Orientational disordering in crystals—II: A model for the evaluation of thermodynamic properties of orientational disordering in crystals

A statistical mechanical model for the evaluation of thermodynamic properties of orientational transitions in crystals developed by Aston is generalised by taking into account the existence of more than two allowed molecular orientations (nγ 2) in the rotator crystal phase explicitly. An orientational transition work function is derived in order to generate full thermodynamic functions leading to a formal expression for the configurational energy change in terms of transition enthalpy change and an entropy integral. The value of n for camphor predicted by this equation compares very well with the one computed from another independent method and that reported by previous workers. A general scheme, based on both spectroscopic and thermodynamic data, by which n and phase eigenstates may be computed including the case where configurational and thermal properties are strongly coupled is presented. An analytical expression is obtained for the relative potential energy barrier ν_eff in a single-lattice model which parallels that defined for a double sub-lattice model of positional disorder by Pople and Karasz and their followers. It is shown that the value of ν_eff for a given value of n is not uniquely defined for all substances which may not have common values of other thermodynamic parameters.