THERMAL TRANSPORT IN THE TRANSITION ZONE

Understanding heat flow requires quantifying the pressure (P) and temperature (T) response of either thermal diffusivity (D) or thermal conductivity [k = ρC_PD, where ρ is density and C_P is heat capacity] for both of two microscopic mechanisms (lattice vibrations or radiative transfer). New laser-flash measurements isolate the lattice component of D for 22 garnets with diverse chemical compositions and several spinels from room temperature up to melting or 1600 K. Cation substitution or hydroxyl incorporation lowers D from end-member values. Once T exceeds ca 1100 to 1500 K, D is constant. This limit (D_sat) is analogous to Dulong and Petit's limit for C_P, and attributable to full population of discrete phonon states. The high T mean free path (computed from D_sat and sound velocities) is slightly larger than the primitive lattice parameter, in accord with localized vibrations having minimal interactions, which allows inference of Dsat for any phase from crystallographic and acoustic data. This result combined with d(ln D)/dP = 2(γ_th+1/3)/K_T, where K_T is bulk modulus and γ_th is the thermal Gruneisen parameter, constrains the lattice contribution in the mantle.

Radiative, diffusive heat transport (k_rad) is calculated from recent optical spectroscopic data for various grain-sizes (d). The following trends hold for olivine, pyroxene, garnet, or spinel: (1) Pressure is unimportant. (2) k_rad depends non-linearly on d, T, and Fe²⁺ content (X). (3) Maxima occur in k_rad(d) when the grains are large enough to emit substantially, but not so large that light is strongly attenuated within a single-grain. (4) The dependence of krad,dif on Fe²⁺ content parallels that with d because absorption is controlled by the product dX (Beer's law). (5) Except for garnet, a local minimum occurs in k_rad near 2000 K for d > 2 mm because at that temperature the peak position of the blackbody curve coincides with that of the strongly absorbing Fe²⁺ peak in the visible. For conditions expected in the transition zone, dk_rad/dT is negative for spinel, which is destabilizing, but positive for garnet, which is stabilizing, and thus thermal response of the transition zone depends strongly on mineral proportions. Linkage of radiative transfer to chemical composition and grain-size suggests that this process impacts planetary evolution.