40 present Bragg peaks of both the

fundamental b.c.c. unit cell and those of the B2

superstructure due to chemical ordering of Fe

atoms and Al atoms on cube-center and cude-edgesites, respectively, or vice versa.

In the X-ray di�raction patterns of Fig. 1, the

100 superstructure peak of the B2 structure is seento gradually disappear during milling which gener-

ates anti-site defects and destroys long-range chemi-cal order. Simultaneously the lattice parameter

increases progressively from the value of the B2 tothat of the b.c.c. solid solution unit cell as evi-

denced by the systematic shift of the fundamentalBragg peaks towards lower angles. At the same

time, nanocrystallization (grain re®nement) leads to

the broadening of Bragg peaks from which the evol-ution of grain size can be deduced using for

example the Scherrer type analysis. These phenom-ena have been amply studied previously [8].

However, it is seen in the middle spectrum of Fig. 1that the fundamental Bragg peaks become asym-

metric after milling and appear to be the convolu-tion of two neighboring peaks. Further milling

leads to the full disappearance of superstructure

peaks such as the (100) and the re-establishment ofthe full symmetry of the fundamental Bragg peaks.

The asymmetry of the fundamental peaks develop-ing during disordering by deformation has not been

previously reported for B2 Fe60Al40.{ This phenom-enon is more clearly seen in Fig. 2 which shows

details of the (110) fundamental peak in the orderedB2 state before milling and after 30 min milling

(partially disordered powder) up to 90 min milling(fully disordered).

Clearly the (110) peak of the partially ordered

powder is composed of a peak positioned at the dif-fraction angle of the ordered powder before milling

and a second peak near the Bragg position of thefully disordered Fe60Al40. It thus appears that the

partially disordered powder consists of nearly fully

ordered grains and nearly fully disordered grains. Ifthis were not the case, instead of splitting, the fun-

damental peaks would gradually broaden and shiftto lower angles with increased deformation until

full disordering. The intermediate broad peakswould in that case correspond to the sum of the

contributions from regions with a full range ofdi�erent intermediate degrees of order.

Deconvolution of contributions to the fundamental

peak intensities from ordered and disordered nano-grains (such as those of the 110 peak after 30 min

milling) allows a new determination of the latticeparameter. Figure 3 shows such a plot derived from

Table 1. EDX-determined nanocrystalline milled powder compo-sition before annealing for re-ordering (average of ®ve measures)

Composition

Al 37.621.5 at.%Cr 2.2620.5 at.%Fe 60.1422.5 at.%

{Asymmetric peaks were reported for some AlxFe1ÿxpowders during mechanical alloying of Al and Fe powdersby Enzo et al. [14].

NEGRI et al.: DEFORMATION INDUCED TRANSFORMATIONS4546

the (110) peak positions of our samples. While the

lattice parameters of the fully ordered and the fully

disordered states are very close to published data,

the evolution of the lattice parameter a0 is di�erent.

More particularly, a0 of the ordered state changes

discontinuously to that of the disordered state withthe destruction of long-range order (LRO) of the

B2 structure. The B2�)b:c:c: transformation is

seen to induce a dilatation DV=V03Da=a003%.

Subsequently with continued milling, a0 of the b.c.c.

lattice continues a slow increase then levels o� after

180 min.

Figure 4 shows the evolution of grain size D with

milling time for the two states of Fe60Al40. Using

the Scherrer [15] method with D00:9l=�D2y�cos yon the 110 Bragg peak's FWHM (D2y), the ®nalgrain size is found to be about 12 nm. There is an

unknown degree of uncertainty in using this for-

mula that is more or less accurate in di�erent

nanostructures with di�erent levels and types of in-

ternal stresses. Strain broadening increases with dif-

fraction angle and a better method is that of

Williamson and Hall [16] which removes strainbroadening using plots of �D2y�cos y vs sin y ex-

trapolated to sin y � 0 before substitution in the

Scherrer method. However, this method requires

several Bragg peaks of the same hkl family. In the

absence of zero y values for �D2y�cos y, the De

Keijser and Langford method [17] for single peakanalysis is used to determine grain size. In this

method, the peak is ®tted to a Voigt-type function

and deconvoluted into Gauss and Cauchy com-

ponents. The Gauss width is then used to estimate

heterogeneous strains and the Cauchy width to de-

rive the grain size from Scherrer's formula.

