Pressure dependence of thermal transport properties

Abstract

Pressure (P) derivatives of thermal conductivity (k) and thermal diffusivity (D) are important to geophysics but are difficult to measure accurately because minerals, being hard and partially transparent, likely incur systematic errors through thermal losses at interfaces and spurious radiative transfer. To evaluate accuracy, repeat experiments for olivine [(Mg(0.9)Fe(0.1))(2)SiO4], quartz (SiO2), and NaCl are examined in detail: these and other data on electrical insulators are compared with theory. At ambient conditions, D is underestimated in proportion to the number of contacts. As temperature (T) increases, spurious radiative transfer more than offsets contact loss. Compression of pore space and contact losses affect pressure derivatives, but these seem independent of T. Accurate (+/-2%) values of D(T) at 1 atm are obtained with the contact-free, laser-flash method. Other optical techniques do not pinpoint D but provide useful pressure derivatives. Published data on (partial differential)(lnk)/(partial differential)P at ambient conditions agree roughly with all available models, the simplest of which predicts (partial differential)(lnk)/(partial differential)P approximately (partial differential)(lnK(T))/(partial differential)P, where K(T) is the bulk modulus. However, derivatives verified by multiple measurements are reproduced accurately only by the damped harmonic oscillator model. An improved database is needed to refine this model and to confidently extrapolate these difficult measurements to geophysically relevant conditions.

Fig. 1.

Thermal diffusivity at room temperature as a function of the number of physical contacts with heaters and/or thermocouples. All lines are least squares linear fits to the data. Squares, diamonds, and triangles, three orientations as labeled of olivine, ∼Mg_1.8Fe_0.2SiO₄ (3, 9, 48, 63, 64); gray symbols, picosecond transient grating spectroscopy measurements of olivine (53), which have problems other than contact (see text); circles, weighted average of the two orientations of quartz, SiO₂ (3, 47, †); +, NaCl (24, 54, 66, 67): LFA results of D = 3.6 mm²/s is the average of 10 measurements on a crystal purchased from IR Crystal Laboratories; ×, NaCl from Pangilinan et al. (44).

Fig. 2.

Recent data on D(T) for hard, dense materials at various pressures. Dark gray, single-crystal garnet (Mg_0.21Fe_0.74Ca_0.05Al₂Si₃O₁₂) from LFA at 1 atm (7); light gray and squares, single-crystal garnet (Mg_0.24Fe_0.74Ca_0.01Al₂Si₃O₁₂) at 8.3 GPa (11): the fit is a third-order polynomial in T; black symbols and lines, olivine, Mg_1.8Fe_0.2SiO₄; dots, aggregates at 10 GPa; filled diamonds, 7 GPa; filled squares, 4 GPa (12); light broken lines, fits to D = a + b/T; solid line, extrapolation of data of Xu et al. (12) to 1 atm; open circles, triangles, and squares, orientated single-crystal olivine at 8.3 GPa (11); heavy broken lines, oriented single-crystal olivine from LFA at 1 atm (9); heavy solid line, orientational average of LFA. High-P contact measurements underestimate D. In addition, single crystals are effected by radiative transfer at high T.

Fig. 3.

Comparison of calculated to measured pressure derivatives of thermal conductivity. Diamonds and long dashed line, prediction using Dugdale and McDonald's model; circles and dotted line, comparison with K′/K_T; gray squares, comparison with optic model (left y axis). Sulfur, NaI, and NaBr data (labeled) strongly affect the slope. For sulfur, the model of Dugdale and McDonald (25) predicts 112%/GPa (as indicated by the arrow). Results for NaCl and NaI are each joined by lines.