Tatiana S. Sokolova, Peter I. Dorogokupets, Alena I. Filippova
{"title":"Equations of state of clino- and orthoenstatite and phase relations in the MgSiO3 system at pressures up to 12 GPa and high temperatures","authors":"Tatiana S. Sokolova, Peter I. Dorogokupets, Alena I. Filippova","doi":"10.1007/s00269-022-01212-7","DOIUrl":null,"url":null,"abstract":"<div><p>The equations of state of MgSiO<sub>3</sub>-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 <i>T–P</i> or <i>T–V</i> 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 MgSiO<sub>3</sub> system are calculated based on the estimated Gibbs energy for studied MgSiO<sub>3</sub>-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 <i>P</i>(GPa) = 0.0021 × <i>T</i>(K) + 4.2. The triple point of equilibrium is determined at 1100 K and 6.5 GPa. Isotropic compressional (<i>P</i>) and shear (<i>S</i>) wave velocities of orthoenstatite and high-pressure clinoenstatite at different pressures are calculated based on the obtained equations of state. The calculated jumps of <i>P</i>- and <i>S</i>-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.</p></div>","PeriodicalId":20132,"journal":{"name":"Physics and Chemistry of Minerals","volume":"49 9","pages":""},"PeriodicalIF":1.2000,"publicationDate":"2022-08-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00269-022-01212-7.pdf","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Physics and Chemistry of Minerals","FirstCategoryId":"89","ListUrlMain":"https://link.springer.com/article/10.1007/s00269-022-01212-7","RegionNum":4,"RegionCategory":"地球科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATERIALS SCIENCE, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 2
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.
期刊介绍:
Physics and Chemistry of Minerals is an international journal devoted to publishing articles and short communications of physical or chemical studies on minerals or solids related to minerals. The aim of the journal is to support competent interdisciplinary work in mineralogy and physics or chemistry. Particular emphasis is placed on applications of modern techniques or new theories and models to interpret atomic structures and physical or chemical properties of minerals. Some subjects of interest are:
-Relationships between atomic structure and crystalline state (structures of various states, crystal energies, crystal growth, thermodynamic studies, phase transformations, solid solution, exsolution phenomena, etc.)
-General solid state spectroscopy (ultraviolet, visible, infrared, Raman, ESCA, luminescence, X-ray, electron paramagnetic resonance, nuclear magnetic resonance, gamma ray resonance, etc.)
-Experimental and theoretical analysis of chemical bonding in minerals (application of crystal field, molecular orbital, band theories, etc.)
-Physical properties (magnetic, mechanical, electric, optical, thermodynamic, etc.)
-Relations between thermal expansion, compressibility, elastic constants, and fundamental properties of atomic structure, particularly as applied to geophysical problems
-Electron microscopy in support of physical and chemical studies
-Computational methods in the study of the structure and properties of minerals
-Mineral surfaces (experimental methods, structure and properties)