Grüneisen Parameter from Thermal Conductivity Measurements under Pressure

Abstract

A relation is discussed from which a Grüneisen parameter γG can be calculated if the thermal conductivity κ with respect to pressure p and the bulk modulus B are known. The relation, γG(κ) = B (∂ lnκ / ∂p)T − 13, is analogous to the widely known expression, γG(s) = B∂(∂ lns / ∂p)T + 13, 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 = ρsΛCı / 3 properly relates κ to s, the density ρ, the phonon mean free path Λ, and the heat capacity Cυ. Further assumptions, Λ∝ρ−1/3 and Cυ is constant, are also used. In an alternative derivation, the same form for γG(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 γG(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 γG by certain other techniques. Our experimental techniques, which involve two types (coaxial cylinders and symmetrical sandwiches) of conductivity-pressure cells, are outlined.