Interpretation of adiabatic decompression measurements of the Grüneisen parameter

Authors

  • Frank D. Stacey


Abstract

The most direct measurement of the thermodynamic Grüneisen parameter γ of a material is by observation of temperature changes accompanying sudden (adiabatic) compressions or decompressions. Measurements over a wide pressure range permit the dependence of γ upon density ρ to be inferred, but if measurements are made below the Debye temperature of the material, interpretation of the results may be confused by the temperature dependence of γ. If the temperature dependence is measured for the same samples, the density dependence may be adjusted to refer to a specimen held at a constant fraction of its Debye temperature, instead of constant temperature, by the equation [−(∂ &#55349;&#56513;n γ/∂ &#55349;&#56513;n ρ)T/θ] = [−(∂ &#55349;&#56513;n γ/∂ &#55349;&#56513;n ρ)T] × [1 + αT(d &#55349;&#56513;n θ/d &#55349;&#56513;n ρ)] − (∂ &#55349;&#56513;n γ/∂ &#55349;&#56513;n T)P(d &#55349;&#56513;n θ/d &#55349;&#56513;n ρ) where (∂ &#55349;&#56513;n γ/∂ &#55349;&#56513;n ρ)T/θ is the more fundamental quantity and for crystals with high Debye temperatures, will commonly be smaller in magnitude than (∂ &#55349;&#56513;n γ/∂ &#55349;&#56513;n ρ)T (both being negative) because (∂ &#55349;&#56513;n γ/∂ &#55349;&#56513;n T)P is positive at T < θ. Ideally, for geophysical purposes, we are interested in (∂ &#55349;&#56513;n γ/∂ &#55349;&#56513;n ρ)T>θ which is probably not very dependent on T and for which (∂ &#55349;&#56513;n γ/∂ &#55349;&#56513;n ρ)T/θ at T < θ appears to be a good approximation, but (∂ &#55349;&#56513;n γ/∂ &#55349;&#56513;n ρ)T for T < θ is not. However, the difference appears to be small for Cu, NaCl, CaF2 and α-SiO2.

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