Thermodynamic properties of MgAl₂O₄ spinel are significant in understanding the phase relations of the Earth’s crust and upper mantle, but available values from experimental measurements are limited at ambient pressure conditions to date. Based on an iterative numerical approach and experimental data from the literature, we determined the self-consistent unit-cell volume, elastic moduli, and, particularly, thermodynamic properties, including thermal expansion, heat capacity, entropy, and the Grüneisen parameter of MgAl₂O₄ spinel over a wide temperature and pressure range. The obtained thermal expansion, heat capacity, entropy, and Grüneisen parameter of MgAl₂O₄ spinel show nonlinearly and are negatively correlated with pressure. Most importantly, we found that the pressure effects on thermal expansion and entropy increase with temperature, whereas the pressure effect on the heat capacity and the Grüneisen parameter decreases to a minimum at ~400 K and ~700 K, respectively, then increases or remains almost constant above this temperature, respectively.

Using an iterative numerical approach, we have obtained the self-consistent thermal expansion, heat capacity, and Grüneisen parameters of diopside (MgCaSi₂O₆) over wide pressure and temperature ranges based on experimental data from the literature. Our results agree well with the published experimental and theoretical data. The determined thermodynamic parameters exhibit nonlinear dependences with increasing pressure. Compared with other minerals in the upper mantle, we found that the adiabatic temperature gradient obtained using the thermodynamic data of diopside is larger than that of garnet while lower than that of olivine, when ignoring the Fe incorporation. Combining our results with thermodynamic parameters of garnet obtained in previous studies, we have estimated the adiabatic temperature gradient and geotherm of an eclogitic upper mantle in a depth range of 200–450 km. The results show that the estimated adiabatic temperature gradient of the eclogite model is ~16% and ~3% lower than that of the pyrolite model at a depth of 200 km and 410 km, respectively. However, the high mantle potential temperature of the eclogite model leads to a similar temperature as the pyrolite model in a depth range of 200–410 km.

The thermodynamic properties of MgSiO₃ akimotoite at high temperatures and high pressures are important for investigating the phase equilibria of the Earth’s transition zone and the upper part of the lower mantle. In this paper, we present the self-consistent unit-cell volume, elastic properties, and in particular, thermodynamic properties including thermal expansion, heat capacity, entropy, and Grüneisen parameter of MgSiO₃ akimotoite at pressures up to 30 GPa and temperatures to 2000 K using an iterative numerical method and available experimental data, which are consistent with the previous studies. The results show that the determined thermal expansion, heat capacity, entropy, and Grüneisen parameter exhibit a nonlinear and negative relationship with increasing pressure. Additionally, the pressure derivatives of these thermodynamic parameters along with the temperature are also presented.

超硅石榴石作为地幔过渡带的重要组成部分，对于理解地球内部的物理化学特性和相平衡十分重要。本研究通过迭代数值方法，并结合前人已发表的实验数据，研究了在较大温度和压力范围内，超硅石榴石的单晶体积和弹性性质，尤其是包括热膨胀系数、等压热容、熵和Grüneisen参数在内的热力学性质。研究发现，随着压力的升高，超硅石榴石的热膨胀系数、等压热容、熵和Grüneisen参数与压力呈现非线性的负相关关系。其中，热膨胀系数、等压热容和Grüneisen参数对压力的一阶导数分别在温度达到约470 K、860 K和1050 K时达到峰值，随后逐渐降低；而压力对熵的影响则在研究的温度范围内持续增强。本研究为我们了解地球内部物质组成特征，特别是地幔过渡带的相变提供了重要的参考。