determination of the magnetocaloric parameters through ......determination of magnetocaloric...
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R. BurrielInstituto de Ciencia de Materiales de AragonCSIC – University de Zaragoza50009 Zaragoza, Spain
Determination of the magnetocaloric parametersthrough magnetic and thermodynamic methods
in first-order transitions
Delft Days on Magnetocalorics, Delft, Netherlands, 30-31 October, 2008
Collaborators:- E. Palacios- L. Tocado- G. Wang
● Determination of magnetocaloric parameters� Calorimetric methods
� Heat capacity. Practical limitations
� Direct measurements of ∆∆∆∆TS and ∆∆∆∆ST
� Magnetic methods� Magnetization. Maxwell relation
� Isothermal. Isofield. Other thermal and field paths� First-order transitions. Overestimation of ∆∆∆∆ST
� Adiabatic pulsed field� Adiabatic and isothermal magnetization
● Applicability of the Maxwell relation. Hysteretic compounds� Errors with isothermal magnetization curves
� Solutions� Magnetization M(T) at constant field
� Isothermal magnetization of appropriate thermal and field history
Outline
� From heat capacity
∫=T
H dTT
TCTS Hp
0
,)(
)(
( )12
)()( HHS STSTT −=∆
∫−
=−=∆T HpHp
HHT dTT
TCTCTSTSS
0
,, 12
12
)()()()(
● Determination of the magnetocaloric parameters
�Calorimetric methods
• Good at low temperatures• Low precision at room T• Scarce C(T)H data
TC
S (T)B
Ent
rop
y, S
Temperature, T
S (T)B = 0
TC
S(T)B=0
S(T)B
∆TS
∆ST
∆ST
� From direct measurements
∆∆∆∆TS = [T(S)H2- T(S)H1
]
∆∆∆∆ST = ∆Q/T = [S(T)H2- S(T)H1
]
L. Tocado, E. Palacios, R. BurrielJ. Magn. Magn. Mater.290-291, 719 (2005).
2 0 0 4 0 0 6 0 0 8 0 00 ,0
1 ,5
3 ,0
4 ,5
t ( s )
Pow
er (
mW
)
Magne
tic F
ield
(T)
- 2 0
- 1 0
0
1 0
2 0
T (m
K)
T = 1 5 4 .2 7 3 K
0
2
4
6
Sample holder
Adiabatic shield
HpTp T
HTM
H
HTS
,,
),(),(
∂∂=
∂∂
� Magnetic methods
� From magnetizationdata
Using the Maxwell relation
dHT
HTM
HTC
TT
Hp
H
S
,0
),(
),(∫
∂∂×=∆
dHT
HTMS
Hp
H
T,
0
),(∫
∂∂=∆
● Limited to ∆∆∆∆ST
� Calculation of ∆∆∆∆TS requires C(T, H)
● Discontinuities in first derivatives� Computational errors
● Maxwell relations valid for state functions� M(T,H) is not a state function in first-order transitions � It depends on history (hysteresis)
● Easy measurements� Isothermal magnetization� At constant field� Other thermal and field history
● Problems
� Adiabatic pulsed fields
� Comparison of magnetization curves in adiabatic and isothermal processes
R.Z. Levitin, V.V. Snegirev, A.V. Kopylov, A.S. Lagutin, A. GerberJ. Magn. Magn. Mater.170, 223 (1997).
relation Maxwell,,
,
2
,
,
2
,
pBpT
pBpT
pTpB
T
M
B
S
T
M
TB
GM
B
G
B
S
BT
GS
T
G
∂∂=
∂∂
∂∂−=
∂∂∂
⇒−=
∂∂
∂∂−=
∂∂∂
⇒−=
∂∂
VdpMdBSdTdG −−−=
● Applicability of the Maxwell relation. Hysteretic compounds
300 320 340 3600
50
100
150
315 320 325 330
50
100
150
0 - 1 T 0 - 2 T 0 - 3 T 0 - 4 T 0 - 5 T 0 - 6 T 0 - 7 T 0 - 8 T 0 - 9 T
-∆S T
(J/
kg·K
)
T (K)
-∆S T
(J/
kg·K
)
T (K)
MnAs
300 320 340 3600
50
100
150
315 320 325 330
50
100
150
0 - 1 T 0 - 2 T 0 - 3 T 0 - 4 T 0 - 5 T 0 - 6 T 0 - 7 T 0 - 8 T 0 - 9 T
-∆S T
(J/
kg·K
)
T (K)
-∆S T
(J/
kg·K
)
T (K)
MnAs
310 320 330 340
7.5
8.0
8.5
9.0
6 T5 T4 T
3 T2 T
1 T0 T
S /
R
T(K)
Application to MnAs
∂S/∂T > 0
0 2 4 6 80
40
80
120
isotherm 1 isotherm 2 isotherm 3 isotherm 4 isotherm 5 isotherm 6
M (
em
u/g
)B (T)
(dM)B
300 310 320 330 3400
2
4
6 65432
dx/dT
