The thermodynamics of charged defects in ionic crystals

Abstract

A generic methodology is developed in this thesis to calculate the thermodynamic contribution due to high concentrations of charged defects in ionic crystals. The aim of this methodology is to allow atomistic defect behaviour, such as correlation between defects, to be included in higher-level simulation techniques, for example, when calculating phase diagrams (using CALPHAD [1, 2]) or obtaining charge-concentration profiles through techniques such as solving the Poisson-Boltzmann equation. A number of Monte Carlo methods (specific-heat integration (SHI) [3], Wang-Landau sampling (WL) [4,5] and nested sampling (NS) [6]) have been applied to a model of a simple solid-electrolyte system. This is an example of a system wherein defects in ionic crystals play a central role in the behaviour. The methods are then used to calculate the thermodynamic properties of the model; for example, it is shown that one can readily obtain the Helmholtz free energy. These properties can in turn be used to parameterise simple regularsolution approaches that allow the provision of a continuum-level description of the free energy. The thermodynamic description obtained from these Monte Carlo methods is compared to those given by more-traditional defect models, such as ideal-solution theory and Debye-Huckel theory, and it is shown that the thermodynamic behaviour of our model system agrees with such a description in the correct limits. The SHI, NS, and WL methods are compared in terms of computational efficiency and ease of implementation, and suggestions are made concerning the applicability of the methods in different regimes. Finally, some suggestions are made as to extensions and further applications of the work.