Spreadsheets to calculate <i>P–V–T</i> relations, thermodynamic and thermoelastic properties of silicates in the MgSiO₃–MgO system

Modified equations of state (EoS) of forsterite, wadsleyite, ringwoodite, akimotoite, bridgmanite and post-perovskite based on the Helmholtz free energy are described using Microsoft Excel spreadsheets. The equations of state were set up by joint analysis of reference experimental data and can be used to calculate thermodynamic and thermoelastic parameters and P–V–T properties of the Mg-silicates. We used Visual Basic for Applications module in Microsoft Excel and presented a simultaneous calculation of full set of thermodynamic and thermoelastic functions using only T–P and T–V data as input parameters. Phase transitions in the MgSiO3–MgO system play an important role in the interpretation of the seismic boundaries of the upper Earth’s mantle and in the D″ layer. Therefore, proposed EoSes of silicates in the MgSiO3–MgO system have clear geophysical implications. The developed software will be interesting to specialists who are engaged to study the mantle mineralogy and Earth’s interior.基于亥姆霍兹自由能（Helmholtz free energy）的镁橄榄石（forsterite）、瓦兹利石（wadsleyite）、林伍德石（ringwoodite）、秋本石（akimotoite）、布里奇曼石（bridgmanite）及后钙钛矿（post-perovskite）的修正状态方程（Equations of State, EoS）以Microsoft Excel电子表格形式呈现。本套状态方程通过联合分析参考实验数据构建完成，可用于计算镁硅酸盐的热力学、热弹性参数以及压强-体积-温度（P-V-T）性质。本研究借助Microsoft Excel中的Visual Basic for Applications（VBA）模块，实现了仅以温度-压强（T-P）与温度-体积（T-V）数据作为输入参数，对全套热力学及热弹性函数的同步计算。MgSiO₃-MgO体系中的相变，对于解释地球上地幔的地震波边界及D''层具有重要意义。因此，本次提出的MgSiO₃-MgO体系硅酸盐状态方程，具备明确的地球物理学应用价值。本研究开发的软件，将对从事地幔矿物学与地球内部研究的专业人员具有参考价值。