Equations of state of clino- and orthoenstatite and phase relations in the MgSiO3 system at pressures up to 12 GPa and high temperatures

The equations of state of MgSiO₃-pyroxenes (low-pressure clinoenstatite, orthoenstatite and high-pressure clinoenstatite) are constructed using a thermodynamic model based on the Helmholtz free energy and optimization of known experimental measurements and calculated data for these minerals. The obtained equations of state allow us to calculate a full set of thermodynamic and thermoelastic properties as depending on T–P or T–V parameters. We offer open working MS Excel spreadsheets for calculations, which are a convenient tool for solving various user’s tasks. The phase relations in the MgSiO₃ system are calculated based on the estimated Gibbs energy for studied MgSiO₃-pyroxenes and clarify other calculated data at pressures up to 12 GPa and temperatures up to 2000 K. The obtained orthoenstatite → high-pressure clinoenstatite phase boundary corresponds to the following equation P(GPa) = 0.0021 × T(K) + 4.2. The triple point of equilibrium is determined at 1100 K and 6.5 GPa. Isotropic compressional (P) and shear (S) wave velocities of orthoenstatite and high-pressure clinoenstatite at different pressures are calculated based on the obtained equations of state. The calculated jumps of P- and S-wave velocities of orthoenstatite → high-pressure clinoenstatite phase transition at a pressure of ~ 9 GPa are 0.7 and 5.1%, respectively. The calculated jump of the density of this phase transition at a pressure of 8 GPa, which corresponds to the depth of ~ 250 km, is 2.9%. These results are used to discuss the location of the seismic X-discontinuity at the depths of 250–340 km, which is associated with phase boundaries in enstatite.