Elasticity of selected icy satellite candidate materials (CO2, C6H6, MgSO4·7H2O and CaSO4·2H2O) revisited by dispersion corrected density functional theory

Abstract

Seismic studies are essential for accurate characterisation of planetary interior structures, but are dependent on modelling for interpretation, requiring data on the elastic properties of likely constituent minerals. With the potential deployment of seismic stations on icy worlds such as Europa and Titan envisioned for the near future, a campaign of study into the elasticity of potential icy ocean world minerals is of paramount importance. In the paper we assess the role of first-principles computer simulations to this problem, in particular focussing on the application of recent advances in simulating dispersion forces in loosely-bonded molecular solids, likely to be the main constituents of icy ocean worlds. This is of particular interest for these kinds of materials, since the complex sample handling, phase transitions and the difficulty of obtaining single crystals often greatly complicates the experimental determination of the full elastic tensor. We focus on CO2, C6H6, MgSO4·7H2O and CaSO4·2H2O as they allow us to benchmark the performance over a wide range of chemical space, structural topologies, crystal symmetries and bonding types, and moreover have accurate experimentally determined unit-cell dimensions, bulk moduli and full elastic tensors for benchmarking purposes. We demonstrate that the dispersion corrected approaches indeed perform better in modelling the experimental density profiles (mean unsigned differences of only 0.04 g/cm3 (CO2), 0.02 g/cm3 (C6H6), 0.003 g/cm3 (MgSO4·7H2O) and 0.013 g/cm3 (CaSO4·2H2O)) and may find application in exploring the compressive parameters of candidate materials, which could then be used in rheological models of icy ocean worlds. Moreover, we have assessed if the elastic constants computed by dispersion corrected density functional theory are accurate enough to be used in a reference data base for the seismic exploration of icy ocean worlds. Despite one approach having demonstrated good accuracy compared with the experimental values in modelling the elasticity of CO2, we instead find average differences from expected P and S wave velocities of around 10 to 25% for the elastically more complex title compounds. In part these differences are due to the large temperature difference between the experimental elasticity data (typically near 300 K) and our calculations, which were performed in the athermal limit.