materials for magnetic refrigeration Ekkes Brck Introduction - - PowerPoint PPT Presentation

Magnetocaloric effect

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materials for magnetic refrigeration

Ekkes Brück Introduction Magnetic cooling Giant magnetocaloric effect Outlook

Review: E. Brück, Magnetic refrigeration near room temperature, Handbook

• f magnetic materials Vol 17 chapt. 4 (2007) ed. K.H.J. Buschow

Magnetocaloric effect

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spins lattice

Basic magnetocalorics

E

• Two energy reservoirs

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• E

Basic magnetocalorics

spins lattice

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Domain movement

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Magnetic cooling: Debye and Giauque 1926 61g Gd2(SO4)3·8H2O, ∆B=0.8T, 1.5K →0.25K Nobel prize 1949

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Zeeman effect for state with total moment J J Jz 2 1

• 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

B H

z P

⋅ − = ⋅ − = µ B µ ) 1 ( 2 ) 1 ( ) 1 ( 2 3 + + − + − = J J S S L L g Lande

z z B Lande P

B J g H E µ >= =<

z B L

B g E µ = ∆

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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

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Z is needed to have the proper normalization The strength of statistical physics is that by calculating Z a lot of information about the system can be derived. The Helmholtz free energy is: while the Gibbs free energy is:

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Thermodynamic relations:

( )

p B

T G p B T S

,

, ,       ∂ ∂ − = ,

( )

p T

B G p B T M

,

, ,       ∂ ∂ − = , (

)

B T

p G p B T V

,

, ,         ∂ ∂ − =

Differential of Gibbs free energy Entropy Magnetization Volume Differential of entropy

dp p S dB B S dT T S dS

B T p T p B , , ,

        ∂ ∂ +       ∂ ∂ +       ∂ ∂ =

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Vdp dB B S dT T C dS

p T p B

α −       ∂ ∂ + =

, ,

Identification of terms Adiabatic process at constant pressure

dB B S C T dT

p T p B , ,

      ∂ ∂ − =

∫

      ∂ ∂ =

B B m

dB T M S ∆

Magnetic entropy Maxwell relations

B T

T M B S       ∂ ∂ =       ∂ ∂

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Easy measurable From definition of specific heat S0 can be set to zero because it is not depending on field

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B T T B T M B T M B T S

i i i i i i i m

∆ − − = ∆

∑

+ + + 1 1 1

) , ( ) , ( ) , (

Experimental determination from magnetic measurements

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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+NT

NJm F 2 1 ln 2 1 2 1 ln 2 1 2 1

2

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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+NT

NJm F 2 1 ln 2 1 2 1 ln 2 1 2 1

4

T=0.0225 J/k T=0.025 J/k T=0.02 J/k

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MCE in iron 0T 3T

Cp [J/mol ·K] T [° C] T [K] ∆T [K]

Magnetic ordering T 10 0.8T 3T 6T

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Total entropy vs reduced temperature of gadolinium in low field (blue) and high field 9T (purple) (Gschneidner et al) MCE in gadolinium

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Magnetic entropy change (green left scale) and Temperature change (red right scale) Derived from specific heat

• data. (Gschneidner et al)

MCE in gadolinium

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8.316

• 0.2
• 0.7
• 4
• 12

~50a Gd2In 8.316 4.4 2.0 37 18.5 194 Gd2In 8.414 6.4 3.2 55 29 265 Gd4Sb3 8.834 6.4 3.2 49 26 273 Gd4(Bi0.75Sb2.25) 9.259 6.5 3.1 47 24 289 Gd4(Bi1.5Sb1.5) 9.679 6.8 3.7 47 27 308 Gd4(Bi2.25Sb0.75) 10.073 4.2 2.2 27 15 332 Gd4Bi3 0-5T 0-2T 0-5T 0-2T Compound 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 457 Niu 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

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9.692

• 1.8c
• 0.4
• 131c
• 68

6.7d TmCu 9.692 3.6c 0.6 118c 25 ~10b TmCu 10.169

• 0.9c
• 0.4
• 55c
• 26

~ 7a TmAg 10.169 4.2c 0.8 74c 11 ~12b TmAg 8.707 8.5 3.0 57 22 323 Gd7Pd3 7.797 4.0 1.9 46 25 325 Nd2Fe17 0-5T 0-2T 0-5T 0-2T Comp. 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. 46 397 Canepa 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 value bMaximum in MCE (no magnetic ordering observed at this temperature) cInterpolated dNéel temperature

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The magnetocaloric properties of selected ternary intermetallic compounds.

