Computational methods for the study of energies of cation distributions: applications to cation-ordering phase transitions and solid solutions

The structural and thermodynamic properties of minerals are strongly affect ed by cation site-ordering processes. We describe methods to determine the main interatomic interactions that drive the ordering process, which are ba sed on parameterizing model Hamiltonians using empirical interatomic potent ials and/or ab initio quantum mechanics methods. The methods are illustrate d by a number of case study examples, including Al/Si ordering in aluminosi licates, Mg/Ca ordering in garnets, simultaneous Al/Si and Mg/Al ordering i n pyroxenes, micas and amphiboles, and Mg/Al non-convergent ordering in spi nel using only quantum mechanical methods.