Anisotropic Lattice Thermal Conductivity of Upper Mantle Minerals at High Temperature

The anisotropic lattice thermal diffusivity of three olivines (Fo0, Fo78, and Fo91) and one orthopyroxene (En91) has been measured to high temperatures via impulsive stimulated light scattering, permitting the calculation of the respective lattice thermal diffusivity tensors. Diffusivities have been combined with calculations of density and specific heat to determine the lattice thermal conductivity tensors. Both the diffusivities and conductivities were found to depart significantly from expectations based on a simple inverse-temperature dependence of the phonon mean free path. The observed behavior is explained in terms of a positive lower bound on the phonon mean free path, and the data thereby constrain a model of thermal conductivity at high temperature. The relative contributions of optic and acoustic modes are evaluated from analysis of published dispersion curves. Several conclusions are reached: The anisotropy of lattice thermal conductivity remains essentially unchanged over the observed range of temperatures, indicating that anisotropy remains significant under upper-mantle conditions, and, in regions displaying preferred alignment, may account for observed lateral variations in the geotherm. Thermal conductivity departs significantly from earlier predictions of its temperature dependence; this may be understood in terms of a minimum phonon mean free path that is a small multiple of the mean interatomic spacing. For olivine, the optic modes have group velocities that are approximately one-third those of the acoustic modes, and do not dominate lattice conduction despite their greater number. Impurity scattering is significant along the olivine Fe-Mg solid solution series, but is not appreciable near the endpoints and therefore likely does not play a major role in the upper mantle. Finally, the historic underestimation of lattice thermal conductivity at temperature has led to an overestimation of radiative conductivity; radiative transport, although significant, plays an even smaller role in the upper mantle than has heretofore been assumed.