Ab initio thermal expansion and thermoelastic properties of ringwoodite (γ-Mg2SiO4) at mantle transition zone conditions

Thermal convection in the Earth’s mantle is driven by lateral variations in temperature and density which are substantially controlled by the local volume thermal expansion of the constituent mineral phases. Ringwoodite is a major component of the lower mantle transition zone, but its thermal expansivity and thermoelastic properties are still affected by large uncertainties. Ambient thermal expansion coefficient (α_V0), for instance, can vary as much as 100% according to different experimental investigations available from the literature. In this work, we perform ab initio density functional theory calculations of vibrational properties of spinel-structured Mg2SiO4 ringwoodite in order to provide reliable thermophysical data up to mantle transition zone conditions. Temperature- and pressure-dependent thermal expansivity has been obtained by phonon dispersion calculations in the framework of quasi-harmonic approximation (QHA) up to 25 GPa and 2000 K. Theoretical analysis of vibrational spectra reveals that accurate prediction of IR and silent modes, along with their relative mode Grüneisen parameters, is crucial to define thermal expansivity. A six-parameter analytical function is able to reproduce ab initio values fairly well in the whole investigated P-T range, i.e. α_V (P,T) = (1.6033·10-5 + 8.839·10-9 T + 11.586·10-3 T-1 – 6.055 T-2 + 804.31 T-3)·exp-(–2.52·10-2 P), with temperature in Kelvin and pressure in Gigapascal. Ab initio static and isothermal bulk moduli have been derived for ringwoodite along with their P, T and cross derivatives, i.e. K_0 = 184.3 GPa, K_(T,300K) = 176.6 GPa; K_0^' = 4.13, K_(T,300K)^' = 4.16; (〖∂K〗_T/∂T)_P = -0.0233 GPa/K and (〖∂^2 K〗_T/∂P∂T)_0= 1.0·10-4 K-1. Computed thermal expansivity and thermoelastic properties supports the evidence that QHA performs remarkably well for Mg2SiO4 ringwoodite up to mantle transition zone temperatures. Since volume thermal expansion of ringwoodite is strongly pressure-dependent and its pressure dependence becomes more marked with the increasing temperature, internally-consistent assessments and empirical extrapolation of thermoelastic data to deep mantle conditions should be taken with care to avoid inaccurate or spurious predictions in phase equilibrium and mantle convection numerical modelling.