Thermodynamic and Elastic Properties of Grossular at High Pressures and High Temperatures: A First‐Principles Study

Abstract

Thermodynamic and elastic properties of grossular (Ca3Al2(SiO4)3, the calcium‐aluminium end‐member of garnet) at high pressures and temperatures are obtained using the first‐principles calculations based on the density functional theory. Our calculated results agree well with available experimental data. The elastic moduli and wave velocities of grossular exhibit the nonlinear pressure and temperature dependences. Although the bulk moduli of grossular are similar to those of pyrope (Mg3Al2(SiO4)3) and almandine (Fe3Al2(SiO4)3), its shear moduli are significantly larger than those of pyrope and almandine. Combining our calculated results with previously calculated elasticity of other upper‐mantle minerals, we estimated density and wave velocity profiles for the pyrolitic and eclogitic compositions along different mantle geotherms. We find that a pyrolitic composition along the normal geotherm can well reproduce the reference velocities and densities for the upper mantle, supporting a pyrolitic upper mantle. Although an eclogitic composition also has similar velocities to reference seismic models above 300 km, it is significantly denser than the pyrolitic composition and the ambient mantle. However, the velocities of eclogite along the cold geotherm are relatively larger than those of the pyrolitic composition, indicating that the presence of eclogite in subduction zones could produce high‐velocity anomalies. In addition, the decomposition of grossular to calcium perovskite and corundum at the conditions of the mantle transition zone can produce considerable velocities and density jumps, which probably provides an interpretation for the seismically observed multiple reflections at ~660 km.

Elasticity of hydrous ringwoodite at mantle conditions: Implication for water distribution in the lowermost mantle transition zone

“…Wu and Wentzcovitch (2011) developed a semi-analytical method that only needs the vibrational properties of unstrained configurations to calculate the high P-T elasticity, which consequently reduces the computational work to the level of less than one-tenth of the conventional method. This approach has been successfully applied to the thermal elasticity of many minerals (Duan et al, 2019;Hao et al, 2019;Hu et al, 2016;Núñez-Valdez et al, 2013;Núñez Valdez et al, 2012;Qian et al, 2018;Shukla et al, 2016Shukla et al, , 2015Wang et al, 2019Wang et al, , 2020Wang and Wu, 2018;Wu et al, 2013;Wu and Wang, 2016;Wu and Wentzcovitch, 2011;Yang et al, 2017;Yang and Wu, 2014;Zou et al, 2018), and so we use it to obtain the elastic properties of hydrous ringwoodite at high P-T conditions in this study. The adiabatic bulk modulus KS and shear modulus G are obtained by using the Voigt-Reuss-Hill averages, and compressional wave velocity (VP) and shear wave velocity (VS) are from elastic moduli and density using 𝑉 \ = ](𝐾 _ + à 𝐺)/𝜌 and 𝑉 _ = e𝐺/𝜌.…”

“…First-principles calculations were performed using the Quantum Espresso package (Giannozzi et al, 2009) based on the density functional theory (DFT), adopting the local density approximation (LDA) for the exchange-correlation function, unless noted otherwise. The pseudopotentials of Mg, Si, H, and O are described in our previous studies (Duan et al, 2019;Hu et al, 2016;Wang et al, 2019). The cutoff energy for the plane wave was 70 Ry.…”

Self-Consistent Thermodynamic Parameters of Diopside at High Temperatures and High Pressures: Implications for the Adiabatic Geotherm of an Eclogitic Upper Mantle

“…Therefore, with the high temperature and high pressure thermodynamic data on diopside and eclogitic garnet, the temperature at a depth of 200 km can be estimated as 1699-1762 K via Equation ( 13) [50]. It is worth noting that the eclogitic garnet is composed of approximately 40% pyrope, 30% almandine, and 30% grossular [67,68].…”

“…However, the temperature of the eclogite model does not show the increase demonstrated in the pyrolite model at the 410 km discontinuity, but maintains the same trend at a depth of 450 km. It is worth noting that, except for olivine, the peridotitic garnet, clinopyroxene, and orthopyroxene are essential compositions in a pyrolite mantle [67,70]. Additionally, the majority of the clinopyroxene in an eclogite mantle is considered to be omphacite, which is mainly composed of diopside and jadeite (NaAlSi 2 O 6 ) [71].…”

Ab initio calculations of third-order elastic coefficients

“…A particular case of the effects of stress on SOECs involves their pressure derivatives, and such derivatives can be analytically expressed in terms of TOECs [see, e.g., 7,[20][21][22]. This could reasonably explain why stressinduced changes in SOECs can be conveniently described in terms of pressure-derivatives of SOECs, as shown in recent studies [4,23]. In this study, we validate relationships between pressure derivatives of SOECs and predictions based on TOECs; a simplified expression thanks to our introduction of effective TOECs is also validated.…”