Computational study of tetrahedral Al-Si and octahedral Al-Mg ordering in phengite

As part of a wider study of the nature and origins of cation order-disorder in micas, a variety of computational techniques have been used to investigate the nature of tetrahedral and octahedral ordering in phengite, K₂^[6](Al₃Mg ^[4](Si₇Al)O₂₀(OH)₄. Values of the atomic exchange interaction parameters J_n used to model the energies of order-disorder were calculated. Both tetrahedral Al-Si and octahedral Al-Mg ordering were studied and hence three types of interaction parameter were necessary: for T-T, O-O and T-O interactions (where T denotes tetrahedral sites and O denotes octahedral sites). Values for the T-T and O-O interactions were taken from results on other systems, whilst we calculated new values for the T-O interactions. We have demonstrated that modelling the octahedral and tetrahedral sheets alone and independently produces different results from modelling a whole T-O-T layer, hence justifying the inclusion of the T-O interactions. Simulations of a whole T-O-T layer of phengite indicated the presence of short-range order, but no long-range order was observed.