Magnetic entropy change

This tells us that the reduced magnetic entropy change will be lower in an antiferromagnetic system than in an uncoupled one, as can be seen below, as the spins are not fully saturated below the conditions of lowest temperature and strongest field. The antiferromagnetic coupling in Gd(III)7 is also a hindrance, with behaviour similar to Gd(III)5, when compared to the relevant Brillouin functions. 

Figure 5.36 Magnetic entropy change and adiabatic temperature change, derived from specific heat data, for [Fei4(bta)606Cl6(0Me)i8] on an applied field change of 7 to 0 T. Solid line is the entropy for an 5 = 25 paramagnet. Reprinted with permission from Evangelisti et al., 2006 [19]. Copyright (2006) Royal Society of Chemistry...

Figure 9.7 The magnetic entropy change, A5J, as a function of temperature and magnetic field for La gCa ...

Also other studies of type-1 EugGaigGe3o have provided evidence for a second feature at a characteristic temperature below Tc- For instance, the magnetic specific heat, in addition to the lambda-type anomaly at Tc, shows a broad shoulder at about 10 K [10]. This anomaly is more clearly revealed by the temperature dependence of the magnetic entropy change [47] that will be further discussed in the context of magnetic refrigeration in the next section. 

Fig. 9.13 Magnetic entropy change (ASm) as a function of temperature (I) for Eu8Gai6Ge3o and Eu4Sr4Gai6Ge3o extracted from M-H-T curves via the Maxwell Eq. 9.9...

The recent reports of "colossal" values of magnetic entropy change of first-order phase transition systems (de Campos et al, 2006 Gama et al., 2004 Rocco et al., 2007) are also discussed, and are shown to be related to the mixed-phase characteristics of the system. We present a detailed description on how the misuse of the Maxwell relation to estimate the MCE of these systems justifies the non-physical results present in the bibliography (Amaral Amaral, 2009 2010). 

Compared to Eq. 24, the derivative 3A/3T directly affects the result. We shall explore the use of Eq. 24 to calculate the magnetic entropy change and compare it to the use of the Maxwell relation. 

Fig. 10. Interpolating a) experimental M H, T) data and b) magnetic entropy change results by mean-field simulations for the second-order phase transition manganite...

Like the previous example of the second-order manganite, the mean-field state function / is fitted to a polynomial function, for calculation purposes. With the Aj and A3 exchange parameters and the / function described, M(H,T) simulations can be performed, and compared to the experimental values. Also, magnetic entropy change can be estimated from the mean-field relation of Eq. 29 and compared to results form the use of the Maxwell relation. Results are shown in Fig. 14. 

Estimating magnetic entropy change from magnetization measurements... 

The sudden, discontinuous entropy change is related to the phase transition itself, and is approximately independent of the applied field. The field shifts the transition only to higher temperatures. This entropy change cannot be calculated from the Maxwell relations, for two reasons (i) It is not a magnetic entropy change, and (ii) M(T) or M(H) is not a continuous, derivable function. For first order transitions, the Clausius-Clapeyron (CC) equation offers a way to calculate the entropy change."... 

Fig. 16. a) schematic diagram of the area for entropy change estimation from the Clausius-Clapeyron equation, from a M vs. H plot of a magnetic first-order phase transition system, and b) magnetic entropy change versus temperature, estimated from the Maxwell relation (full symbols) and corresponding entropy change estimated from the Clausius-Clapeyron relation (open symbols). 

To assess the effects of considering the non-equilibrium solutions of M(H, T) as thermodynamic variables in estimating die magnetic entropy change via the Maxwell relation, we use the three sets of M(H, T) data. The result is presented in Fig. 17(b). 

So if we substitute the above formulation in the integration of the Maxwell relation, used to estimate magnetic entropy change, we can establish entropy change up to a field H as... 

Fig. 21. a) Isothermal M versus H plots of a simulated mixed-phase system, from 295 to 350 K (0.5 K step) and b) magnetic entropy change values resulting from the direct use of the Maxwell relation. 

The above physical quantity, denoted by AS and expressed in J K , is called the field-induced isothermal magnetic entropy change or simply isothermal magnetic entropy change. 

From the magnetic entropy change it is easy to calculate the cooling capacity Q of the magnetic material, that is, the amount of heat that can be extracted from the cold end to the hot end of a refrigerator in one ideal thermodynamic cycle by integrating the following differential equation ... 

This variation, called the adiabatic temperature change calculation of the isothermal magnetic entropy change, is based on the following Maxwell relation ... 

Therefore the specific magnetic entropy change can then be calculated from magnetization data by the integration of the above equation ... 

For most paramagnetic and ferromagnetic materials, the isothermal magnetic entropy change per unit of magnetic induction usually ranges from 1 to 4 J.kg .K .T . 

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