ekkes brück introduction magnetic cooling giant...
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Magnetocaloric effect
1
materials for magnetic refrigeration
Ekkes Brück
Introduction
Magnetic cooling
Giant magnetocaloric effect
OutlookReview: E. Brück, Magnetic refrigeration near room temperature, Handbook of magnetic materials Vol 17 chapt. 4 (2007) ed. K.H.J. Buschow
Magnetocaloric effect
2
spins lattice
Basic magnetocalorics
E
�Two energy reservoirs
Magnetocaloric effect
3
�
E
Basic magnetocalorics
spins lattice
Magnetocaloric effect
4
Domain movement
Magnetocaloric effect
5
Magnetic cooling: Debye and Giauque 1926
61g Gd2(SO4)3·8H2O, ∆B=0.8T, 1.5K →0.25K Nobel prize 1949
Magnetocaloric effect
6
Zeeman effect for state with total moment J
J
Jz210-1-2
B
• Ground state J is 2J+1 times degenerated: Jz=-J, -J+1, … J• Splits in magnetic field into sublevels• Spectroscopic splitting factor gLandee depends on L, S, and J• Splitting at B=1 Tesla in the order of meV• Atom behaves as if it has effective moment: µeff=-gLµBJ
BH zP ⋅−=⋅−= µBµ)1(2 )1()1(23 +
+−+−= JJ SSLLg Lande zzBLandeP BJgHE µ>==<zBL BgE µ=∆
Magnetocaloric effect
7
When a system, in contact with a heat bath at temperature T can be in a state with energy E, the probability for this is given by the Gibbs rule:
where k is Boltzmann's constant. Z is called the partition sum,
Statistical physics description
Magnetocaloric effect
8
Z is needed to have the proper normalization
The strength of statistical physics is that bycalculating Z a lot of information about the system can be derived.
The Helmholtz free energy is:
while the Gibbs free energy is:
Magnetocaloric effect
9
Thermodynamic relations:
( )pBT
GpBTS
,
,, ∂∂−= , ( )
pTBG
pBTM,
,, ∂∂−= , ( )
BTpG
pBTV,
,, ∂∂−=
Differential of Gibbs free energy
Entropy Magnetization Volume
Differential of entropy
dppS
dBBS
dTTS
dSBTpTpB ,,,
∂∂+
∂∂+
∂∂=
Magnetocaloric effect
10
VdpdBBSdTT
CdS pTpB α−
∂∂+= ,,Identification of terms
Adiabatic process at constant pressure
dBBS
CTdT pTpB ,,
∂∂−=
∫
∂∂=
B
Bm dB
TM
S 0∆Magnetic entropy
Maxwell relations BT TM
BS
∂∂=
∂∂
Magnetocaloric effect
11Easy measurable
From definition of specific heat
S0 can be set to zero because it is not depending on field
Magnetocaloric effect
12
BTT
BTMBTMBTS i ii iiiim ∆−−=∆ ∑
+
++ 111 ),(),(),(
Experimental determination from magnetic measurements
Magnetocaloric effect
13
Continuous phase transition
In the absence of an external field, H=0, the system with exchange interaction J/k=1may spontaneously order.
T=0.3J/k
T=0.25J/k
T=0.2J/k
−= +m)(+m)-m)+((-m)(- NHm+NTNJmF21ln
21
21ln
21
21 2
Magnetocaloric effect
14
First order phase transition
If interactions with quartets play a role this may result in local minima in the free energy.