7.961

• 171

100 10 HoCoAl 9.358 8.6 3.2 142 42 17 GdPd2Si 7.619

• 125

70 37 DyCoAl 7.649

• 80

41 70 TbCoAl 7.575

• 79

37 100 GdCoAl 0-5T 0-2T 0-5T 0-2T Compound Dens. (g/cm3) ∆Tad (K)

• ∆SM

(mJ/cm3K) TC

a

Zhang X X, Wang F W and Wen G H 2001 J. Phys.: Condens. Matter 13 L747

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Temperature, T (K)

50 100 150 200 250 300

Lattice heat capacity, CL/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)

50 100 150 200 250 300

Lattice heat capacity, CL/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 Debye temperatures, ΘD, vs. temperature

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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

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Magnetic refrigeration: External magnetic field changes entropy of magnetic moments No CFCs, easy scalable, high efficiency, permanent magnets

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Chubu and Toshiba Refrigerator 2003

Gd metal Rotating magnet 0.76 T Cooling power 60 W T span 20 K

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Magnetocaloric effect

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∆T 50K 2.0 (S) Gd , Gd.74Tb.26

Gd.85Er.15

reciprocatin g University of Victoria (Gao et al. 2006) COPT 25 2.18 (E) Gd spheres; Gd5(Si,Ge)4 pwdr. reciprocatin g

Xian Jiaotong Univ.

(Vasile et al. 2006) Torque 10 Nm 1 (P) Gd plates rotary

Natl Inst.

• Appl. Sci. /

Cooltech (Zimm et

• al. 2006)

4 Hz 1.5 (P) Gd, Gd-Er, spheres LaFeSiH particles rotary Astronautics

(Clot et al. 2003)

COPR 2.2 0.8 (P) Gd foil reciprocatin g

• Lab. Electric

Grenoble

(Richard et

• al. 2004)

epoxy bonded pucks 2 (S) Gd , Gd.74Tb.26 reciprocatin g University of Victoria

(Bohigas et

• al. 2000)

Olive oil 0.3 (P) Gd foil rotary Barcelona

(Zimm et

• al. 1998)

COPT 10 5 (S) Gd spheres reciprocatin g Ames Laboratory/ Astronautics Ref. Remarks Magnetic Field (T) AMR Material AMR Type Name

Other AMR prototypes

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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

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Giant magnetocaloric effect in Gd5Ge2Si2 Magnetically dilute yet higher effect double transition?

Pecharsky & Gschneidner PRL 78 (1997) 4494

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Crystal growth Crystal 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

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• Extraordinary magnetic behavior: first-order character of the

paramagnetic-ferromagnetic transition.

Unusual behavior Unusual behavior

50 100 150 200 250 300 350 400 0.0 0.5 1.0 1.5 2.0 2.5 3.0

Gd5Si1.65Ge2.35 Crystal Sphere d=4mm B=0.05T Stepwise heating mode

a b c

M (µB /f.u.) T (K)

1 2 3 4 5 10 20 30 40

Gd5Ge2.35Si1.65 crystal Sphere d=4mm at 5K

a b c

M (µB/f.u) B (T)

20 40 60 80 100 120 140 160 180 200 220 240 260 50 100 150 200 250 300 350 400 450 500 550 600

C (J/mol·K) T (K)

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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 behavior Unusual behavior

Crystallographic data comes from W Choe PRL v84, n20, p4617, 2000

>Tc: P1121/a, No.14 <Tc: Pnma, No.62

b b

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• 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 behavior Unusual behavior

Normal: Unusual:

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Gd5Si4 based

• rthorhombic

Pnma Ferro magnet Q.L.Liu et al.

