Simulation studies on the pyrope-grossular garnet solid solution

The local structural response of Ca/Mg substitution and the energetic effec ts associated with dodecahedral ordering in the pyrope-grossular garnet sol id solution are derived from a combination of static lattice energy calcula tions and Monte Carlo simulations. We start with a thorough analysis of the goodness of the empirical potential models used for the modelling of alumi nosilicate garnets. The degree of polyhedral distortion was found to be a s ensitive indicator for the quality of the model and, by comparison with exp erimental data, was used to select the best of several available empirical potentials. The Ca/Mg substitution on the dodecahedral site in garnet was f ound to produce strong local distortions in the surrounding tetrahedral and octahedral polyhedra. This arises from the absence of rigid unit modes (RU MS) in the garnet structure, because local rotations of otherwise rigid SiO 4 tetrahedra and AlO6 octahedra cannot occur in order to accommodate differ ent-sized divalent cations in the dodecahedral sites. Strain effects. there fore. mainly govern the dodecahedral substitution, and the corresponding st rain field around a dodecahedral site has a minimum radius of 5 Angstrom. P yrope-grossular solid solution compositions were modelled using a supercell approach. For several garnet compositions many different configurations re presenting individual disordered arrangements were relaxed. The resulting e nergies were analyzed in terms of different-neighbour interactions to deter mine the parameters of a model Hamiltonian. The corresponding interaction e nergies were found to be virtually independent of composition. Surprisingly , the nearest neighbour interaction between edge-sharing dodecahedra is of no particular significance in the garnets. Instead, the strongest interacti on is only via the third-nearest neighbours, i.e. dodecahedra that are edge -shared to a common SiO4 tetrahedron. This cannot lead to dodecahedral long -range order in garnets, but can produce significant amounts of short-range order. Monte Carlo simulations were performed on several compositions to d etermine the macroscopic effects such as NMR-based cluster occupancy, order ing energy and configurational entropy of the short-range ordering process. As expected, the samples tend to random disorder at high temperatures, and at low temperatures it is compositions nearer Py50Gr50 that depart most st rongly from random mixing. For example, a maximum reduction of 3.5 J mol(-1 ) K-1 is predicted for Py75Gr25 and similar to 10 J mol(-1) K-1 for Py50Gr5 0. A comparison of NMR cluster occupancy with experimental Si-29 MAS NMR re sonance intensity is partly successful. However, the changes in NMR cluster occupancy are relatively low (similar to 5%) compared to changes in config urational entropy (similar to 30%), implying that it might be difficult to estimate exact entropy data from Si-29 MAS NMR line intensities.