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R. Burriel, October 24 - 25, 2011 – Delft, The NetherlandsDDMC 2011
R. BurrielInstituto de Ciencia de Materiales de Aragón
CSIC – University de Zaragoza, 50009 Zaragoza, Spain
Methods and problemsin the characterization ofmagnetocaloric materials
R. Burriel, October 24 - 25, 2011 – Delft, The NetherlandsDDMC 2011
We need reliable values for themagnetocaloric parameters
How reliable and how useful are the reported valuesfor ΔTS, ΔST , RC
How valid are for hysteretic transitionsResults from CB(T) : Good, but depends on the T rangeDirect measurementsResults obtained from M(B), M(T)Considerations in hysteretic compounds:
Mixed phase, irreversibility
R. Burriel, October 24 - 25, 2011 – Delft, The NetherlandsDDMC 2011
Effect of a magnetic field change on T and S• Adiabatic temperature change, ΔTS• Isothermal entropy change, ΔST
TC,B
S (T)B
Ent
ropy
, S
Temperature, T
S (T)B = 0
TC,B=0
-ΔST
ΔTS
Magnetocaloric parameters
R. Burriel, October 24 - 25, 2011 – Delft, The NetherlandsDDMC 2011
12)()( BBS STSTT −=Δ
∫−
=−=ΔT BB
BBT dTT
TCTCTSTSS
012
12
)()()()(
TC
S (T)B
Ent
ropy
, S
Temperature, T
S (T)B= 0
TC
ΔTSΔST
Specific heat
Calorimetric methods
∫=T
B dTTTC
TS B
0
)()(
Determination of ΔTS and ΔST
R. Burriel, October 24 - 25, 2011 – Delft, The NetherlandsDDMC 2011
4.2 K – 350 K
Magnetic Field up to 9 T
Heat capacity:
Heat pulse method.
Continuous cooling and
heating thermograms.
Transition enthalpy.
Direct measurement of the
MCE parameters.
Adiabatic field cycles.
Adiabatic installation
Pt thermometer
Thermocouple
Adiabatic shield
Sample holder
CernoxTM
thermometers
R. Burriel, October 24 - 25, 2011 – Delft, The NetherlandsDDMC 2011
0 100 200 3000
10
20
30 0T 1T 2T 3T 4T 5T
CB /
R
T (K)
Adiabatic calorimetryFields B = 1, 2, 3, 4, 5 TFirst-order transitionFerro Para
Heat pulse: Quasiestatic heat, C(T)B = Q/(T2−T1)
Mn1.18Fe0.82P0.75Ge0.25
Experimental techniques for ΔST and ΔTS
R. Burriel, October 24 - 25, 2011 – Delft, The NetherlandsDDMC 2011
Thermograms
• Map the heat capacity of sharp transitions• Cooling and heating thermograms: Thermal hysteresis
dtdTTTC
TTTTdtdQ
dtdTC
dtdT
dTdQ
dtdQ
B
B
δσα
δσδα
)(
])[('
3
44
+≅⇒
−++=
==
Experimental methodδT = Tsample – Tadiabatic shield
0 10000 20000 30000 40000
300
310
320
330
T (K
)
t (s)
Heating thermogram Cooling thermogram
Tocado et al, J. Therm. Anal. Calorim. 84, 213 (2006)
R. Burriel, October 24 - 25, 2011 – Delft, The NetherlandsDDMC 2011
295 300 305 310 315 320 325 33010
20
30
40 0T 1T 2T 3T 4T 5T
CB /
R
T (K)
pulse / cool
Mn1.18Fe0.82P0.75Ge0.25
R. Burriel, October 24 - 25, 2011 – Delft, The NetherlandsDDMC 2011
290 300 310 320 330 340