However, our previous analysis indicates that the

De Keijser and Langford method grossly overesti-

mates grain size [18] in these materials probably

because strain and crystal size broadening are not

necessarily Gauss and Cauchy in shape, respect-

ively. The method of Gangulee [19], which also cor-

rects for strain broadening, gives values very close

to those obtained using the original Scherrer re-

lation [18]. Close observation of transmission elec-

tron microscope (TEM) images such as the bright

®eld picture of Fig. 5 leads to broad crystallite size

histograms tailing at 6 and 16 nm and centered

around 10±12 nm. The Scherrer value D012 nm

for the mean coherent domain size after long time

(2 h) milling is therefore nearly accurate. In Fig. 4,

it can be seen that, as expected, the disordered

Fig. 1. X-ray di�raction pattern of B2 Fe60Al40 orderednanocrystalline powder (with Si added as internal refer-ence). From bottom to top: before milling; after 30 minmilling showing asymmetric Bragg peaks; the disordered

b.c.c. solid solution after 180 min milling.

Fig. 2. (110) Bragg peaks of Fig. 1, showing intermediatestate (30 min milling) as convolution of the ordered B2

and disordered b.c.c. peak intensities.

NEGRI et al.: DEFORMATION INDUCED TRANSFORMATIONS 4547

b.c.c. grains are smaller than the B2 grains having

thus undergone grain re®nement along with disor-

dering. They undergo further grain re®nement with

milling time up to 90 min to D012 nm but D

remains constant afterwards. Comparison of Figs 3

and 4 indicates that the continued evolution of the

lattice parameter after 90 min milling time occurs at

constant b.c.c. nanograin size D and is therefore

due to continued evolution of the atomic environ-

ment inside the grains as deformation destroys

CSRO within the b.c.c. solid solution.

B2 Fe60Al40 which is paramagnetic at room tem-

perature becomes ferromagnetic in its b.c.c. poly-

morph. In the ferromagnetic state, through nuclear

Zeeman hyper®ne ®eld interactions, the local mag-

netic ®eld H splits the nuclear energy levels leading

to the typical sextet MoÈ ssbauer resonance pattern.

The sextets thus appear during milling as disorder-

ing increases the average number of Fe±Fe nearestneighbors Nnn(Fe±Fe) among Z � 8 total nearest

neighbors around an Fe atom. In an Fe1ÿxAlx B2-

type ordered alloy with X < 0:5, the fraction of Al

sites actually occupied by Al atoms XAl sitesAl goes

from X/0.5 for maximum order to XAl sitesAl � X in

the fully disordered random solid solution. In this

notation, Nnn�Fe±Fe� � �1ÿ XAl sitesAl �Z for Fe60Al40

would go from 1.6 in the B2 ordered state to 4.8 in

the fully disordered b.c.c. solid solution environ-

ment thus making MoÈ ssbauer spectroscopy a choice

method for following the evolution of local order in

Fe60Al40. The powders previously used for the X-

ray di�raction experiments (from the fully ordered

to the fully disordered states) were therefore exam-

ined by MoÈ ssbauer spectroscopy at room tempera-

ture.

Figure 6 shows typical MoÈ ssbauer spectra of

ordered B2 Fe60Al40 and evolution with milling

time. The central peak due to the paramagnetic en-

vironment (H � 0) is progressively replaced by a

broadened sextet. It is interesting to note that pre-

viously reported MoÈ ssbauer studies of ball milled

Fe60Al40 powders with initially macroscopic grain

size present di�erent aspects including a continued

presence of a strong central part in the resonance

spectrum [8]. Using the NORMOS ®tting routine

[12], the corresponding HF distribution has been

derived and a typical example is given in Fig. 7.

The HF distribution is seen to spread around two

maxima, 13 and 22 T, and indicates that the

MoÈ ssbauer resonance from ferromagnetic sites is

best resolved by deconvolution into two main con-

tributions due to two di�erent local ferromagnetic

environments as suggested by the light lines in Fig.

