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

ABSTRACT

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.

KEYWORDS:

• Equation of state
• silicates
• Helmholtz free energy
• mantle
• excel spreadsheets

Acknowledgments

We thank Dr. Yuliya Cherepanova for support in sound wave velocity calculations.

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Tatiana S. Sokolova http://orcid.org/0000-0003-1307-6963

Peter I. Dorogokupets http://orcid.org/0000-0002-2514-1470

Additional information

Funding

This work was supported by the Russian Foundation of Basic Research [project No 16-35-00061]. KL and AD thanks for the partial support from the RF state assignment [project No 0330-2016-0006].