Abstract
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.
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Acknowledgements
The authors are grateful to Taku Tsuchiya, editor of Physics and Chemistry of Minerals, and the Reviewers for their valuable comments, thanks to which this study has been significantly improved. The study was supported by the Russian Science Foundation, Grant No. 21-77-10070. The calculation of thermodynamic functions for the studied MgSiO3-pyroxenes was made using the program registered in the Russian Federation (Certificate No. 2019610474).
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Russian Science Foundation, 21-77-10070.
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Conceptualization: TSS, PID and AIF; Methodology: PID; Software: TSS; Writing-original draft preparation: TSS, PID and AIF; Visualization, TSS, PID and AIF; Funding acquisition: TSS and AIF; Supervision: PID. The first draft of the manuscript was written by TSS and all authors read and approved the final manuscript.
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Sokolova, T.S., Dorogokupets, P.I. & Filippova, A.I. Equations of state of clino- and orthoenstatite and phase relations in the MgSiO3 system at pressures up to 12 GPa and high temperatures. Phys Chem Minerals 49, 37 (2022). https://doi.org/10.1007/s00269-022-01212-7
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DOI: https://doi.org/10.1007/s00269-022-01212-7