6. Figure 8 shows the evolution of the fraction of

Fe atoms on each type of site derived from the

MoÈ ssbauer spectra vs milling time. It would be

expected that the stronger ferromagnetic contri-

bution (ferro 1) be due to Fe atoms in disordered

environments in the grain volumes and the weaker

ferromagnetic contribution (ferro 2) with HF

around 13 T to Fe atoms in the grain boundaries

or intercrystalline regions and this will be demon-

strated in the next section.

Fig. 3. Lattice parameter a0 of Fe60Al40 showing discon-tinuous increase from the value of the ordered B2 to that

of the disordered b.c.c. lattice.

Fig. 4. Grain size D derived from Bragg peak pro®les ofFe60Al40 B2 and b.c.c. solid solution vs milling time.

Fig. 5. Typical bright ®eld transmission electron micro-scope (TEM) image of fully disordered Fe60Al40 powdershowing broad crystallite size distribution between 5 and

16 nm and centered around 10±12 nm.

NEGRI et al.: DEFORMATION INDUCED TRANSFORMATIONS4548

4. DISCUSSION

When ordered B2 Fe60Al40 is subjected to heavydeformation, analysis of the di�raction data indi-

cates the occurrence of three types of structural

changes: nanocrystallization, loss of LRO

(B2�)b:c:c:) and destruction of CSRO [Al±Fenearest neighbors (nn) Nnn(Al±Fe) in the b.c.c.

solid solution]. Comparison of Figs 3 and 4 indi-

cates that grain re®nement and the B2�)b:c:c:transformation occur over the same time scale and

are completed after milling time t � 90 min.However, the lattice parameter a0 of the nanocrys-

talline b.c.c. solid solution continues to slowly

increase further and at least up to t � 180 min. The

determination of the grain size D from the funda-

mental peak (110 for example) broadening (Fig. 4)

depends sensitively on the successful deconvolution

of B2 and b.c.c. Bragg peak intensities as nanocrys-

tallization and disordering are occurring simul-

taneously. Without this deconvolution, the peaks

appear broader.

The resolution of the Bragg peaks for the disor-

dered phase in the time/deformation range before

the disappearance of the B2 phase also allows a

Fig. 6. Typical MoÈ ssbauer spectra of ordered B2 Fe60Al40 and evolution with milling time t.

NEGRI et al.: DEFORMATION INDUCED TRANSFORMATIONS 4549

new estimate of the evolution of the ordered volumefraction Vordered/V with milling time t. While con-ventionally the ordered fraction is estimated fromthe superstructure Bragg peak intensities such as

IB2-100:

V�t�ordered=V � fI�t�B2-100=�I�t�b:c:c:-110� I�t�B2-110�g=fI�t0�B2-100=I�t0�B2-110g:

�1�Here it is also possible to obtain the ordered frac-tion from the fundamental Bragg peak intensities ofthe B2 phase using

V�t�ordered=V � I�t�B2-110=fI�t�b:c:c:-110 � I�t�B2-110g �2�where B2-110 and b.c.c.-110 intensities are obtained

from deconvolutions such as that of Fig. 2. Figure9 compares the two estimates which are in near

agreement but also show the limits of their pre-cision. Also shown on this ®gure is the evolution of

the fraction of Fe atoms on paramagnetic (ordered)sites derived from the central MoÈ ssbauer resonance

peak reproduced from Fig. 8. MoÈ ssbauer spec-troscopy is seen to be more precise than X-rays for

determination of the remaining ordered fraction.In Fig. 3, precise measurement of fundamental

Bragg peak shifts with milling time has allowed forthe ®rst time, the determination of the b.c.c. phase

lattice parameter a0 from the start and before fulldisappearance of the B2 phase. The initial lattice

parameter values of the b.c.c. solid solution hadpreviously been masked by the convolution of the

