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American Mineralogist

Journal of Earth and Planetary Materials

Ed. by Baker, Don / Xu, Hongwu / Swainson, Ian


IMPACT FACTOR 2018: 2.631

CiteScore 2018: 2.55

SCImago Journal Rank (SJR) 2018: 1.355
Source Normalized Impact per Paper (SNIP) 2018: 1.103

Online
ISSN
1945-3027
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Volume 86, Issue 10

Issues

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

A. M. Hofmeister
Published Online: 2015-03-26 | DOI: https://doi.org/10.2138/am-2001-1008

Abstract

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 = [ρ/(3ZM)] Cv [(uP + us)/2]2/ <Γ>, where ρ is density, Z is the number of formula units in the primitive unit cell, M is the molar weight, Cv is heat capacity, u is the sound speed (P denotes compression; S denotes shear), and <Γ> 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 Mg0.5Fe0.5Al2O4 and γ-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 kj/k0 =(V/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 γ-Mg2SiO4, 6.5 ± 0.7 W/m-K for γ-Mg12Fe0.8SiO4, and 6.9 ± 0.3 W/m-K for β-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

About the article

Received: 2000-10-06

Accepted: 2001-06-17

Published Online: 2015-03-26

Published in Print: 2001-10-01


Citation Information: American Mineralogist, Volume 86, Issue 10, Pages 1188–1208, ISSN (Online) 1945-3027, ISSN (Print) 0003-004X, DOI: https://doi.org/10.2138/am-2001-1008.

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© 2015 by Walter de Gruyter Berlin/Boston.

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