R. Burriel Instituto de Ciencia de Materiales de Aragon CSIC – University de Zaragoza 50009 Zaragoza, Spain Determination of the magnetocaloric parameters through 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
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Determination of the magnetocaloric parameters through ......Determination of magnetocaloric parameters Calorimetric methods Heat capacity. Practical limitations Direct measurements
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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