Bragg peaks with intensities from remaining B2grains. The evolution of a0 of the b.c.c. solid sol-

ution with milling time (Fig. 3) shows two charac-teristics. First we see a jump to higher values from

the initial a0 of the B2 superstructure, the change isof the order of 1% corresponding to a volume peratom DVexpansion of about 3%. Subsequently, a0continues to increase slowly with further milling atconstant grain size D012 nm and in the absence of

any B2 phase. This continued change of a0 withfurther milling up to at least 180 min is attributable

to reduction of CSRO or the number of Al±Fe het-eroatomic ``bonds'' Nnn(Fe±Al). The atomic

volumes of f.c.c. Al and b.c.c. Fe at room tempera-ture as derived from pure component lattice par-

ameter a0 values are VAl016:6 A3 andVFe011:78 A3 and for the Fe60Al40 alloy, Vegard's

law gives the value of VVegard�Fe60Al40�013:71 A3.The measured lattice parameter a002:896 A of

ordered B2 Fe60Al40 corresponds to a volume peratom VB2012:15 A3 as compared to the Vegard

law value and indicates a negative volume of mixingDVmix=VVegard011:36%. Like the formationenthalpy DHmixing or the heat of mixing, in the

regular solution model [20], the volume of mixingDVmix can be attributed to ®rst nearest neighbor in-

Fig. 7. Typical hyper®ne ®eld (HF) distribution derivedfrom the as-measured MoÈ ssbauer resonance sextets of Fig.6. The HF distribution is seen to spread around two max-ima, 13 and 22 T. Deconvolution of the MoÈ ssbauer spec-tra due to these two local ferromagnetic environments is

indicted by light lines (Fig. 6).

Fig. 8. Evolution of the fraction of Fe atoms on sites cor-responding to HF distributions around 22 T (ferro 1) and13 T (ferro 2), the latter scaling with the grain size (see

Fig. 10).

Fig. 9. Evolution of the ordered volume fraction Vordered/V with milling time derived from the intensity ratiosI�t�B2-100=fI�t�b:c:c:-110 � I�t�B2-110g=fI�t0�B2-100=fI�t0�B2-110gand I�t�B2-110=fI�t�b:c:c:-110 � I�t�B2-110g and from MoÈ ssbauer

spectrometry (see text).

NEGRI et al.: DEFORMATION INDUCED TRANSFORMATIONS4550

teractions as a ®rst approximation. Since the num-

ber of nearest neighbors in b.c.c. or B2 structures isZ � 8, the number of Al±Fe nearest neighborsNnn(Al±Fe) around the minority Al atoms in

Fe60Al40 goes down from 8 in the fully orderedstate to �1ÿ X �Z � 4:8 in the fully disordered state.If we assume that DVmix/VVegard is proportional to

Nnn(Al±Fe), then going from Nnn�Al±Fe� � 8 in theB2 state to Nnn�Al±Fe� � 4:8 in the disordered b.c.c.

state should lead to an expansionDVexpansion0�DVmix=VVegard��8ÿ 4:8�=804:5% ascompared to the observed DVexpansion03% which

strongly suggests that the b.c.c. phase still containsstrong CSRO or associations and that it is not afully random solid solution. Furthermore, while the

®rst nn approximation is good for close-packedstructures [20], it is expected to be poor for b.c.c.

lattices where strong second nn interactions areexpected. The second nn atoms around Al atomsare again on the Al sublattice of the ordered B2

state and their occupancy is only 20% Fe but thisFe second nn fraction goes up to 60% in the disor-dered random b.c.c. solid solution thus contributing

to Al±Fe attractive interactions and to the negativevolume of mixing. It is therefore reasonable to ob-

serve only 3% volume expansion during theB2�)b:c:c: transformation instead of the expected4.5% for the nn approximation. The slow part of

the expansion (increase in a0) observed after the dis-appearance of the B2 phase is attributable tofurther destruction of CSRO [Nnn(Al±Fe)] in the

solid solution.Comparison of the di�raction results with the

analysis of disordering using the evolution of theMoÈ ssbauer resonance signal during deformation isvery useful as the latter probes directly the local en-

vironment of the Fe atoms. The coupling betweenthe atomic chemical and topological order in

