Magnetocaloric effects in intermetallic compounds

• Introduction

• Experimental results & discussion

• Conclusions

- Magnetic phase transitions- Magnetocaloric effects & Magnetic refrigeration

- Magnetic-refrigerant materials

- 2nd order phase transition & MCE - 1st order phase transition & MCE

0 50 100 150 200 250 300 350 4000

20

40

60

80

100

120

140

160

180

200

M (

Am

2 /kg

)

T (K)

Tc

Introduction Magnetic phase transitions

FM PM

0 50 100 150 200 2500

5

10

15

20

25

PMAFM

M (

Am2 /k

g)

T (K)

TNTN

0 1 2 3 4 50

5

10

15

20

25

FM

PM

M (

Am

2 /kg

)

0H (T)

Magnetic field-induced transition

pT

GS

TP

GV

M

P T B

GM

,

Entropy

Magnetization

Volume

First-order phase transition

PT

GTCp

2

2

Second-order phase transition

TC

T T+ΔT

TT-ΔT

ΔQΔQ

Magneto-caloric effect & Magnetic refrigeration

Absorb heat

Adiabatic

ΔTad

Isothermal ΔSm

N

S N

S

Cooling effect

dpp

SdB

B

SdT

T

SdS

BTpTpB ,,,

B

B

mdB

T

MS

0

dBT

M

C

TT

B

pBpB

ad

0,,

Thermodynamics

T

M

Large

Small CB,p

Large ΔB

Superconducting magnet

Gd

Metal Gd sphere 3 kg

Energy efficiency 20%-60%

Cooling power 200 W-600 W

C.O.P 2-9

ΔT = 4.5 K for 1.5 T ΔT = 11K for 5 T

Magnetic field

Permanent magnetic field

Space: 114 x 128 x 12.7 mm3

Field strength: 2 T

Lee et al. JAP (2002)

Nd2Fe14B magnet

Magnetic refrigerant materials

270 280 290 300 310 320 3300

5

10

15

20

25

30

B: 0--2 T

MnAs

Fe49Rh51

MnFeP0.45As0.55

Gd

La(Fe0.89Si0.11)13H1.3

Gd5Si2Ge2

T (K)

- S

m (

J/k

gK

)

Adiabatic temperature change

270 280 290 300 310 320 3300

2

4

6

8

B: 0--2 T

MnAs

Fe49Rh51

Gd

La(Fe0.89Si0.11)13H1.3

Gd5Si2Ge2

T (K)

Tad (K

)

240 260 280 300 320 340 3601

2

3

4

5

6

7

8

9Gd-S

M (max)

TC

TFWHM-

Sm

(J/k

gK)

T (K)

Ordering T: TC = 295 K

Field change: ΔB = 5 T

FWHM : δTFWHM = 65 K

MAX entropy change: -ΔSm(max) = 8.5 J/kgK

Relative cooling power

RCP(S) = -ΔSm(max)*δTFWHM

=552 J/kg

Cooling power

What are important for MR?

2

1

)(T

Tm dTTSQ

Experimental results & discussion

240 260 280 300 320 340 3600

1

2

3

4

5

6

7

8

9

0-1T 0-2T 0-3T 0-4T 0-5T

Gd

-S

m(J

/kg

K)

T(K)

0 50 100 150 200 250 300 3500

20

40

60

80

100

120

140

160

180

200

FMPM

Tc

M (A

m2 /k

g)

T (K)

Gd

Second order magnetic phase transition & MCE

Sth(max) = RLn(2J+1)=17.3 J/molK; Sth(max) = 110 J/kgK <10%

TC = 298 K

ΔB = 2 T

ΔTad = 1.7 K

Hashimoto et al (1982)

255 270 285 300 315 3300

2

4

6

8

10Mn5Ge3

0-2 T 0-5 T

-S

m(J

/kg

K)

T(K)

0 1 2 3 40

50

100

150

200

250

300

350

400

PM

PM

Phase diagram of Gd5Ge4-xSix

Gd5Ge4 Gd5Si4

PM

AFM

FMFMFM

Monoclinic Orthorhombic

T

(K

)

X

First-order magnetic phase transition & MCE

Pecharsky et al (1997)

Orthorhombic

Orthorhombic

What makes Gd5Ge4-xSix have giant MCE?

