Comparative study of quasiharmonic lattice dynamics, molecular dynamics and Debye model applied to MgSiO 3 perovskite

Abstract

We consider three independent methodologies for calculating thermal equation of state (EOS) of the major earth-forming mineral, orthorhombic MgSiO 3 perovskite: molecular dynamics (MD), lattice dynamics (LD) and Debye model (DM). Using the most recent developments in the GULP code, we derive a new interatomic potential, which is demonstrated to be extremely robust at both high temperatures and high pressures. With this potential we construct a quasiharmonic self-consistent DM based on elastic properties of the crystal, and compare its results with results of more rigorous LD and MD simulations with the same potential model. We show that the DM reproduces quite accurately harmonic constant-volume heat capacity above 500 K, but gives thermal expansion and Grüneisen parameter ( γ) that are too small. We conclude that MgSiO 3 perovskite is not a Debye-like solid, in contrast to what has often been assumed in geophysical literature. Acoustic γ, often used in geophysical studies, are a very crude approximation to the true γ. To obtain good accuracy, one needs to know the γ( V) function more accurately than the DM can give. However, analytical functions, given by the Debye theory, are useful for fitting thermal expansion and related parameters at elevated temperatures. A common assumption that q= d ln γ/ d ln V is constant is found to be inadequate: in fact, q varies strongly with volume and can reach negative values towards the base of the lower mantle. This can be relevant for discussion of the anomalous properties of the core-mantle boundary (D″) layer. Comparison of results of LD and MD indicates importance of intrinsic anharmonic contributions in the thermal expansion and γ. Therefore, MD is the most suitable technique for simulating minerals at the Earth’s mantle conditions.