Recent XRD investigation

reported that Gd5(SixGe1-x)4 alloys form a completely miscible solid-solution crystallized in the Gd5Si4-type Pnma structure below TC regardless of the composition. Ground state is low temperature (Gd5Si4–based) orthorhombic ferromagnet

Temperature of structural phase

transition always coincides with Curie temperature TC.

Unusual behavior Unusual behavior

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x > 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(T2

6-)2(3e-) (Gd3+)5(T2 6-)1.5(T4-)(2e-) (Gd3+)5(T2 6-) (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 superexchange Breaking and making bond RKKY or Breaking and making bond RKKY or superexchange superexchange

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Magnetically driven 1st order structural transition below 270 K. Gd5Ge2Si2 monoclinic above magnetic transition

• rthorhombic below.

Anisotropy on X-tals. Exceptional coupling of lattice with s-state 4f-magnetism. Hysteretic transition: locking of structure? Mechanical stability?

Summary Gd5Ge2Si2

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Transition-metal compounds

High abundance (low price) Intermediate magnetic moment (moderate MC effect) Strong coupling to lattice (Simultaneous magnetic and structural transitions or metamagnetism)

• ther alternative

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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.

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Concentration dependence of Curie temperature and moment

Palstra et al. 1983

Tc increase with dilution

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LaFe13 system

APL Zhang et al 2000 Fujieda et al 2002

MCE decrease with dilution

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PRB Fujita et al 2003

Tc increase with hydrogen! Sharp transition maintained! LaFe13 system with hydrogen

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PRB Fujita et al 2003

LaFe13 system with hydrogen MCE almost not affected with hydrogen

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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

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MnFeP1-xAsx Hexagonal Fe2P type of structure Bacmann, JMMM 1994 Space group: P62m Mn 3g sites Fe 3f sites P/As 1b&2c sites _

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Sample preparation

Starting Fe2P, Mn2As3, Mn & P mechanical alloying sintering 1000oC annealing 800oC

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Temperature dependence of magnetization with different compositions Tc tunable

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Temperature dependence in different fields Strong shift of Tc with field

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Magnetization process near Tc Field induced transition with small hysteresis

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0.2 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.

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Comparison with Gd metal Step-like transition first order but very little hysteresis

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Comparison of magnetocaloric effect in different materials Entropy change concentrated in relevant T interval

Tegus et al. Nature 415

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150 200 250 300 350 5 10 15 20 25 30 35

2 T 5 T x=0.35 x=0.5 x=0.25 x=0.65 x=0.55 x=0.45

MnFeP1-xAsx

• ∆

∆ ∆ ∆Sm(J/kgK) T (K)

MCE as function of composition Broad T interval covered

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285 290 295 300 305 310 315 1 2 3 4 5

∆ ∆ ∆ ∆B = 1.45 T MnFeP0.45As0.55 MnFeP0.47As0.53 Mn1.1Fe0.9P0.47As0.53 ∆ ∆ ∆ ∆Tad (K)

T (K)

Direct measurements MSU Adiabatic temperature-change Sample dependence need for careful preparation

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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)

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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
• ther element.

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Cooltech current N°4 Prototype

IMPORTANT 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

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Availability

60t? WW prod=90t, avail 10t ? Ga Ni0.501Mn0.227Ga0.258 4000 4000 none WW prod=90t, avail 10t ? 1000 Estimated availability 7000t La Manganites

LaMnO3

22000t La Lathanum alloys

La(Fe13-xMx)

No limitation for an industrial production none Manganese alloys

Mn(As1-xSbx) MnFe(P1-xAsx)

140t Ge Gadolinium Silicon alloys Gd4(Si1-xGex)5 1000t Gd Gd metal Total availability of MC material Limiting ingredient

Data : Cooltech source and USGS.GOV

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25 20 15 10 5 0 20 40 60 80

T (C0) ∆S (J/K·kg) Increased T span with active magnetic regenerator containing different materials with tailored TC