0 50 100 150 200 250 300 350 4000

5

10

15

20

25

// a-axis // b-axis // c-axis

Gd5Si1.7Ge2.3

M (

Am

2 /kg)

T (K)

0.05 T

TC=240.4±1 KSingle crystal

Gd5Si1.7Ge2.3

Monoclinic (P1121/a)

a = 7.585 Åb = 14.800 Åc = 7.777 Å β = 93.290

B-T phase diagram

0 1 2 3 4 5 60

10

20

30

40

5 K

240 K

230 K

252.5

K

257.5

K

260 K

B//a-axis

Gd5Si

1.7Ge

2.3M

( B

/f.u

.)

0H(T)

Magnetization

Field-induced magnetic phase transition

PM FM

Field hysteresis1 T

200 220 240 260 280 300 320

0

10

20

30

40

50

// c-axis 1T 2T 3T 4T 5T

T (K)

0

10

20

30

40

50

// a-axis

1T 2T 3T 4T 5T

-S

m (

J/k

gK)

0

10

20

30

40

50

// b-axis

1T 2T 3T 4T 5T

Magnetic entropy changes

TC = 240 K

ΔB = 5 T

ΔS(max) = 30.5J/kgK

δTFWHM = 18K

RCP(S) = 549 J/kgK

Effect of magnetic anisotropy is small

0 50 100 150 200 250 3000

1

2

3

4

5

6

7

8

D = 237 K

= 32.3 mJ/mol.K2

Tc = 239 K

c p/T (J

/mol

K2 )

T (K)

Specific heat capacity

230 235 240 245 250 255330

335

340

345

350

355

360

365

370

S (

J/kg

K)

T (K)

at TC ΔS = 11.0 ± 0.5 J/molK

Latent heat L = 2.63 ± 0.12 kJ/mol

Gd5Si1.7Ge2.3

195 210 225 240 255 2700

250

500

750

1000

1250

1500

1750

T'c = 245.6 K

Tc = 239 K

0 T 2 T

TC/B = 3.3 K/T

Gd5Si

1.7Ge

2.3

c p (J

/mol

.K)

T (K)

ΔTad

= Tc•ΔSm/Cp

> 15 K

Transition at TC = 240.0 ±1.0 KT’C = 236.0 ±1.0 K

Thermal hysteresisΔT = 4 K

ΔLa/La = 6.8x10-3 >0ΔLb/Lb = -2.0x10-3 <0ΔLc/Lc = -2.1x10-3 <0

Relative volume changeΔV/V = 2.7x10-3

Clausius-Clapeyron relation

dTC/dp = 3.2 ± 0.2 K/kbarM. Nazih et al. 2002

Thermal expansion ΔL/L = (L(T)-L(T = 5 K))/L(T = 5 K)

Transition-metal based compound: MnFeP1-xAsx

Crystal structure (0.15 x 0.65)

Fe2P-type; Hexagonal

Space group P-62m

Fe-layer

Mn-layer

Fe-layer

3g 1b/2c 3f

At transition

Δc/c > 0 Δa/a < 0 ΔV/V < 0

There is no crystallographicsymmetry change.

Magnetic moment 4 µB/f.u.