−= +m)(+m)-m)+((-m)(- NHm+NTNJmF21ln
21
21ln
21
21 4
T=0.0225 J/k
T=0.025 J/k
T=0.02 J/k
Magnetocaloric effect
15
MCE in iron
0T
3T
Cp
[J/m
ol ·
K]
T [°C]
T [K]
∆T [K
]
Magnetic ordering T
10
0
0.8T
3T
6T
Magnetocaloric effect
16
Total entropy vs reduced temperature of gadolinium in low field (blue) and high field 9T (purple) (Gschneidner et al)
MCE in gadolinium
Magnetocaloric effect
17
Magnetic entropy change (green left scale) and
Temperature change (red right scale)
Derived from specific heat data. (Gschneidner et al)
MCE in gadolinium
Magnetocaloric effect
188.316-0.2-0.7-4-12~50aGd2In
8.3164.42.03718.5194Gd2In
8.4146.43.25529265Gd4Sb3
8.8346.43.24926273Gd4(Bi0.75Sb2.25)
9.2596.53.14724289Gd4(Bi1.5Sb1.5)
9.6796.83.74727308Gd4(Bi2.25Sb0.75)
10.0734.22.22715332Gd4Bi3
0-5T0-2T0-5T0-2TCompound
Dens.(g/cm3)
∆Tad(K)
-∆SM(mJ/cm3K)
TC(K)
Ilyn M I, Tishin A M, Gschneidner K A Jr, Pecharsky V K and Pecharsky A O 2001 Cryocoolers 11 ed R G Ross Jr (New York: Kluwer Academic/Plenum) p 457Niu X J, Gschneidner K A Jr, Pecharsky A O and Pecharsky V K 2001 J. Magn. Magn. Mater. 234 193
The magnetocaloric properties of selected binary intermetallic compounds
aTemperature at which ∆SM has the largest positive value and ∆Tad has largest negative MCE value
Magnetocaloric effect
199.692-1.8c-0.4-131c-686.7dTmCu
9.6923.6c0.6118c25~10bTmCu
10.169-0.9c-0.4-55c-26~ 7aTmAg
10.1694.2c0.874c11~12bTmAg
8.7078.53.05722323Gd7Pd3
7.7974.01.94625325Nd2Fe17
0-5T0-2T0-5T0-2TComp.
Density
(g/cm3)
∆Tad(K)
-∆SM(mJ/cm3K)
TC(K)
Dan’kov S Yu, Ivtchenko V V, Tishin A M, Gschneidner K A Jr and Pecharsky V K 2000 Adv. Cryog. Engin. 46 397Canepa F, Napoletano M and Cirafici S 2002 Intermetallics 10 731 Rawat R and Das I 2001 J. Phys.: Condens. Matter 13 L379
The magnetocaloric properties of selected binary intermetallic compounds
aTemperature at which ∆SM has the largest positive value and ∆Tad has largest negative MCE valuebMaximum in MCE (no magnetic ordering observed at this temperature) cInterpolated dNéel temperature
Magnetocaloric effect
20
The magnetocaloric properties of selected ternary intermetallic compounds.
7.961------17110010HoCoAl
9.3588.63.21424217GdPd2Si
7.619------1257037DyCoAl
7.649------804170TbCoAl
7.575------7937100GdCoAl
0-5T0-2T0-5T0-2TCompound
Dens.(g/cm3)
∆Tad(K)
-∆SM(mJ/cm3K)
TCa
Zhang X X, Wang F W and Wen G H 2001 J. Phys.: Condens. Matter 13 L747
Magnetocaloric effect
21Temperature, T (K)0 50 100 150 200 250 300
Latti
ce h
eat c
apac
ity, C
L/R
0.0
0.2
0.4
0.6
0.8
1.0
ΘD = 150 K
ΘD = 350 K
ΘD = 250 K
Temperature, T (K)0 50 100 150 200 250 300
Latti
ce h
eat c
apac
ity, C
L/R
0.0
0.2
0.4
0.6
0.8
1.0
ΘD = 150 K
ΘD = 350 K
ΘD = 250 K
dimensionlless lattice heat capacity of three solids with different Debyetemperatures, ΘD, vs. temperature
Magnetocaloric effect
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Rules for magnetocaloric effect
Larger moment ⇒ larger ∆S & ∆T
Lower temperature ⇒ larger ∆S & ∆T
