Progress in Modeling Heat Capacity versus Temperature Morphology *

After discussion of other models for representing heat capacities, the volumetric model used in resolution of lanthanide Schottky contributions over the cryogenic range and a more recent single-parameter formula to represent the lattice heat capacity, to resolve excess heat capacity contributions, to extrapolate lattice heat capacity beyond the measured temperature regions, and to predict thermodynamic properties of a compound in a series of known isostructural compounds is described. It is based on a new phonon distribution function improved over the Debye model by distinguishing between transverse and longitudinal modes, differences in the masses of the constituent atoms, the actual shape of the first Brillouin zone, the discreteness of the crystal structure, etc. Several other parameters included in the formula are uniquely determined from chemical, crystallographic, and elastic data. The single characteristic temperature (0), is retained in the formula as a parameter to be determined by fitting the calorimetric data. The success of the model was checked by plotting the apparent characteristic temperature against temperature for experimental heat-capacity data of compounds with purely lattice heat capacities.