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

Composition dependence of TC

Bacmann et al. JMMM(1994)

X-T phase diagram

FM

PM

T

H

O

AF

X

160-330 K

270 285 300 315 330 345 3600

20

40

60

80

100

120

B = 1 T

MnFeP0.45

As0.55

M (A

m2 /kg

)

T (K)

Magnetization

Field hysteresis 0.5 TThermal hysteresis 3.4 K

0 1 2 3 4 50

20

40

60

80

100

120MnFeP

0.45As

0.55

300 K304 K308 K312 K312 K

M(A

m2 /kg

)

0H(T)

300 304 308 312 316 320 324 3280

1

2

3

4

5

6

MnFeP0.45

As0.55

PM

FM = 3.8 K

B (T

)

T (K)

B – T phase diagram of MnFeP0.45As0.55

Ordering T:

TC = 306 KT’C = 302.2 K

Thermal hysteresis:

3.8 K

ΔTC/ΔB = 4.2 K/T

First order phase transition

240 260 280 300 320 340 360 380 4000

200

400

600

800

1000

1200

1400

cooling

Tp = 296 K

MnFeP0.45As0.55

Zero field

c p (

J/kg

K)

T (K)

Tp= 296 K

Latent heat :

L = 526 J/mol

Cp = 550 J/kgK (T > 300 K)

Specific heat capacity

280 290 300 310 320 330 340

0

2

4

6

8

10

12

14

16

18

20

5 T

2 T

Decreasing field

MnFeP0.45

As0.55

lS

Ml (

J/kg

K)

T (K)

Magnetic entropy changes

TC = 306 K

ΔB = 5 T

-ΔS(max) = 18.3 J/kgK

δT = 21.3 K

RCP(S) = 390 J/kg

ΔTad =Tc•ΔSM/Cp

ΔTad = 10 K (ΔB=5 T)

Isothermal magnetic entropy changes:

150 175 200 225 250 275 300 325 350 375

0

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

MnFeP1-x

Asx

-

Sm(J

/kg

K)

T (K)

Magnetic entropy change in different compositions

MnFeP1-xAsx

Conclusions

1. MCE is closely related to the critical behavior of magnetic phase transition.

Second order transition gives broad MCE peak. MCE is small.First order transition gives sharp MCE peak. MCE can be large.

2. Gd5Si1.7Ge2.3 has a simultaneous structural and magnetic phasetransition at 239 K. This transition is a first order transition with thermal hysteresis 7.4 K and with field hysteresis 1 T.The MCE related with first order phase transition is quite large.Effect of magnetic anisotropy on MCE in this material is negligible.

3. MnFeP1-xAsx (0.25<x<0.65) has a first order phase transitionwith thermal hysteresis 3.4 K and field hysteresis 0.5 T.The MCE related with this transition is also quite large.

4. Advantages of MnFeP1-xAsx as a magnetic refrigerant

1. Large MCE2. Tunable ordering temperature( between 168 and 332 K)3. Small hysteresis 4. Lower cost : MnFe(P,As):

Mn,Fe,P,As(99%, 150$/kg) Gd-Si-Ge Gd: Gd(4N): 4000 $/kg. Fe-Rh: Rh: 12000$/kg

Acknowledgment

This work is supervised by E. Brück, J.H.K. Buschow, F.R. de Boer.

Collaborators: L. Zhang, W. Dagula, X.W. Li

Financially supported by the STW.

Bean-Rodbell model

Gibbs free energy

G = Gex + GH + Gdist + Gentr + Gpress

Volume change is due to the effect of magnetization.

]1[0

00 V

VVTTC

0V

G.2/2

00

0 pKTNKkV

VVB

N: number of atoms/V0

K: compressibilityσ: relative magnetization(J =1/2)

Tc: Curie temperatureT0: Curie temperature (not compressible)V : volumeV0 : volume(absent of exchange interaction)

.2/3

)3/1)(tanh/(/

0

20

210

KTNk

pKTT

G

B

Set P = 0η = 0; σ = 0 TC = T0 η < 1 corresponds to 2nd order phase transitionη > 1 corresponds to 1st order phase transition

For MnFeP0.5As0.5 η = 1.62, J = 2, T0 =250 K

R. Zach et al. JAP (1998)

J=1/2σ

η = 01 2

Bean et al. PR(1962)

Heat capacity in field Adiabatic T change