Smag ≈ J
Lower thermal agitation Lower heat capacity
Magnetocaloric effect
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Magnetic refrigeration:
External magnetic field changes entropy of magnetic moments
No CFCs, easy scalable, high efficiency, permanent magnets
Magnetocaloric effect
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Chubu and Toshiba Refrigerator 2003
Gd metal
Rotating magnet
0.76 T
Cooling power
60 W
T span 20 K
Magnetocaloric effect
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Magnetocaloric effect
26(Rowe et al. 2006)∆T 50K2.0 (S)Gd , Gd.74Tb.26Gd.85Er.15reciprocatingUniversity of Victoria (Gao et al. 2006)COPT 252.18 (E)Gd spheres; Gd5(Si,Ge)4pwdr.reciprocatingXian JiaotongUniv. (Vasile et al. 2006)Torque 10 Nm1 (P)Gd platesrotaryNatl Inst. Appl. Sci. / Cooltech (Zimm et al. 2006)4 Hz1.5 (P)Gd, Gd-Er, spheres LaFeSiHparticlesrotaryAstronautics (Clot et al. 2003)COPR 2.20.8 (P)Gd foilreciprocatingLab. ElectricGrenoble (Richard et al. 2004)epoxy bonded pucks2 (S)Gd , Gd.74Tb.26reciprocatingUniversity of Victoria (Bohigas et al. 2000)Olive oil0.3 (P)Gd foilrotaryBarcelona (Zimm et al. 1998)COPT 105 (S)Gd spheresreciprocatingAmes Laboratory/ Astronautics Ref.RemarksMagnetic Field(T)AMRMaterialAMRTypeNameOther AMR prototypes
Magnetocaloric effect
27
1990 FeRh (Nikitin et al.)1997 Gd5Si2Ge2((Percharsky & Gschneidner Jr.)1998 RCo2 (Foldeaki et al. )2000-2002 La(Fe,Si)13 (Zhang et al., Fukamichi et al.) 2001 MnAs1-xSbx (Wada et al.)2002 MnFe(P,As) (Tegus et al.)2003 Co (S1-xSex)2 (Yamada & Goto)
Replace Gd with material with large MCE
Magnetocaloric effect
28
Giant magnetocaloric effect in Gd5Ge2Si2
Magnetically dilute yet higher effect
double transition?
Pecharsky & GschneidnerPRL 78 (1997) 4494
Magnetocaloric effect
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Crystal growthCrystal growth
D=4mm Sphere was cut by spark erosion from as grown rod
Crystal was grown in a mirror furnace by means of traveling solvent floating zone method
Magnetocaloric effect
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� Extraordinary magnetic behavior: first-order character of the paramagnetic-ferromagnetic transition.
Unusual behaviorUnusual behavior
0 50 100 150 200 250 300 350 4000.0
0.5
1.0
1.5
2.0
2.5
3.0
Gd5Si
1.65Ge
2.35 Crystal
Sphere d=4mmB=0.05T Stepwise heating mode
a b c
M (
µ B /f
.u.)
T (K)
0 1 2 3 4 50
10
20
30
40
Gd5Ge
2.35Si
1.65 crystal
Sphere d=4mm at 5K
a b c
M (
µ B/f.
u)
B (T)
0 20 40 60 80 100 120 140 160 180 200 220 240 2600
50
100
150
200
250
300
350
400
450
500
550
600
C (
J/m
ol·K
)
T (K)
Magnetocaloric effect
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� The high temperature paramagnetic monoclinic phase transforms to the low temperature ferromagnetic orthorhombic phase. The low temperature phase has a higher symmetry than the high temperature, which is the opposite of what is normally observed for other polymorphic systems.
