Enhancement of radiative transfer in the upper mantle by OH^- in minerals

Diffusion of heat by radiation in the mantle has previously been associated with absorption of light by Fe²⁺. The near-IR absorptions of structurally incorporated OH^- provide another mechanism to convert the energy of photons into lattice vibrations. The effective diffusive radiative thermal conductivity due to protonation ( k _rdf,wet) may be important within the mantle because low absorption strengths, as expected for trace to minor OH^- contents, allow light to travel long distances in the medium. Available calibrations of band strength with OH^- content are used to develop a formula for k _rdf,wet as a function of temperature, grain size, and hydroxyl concentration that is generally applicable to mantle phases. These results are compared to new data on the phonon contribution for olivine and to calculations of Fe²⁺ radiative transfer. As T increases, k _rdf,wet increases. As OH^- content increases, k _rdf,wet initially increases, reaches a maximum near 100-1000 ppm hydroxyl content as H₂O, and then decreases at higher concentrations. A similar dependence on grain size exists, with the maximum k _rdf,wet near d ∼ 1 cm. Grain sizes and OH^- contents of hydrous upper mantle samples foster radiative transport via protonation. For example, at 1500 K, sub-cm grain sizes with ∼10-100 ppm H₂O, provide k _rdf,wet that is ∼1/4 of k _rdf arising from the combined effect of overtones and Fe²⁺ transitions, and ∼1/8 of the lattice contribution to k of olivine. Given that OH^- concentrations vary among mantle minerals, the above results suggest that mantle heat flow is heterogeneous and anisotropic. The dependence of both k_rdf and viscosity on grain size and hydration suggests that the dynamical behavior in or near subducting slabs will be complex.