Phase transitions magnetic field

Consider how the change of a system from a thennodynamic state a to a thennodynamic state (3 could decrease the temperature. (The change in state a —> f3 could be a chemical reaction, a phase transition, or just a change of volume, pressure, magnetic field, etc). Initially assume that a and (3 are always in complete internal equilibrium, i.e. neither has been cooled so rapidly that any disorder is frozen in. Then the Nemst heat... 

Here we shall consider two simple cases one in which the order parameter is a non-conserved scalar variable and another in which it is a conserved scalar variable. The latter is exemplified by the binary mixture phase separation, and is treated here at much greater length. The fonner occurs in a variety of examples, including some order-disorder transitions and antrferromagnets. The example of the para-ferro transition is one in which the magnetization is a conserved quantity in the absence of an external magnetic field, but becomes non-conserved in its presence. 

In the inset of Fig. 9 we show the mean field frequency 0 = 0// as a function of density for T = 1. At this temperature the system undergoes a phase transition from a paramagnetic to a ferromagnetic fluid at a density whose mean field value is p mf = 0-4- For densities below this value we obtain 0 = cjq, which agrees with the frequency value of the low-order virial expansion (see Eq. (34)). For p > Pc,mF) increases with the density due to increase of the magnetization. 

Figure 4.7 Temperature dependence of the contribution to the total specific heat, reveals magnetization in 5 0e applied field of a pow- two distinct phase transitions. (Redrawn der sample of Gd(hfac)3NIT-Et n evidencing from Ref. [53] with data kindly provided by a phase transition around 1.8K. In the inset A. Lascialfari. (Published by American the magnetic contribution to the specific physical society).) heat, evaluated by subtracting the lattice...

In order to focus on the driving force for phase transitions induced by a magnetic field it is advantageous to use the magnetic flux density as an intensive variable. This can be achieved through what is called a Legendre transform [12], A transformed Helmholtz energy is defined as... 

Figure 2.9 The B-Tphase diagram of MnP [13] with the magnetic field along the b-axis. Three different magnetically ordered phases - ferro, fan and screw - are separated by first-order phase transitions. The transitions to the disordered paramagnetic state are of second order and given by a dashed line.

Electronic transitions like insulator-metal transitions, magnetic order-disorder transitions, spin transitions and Schottky-type transitions (due to crystal field splitting in the ground state in/element-containing compounds) profoundly influence the phase stability of compounds. A short description of the main characteristics of these transitions will be given below, together with references to more thorough treatments. 

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