Olivine, the most abundant mineral in the upper mantle, plays a key role in controlling the thermodynamic properties in the Earth’s and planetary interiors, like the temperature distribution along the adiabatic geotherm. In this study, we conducted simultaneous high-pressure (P) and high-temperature (T) Raman measurements on a San Carlos olivine sample in an externally heated diamond-anvil cell (DAC). The intrinsic anharmonic parameters, ai, are calculated as functions of both pressure and temperature, and the isochoric (CV) and isobaric (CP) heat capacities are computed at various P-T conditions with the anharmonic correction. The harmonic heat capacities are CV = 807.7 J/kg/K and CP = 815.4 J/kg/K at ambient conditions, with anharmonic contribution of ΔC = 7.9 J/kg/K. Relative to the previous vibrational measurements conducted at high-P or high-T conditions, this simultaneous high-P-T experiment indicates that the anharmonic contribution to heat capacities is overestimated if the anharmonic parameters (ai) are treated as constants, as done previously. The pressure effect is marginal on the intrinsic anharmonic contribution to thermodynamic properties, whereas it has a much more significant effect on the external anharmonicity (thermal expansivity). The pressure dependence of CP (dCP/dP, in J/kg/K/GPa) increases from –3.14 at 300 K to –1.94 at 700 K, and then decreases smoothly to –5.03 at 1800 K. Combining the derived high-P-T capacity with a reliable P-V-T equation of state (EoS) for olivine, we further modeled the thermodynamic Grüneisen parameter, γ(P-T). The Grüneisen parameter is important for the connection between isothermal and adiabatic compressions of minerals, which can be decreased by approximately 5% with the anharmonic correction at high temperatures. The modeled adiabatic bulk modulus and bulk sound velocity can be expressed as: KS(T,P) (GPa) = 127.5(1) + 4.32(5)∙P – 0.018(1)∙(T – 300) and VΦ(T-P) (km/s) = 6.22(2) + 0.069(3)∙P – [3.74(15)–0.075(13)∙P]∙10–4∙(T – 300). The adiabatic temperature gradient, dTS/dP, which is almost independent of pressure, equals 13.40(16) and 12.35(16) K/GPa in the harmonic and anharmonic models, respectively. This study provides a useful example for modeling the radial temperature distribution in adiabatic planetary mantles.

You do not have access to this content, please speak to your institutional administrator if you feel you should have access.