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Thermal diffusivity of garnets at high temperature

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Abstract

Thermal diffusivity (D) of garnets with diverse chemical compositions was measured using the laser-flash technique, which is accurate (±2%) and isolates the lattice component from direct radiative transfer. Temperatures ranged from ~290 to ~1,600 K (unless limited by melting). Seven synthetic (e.g., YAG, GGG) and 15 natural garnets with two types of ionic substitution [Ca3(Fe,Al)2Si3O12 and (Mg,Fe,Ca)3Al2Si3O12] and varying amounts of OH- were examined. Cation substitution or hydroxyl incorporation lowers D from end-member values. Thermal diffusivity is constant once the temperature (T) exceeds a critical value (T sat) of ~1,100 to 1,500 K. From ~290 K to T sat, the measurements are best represented by 1/D=A+BT+CT 2 where A, B, and C are constants. These constants vary little among diverse chemical compositions, suggesting that the oxygen sublattice controls heat transport. Higher order terms are needed only when T sat is low, such as Ant Hill garnet wherein 1/D=0.049403+0.0032299T−2.3992T 2×10−6+6.0168T 3×10−10(1/D in s/mm2; T in K). The mean free path (λ, computed from D and sound velocities) is slightly larger than the lattice parameter above T sat, in accord with phonon–phonon interactions requiring non-localized modes. At most temperatures, λ is nm-sized. Large values of λ are obtained by extrapolation to a few Kelvins, suggesting that boundary scattering can only be important at extremely cold temperatures. The observed behavior with T and chemical composition is consistent with the damped harmonic oscillator model. Phonon transport is best represented by inverse thermal diffusivity wherein 1/D goes as T n where n is between 1 and 3 up to ~200 K, depends on a quadratic or cubic polynomial at moderate T, but is constant above T sat. The predicted and observed temperature response of 1/D mimics the well-known form for heat capacity, in that acoustic modes control heat transport near cryogenic temperatures, optic phonons dominate above ambient temperature, and a limit analogous to that of Dulong and Petit is reached at very high temperature, due to full population of discrete phonon states.

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Acknowledgements

Support was provided by NSF EAR 0132275 and 0206121. I thank Gretchen Benedix for providing microprobe analyses.

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  1. Department of Earth and Planetary Sciences, Washington U, 1 Brookings Dr, St Louis, MO, 63130-4899, USA

    Anne M. Hofmeister

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Hofmeister, A.M. Thermal diffusivity of garnets at high temperature. Phys Chem Minerals 33, 45–62 (2006). https://doi.org/10.1007/s00269-005-0056-8

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