A thermodynamic theory of the Grüneisen ratio at extreme conditions: MgO as an example |
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| Authors: | Orson L Anderson Hitoshi Oda Anastasia Chopelas Donald G Isaak |
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| Institution: | 1. Center for Earth and Planetary Interiors, Institute of Geophysics and Planetary Physics UCLA, 90024, Los Angeles, CA, USA
2. Max Planck Institut für Chemie, Postfach 3060, W-6500, Mainz, Germany
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| Abstract: | The Grüneisen ratio, γ, is defined as γy=αK TV/Cv. The volume dependence of γ(V) is solved for a wide range in temperature. The volume dependence of αK T is solved from the identity (? ln(αK T)/? ln V)T ≡ δ T-K′. α is the thermal expansivity; K T is the bulk modulus; C V is specific heat; and δ Tand K′ are dimensionless thermoelastic constants. The approach is to find values of δ T and K′, each as functions of T and V. We also solve for q=(? ln γ/? ln V) where q=δ T -K′+ 1-(? ln C V/? ln V)T. Calculations are taken down to a compression of 0.6, thus covering all possible values pertaining to the earth's mantle, q=? ln γ/? ln V; δ T=? ln α/? ln V; and K′= (?K T/?P)T. New experimental information related to the volume dependence of δ T, q, K′ and C V was used. For MgO, as the compression, η=V/V 0, drops from 1.0 to 0.7 at 2000 K, the results show that q drops from 1.2 to about 0.8; δ T drops from 5.0 to 3.2; δ T becomes slightly less than K′; ? ln C V/? In V→0; and γ drops from 1.5 to about 1. These observations are all in accord with recent laboratory data, seismic observations, and theoretical results. |
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