Thermal conductivity of spinels and olivines from vibrational spectroscopy: Ambient conditions

The damped harmonic oscillator model for thermal conductivity of insulators is improved, leading to a formula that predicts thermal conductivity at am bient conditions (k(0)) from various physical properties, most of which are commonly measured. Specifically, k(0) = [rho/(3ZM)] C-V [(u(P) + u(S))/2]( 2)/ < Gamma >, where rho is density, Z is the number of formula units in th e primitive unit cell, M is the molar weight, C-V is heat capacity, u is th e sound speed (P denotes compression; S denotes shear), and < Gamma > is th e average of the damping coefficients determined from peak widths in infrar ed reflectivity spectra, or from suitable Raman and Brillouin spectra. The classical physics and quantum-mechanical basis for this model is discussed, with emphasis on the effect of phonon-phonon interactions on mode properti es. The calculated values of k(0) all lie within the experimental uncertain ty of the measurements for all samples with the spinel or olivine structure examined by Horai (1971) with known or approximately correct chemical comp ositions. Other divergent measurements of k for MgAl2O4 are discounted for various reasons. Early studies of Fe-bearing spinels are not generally reli able, but rough estimates from the above equation are consistent with all d ata, and good agreement is obtained for samples such as Mg0.5Fe0.5Al2O4 and gamma -Fe2SiO4 for which the previous authors obtained chemical data, and for which IR reflectivity data exist. The theory reproduces the measured de pendence of k(0) on composition and structure, Anisotropy in k(0) results m ainly from differences in lattice constants (j): the equation for olivine i s k(j)/k(0) = (V-1/3/j)(0.73) which predicts the ratios within 3%. For soli d solutions between Fe and Mg, the model provides a non-linear dependence o f k(0) on mol% Fe, with the damping coefficient being the key factor produc ing non-linearity. Predicted ambient values are 11.3 +/- 0.4 W/m-K for gamm a -Mg2SiO4, 6.5 +/- 0.7 W/m-K for gamma -Mg1.2Fe0.8SiO4, and 6.9 +/- 0.3 W/ m-K for beta -Mg2SiO4. The high k(0) for ringwoodite suggests that heat in Earth's transition zone should be conducted twice as efficiently as in the adjacent upper and lower mantles: this discontinuous depth dependence of k could impact thermal models of conduction in subducting stabs and of mantle convection.