Thermal Diffusivity and Conductivity Measurements: Effect of Sample Length and Radiation

Measurements of thermal diffusivity D and conductivity κ commonly show an upturn as a function of temperature. The upturn is very apparent in semi-transparent materials such as upper mantle minerals at absolute temperatures T of the order of 600-700 K. Although the effect is readily attributed to a radiative component, it shows a temperature dependence that is more characteristic of a black body (e.g., T3) than that expected from actual optical absorption spectra at high temperature for very large dimensions. When radiative conductivity κr is obtained from optical methods, it tends begin at lower temperatures and to level off as absorption increases with T. Part of the discrepancy can be assigned to the fact that photon mean free path mfp( T) is usually comparable with sample dimensions. However, the problem is worsened in portions of the spectra by spectral path lengths (reciprocal absorption coefficients) substantially longer than sample lengths, an effect manifested in length-dependent radiative diffusion. For olivine (Mg0.91,Fe0.09)2SiO4 we have used a model of 1-dimensional spectral absorption and emission between volume elements to demonstrate that as sample length increases, κr approaches that expected from spectral methods.