Pressure dependence of the thermal Grüneisen parameter, with application to the earth's lower mantle and outer core

Details Pressure dependence of the thermal Grüneisen parameter, with application to the earth's lower mantle and outer core Pressure dependence of the thermal Grüneisen parameter, with application to the earth's lower mantle and outer core

Nov 1975

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1975pepi...11..157i&link_type=abstract

Physics of the Earth and Planetary Interiors, Volume 11, Issue 2, p. 157-165.

Physics

14

Scientific paper

By considering high-temperature (classical) thermal oscillations of atoms in certain simple crystal structures with purely central interatomic forces, the treatment of anharmonic oscillations is generalised to random three-dimensional motion, yielding the Vashchenko and Zubarev relationship for the Grüneisen ratio γ at any pressure. If one-dimensional atomic oscillations only are considered the equation reduces to the Dugdale-MacDonald expression. To account for non-central forces additional terms must be introduced, giving: γ=1/2dK/dP-5/6+2/9P/K-f/18K+1/6df/dP/1-4/3P/K+f/3K where f = 0 for purely central forces. Calculations of f in terms of the Poisson ratio for different crystal structures have not been made, but for many materials the central-force approximation suffices. This is believed to be true both for the outer core (γ~1.4) and for the close-packed structures of the lower mantle (γ~1.0). For the upper mantle non-central atomic forces are important and we have no estimate of (γ independently of laboratory values for plausible minerals which suggest γ ~ 0.8.

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