8,8
9,6
10,4 heat cool 0T 1T 2T 3T 4T 5T
(S −
S0)/
R
T (K)
( )∫=T
BB dTTCTS0
)(
Mn1.18Fe0.82P0.75Ge0.25
R. Burriel, October 24 - 25, 2011 – Delft, The NetherlandsDDMC 2011
• Good at low T
S(T)B=0 >> S(T)B=5Precision of ΔS T and S T are similar
• Low precision at high T
ΔS T < 5% of S TError in ΔS T > 20 times the error in S T
Pecharsky and Gschneidner, J. Appl. Phys. 86, 565 (1999)
Problems from specific heat determinations of S
R. Burriel, October 24 - 25, 2011 – Delft, The NetherlandsDDMC 2011
Pecharsky, Gschneidner, J. Appl. Phys. 86, 565 (1999)
• Improvement combining CB with direct measurements• Avoids the need of CB at low temperatures• Without increased error at high T
R. Burriel, October 24 - 25, 2011 – Delft, The NetherlandsDDMC 2011
Adiabatic systemPt thermometer
Thermocouple
Adiabatic shield
Sample holder
CernoxTM
thermometers
Direct measurements
Control of T, Q and B in the sample and in the surrounding shield
R. Burriel, October 24 - 25, 2011 – Delft, The NetherlandsDDMC 2011
∫=T
H dTT
TCTS Hp
0
,)(
)(
TC
S (T)B
Ent
ropy
, S
Temperature, T
S (T)B = 0
TC
S(T)B
S(T)B=0
ΔTS
ΔTS = [TS(B2) - TS(B1)]
0
2
4
6
0 300 600 900
237,6
238,0
238,4
238,8
Temperature
ΔTS(6T-0)
ΔTS(5-6T)
ΔTS(3-5T)
ΔTS(1.5-3T)
t (s)
T (K
)
ΔTS(0-1.5T)
0T
6T
5T
3T
1.5T
B (T
)
Field
0T
R. Burriel, October 24 - 25, 2011 – Delft, The NetherlandsDDMC 2011
∫=T
H dTT
TCTS Hp
0
,)(
)(
TC
S (T)B
Ent
ropy
, S
Temperature, T
S (T)B = 0
TC
S(T)B
S(T)B=0
-ΔST
ΔST = Q/T = [ST(B2) - ST(B1)]
200 400 600 800
-8
-4
0
4
80.0
1.5
3.0
4.5
t (s)
P (m
W)
B
(T)
0
2
4
6
δT (m
K)
Other methods: Peltier cellBasso et al, Rev. Sci. Instrum. 79, 63907 (2008)
R. Burriel, October 24 - 25, 2011 – Delft, The NetherlandsDDMC 2011
∫+=T
TB
BB dTTTCTSTS
0
)()()( 0 )()()( 0000 TSTSTS TBB Δ+= =
Measured290 300 310 320 330 340
8,4
9,1
9,8
10,5
B = 0 B = 5T
330 332 334 336 33810.1
10.2
10.3
10.4
(S −
S0)/
RT (K)
(S −
S0)/
R
T (K)
direct ΔST
Combined CB(T)and direct ΔST
Entropy curves from- CB, unknown S0- Direct ΔST, common S0
Mn1.18Fe0.82P0.75Ge0.25 Solution to S calculation from CB(T)
R. Burriel, October 24 - 25, 2011 – Delft, The NetherlandsDDMC 2011
260 280 300 3200
4
8
12
16
-ΔS T (
J/kg
·K)
T (K)
1T-0 2T-0 3T-0 5T-0
260 280 300 3200
2
4
6 0 - 1T 0 - 2T 0 - 3T 0 - 4T 0 - 5T
ΔTS (
K)
T (K)
Mn1.26Fe0.74P0.75Ge0.25
Full symbols: Results from direct measurementsContinuous lines: From CB
R. Burriel, October 24 - 25, 2011 – Delft, The NetherlandsDDMC 2011
Magnetocaloric parameters from magnetic measurements
dBT
BTMSB
B
T ∫ ⎟⎠⎞
⎜⎝⎛
∂∂
=Δ0
),(
Gibbs free energyG = U – TS – BMdG = – S dT – MdB
Maxwell relation
⎟⎟⎠
⎞⎜⎜⎝
⎛∂∂
∂=⎟⎟
⎠
⎞⎜⎜⎝
⎛∂∂
∂BT
G TB
G 22
BT TM
BS
⎟⎠⎞
⎜⎝⎛
∂∂
=⎟⎠⎞
⎜⎝⎛
