A computational study of magnesium point defects and diffusion in forsterite

We have studied the formation and migration of point defects within the magnesium sub-lattice in forsterite using a combination of empirical and quantum mechanical modelling methodologies. Empirical models based on a parameterised force field coupled to a high throughput grid computing infrastructure allow rapid evaluation of a very large number of possible defect configurations. An embedded cluster approach reveals more accurate estimates of defect energetics for the most important defect configurations. Considering all defects in their minimum energy, equilibrium positions, we find that the lowest energy intrinsic defect is the magnesium Frenkel type, where a magnesium atom moves from the M1 site to form a split interstitial defect. This defect has 2 four-co-ordinated magnesium atoms located outside opposite triangular faces of an otherwise vacant M1 octahedron. The split interstitial defect is more stable than regular interstitials where magnesium is located in either of the two structurally vacant octahedral sites in the hexagonally close packed oxygen lattice. M1 vacancies are also found to form when iron(II) oxidises to iron(III). The energy of the defects away from the equilibrium positions allows the energy barrier to diffusion to be calculated. We have considered the migration of both magnesium vacancies and interstitials and find that vacancies are more mobile. When the contribution from the formation energy of the defects is included we arrive at activation energies for vacancy diffusion that are in agreement with experiment.