Lattice Statistics of Hydrogen Bonded Crystals. II. The Slater KDP Model and the Rys F-Model

The Slater KDP model, a simple hydrogen bonded ferroelectric model, and the Rys F-model, a simple hydrogen bonded antiferroelectric model, have been treated using both high- and low-temperature series for the partition function. The high-temperature series is a modification of the residual entropy of ice series discussed in I. For each model a temperature is found at which the high-temperature series and the low-temperature series are identically equal. For the KDP model this equality gives a transition temperature and a latent heat is easily calculated, both of which are exact. It so happens that these exact results agree with previous analyses which used only mean field approximations. For the F-model the formal equality of the series gives the first evidence for a phase transition. Although the latent heat calculation throws some doubt on the existence of a transition, after further discussion of the series it is concluded that there most probably is a phase transition.