Unusual behaviorUnusual behavior
Crystallographic data comes from W Choe PRL v84, n20, p4617, 2000
>Tc: P1121/a, No.14<Tc: Pnma, No.62
bb
Magnetocaloric effect
32
� Volume decreases when cooling through the transition, i.e., the cell volume in the low-temperature ferromagnetic phase is smaller ( ∆v>0.4%) than in the high-temperature paramagnetic one. This is in contrast with the general physical picture of the magnetovolume effects which are transtions from a low-volume low-moment to a high-volume high-moment state.
Unusual behaviorUnusual behavior
Normal:Unusual:
Magnetocaloric effect
33Gd5Si4 based orthorhombic Pnma Ferro magnetQ.L.Liu et al.
� Recent XRD investigation reported that Gd5(SixGe1-x)4alloys form a completely miscible solid-solution crystallized in the Gd5Si4-type Pnma structure below TCregardless of the composition. Ground state is low temperature (Gd5Si4–based) orthorhombic ferromagnet� Temperature of structural phase transition always coincides with Curie temperature TC.
Unusual behaviorUnusual behavior
Magnetocaloric effect
34x > 0.5 0.4 < x < 0.5 x < 0.3
Gd5Si4 type Pnma Gd5Si2Ge2 type P1121/a Gd5Ge4 type Pnma
T=Si, Ge (Gd3+)5(T26-)2(3e-) (Gd3+)5(T2
6-)1.5(T4-)(2e-) (Gd3+)5(T26-) (T2
6-)2 (1e-)
V. K. Pecharsky and K. A. Gschneidner, Jr., J. Alloys Compd. 260, 98-106 (1997)
b a
What is responsible for the unusual behaviors? What is responsible for the unusual behaviors?
Breaking and making bond RKKY or superexchangeBreaking and making bond RKKY or Breaking and making bond RKKY or superexchangesuperexchange
Magnetocaloric effect
35
Magnetically driven 1st order structural transition below 270 K.
Gd5Ge2Si2 monoclinic above magnetic transition
orthorhombic below.
Anisotropy on X-tals. Exceptional coupling of lattice with s-state 4f-magnetism.
Hysteretic transition: locking of structure?Mechanical stability?
Summary Gd5Ge2Si2
Magnetocaloric effect
36
Transition-metal compounds
High abundance (low price)
Intermediate magnetic moment (moderate MC effect)
Strong coupling to lattice (Simultaneous magnetic and structural transitions or metamagnetism)
other alternative
Magnetocaloric effect
37
La(Fe,Si)13 compound
Cubic CaZn13 type of structure stabilized by addition of 10% Si(Kripyakewich et al. 1968)Invar type of behavior and unusual magnetic transition(Palstra et al 1983)Difficult to obtain single phase.
Magnetocaloric effect
38
Concentration dependence of Curie temperature and moment
Palstra et al. 1983
Tc increase with dilution
Magnetocaloric effect
39
LaFe13 system
APL Zhang et al 2000
Fujieda et al 2002
MCE decrease with dilution
Magnetocaloric effect
40PRB Fujita et al 2003
Tc increase with hydrogen!
Sharp transition maintained!
LaFe13 system with hydrogen
Magnetocaloric effect
41PRB Fujita et al 2003
LaFe13 system with hydrogen
MCE almost not affected with hydrogen
Magnetocaloric effect
42
Field driven 1st order metamagnetic transition around 200 K .
La(Fe,Si)13 cubic above magnetic transition
cubic below
volume change 1.5%.
Low Tc can be increased by addition of Cobalt or Hydrogen.
Hysteretic transition: powder after hydrogenation?Mechanical stability?
Summary La(Fe,Si)13
Magnetocaloric effect
43
MnFeP1-xAsx
Hexagonal Fe2P type of structure
Bacmann, JMMM 1994
Space group:
P62m
Mn 3g sites
Fe 3f sites
P/As 1b&2c sites
_
Magnetocaloric effect
44
Sample preparation
Starting Fe2P, Mn2As3, Mn & P
mechanical alloying
sintering 1000oC
annealing 800oC
Magnetocaloric effect
45
Temperature dependence of magnetizationwith different compositions
Tc tunable
Magnetocaloric effect
46
Temperature dependence in different fields
Strong shift of T cwith field
Magnetocaloric effect
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Magnetization process near Tc
Field induced transition with small hysteresis
Magnetocaloric effect
480.2 0.3 0.4 0.5 0.6 0.7
160
180
200
220
240
260
280
300
320
340
PM
FM
T (
K)
X
Concentration dependence of TC for MnFeP1-xAsx
Somewhat higher TC compared with lit.
