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

摘要

Locally diffusive, radiative heat transport inside the earth is represented by an effective thermal conductivity (k_(rad,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 k_(rad,dif) are estimated from recent visible spectra of olivine combined with new IR data. The following trends hold for k_(rad,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 Fe~(2+) content (X), (3) maxima occur in k_(rad,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 k_(rad,dif) on Fe~(2+) content parallels that with d because absorption is controlled by the product dX (Beer's law), and (5) a local minimum occurs in k_(rad,dif) near 2000 K for d > 2mm because at that temperature the peak position of the blackbody curve coincides with that of the strongly absorbing Fe_(2+) peak in the visible. Larger k_(rad,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, partial deriv k_(rad,dif)/partial deriv 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 com- position and grain-size suggests that this process impacts planetary evolution through the non-linear feedback with rheology.