Paramagnetic phases

Variable temperature EPR and variable temperature susceptibility measurements showed that, analogous to BDTA, the LT phase is diamagnetic and the HT phase paramagnetic. In this case, however, both HT and LT X-ray structures have been determined (Figure 3.30), demonstrating clearly the dimerisation in the LT phase that leads to the diamagnetic behaviour. The HT phase, in contrast, consists of uniformly stacked... 

The transition from a ferromagnetic to a paramagnetic state is normally considered to be a classic second-order phase transition that is, there are no discontinuous changes in volume V or entropy S, but there are discontinuous changes in the volumetric thermal expansion compressibility k, and specific heat Cp. The relation among the variables changing at the transition is given by the Ehrenfest relations. 

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. 

For conventional Ising-spin systems, Pising(o ) takes on the expected simple forms namely, either Puingiq) = < (0) in the (high-temperature, zero magnetization) paramagnetic phase or the double-peaked Pising(o ) = 5(q + M ) + 6 q — M ) for temperatures below the Curie critical temperature, T < Tc. 

Let us mention some examples, that is, the passivation potential at which a metal surface suddenly changes from an active to a passive state, and the activation potential at which a metal surface that is passivated resumes active dissolution. In these cases, a drastic change in the corrosion rate is observed before and after the characteristic value of electrode potential. We can see such phenomena in thermodynamic phase transitions, e.g., from solid to liquid, from ferromagnetism to paramagnetism, and vice versa.3 All these phenomena are characterized by certain values... 

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