Order-disorder in positions and orientations

The simplest treatment of the melting of inert gas crystals is that due to Lennard-Jones and Devonshire (LJD) who regarded the mechanism of fusion as a positional order-disorder phenomenon. They postulated that 

Crystals in which the rotational transition precedes the melting  

5-sites, Lennard-Jones and Devonshire showed that the melting parameters predicted by the theory agree well with the data for a number of spherical or nearly spherical molecules. 

However, the theory fails for anisotropic molecules where the effects of orientational disorder become important. The thermodynamic data on melting suggest that there are two classes of molecular crystals those which undergo phase transitions associated with rotational motions at temperatures below the melting point and those in which the rotational and melting transitions coalesce. The former have entropies of fusion lower than the inert gas crystals, while the latter have much higher entropies of fusion (table 2.1.1). 

Pople and Karasz proposed a simple extension of the LJD model which at once provides an interpretation of these variations in the melting properties. They assumed that the molecule can take up one of two orientations on any site, so that it now has four possibilities, / , A, 5, and The state of perfect order (or the solid at zero temperature) may then be regarded as one in which all molecules occupy sites and orientations of the same type, say A, and the state of complete disorder (or the liquid phase) as one in which all four configurations are equally populated. Clearly, there can also be states with positional order and no orientational order and vice versa. 

---