## Modelling forsterite in the mantle: accuracy of interatomic potentials

Olivine (Mg,Fe)_{2}SiO_{4} is the most abundant mineral in the Earth’s upper mantle, therefore knowledge of its deformation mechanisms is of the uttermost importance. In addition to experimental investigations, simulations can provide insight on the elementary mechanisms at the atomic scale, at the condition of disposing of accurate models. Ab initio calculations provide the most accurate basis, but are restricted to relatively small systems, typically fewer than 1,000 atoms. Modelling extended defects such as dislocations or grain boundaries require larger simulation cells, of the order of 10,000 up to millions of atoms. To keep atomic resolution at such scales, one must turn to semi-empirical potentials, at the risk of loosing accuracy.

Since the 1980s several interatomic potentials were proposed to described forsterite, the Mg-rich end-member of olivine. We compare five of them with data from literature obtained experimentally or with *ab initio *calculations. We find that all interatomic potentials reproduce bulk properties with a good fidelity, but their accuracy differ when defects are involved. In particular, modelling generalized stacking faults (GSF) shows that most potentials fail to reproduce the energies of these defects, even qualitatively (Fig. 1). Only the shell-model three-body potential (THB1) proposed by Price et al in 1987 produces energies comparable to ab initio calculations. The rigid-ion potential fitted by Pedone in 2006 gives a correct qualitative trend, but underestimates the energies by a factor of 2. Other rigid-ion potentials fail completely because they produce a metastable stacking fault in the (010) plane, which is inconsistent with ab initio data. The accuracy on GSF energies is critical because they are closely related to the properties of dislocations, which are involved in the plastic deformation. Failing this test means that a potential is inadequate for modelling dislocations in forsterite, and for modelling other planar defects as well.

In the end, only the THB1 potential (Price et al 1987) is the best match to experimental and ab initio data for all properties studied. The Pedone potential gives good overall agreement, even if it is only qualitative agreement in the case of some stacking faults energies. Other rigid-ion potentials fail at describing planar defects.

This work paves the way for using interatomic potentials for studying complex defects like grain boundaries in forsterite, which is the goal of the NuMoGO project.

*Fig. 1 – Generalized stacking fault (GSF) energies in the (010) plane of forsterite, along [100] (top) and [001] (bottom) directions, at 0 GPa (left) and 10 GPa (right). Results obtained with interatomic potentials (lines) are compared with ab initio calculations published by J. Durinck et al (blue squares). On the right: atomic representation of the (010)[001] stacking fault. Mg ions are represented as orange spheres, and SiO4 tetrahedra in blue. This configuration is expected to be unstable from ab initio calculations, however several interatomic potentials fail to reproduce that behaviour.*

**To learn more: **

P. Hirel, J. Furstoss, P. Carrez (2021) A critical assessment of interatomic potentials for modelling lattice defects in forsterite Mg2SiO4 from 0 to 12 GPa, Physics and Chemistry of Minerals, 48, 12, https://doi.org/10.1007/s00269-021-01170-6