Stable, Metastable and Unstable Solutions of the Modified Pople-Karasz Model

Authors: Şükrü ÖZGAN, Mustafa YAZICI

Abstract: The theory of melting of molecular crystals with orientational degrees of freedom developed by Pople and Karasz[1] is modified using a third energy parameter W'' in our recent paper[2]. W'' is the interaction between molecules on differnet sites and different orientations. W'' is combined with the previous two energy parameters, of which W is the interaction between molecules on different sites with the same orientation and W' is the interaction between molecules on the same wite with different orientations, using the arithmetic mean. In this work, we study the equilibrium behaviour of the modified model, where W'' is combined with W and W' by the geometric mean, using the lowest approximation of the cluster variation method[3]. Especially, metastable and unstable solutions of positional Q and orientational S order parameters are found beside the stable solutions and the thermal variation of these solutions is investigated as a function of the reduced temperature. This model is also used to study how a system will "freeze" in a metastable state with two long range order parameters. The phenomenon of freezing-in in the metastable state is shown by two different methods: 1 - Displaying free energy surfaces in the form of the contour mapping, 2 - Solving the dynamical equations, which were constructed by introducing a detailed balancing condition directly, by means of the flow diagram. Finally, the results obtained with these two methods coincide with each other exactly.

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