Magnetocaloric effects in intermetallic compounds Introduction Experimental results & discussion...
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Transcript of Magnetocaloric effects in intermetallic compounds Introduction Experimental results & discussion...
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