Fe60Al40 during simultaneous disordering and nano-crystallization is such that the chemically ordered(B2) regions will be paramagnetic and the disor-

dered regions will be ferromagnetic. Atoms in disor-dered regions within grains and in the grainboundaries will couple ferromagnetically but in the

latter cases the local ®elds are expected to be di�er-ent (and lower [22]) due to di�erences in topological

order. The appearance of two well-de®ned maxima(near 13 and 22 T) in the HF distributions derivedfrom the MoÈ ssbauer spectra of Fig. 6 as exempli®ed

in Fig. 7 justi®es the deconvolution of theMoÈ ssbauer sextet signal into two components corre-sponding to the two observed HF distributions. The

areal contributions of these two components to thetotal resonance from Fe atoms in ferromagnetically

coupled (disordered) sites (along with the centralparamagnetic signal from Fe atoms in B2 regions)are presented in Fig. 8 as ferro 1 and ferro 2. Of

course, the state of local order as de®ned byNnn(Al±Fe) and Nnn(Fe±Fe) also has a distributionin each type of region, but ¯uctuates around aver-

age values that are di�erent. Thus, while some Fe

atoms in regions with predominantly B2 order maycontribute to the HF interactions ferromagnetically,some in disordered regions and grain boundarieswill contribute paramagnetically [21] but while

recognizing this distribution of local con®gurationsand the three types of regions, the three com-ponents of the area representing the resonance sig-

nal can still be considered proportional to Fe atomson the three types of geographical sites: B2, b.c.c.and grain boundary or intercrystalline local en-

vironments. The stronger ferromagnetic contri-butions would be due to Fe atoms in disorderedenvironments in the grain volumes and the weaker

ferromagnetic contribution to Fe atoms in the grainboundaries. If this attribution is correct, the evol-ution of ferro 2 MoÈ ssbauer signal intensity of Fig. 8

should scale with the grain size D. Con®rmationcomes from Fig. 10 which plots these data together.As with the X-ray determined b.c.c. grain size re-

duction with milling time (Fig. 4), the areal fractionof the weaker MoÈ ssbauer sextet ceases to evolve(increase) with milling time after 90 min milling.

With further milling, while b.c.c. grain (coherentdomain) size remains constant, the stronger sextetsignal continues to increase slowly as does the X-

ray determined b.c.c. lattice parameter (Fig. 3) indi-cating a slow increase in Nnn(Fe±Fe) with continueddestruction of CSRO in the b.c.c. solid solution.Identi®cation, using MoÈ ssbauer spectroscopy, of

increase in grain boundary atoms during nanocrys-tallization and disordering of Fe60Al40 has not beenpreviously reported and has been rendered possible

by the new X-ray di�raction analysis [10] (for adetailed review of MoÈ ssbauer studies on B2 andmetastable b.c.c. states of Fe60Al40 see Ref. [8]).

Fultz et al. [23] determined the grain boundaryatom contributions to MoÈ ssbauer spectra in variousnanocrystalline Fe-based alloys with b.c.c. unit cells

and determined the grain boundary thickness to beslightly larger than 1 nm. Using this thickness, wecan estimate the expected fraction of Fe atoms in

Fig. 10. Evolution with milling time, of the fraction of Featoms with HF distribution around 13 T (ferro 2 of Fig.

8) and the grain size Db.c.c. of Fig. 4.

NEGRI et al.: DEFORMATION INDUCED TRANSFORMATIONS 4551

the grain boundaries in our Fe60Al40 alloy as afunction of milling time. For grain size less than

12 nm, the contribution of triple boundariesbecomes signi®cant and must be taken into con-sideration [24] but for the present powders they are

not expected to represent a signi®cant volume frac-tion. Consider grain boundaries of thicknessdgb11:25 nm between grains of diameter D. Since

in the early stages of milling we have a non-zeroordered (B2) volume fraction Vord/V (Fig. 9) withmean grain size DB2 (Fig. 4) together with a b.c.c.

