Dependence of diffusive radiative transfer on grain-size, temperature, and Fe-content: Implications for mantle processes

Locally diffusive, radiative heat transport inside the earth is represented by an effective thermal conductivity (krad,dif), calculated from spectra. Previous geophysical models assumed that emissivity (ξ) equals unity, which violates local radiative equilibrium in an internally heated, grainy medium. Our new formulation accounts for ξ depending on frequency, physical scattering depending on grain-size (d), and for light lost through back-reflections at interfaces. Mantle values of krad,dif are estimated from recent visible spectra of olivine combined with new IR data. The following trends hold for krad,dif calculated from olivine spectra, and should be equally valid for pyroxene and spinel: (1) pressure is unimportant, (2) radiative thermal conductivity depends non-linearly on d, temperature (T), and Fe2+ content (X), (3) maxima occur in krad,dif(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), and (5) a local minimum occurs in krad,dif 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. Larger krad,dif exists at lower and higher temperatures because mean free paths are long in the transmitting near-IR and UV spectral regions. As integration smooths over spectral details, the above representation based on olivine becomes increasingly accurate for other phases as grain-size decreases. For conditions expected in the transition zone, ∂krad,dif/∂T is negative, which is destabilizing [Dubuffet, F., Yuen, D.A., Rainey, E.S.G., 2002. Controlling thermal chaos in the mantle by positive feedback from radiative thermal conductivity. Nonlinear Proc. Geophys. 9, 1-13]. In the lower mantle, photon transport dominates phonon, promoting stable, weak convection. That radiative transfer is linked to chemical composition and grain-size suggests that this process impacts planetary evolution through the non-linear feedback with rheology.