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High‐temperature elastic constant data on minerals relevant to geophysics
Author(s) -
Anderson Orson L.,
Isaak Donald,
Oda Hitoshi
Publication year - 1992
Publication title -
reviews of geophysics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 8.087
H-Index - 156
eISSN - 1944-9208
pISSN - 8755-1209
DOI - 10.1029/91rg02810
Subject(s) - thermodynamics , extrapolation , thermal expansion , anharmonicity , helmholtz free energy , thermoelastic damping , adiabatic process , bulk modulus , geothermal gradient , enthalpy , geophysics , thermal , debye model , physics , mineralogy , geology , condensed matter physics , mathematics , mathematical analysis
The high‐temperature measurements of elastic constants and related temperature derivatives of nine minerals of interest to geophysical and geochemical theories of the Earth's interior are reviewed and discussed. A number of correlations between these parameters, which have application to geophysical problems, are also presented. Of especial interest is α, the volume coefficient of thermal expansion, and a section is devoted to this physical property. Here we show how α can be estimated at very high temperatures and how it varies with density. An estimate of α for Mg‐perovskite at deep‐mantle conditions is made. The formula for the Grüneisen ratio γ as a function of V and T is presented, including plots of the numerical values of γ over a wide T and V range. An example calculation of γ for MgO is made. The high‐ T ‐high‐ P values of γ calculated here agree well with results from the ab initio method of calculation for MgO. The use of the thermoelastic parameters is reviewed, showing application to the understanding of thermal pressure, thermal expansivity, enthalpy, and entropy. We review an extrapolation formula to determine K s , the adiabatic bulk modulus, at very high T . We show that the thermal pressure is quite linear with T up to high temperatures (∼1800 K), and, as a consequence, the anharmonic contribution to the Helmholtz free energy is sufficiently small, so that it can and should be ignored in thermodynamic calculations for mantle conditions.