(disordered) volume fraction (1ÿ Vord=V) withgrain size Db.c.c. (Fig. 4), we will use a volume-aver-age grain size D � �Vord=V �DB2 � �1ÿ Vord=V �Db:c:c:.Assuming spherical grains with total radius r � D=2including a super®cial grain boundary thicknessdgb=210:62 nm, the fraction of grain boundaryatoms ngb/ntotal can be approximated using

ngb=ntotal1f1ÿ ��Dÿ dgb�=D�3g: �3�Figure 11 shows a plot of equation (3) using the

values of the mean grain size vs milling time. Alsoshown is the time dependence of the ferro 2 (seeFig. 8) contribution of the grain boundary Fe

atoms to the total MoÈ ssbauer resonance signal. Theagreement is seen to be good. While in the earlystages of milling, the atomic fraction of grain

boundary atoms estimated from X-ray grain sizedi�ers from the estimate from the MoÈ ssbauer spec-tra [due to the limits of precision of the X-raydeconvolution of the B2 and the b.c.c. 110 Bragg

intensities and the above assumptions about themean grain size used in equation (3)], the ®nalvalues from X-ray data after disappearance of the

B2 Bragg peaks superimpose nicely those from theMoÈ ssbauer data.The close agreement of the two sets of ®nal

values for the fraction of grain boundary atoms issigni®cant for several reasons. Firstly, it is a con®r-mation of the deconvolution of the MoÈ ssbauer sig-

nal into contributions from Fe atoms in the grain

boundaries and in the bulk of the b.c.c. nanograins.

Secondly, since equation (3) assumes the sameatomic number density in the bulk and the nano-grain boundaries, the agreement of results presented

in Fig. 11 con®rms that the grain boundaries in ma-terials nanocrystallized by heavy deformation arenearly as dense as the bulk as compared to atomic

densities in grain boundaries of compacts of nano-materials prepared by inert gas condensation which

are reputed to be gas-like.Further information about this point can be

obtained by considering the magnetic properties as

a function of the number of Fe±Fe nearest neigh-bors Nnn(Fe±Fe). For Fe60Al40, as stated earlier,there are Nnn�Fe±Fe� � �1ÿ XAl sites

Al �Z � 1:6 around

an Fe atom in the ordered state and 4.8 in the dis-ordered state, the former environment being para-

magnetic and the latter ferromagnetic at roomtemperature. However, we also know that inFe50Al50, the disordered state with Nnn�Fe±Fe� ��1ÿ XAl sites

Al �Z � �1ÿ 0:5�Z � 4 is still paramagneticat room temperature. The room temperature tran-sition from para- to ferromagnetic environment

therefore occurs in the range 4 < Nnn�Fe±Fe� < 4:8.The fact that the HF of grain boundary Fe atoms

is distributed around 13 T indicates that in thenanograin boundaries, Nnn(Fe±Fe) is between 4 and4.8. A linear extrapolation from room temperature

HF � 23 T for Nnn�Fe±Fe� � 4:8 corresponding tobulk Fe atoms to H � 0 for Nnn�Fe±Fe� � 4 yieldsNnn�Fe±Fe�14:4 for HF113 in the grain bound-

aries. Of course, these room temperature extrapol-ations are highly approximate (Curie point beingnear room temperature for some local environ-

ments) but are a useful demonstration that theatomic number density in the nanograin boundaries

can be only about 10% less than that of the bulk inour samples and con®rms the conclusions concern-ing grain boundary atom densities drawn from the

data of Fig. 11.Finally, we need to understand the reason why in

spite of several previous investigations, our X-ray

di�raction data are the ®rst to clearly allow decon-volution of the B2 and b.c.c. fundamental Bragg

peak intensities during deformation induced disor-dering of Fe60Al40.Figure 2 shows that while the 110 intensity from

disordered b.c.c. crystallites is developing on thelow angle tail side, the position of the initial B2

ordered 110 peak hardly changes as it diminishes inintensity. This would suggest that while someregions are becoming fully disordered, others are

intact in their B2 order.One possible reason for this may come from our

use of initially nanocrystalline (D125 nm) B2 pow-

ders as opposed to bulk grains, together with theuse of a vibrating mill with a single 6 cm diameter

ball. Indeed the powder volume subjected to heavydeformation upon each impact of our ball is esti-mated to have linear dimensions less than 100 mm

Fig. 11. Fraction of grain boundary atoms ngb/ntotal esti-mated from the average grain size D and a grain boundarythickness dgb11:25 nm [23] as compared to the fraction ofFe atoms with HF distribution around 13 T vs milling

time.