∂∂
[ ] dBTMTMTT
dBT
BTMSB
B
B
B
T ∫∫ −−
=⎟⎠⎞
⎜⎝⎛
∂∂
=Δ0 12
120
)()(1),(
R. Burriel, October 24 - 25, 2011 – Delft, The NetherlandsDDMC 2011
Problem with derived “spikes” from Maxwell relation
The colossal effect for Mn1-xFexAsNature Materials 5, 804 (2006)
R. Burriel, October 24 - 25, 2011 – Delft, The NetherlandsDDMC 2011
260 280 300 3200
20
40
60
0T 0T 0T 1T 1T 3T 3T 6T 6T 6T
C
p,B
/ R
T (K)
x = 0.01
Mn1-xFexAs (x=0.01)
Heat pulseHeating thermogramsCooling thermograms
G.F. Wang et al.Magneto-Science 2011,Shanghai
R. Burriel, October 24 - 25, 2011 – Delft, The NetherlandsDDMC 2011
260 280 300 3200
10
20
30
40
1T 1T 3T 3T 6T 6T 6T 6T
-ΔS
T (J/k
gK)
T (K)
x = 0.01
260 270 280 290 300 310 3200
5
10
15
20
ΔTS (K
)
T (K)
1T 2T 3T 4T 5T 6T 1T 3T 6T 1T 3T 6T
x = 0.01
Mn1-xFexAs (x=0.01)
Symbols: from direct measurements. Dotted and solid lines: from heat capacityon cooling and heatingGiant MCE but not colossal
G.F. Wang et al.Magneto-Science 2011, Shanghai
R. Burriel, October 24 - 25, 2011 – Delft, The NetherlandsDDMC 2011( )∫
=
=
Δ−=Δ
tB
B
BanPFex dB
HTCMMS
0 0
0)()(
0
1
2
3
4
5
6
7
8
9
220 230 240 250 260 270 280
T (K)
B (T
)
(dS)T
(dM)B
Para
Ferro
History
depe
nden
t
.
Hysteretic compounds
Mixed phase:
M = x·MP + (1-x)·MF
Calculation from M(B)T
ΔST = ΔS + ΔSex
∫ ⎟⎠⎞
⎜⎝⎛
∂∂
−=ΔtB
BPFex dB
TxMMS
0
)(
Tocado et al, J. Appl. Phys. 105, 093918 (2009)
R. Burriel, October 24 - 25, 2011 – Delft, The NetherlandsDDMC 2011
220 240 260 2800
10
20
30
-ΔS
T (J/k
g.K
)
T (K)
cooling from M(B)
T
from M(T)B
Same results for ΔST from:• Field dependent magnetization M(B)T
with complete phase conversion• Temperature dependent magnetization
M(T)B• And also from Cp,B(T) and direct values
220 240 260 2800
10
20
30
40
50
60
70
80
-ΔS
(J/k
gK)
T (K)
ΔB=1T ΔB=2T ΔB=3T ΔB=4T ΔB=5T ΔB=6T ΔB=7T ΔB=8T ΔB=9T
Increasing Field
Results for ΔST from M(T)B, M(B)T, and M(B)T with cycling in T(same scale)
R. Burriel, October 24 - 25, 2011 – Delft, The NetherlandsDDMC 2011
Heating process:• D A, Stable phase Ferro-• A B, Transition to Para-
Cooling process:• B C, Stable phase Para-• C D, Transition to Ferro-
A to C, unstable ∂S/∂T < 0
Phase equilibrium at TeqGE = GG
300 320
7.4
7.6
7.8
8.0
8.2
S/R
T(K)
Paramagnetic
Ferromagnetic
A
B
C
D Teq
E
F
GAACB
Entropy curve
Irreversibility: Entropy dS ≥ dQ/T
R. Burriel, October 24 - 25, 2011 – Delft, The NetherlandsDDMC 2011
( )
A
BpACBA
A
BBBAAA
ACB
B
ABA
THS
dTTCHAHST
STHSTHSTH
ASdTGG
Δ>Δ⇒
=Δ>+Δ=Δ
⇔>Δ+Δ−=+−−=
==−
∫
∫
,
0
Estimation of the area AACB (as a triangle):
300 320
7.4
7.6
7.8
8.0
8.2
S/R
T(K)
Paramagnetic
Ferromagnetic
A
B
C
D Teq
E
F
GAACB
( ) )(21)(
21
CACAABACB TTSTTSSA −Δ=−−≅
CA
Aheatheat TT
TSS+
Δ≅Δ2'
Heating