ParamagneticOrthorhombicB
(T
)
T (K)
dx/dB
FerromagneticHexagonal
1
Isothermal magnetization measurements:M(B)T
Ferromagnetic phase (x = 1) � Isotherms 1 and 2
Ferromagnetic phase (x) + Paramagnetic phase (1-x) � Isotherms 3 and 4
Paramagnetic phase (x = 0) � Isotherms 5 and 6
Phase diagram from M and Cp measurements
MnAs
310 320 330
2 3 4 5 61
(dM)B(dS)T
310 320 330 340 3500
50
100
150 0 - 1 T 0 - 2 T 0 - 3 T 0 - 4 T 0 - 6 T 0 - 9 T
-∆S T
(J/
kg·K
)
T (K)
M = x·MF + (1-x)·MPB
PF
B
F
B
P
B T
xMM
T
Mx
T
Mx
T
M
∂∂−+
∂∂+
∂∂−=
∂∂
)()1(
dBB
xMMdB
T
MxdB
T
MxdS
TPF
B
F
B
P
∂∂−+
∂∂+
∂∂−= )()1(
∫
∂∂−
Bt
BPF dB
T
xMM
0
)(
( )( ) 0
0,
0 =
=
= ∆=
∂∂
B
anomBp
B H
C
T
x
Calculation in a real process (isothermal magnetization)
dBT
MdS
B
∂∂=
dS = dS’ + dSex
Solutions for hysteretic compounds
● Magnetization at constant fields M(T)B
● Isothermal magnetization (for increasing fields) after forcing the P state by heating and cooling
● Isothermal magnetization (for decreasing fields) after forcing the F state by cooling and heating
0
2
4
6
8
220 230 240 250 260 270 280
T (K)
B (
T)
Cooling
HeatingField
Temperature
0
2
4
6
8
220 230 240 250 260 270 280
T (K)
B (
T)
Cooling
HeatingField
Temperature
Mn1.1Fe0.9P0.82Ge0.18
200 220 240 260 280 3000
30
60
90
120
150
M (
Am
2 /kg)
T (K)
Cooling B = 1 T B = 2 T B = 3 T B = 4 T B = 5 T B = 6 T B = 7 T B = 8 T B = 9 T
200 220 240 260 280 3000
30
60
90
120
150
M (
Am
2 /kg)
T (K)
Heating B = 1 T B = 2 T B = 3 T B = 4 T B = 5 T B = 6 T B = 7 T B = 8 T B = 9 T
210 220 230 240 250 260 270 280 2900
10
20
30
40
-∆S
(J/
kgK
)
T (K)
∆B = 1 T ∆B = 2 T ∆B = 3 T ∆B = 4 T ∆B = 5 T ∆B = 6 T ∆B = 7 T ∆B = 8 T ∆B = 9 T
Heating
210 240 2700
10
20
30
-∆S
(J/
kgK
)
T (K)
∆B = 1 T ∆B = 2 T ∆B = 3 T ∆B = 4 T ∆B = 5 T ∆B = 6 T ∆B = 7 T ∆B = 8 T ∆B = 9 T
Cooling
Mn1.1Fe0.9P0.82Ge0.18
200 220 240 260 280 3000
5
10
15
20
25
30
35
-∆S
(J/
kgK
)
T (K)
∆B=1T ∆B=2T ∆B=3T ∆B=4T ∆B=5T ∆B=6T ∆B=7T ∆B=8T ∆B=9T
Increasing Field
220 230 240 250 260 270 280 290 3000
10
20
30
40
-∆S
(J/
kgK
)
T (K)
∆B=1T ∆B=2T ∆B=3T ∆B=4T ∆B=5T ∆B=6T ∆B=7T ∆B=8T ∆B=9T
Decreasing Field
220 240 260 2800
20
40
60
80
-∆S
(J/
kgK
)
T (K)
∆B=1T ∆B=2T ∆B=3T ∆B=4T ∆B=5T ∆B=6T ∆B=7T ∆B=8T ∆B=9T
Decreasing Field
210 220 230 240 250 260 270 280 2900
20
40
60
80
-∆S
(J/
kgK
)
T (K)
∆B=1T ∆B=2T ∆B=3T ∆B=4T ∆B=5T ∆B=6T ∆B=7T ∆B=8T ∆B=9T
Increasing Field
Isothermal magnetizationIsothermal magnetization
from P or F state
MnAs
Adiabatic temperature changefor MnAs
• Direct ∆TS (symbols)• From Cp (lines)
MnAs
Isothermal entropy changefor MnAs• Direct results (symbols)• From Cp (lines)
L. Tocado, E. Palacios, R. Burriel
J. Therm. Anal. Calorim.84, 213 (2006).
� Importance of reliable estimates of ∆∆∆∆TS and ∆∆∆∆ST
� Practical results from M(T,H) in paramagnets and in second order transitions
� Materials with giant MCE: first-order transitions� Incorrect results from M(T,H)
� Overvaluedcalculations
� Limitations from Cp results for high temperature ∆∆∆∆ST calculations
� Direct measurement of ∆∆∆∆TS and ∆∆∆∆ST
� Importance of thermal history in M(H) measurements� Use ofisofield magnetization curves orcontrolled isothermal
curves� Practical results in first-order transition compounds
� Absence of spurious spikes, no evidence of colossal MCE
� Calculation of the spurious spikes
Conclusions
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