The lattice dynamics of forsterite

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Abstract
We use an approach based upon the atomistic or Born model of solids, in which potential functions represent the interactions between atoms in a structure, to calculate the infrared and Raman vibrational frequencies of forsterite. We investigate a variety of interatomic potentials, and find that although all the potentials used reproduce the structural and elastic behaviour of forsterite, only one potential (THB1) accurately predicts its lattice dynamics. This potential includes ‘bond-bending’ terms, that model the directionality of the Si-O bond, which we suggest plays a major role in determining the structural and physical properties of silicates. The potential was derived empirically from the structural and physical data of simple oxides, and its ability to model the lattice dynamics of forsterite is a significant advance over previous, force-constant models, which have been simply derived by fitting to the spectroscopic data that they aim to model. The success that we have had in predicting the lattice dynamics of forsterite indicates that the potential provides the previously elusive yet fundamental, quantitative link between the microscopic or atomistic behaviour of a mineral and its macroscopic or bulk thermodynamic properties.

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