Almost linear concentration dependence.
Magnetocaloric effect
49
Comparison with Gd metal
Step-liketransition
first order
but very littlehysteresis
Magnetocaloric effect
50
Comparison of magnetocaloric effect in different ma terials
Entropy changeconcentrated inrelevant T interval Tegus et al. Nature 415
Magnetocaloric effect
51150 200 250 300 3500
5
10
15
20
25
30
35
2 T 5 T
x=0.35
x=0.5
x=0.25
x=0.65x=0.55
x=0.45
MnFeP 1-xAs x
- ∆∆ ∆∆S
m(J
/kgK
)
T (K)
MCE as function of composition
Broad T interval covered
Magnetocaloric effect
52285 290 295 300 305 310 3150
1
2
3
4
5∆∆∆∆B = 1.45 T
MnFeP0.45
As0.55MnFeP
0.47As
0.53
Mn1.1
Fe0.9
P0.47
As0.53
∆∆ ∆∆Tad
(K
)
T (K)
Direct measurements MSU
Adiabatic temperature-change
Sample dependence need for careful preparation
Magnetocaloric effect
53
Field driven 1st order magnetoelastic transition 150 K < Tc < 450 K .
MnFe(P,As) hexagonal above magnetic transition
hexagonal below.
Hardly any volume change( 0.1 %) but change of c/a.
Hysteretic transition: Hysteresis depends on grain size?High chemical stability allows As content?
Summary MnFe(P,As)
Magnetocaloric effect
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Conclusions
• First order magnetic transition common to the different systems!
• Structural transition may cause extra hysteresis.
• Control of hysteresis very important.
• Evaluation of entropy change needs care.
• Fe and Mn based systems with much lower materials costs.
• Relevant T range covered by La(Fe,Si)13Hx and MnFe(P,As,Si,Ge).
• Sample preparation simplest for MnFe(P,As) with As replaced by other element.
Magnetocaloric effect
55
Cooltech current N°4 PrototypeIMPORTANT issues:1 – The AMRR Cycle (Active Magnetic Regenerator Refrigeration): with Gd inserts as cross-flow plate heat-exchangers.2 - Amplification of ∆Τ∆Τ∆Τ∆Τ by accumulation of cycles.3 - Reduction in torque (10 Nm) obtained by ensuring a ferromagnetic continuity on the disc.4 - Very low level of noise and vibrations (< 25 dB)5 - Creation of magnetic fields of 0.7 to 2 Tesla with standard permanent magnets.6 - Low thermal losses, completely separate “hot” and “cold” fluid circuits.
Registered Patents, Brand and Models
Outlook
Magnetocaloric effect
56
Availability
60t?WW prod=90t, avail
10t ?GaNi0.501Mn0.227Ga0.258
4000
4000
none
WW prod=90t, avail 10t ?
1000
Estimated availability
7000tLaManganites
LaMnO3
22000tLaLathanum alloys
La(Fe13-xMx)
No limitation for an industrial production
none
Manganese alloys Mn(As1-xSbx)
MnFe(P1-xAsx)
140tGeGadolinium Silicon alloys Gd4(Si1-xGex)5
1000tGdGd metal
Total availability of MC material
Limiting ingredient
Data : Cooltech source and USGS.GOV
Magnetocaloric effect
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2520151050 0 20 40 60 80T (C0)
∆S (
J/K
·kg)
Increased T span with active magnetic regenerator containing different materials with tailored TC