THERMAL DIFFUSIVITY OF GARNETS AT HIGH TEMPERATURE

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 (Tsat) of ~1,100 to 1,500 K. From ~290 K to Tsat, the measurements are best represented by 1/D =A+BT+CT2 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 Tsat is low, such as Ant Hill garnet wherein 1/D =0.049403+0.0032299T-2.3992T2×106 +6.0168T3×10-10(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 Tsat, 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 Tn 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 Tsat. 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. © Springer-Verlag 2006.