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

Department of Earth and Planetary Sciences, Washington University, St. Louis, Missouri 63130, U.S.A.

Correspondence: ^* E-mail: hofmeist{at}levee.wustl.edu

The damped harmonic oscillator model for thermal conductivity of insulators is improved, leading to a formula that predicts thermal conductivity at ambient conditions (k₀) from various physical properties, most of which are commonly measured. Specifically, k₀ = [/(3ZM)] C_V [(u_P + u_S)/2]²/< >, where is density, Z is the number of formula units in the primitive unit cell, M is the molar weight, C_V is heat capacity, u is the sound speed (P denotes compression; S denotes shear), and < > is the average of the damping coefficients determined from peak widths in infrared 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 properties. The calculated values of k₀ all lie within the experimental uncertainty of the measurements for all samples with the spinel or olivine structure examined by Horai (1971) with known or approximately correct chemical compositions. Other divergent measurements of k for MgAl₂O₄ are discounted for various reasons. Early studies of Fe-bearing spinels are not generally reliable, but rough estimates from the above equation are consistent with all data, and good agreement is obtained for samples such as Mg_0.5Fe_0.5Al₂O₄ and -Fe₂SiO₄ for which the previous authors obtained chemical data, and for which IR reflectivity data exist. The theory reproduces the measured dependence of k₀ on composition and structure. Anisotropy in k₀ results mainly from differences in lattice constants (j): the equation for olivine is k_j/k₀ =(V^1/3/j)^0.73 which predicts the ratios within 3%. For solid solutions between Fe and Mg, the model provides a non-linear dependence of k₀ on mol% Fe, with the damping coefficient being the key factor producing non-linearity. Predicted ambient values are 11.3 ± 0.4 W/m-K for -Mg₂SiO₄ , 6.5 ± 0.7 W/m-K for ß-Mg_1.2Fe_0.8SiO₄, and 6.9 ± 0.3 W/m-K for ß-Mg₂SiO₄. The high k₀ 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 slabs and of mantle convection

This article has been cited by other articles:

				A. M. Hofmeister and M. Pertermann Thermal diffusivity of clinopyroxenes at elevated temperature European Journal of Mineralogy, August 1, 2008; 20(4): 537 - 549. [Abstract] [Full Text] [PDF]

				A. M. Hofmeister Thermal diffusivity of aluminous spinels and magnetite at elevated temperature with implications for heat transport in Earth's transition zone American Mineralogist, November 1, 2007; 92(11-12): 1899 - 1911. [Abstract] [Full Text] [PDF]

				A. M. Hofmeister High-Pressure Geoscience Special Feature: Pressure dependence of thermal transport properties PNAS, May 29, 2007; 104(22): 9192 - 9197. [Abstract] [Full Text] [PDF]

				M. Pertermann and A. M. Hofmeister Thermal diffusivity of olivine-group minerals at high temperature American Mineralogist, November 1, 2006; 91(11-12): 1747 - 1760. [Abstract] [Full Text] [PDF]