Anisotropic Lattice Thermal Conductivity in Enstatite as a Function of Pressure and Temperature

Abstract

Summary Principal lattice thermal conductivity coefficients have been determined from measurements of heat flux and temperature gradient in oriented samples of enstatite single crystals at pressures between 19 and 56 × 1018 Nm−21 and at temperatures between 300° and 400°K. A noticeable change in the rate of increase of conductivity with pressure near 38 × 1018 Nm−2 is interpreted as the onset of a reversible polymorphic transition from orthorhombic enstatite to monoclinic clinoenstatite. The two structures are derivable from one another by twinning and untwinning processes and a gradual transition is considered to proceed by the formation of an increasing number of stacking faults in the orthorhombic structure. This, obviously, increases the amount of phonon scattering, and observed thermal conductivity changes can thus be used to determine stacking fault densities. Figures for the minimum in lattice thermal conductivity have been derived from observed Δλ/ΔP and Δλ/ΔT values terms of hypothetical values of depth and temperature within the Earth. Estimates of ∂T/∂P at constant entropy, as determined from Δλ/ΔP and Δλ/ΔT values, suggest that in the case of enstatite conditions for convection are not fulfilled within the region of appreciable transformation at pressures greater than about 35 × 108 Nm−2. Straight line graphs are obtained if log (Δλ/ΔT) is plotted versus 1/T yielding activation energies of the order of 3.2 × 10−20 J (0.2 ev) for processes controlling the variation of lattice thermal conductivity with temperature. In the Appendix a two layer model is discussed to illustrate possible deviations of the terrestrial heat flow vector from the direction of maximum temperature gradient in the presence of an anisotropic structure such as enstatite.