General thermodynamic treatment of ammonium chloride system close to phase transitions

Abstract

In ammonium halides the optical and acoustical phonons may be represented by the Einstein and Debye models. Close to the λ-phase-transition, the model for the lattice vibrations in these crystals requires an extra component which can be described by an Ising model. In this study we have developed an Ising model superimposed on an Einstein and/or Debye model and have applied it to the NH 4Cl system. In this application we have used the Raman frequency of the ν 5(174cm −1) phonon of NH 4Cl to characterize the corresponding Einstein and Debye frequency for this crystal system. Thus from our observed frequencies for the 174cm −1 (TO) mode we have obtained an approximation for the lattice vibrational contribution to the specific heat C y of NH 4Cl. The critical behaviour of the specific heat has been obtained for the Ising model, since the Einstein or Debye model is considered to show no anomaly in C v near the phase transition. The predicted values are close to observed C p data but differ significantly from the only observed C v data available, (Sakamoto, 1954) It is suggested that the observed C y data is unreliable in the vicinity of the λ-transition. The present model, or modifications of it should be capable of giving quite precise descriptions of the thermodynamic properties of solids close to second-order (or nearly second-order) phase transitions.