Quantum mechanical aspect of first order phase transition of crystals

Abstract

It has been generally believed that some external physical porperties, e.g. volume, enthalpy, and entropy, etc. change discontinuously at first order phase transition temperatures, since Ehrenfest’s proposition. However, the deviation from this proposition was often found in many crystals. As the progress of experimental methods and the accuracy develop the number of crystals that manifest unusual transition processes is increasing. Notably aberrant phenomena are as follows. An intermediate phase appears whose crystal structure is undoubtedly different from those of the low and high temperature forms. The peak of differential thermal analysis of specific heat is splitted into two as if one transition inevitably induces another. The interpretation of these abnormal behaviors in the vicinity of the transition is certainly beyond reach of thermodynamic ideas. We assumed that the eigenkets of Boltzmann’s H of each phase in the vicinity of the transition temperature interact to produce perturbing state. Then the intermediate phase named M phase emerges, and its eigenket is the superposition of eigenkets of commuting Hamiltonian of the two temperature phases. It is natural that the new M phase has different structure from those of the two phases. The above mentioned phenomena occurring in dichlorobenzophenone, NaNO2, 1-Ethyl-3-(4-methylpentanoyl)urea, and VO2 are explained by this quantum mechanical theory.