Estimation of the real entropy jump
A
'
THS Δ
=Δwhere the pseudo-entropy
R. Burriel, October 24 - 25, 2011 – Delft, The NetherlandsDDMC 2011
300 320
7.4
7.6
7.8
8.0
8.2
S/R
T(K)
Paramagnetic
Ferromagnetic
A
B
C
D Teq
E
F
GA
ACB
( )CA
CAcoolheat
B
Ccoolheat
coolBpA
D
heatBp
DAABBCCD
TTTTSSSS
TdTTC
TdTTC
SSSSSSSSdS
+−
Δ+Δ+Δ−Δ+−
≅−+−+−+−==
∫∫
∫''''
)()(
0
,,,,
Estimation of the real entropy jump
Similarly, on cooling
A
CADDC
TH
S
AGGΔ
<Δ⇒
=−
CA
Ccoolcool TT
TSS+
Δ≅Δ2'
Heating-cooling cycle DABCD
R. Burriel, October 24 - 25, 2011 – Delft, The NetherlandsDDMC 2011
Error in the measurement of the entropy cycle
200 220 240 260
8
10
ΔS'cycle
ΔS'coolS'/R
T(K)
Pseudo-entropy by integration of Cp/T
Mn1.1Fe0.9P0.82Ge0.18TA
TC
ΔS'heatB = 6 T
( )coolheatcrit
coolheathys
crit
crit
hyscycle
TTT
TTTT
HS
TT
SS
+=
−=Δ
Δ=Δ
Δ−≅
Δ
Δ
2/1
'
''
It coincides with theexperimental value: 6%
R. Burriel, October 24 - 25, 2011 – Delft, The NetherlandsDDMC 2011
Hysteresis: possible mixed phase
Wrong application of the Maxwell relation in M(B)T measurements
Unphysical “colossal” effect ΔSex
Irreversibility: Entropy dS ≥ dQ/T
Cycle of pseudo-entropy fromcalorimetric measurements
Effects of hysteresis and irreversibility
crit
hyscycle
TT
SS Δ
−≅Δ
Δ
''
( )∫=
=
Δ−=Δ
tB
B
BanompPFex dB
HTC
MMS0 0
0, )()(
Paramagnetic
Q
G
F
E
D
C
B
AEn
trop
y
Temperature
P
Ferromagnetic
GC < GBGA < GD
R. Burriel, October 24 - 25, 2011 – Delft, The NetherlandsDDMC 2011
0
1
2
3
4
5
6
7
8
9
220 230 240 250 260 270 280
T (K)
B (T
)
Para
Ferro
History
depe
nden
t
Hysteretic compounds
Reduction of the efficientT region in practical cycles
Reduced effectiveparameters and coolingefficiency
R. Burriel, October 24 - 25, 2011 – Delft, The NetherlandsDDMC 2011 0 20 40 60 80 1000
10
20
30
0
10
20
300
40
80
120
B (a
.u.)
B0
B1
Ferro
Para
Hystere
tic
ΔTS (a
.u.)
T (a.u.)
-ΔS T (a
.u.)
S (a
.u.)
S(B0)
S(B1)
Phase diagram• Ferro - para• First order• Hysteresis
Entropy curves at fields B0 and B1,heating and cooling
Derived entropychange ΔST
Derived temperaturechange ΔTS
R. Burriel, October 24 - 25, 2011 – Delft, The NetherlandsDDMC 2011
Conclusions
Precise determination of the MCE parameters.
Measurement and control of: Q, T, and B ΔTS and ΔST
Determinations from CB, good at low T, no precision at high T.Solved with CB around Tc plus one direct measurement of ΔST.
Hysteretic compounds. Spike problem from M(B)T
Irreversible entropy. Small correction.
Hysteresis: reduces the effetive ΔTS, ΔST and RC
R. Burriel, October 24 - 25, 2011 – Delft, The NetherlandsDDMC 2011
Contributors to this work at theInstitute of Materials Science of Aragon (ICMA)
Ramon BurrielElias PalaciosLeticia TocadoGaofeng Wang