Statistical thermodynamics -- A tool for understanding point defects in intermetallic compounds

The principles of the derivation of statistical-thermodynamic models to interpret the compositional variation of thermodynamic properties in non-stoichiometric intermetallic compounds are discussed. Two types of models are distinguished: the Bragg-Williams type, where the total energy of the crystal is taken as the sum of the interaction energies of all nearest-neighbor pairs of atoms, and the Wagner-Schottky type, where the internal energy, the volume, and the vibrational entropy of the crystal are assumed to be linear functions of the numbers of atoms or vacancies on the different sublattices. A Wagner-Schottky type model is used for the description of two examples with different crystal structures: for β'-FeAl (with B2-structure) defect concentrations and their variation with composition are derived from the results of measurements of the aluminum vapor pressure, the resulting values are compared with results of other independent experimental methods; for Rh3Te4 (with an NiAs-derivative structure) the defect mechanism responsible for non-stoichiometry is worked out by application of a theoretical model to the results of tellurium vapor pressure measurements. In addition it is shown that the shape of the activity curve indicates a certain sequence of superstructures. In principle, there are no limitations to the application of statistical thermodynamics to experimental thermodynamic data as long as these are available with sufficient accuracy, and as long as it is ensured that the distribution of the point defects is truly random, i.e. that there are no aggregates of defects