The lattice dynamics and thermodynamics of the Mg2SiO4 polymorphs

We use an approach based upon the Born model of solids, in which potential functions represent the interactions between atoms in a structure, to calculate the phonon dispersion of forsterite and the lattice dynamical behaviour of the beta-phase and spinel polymorphs of Mg₂SiO₄. The potential used (THB1) was derived largely empirically using data from simple binary oxides, and has previously been successfully used to model the infrared and Raman behaviour of forsterite. It includes ‘bond bending’ terms, that model the directionality of the Si-O bond, in addition to the pair-wise additive Coulombic and short range terms. The phonon dispersion relationships of the Mg₂SiO₄ polymorphs predicted by THB1 were used to calculate the heat capacities, entropies, thermal expansion coefficients and Gruneisen parameters of these phases. The predicted heat capacities and entropies are in outstandingly good agreement with those determined experimentally. The predicted thermodynamic data of these phases were used to construct a phase diagram for this system, which has Clausius-Clapeyron slopes in very close agreement with those found by experiment, but which has predicted transformation pressures that show less close agreement with those inferred from experiment. The overall success, however, that we have in predicting the lattice dynamical and thermodynamic properties of the Mg₂SiO₄ polymorphs shows that our potential THB1 represents a significant step towards finding the elusive quantitative link between the microscopic or atomistic behaviour of minerals and their macroscopic properties.