Thermodynamics of Condensed Phases: Formula Unit Volume, Vm, and the Determination of the Number of Formula Units, Z, in a Crystallographic Unit Cell

Abstract

Formula unit (or molecular) volume, Vm, is related to many thermodynamic and physical properties of materials, so that knowledge of Vm is useful in prediction of such properties for known and even hypothetical materials. The symbol Z represents the number of formula units in a crystallographic unit cell; Z thus permits calculation of Vm from the unit-cell volume. Unfortunately, Z is sometimes omitted from published crystal constants (for obscure reasons).We discuss methods for evaluation of Z and Vm, and some of the complications in the assessment of Z. We show how entropy, lattice energy, and bulk isothermal compressibility (a thermoelastic property) are calculated using thermodynamic correlations, with the chalcopyrite CuAlS2 as an example.