NEGRI et al.: DEFORMATION INDUCED TRANSFORMATIONS4552

such that entire nanograins are deformed on eachimpact whereas impact on bulk grains would only

result in deformation in local shear bands in partsof the grain. Coherency between ordered and disor-dered regions in such bulk B2 grains containing

anti-phase domain boundaries would be expected tolead to intermediate lattice parameter values andbroadened but not split Bragg peaks.

Another mechanism that may lead to near fulldisordering of some nanograins (or powder par-ticles) before the process occurs in others, may be

provided by the change with disordering, of themechanical properties of the powder. It is wellknown that fully ordered intermatallics are gener-ally much more brittle than their chemically disor-

dered states [25] and although disordering anddeformation are known to lead to mechanical hard-ening, they also result in ductilization. It is also well

known that during attrition/milling, powdersundergo multiple fracture events during impacts.We suggest that the fully ordered regions being

more brittle, may more often undergo brittle frac-ture as compared to partially disordered regionsthat will undergo more plastic deformation and

ductile fracture. This, we suggest, may render themeven more disordered accordingly.

5. CONCLUSIONS

When ordered B2 Fe60Al40 is subjected to heavy

deformation, analysis of the di�raction data indi-cates the occurrence of three types of structuralchanges: nanocrystallization, loss of LRO

(B2�)b:c:c:) and destruction of CSRO (Al±Fe nnin the b.c.c. solid solution). Grain re®nement andthe B2�)b:c:c: transformation occur over the sametime scale and are completed after milling time

t � 90 min. However, the lattice parameter a0 of thenanocrystalline b.c.c. solid solution continues toslowly increase further and at least up to

t � 180 min.Precise measurement of fundamental Bragg peak

shifts with milling time has allowed for the ®rst

time, the deconvolution of the 110 fundamentalBragg peak intensities of the b.c.c. disorderedregions and of the ordered B2 regions from thestart and before full disappearance of the B2 phase.

While previously the ordered fraction was esti-mated from the low resolution superstructure Braggpeak intensities such as IB2-100, this deconvolution

has allowed an independent estimation of theordered fraction from the fundamental Bragg peakintensities of the b.c.c. and B2 phases.

The evolution of the lattice parameter a0 of theb.c.c. solid solution with milling time shows twocharacteristics. First a jump to higher values from

the initial a0 of the B2 phase, with a change Da0which is of the order of 1% corresponding to avolume per atom DVexpansion of about 3%.Subsequently a0 continues to increase slowly with

further milling at constant grain size D and in theabsence of any B2 phase. This continued change of

a0 with further milling up to at least 180 min is at-tributable to reduction of CSRO or the number ofAl±Fe heteroatomic ``bonds''.

The appearance of two well-de®ned maxima(near 13 and 22 T) in the HF distributions derivedfrom the MoÈ ssbauer spectra indicated the presence

of two ferromagnetic MoÈ ssbauer signals. The majorcomponent (ferro 1) was attributed to Fe atoms inthe bulk of the b.c.c. disordered grains and the

smaller component (ferro 2) to grain boundary Featoms. The evolution of the second contribution tothe MoÈ ssbauer sextet signal scales with the grainsize D. Using the mean grain size D derived from

X-ray Bragg peak pro®les and TEM observationstogether with the grain boundary thickness dgb of1 nm determined by Fultz et al. [23] for b.c.c. Fe-

based alloys, the fraction of grain boundary atomsngb/ntotal was estimated and found to match thefraction of Fe atoms contributing to the minor

component of the broad MoÈ ssbauer sextet signal.This grain boundary atom count using both

methods con®rms that the grain boundaries in ma-

terials, nanocrystallized by heavy deformation, arenearly as dense as the bulk as compared to atomicdensities in grain boundaries of compacts of nano-materials, prepared by inert gas condensation,

which are reputed to be gas-like. Comparison ofbulk and grain boundary HF values also indicatesthat atom number densities in nanograin bound-

aries are only about 10% less than in the bulk ofdisordered b.c.c. Fe60Al40.Finally, it was found that while the 110 Bragg

intensity from disordered b.c.c. crystallites is devel-oping at lower angles, the angular position of theinitial B2 ordered 110 peak hardly changes as itdiminishes in intensity. This would suggest that

while some regions are becoming fully disordered,others are intact in their B2 order. This may bebecause unlike in bulk grains, our grains are much

smaller than the powder volume undergoing heavydeformation on each impact.Also, it may be that the fully ordered B2 regions

being more brittle, they may more often undergobrittle fracture during impact as compared to par-tially disordered regions that will undergo more

plastic deformation and ductile fracture. This mayrender them even more disordered accordingly.

