6. Conclusion and scope for future work 1. Conclusions
1.3. MAGNETO-CALORIC EFFECT
Magneto-caloric effect (MCE) refers to the thermal response of a material subjected to an external magnetic field which is due to the inter-dependence of thermal and magnetic properties of the material. This effect first observed by Emil Warburg in 1881 in pure Iron, which was found to warm up under an applied magnetic field [WARB81a]. In 1905, Langevin demonstrated the reversible temperature change caused by magnetizing a paramagnet [LANG05a]. But, it was only in the late 1920s that the origin of MCE was explained independently by Debye [DEBY26a] and Giauque [GIAU27a] who also suggested a new method of achieving low temperatures by adiabatic demagnetization. A few years later, Giauque and MacDougall experimentally demonstrated adiabatic demagnetization of a paramagnetic salt and also reached an ultra low temperature of 0.25 K using this process [GIAU33a].
Normally, MCE is an intrinsic property of a magnetic material and the strength of this effect can be characterized by the change in temperature arising from the application or removal of an external magnetic field. If a magnetic material is exposed to an external magnetic field under isothermal condition, the magnetic moments are aligned by the magnetic field and the entropy decreases (which is evident from Figure 1.11). But, under adiabatic condition, the total entropy is constant. In this case, the difference in magnetic entropy is transferred to lattice entropy via spin and lattice coupling. This transformation makes the atoms vibrate more rapidly. As a result,
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temperature of the material increases. On the other hand, the adiabatic removal of the external field causes the moments to re-randomize, thereby removing the entropy from the lattice or creating a cooling effect (as illustrated in Figure 1.11). Thus, the coupling of spin sub lattice with the magnetic field produces the MCE.
Figure 1.11: The basic mechanism of MCE when a magnetic field is applied to or removed from a magnetic system under different thermodynamic conditions [ROME13a].
The peak value of MCE can be obtained around temperatures where rapid changes in magnetization (M) with respect to temperature occur i.e. at the phase transition temperatures.
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1.3.1. Magneto-caloric materials
There are several classes of materials which exhibit MCE. For a long period, the search for magneto-caloric compounds for applications was focused on rare-earth-based compounds because of the large MCE exhibited by them around room-temperature [GSCH94a, GSCH96a, BRUC08b]. The largest value of MCE was found in Gd, where the value of ǻSM and ǻTad near the Curie temperature TC = 293 K are about -9.8 Jkg-1K-1 and 11.6 K, respectively for ǻH of 5 T [GSCH00b]. But its commercial usage is somehow limited because Gd is quite expensive (~$4500 kg-1).
In 1997, when Pecharsky and Gschneidner discovered the giant MCE in the Gd5Si2Ge2 compound [PECH97a], the interest of MCE materials was reawakened. While undergoing a first-order phase transition near a magnetic phase transition, Gd5Si2Ge2 exhibits large MCE which is about twice of that in Gd. More importantly, this alloy not only showed enhanced MCE but also opened the door to domestic applications such as home and automotive air conditioning [PECH05a]. Nonetheless, the TC of Gd5Si2Ge2 is about 276 K, which is much lower than that of Gd (293 K), making this alloy difficult for use in room-temperature applications [BRUC05a]. To overcome these difficulties, several other families of MCE materials have been (and are being) explored, especially materials without rare-earth elements, such as, Ni–Mn–Ga alloys [HUFS01a], Mn–As–
Sb alloys [WADA01a], La–Fe–Co–S alloys [FUJI02a], Mn–Fe–P–As alloys [TEGU02a], La–Ca–Sr–Mn–O manganites [PHAN05a], Ni–Mn–Sn alloys [KREN05a], Ni–Mn–In [KREN07a] alloys, etc. According to theoretical analyses as well as the experimental results of existing magneto-caloric materials [PECH05a, BRUC05a,
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PHAN07a], the criteria for selecting materials for active MCE applications are following:
Materials should exhibit large ǻSM and ǻTad (i.e., large MCE).
Materials should have large density of magnetic entropy but small lattice entropy.
Thermal and magnetic hysteresis should be small (these are related to the reversibility and working efficiency of the MCE material).
Materials with small specific heat and large thermal conductivity to ensure large temperature change and rapid heat exchange.
Materials should also have high chemical stability, easily available with low cost and simple synthesis route.
1.3.2. Magneto-caloric parameters
Normally the strength of MCE is measured by the isothermal magnetic entropy change (∆SM)T and adiabatic temperature change (∆Tad). In order to understand the relation between these two important MCE parameters, one can start with the general thermodynamic potentials (the internal energy U of the system, the enthalpy H, Helmholtz free energy F and Gibbs free energy G) which are related to the magnetic as well as thermodynamic variables as follows [SWAL62a, BAZA64a, VONO74a, TISH99b, TISH03a]:
) , , (S V M U
U =
ST U F = −
and G=U−ST+PV−MH
(1.8)
where P, V, T, S, H and M are pressure, volume, absolute temperature, entropy, magnetic field and magnetization, respectively. Now, differential forms of U, F and G are
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dU=TdS−PdV+HdM (1.9)
dF = −SdT−PdV +HdM (1.10)
dG = VdP − SdT − MdH
(1.11)Using above equations, the variables P, V, S, H and M can be determined by the following equations of state:
T
V H
V F H T P
,
) , ,
( ¸
¹
¨ ·
©
§
∂
− ∂
= (1.12)
,
( , , )
H T
V T H P G
P
§∂ ·
=¨ ¸
©∂ ¹ (1.13)
V
T H
V F H T S
,
) , ,
( ¸
¹
¨ ·
©
§
∂
− ∂
= or,
P
T H
P G H T S
,
) , ,
( ¸
¹
¨ ·
©
§
∂
− ∂
= (1.14)
,
( , , )
V T
H T M V F
M
§ ∂ ·
=¨ ¸
©∂ ¹ (1.15)
P
H T
P G H T M
,
) , ,
( ¸
¹
¨ ·
©
§
∂
− ∂
= (1.16)
From these equations of state, it is possible to derive the thermodynamic Maxwell relations
, ,
T P H P
S M
H T
∂ ∂
§ · § ·
=
¨ ¸ ¨ ¸
∂ ∂
© ¹ © ¹ (1.17)
, ,
T H H P
S V
P T
∂ ∂
§ · § ·
¨ ¸ = −¨ ¸
∂ ∂
© ¹ © ¹ (1.18)
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, ,
T P M P
S H
M T
∂ ∂
§ · § ·
¨ ¸ = −¨ ¸
∂ ∂
© ¹ © ¹ (1.19)
Considering S as a function of T, P and H, the total differential of S can be written as