Second order, phase change

The change from an ordered state to a disordered state is a second-order phase change. In a first-order phase change, thermodynamic properties such as enthalpy and entropy undergo abrupt changes. In contrast, there is no heat of... 

MEAN-FIELD THEORIES OF THE SECOND-ORDER, PHASE-CHANGE... 

The second-order, phase-change exhibited by ferromagnets (Section 6), antiferromagnets (Section 7) and by superconductors (Section 8) have a phenomenological description in terms of the mean-field equation,... 

In this section we give the freeon theory of ferromagnetism. As pointed about above ferromagnetism is a second order-phase change which is well-defined by mean-field theory. In Section 6.2 we give the uniform interaction derivation of mean-field theory and in Section 6.3 we compare prediction with observation. 

HDU had an apparent change from 91-92 C. The fibrous nature of the sample made observation somewhat difficult. Measurement using a differential scanning calorimeter showed a slight change of curvature indicating the possibility of a second order phase change at 117 C. The "transition" does not appear to be reversible. No return to the LT color was observed after two weeks of observation. 

Thus the second-order phase change would be observed about 50 K below Tg for an experiment carried out infinitely slowly. 

One example of a second-order phase change is the structural rearrangement of quartz, where G, S, and V are continuous across the coexistence line, but the constant-pressure heat capacity, which is related to the second temperature derivative of the Gibbs energy,... 

Fig. 23. Entropy and volume changes in a supposed second-order phase change.

The question of whether the normally first-order smectic-A to nematic phase transition can be second order in some materials is somewhat controversial. All of the published mean-field theories " of the smectic-A phase do exhibit second-order phase changes for certain values of the potential parameters. In both McMillan s theory and that of Lee et al, the second-order transition is predicted to occur at that end of homologous series having short chain lengths. More specifically, these models predict the second-order changes to occur when the ratio of transition temperatures Tan/Tni (or Tac/Tci) is at or below about 0.88 (see Fig. 5). 

In the smectic-A phase, the single-molecule distribution function, Eqs. [7] and [10] can likewise be represented as a (one-dimensional) Fourier series in which all the coefficients may be considered order parameters. The disappearance of smectic-A order requires the simultaneous vanishing of all the order parameters. That they all can vanish simultaneously and continuously before the free energy of the smectic-A phase exceeds that of the nematic phase seems just as unlikely here as in the (empirically verified) case of the crystalline solids. It seems clear to me that the reason the various theoretical treatments mentioned above can exhibit second-order phase changes is that an insufficient number of order parameters is included. In all the treatments, either the potential, the potential of mean force, or the distribution function are expressed in terms of highly truncated Fourier series. Such truncation automatically limits the number of order parameters. Small numbers of order parameters can then vanish simultaneously and continuously under certain conditions providing the spurious second-order phase transitions. 

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