AcknowledgementsÐThe authors are happy to acknowl-edge fruitful discussions with Ge rard Le CaeÈ r, Director ofResearch at the CNRS. Katerina Tousimi (Ph.D. 1999)performed the TEM observations. Daniela Negri (Ph.D.1999) is recipient of a fellowship of the Italian ResearchCouncil for her work in Grenoble.

REFERENCES

1. Yavari, A. R., Ann. Chim. Sci. Mat., 1997, 22, 373.

NEGRI et al.: DEFORMATION INDUCED TRANSFORMATIONS 4553

2. Yavari, A. R., Acta metall. mater., 1993, 41, 1391.3. Navarro, E., Hernando, A. and Yavari, A. R.,

Nanostruct. Mater., 1999, 35, 307.4. Benameur, T. and Yavari, A. R., J. Mater. Res., 1992,

7, 2971.5. Yavari, A. R., Gialanella, S., Benameur, T., Cahn, R.

W. and Bochu, B., J. Mater. Res., 1993, 8, 242.6. Taylor, A. and Jones, R. M., J. Phys. Chem. Solids,

1958, 6, 16.7. SurinÄ ach, S., Amils, X., Gialanella, S., Lutterotti, L.

and Baro , M. D., Mater. Sci. Forum, 1997, 235±238,415.

8. Gialanella, S., Amils, X., Baro , M. D., Delcroix, P.,Le CaeÈ r, G., Lutterotti, L. and SurinÄ ach, S., Actamater., 1998, 46, 3305.

9. Enzo, S., Frattini, R., Gupta, R., Macri, P. P.,Principi, G., Schi�ni, L. and Scipione, G., Actamater., 1996, 44, 3105.

10. Yavari, A. R., Negri, D., Navarro, E., Deriu, A.,Hernando, A. and Botta, W. J., Mater. Sci. Forum,1999, 312±314, 229.

11. Secondi, J., Ph.D. thesis, Metastable andNanocrystalline Materials (Euronano), InstitutNational Polytechnique de Grenoble, 1994.

12. Brand, R. A., Nucl. Instrum. Meth., 1987, B28, 398.

13. Billard, L. and Chamberod, A., Solid St. Commun.,1975, 17, 113.

14. Enzo, S., Mulas, G. and Frattini, R., Mater. Sci.Forum, 1998, 269±272, 385.

15. Scherrer, P., Nachr. Ges. Wiss. GoÈttingen, 1918, 26, 98.16. Williamson, G. K. and Hall, W. H., Acta metall.,

1953, 1, 22.17. De Keijser, Th. H., Langford, J. I., Mittemeijer, E. J.

and Vogels, B. P., J. appl. Crystallogr., 1982, 15, 308.18. Drbohlav, O., Ph.D. thesis, Metastable and

Nanocrystalline Materials (Euronano), InstitutNational Polytechnique de Grenoble, 1995.

19. Gangulee, A., J. appl. Crystallogr., 1974, 7, 434.20. Yavari, A. R., Gialanella, S., Baro , M.-D. and Le

CaeÈ r, G., Phys. Rev. Lett., 1997, 78, 4954.21. Le CaeÈ r, G., Private communication, 1999.22. Le CaeÈ r, G. and Delcroix, P., Nanostruct. Mater.,

1996, 7, 127.23. Fultz, B., Kuwano, H. and Ouyang, H., J. appl. Phys.,

1995, 77, 3458.24. Wang, N., Palumbo, G., Wang, Z., Erb, U. and Aust,

K. T., Scripta metall. mater., 1995, 28, 253.25. Cahn, R. W., in Springer Series in Material Sciences,

Vol. 27, ed. F. E. Fujita. Springer-Verlag, Berlin,1994, pp. 178±225.

NEGRI et al.: DEFORMATION INDUCED TRANSFORMATIONS4554