Grüneisen Parameter from Thermal Conductivity Measurements under Pressure

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Abstract
A relation is discussed from which a Grüneisen parameter γ G can be calculated if the thermal conductivity κ with respect to pressure p and the bulk modulus B are known. The relation, γ G (κ) = B (∂ ln κ / ∂p) T − 1 3 , is analogous to the widely known expression, γ G (s) = B∂(∂ ln s / ∂p) T + 1 3 , which is used to obtain a Grüneisen parameter from measurements of sonic speed s vs p . The first relation can be derived from the second if the Debye equation κ = ρsΛC ı / 3 properly relates κ to s , the density ρ , the phonon mean free path Λ , and the heat capacity C υ . Further assumptions, Λ∝ρ −1/3 and C υ is constant, are also used. In an alternative derivation, the same form for γ G (κ) follows from the assumption that thermal conduction corresponds to the leakage of a fraction of the energy during each vibration, from each localized vibrational mode, i.e., κ = Jν where ν is the frequency and J is a coupling parameter. Estimates of γ G (κ) based on data for several polymers, minerals, and inorganic glasses indicate that it is significantly larger (4–20) than values (0.05–5) obtained for γ G by certain other techniques. Our experimental techniques, which involve two types (coaxial cylinders and symmetrical sandwiches) of conductivity‐pressure cells, are outlined.