Modelling in relation to cation ordering

We review the methodology of using computer models to obtain quantitative i nformation about cation ordering. Empirical interatomic potentials or ab in itio electronic structure calculations are used to generate the energies fo r many configurations containing disordered arrangements of cations, and th e parameters in model Hamiltonians can be determined from these energies. M onte Carlo simulations are then used to generate ensemble averages as funct ions of temperature or chemical composition. Analysis of the Monte Carlo en sembles directly yields the temperature dependence of long-range and short- range order, and thermodynamic quantities such as energy and heat capacity. Use of thermodynamic integration allows for the calculation of entropy and free energy. The methods are illustrated by examples showing long-range or der/disorder phase transitions (feldspars), short-range order in solid solu tions (pyrope-grossular), and non-convergent ordering (magnesium aluminate spinel); where comparisons with experimental data are possible, the model c alculations are seen to give results that are reasonably accurate. The exam ple in which ab initio electronic structure calculations are used show that it is now possible to extract accurate thermodynamic data for ordering pro cesses using models that require no prior experimental data.