Thermal Conductivity of Deep Mantle Phases: Grain-size as a Primary Control of Radiative Transfer

The assumed dependence of thermal conductivity (k) on temperature (T) strongly influences results from mantle convection models due to feedback in the temperature equation. Numerical calculations have show that the exponential dependence of viscosity on T has a lesser influence on the style of mantle convection than does a T³ dependence of k. Several constraints can be set on k of the deepest mantle phases through comparison. The phonon component of thermal conductivity (k_lat) for minerals is provided by laser-flash measurements. For 20 silicates and oxides examined so far, k_lat becomes independent of temperature above roughly 1200 to 1900 K. This behavior arises because discrete phonon states only exist at low frequency, and these states are all populated by about 1500 K. Invariant k_lat(T) at high T is thus universal, and expected for the perovskite (pv) and post-pv phases, regardless of chemical composition. Deep mantle behavior thus depends on diffusion of photons. The formulation for an effective thermal conductivity due to radiative transfer was recently revised to account for physical scattering and emission characteristics of a solid medium. We applied this formulation to phases with very different spectra (perovskite, garnet, olivine), with and without Fe³⁺-Fe²⁺ charge transfer bands, and with and without d-d transitions of Fe²⁺. We find that grain-size and Fe content are key variables, whereas charge transfer and mineral structure have relatively little effect. For grain-size = 0.1 cm and Fe/(Fe+Mg) = 0.1, k_rad is roughly 0.1377-0.000612T+6.28T²/10⁷ in W/m-K. Lowering grain size and either raising or lowering Fe content lowers k_rad. Increasing grain-size raises k_rad at low T. The high temperature behavior for large grain-size is difficult to predict because absorptions shift and intensify with temperature, but few measurements exist. Transparent materials such as Fe-free phases and minerals with low spin Fe can have large k_rad at high T when grain-size nears 1 cm. However, in D", phases should bear Fe, due to interactions with the core, and high spin Fe is stable, as this disordered state is promoted at high T by its large magnetic and electronic entropy (large positive Clapeyron slope). Therefore, k_rad of the ppv phase in D" can be modeled with the above equation. The power law dependence on T weakens convection in D". The stability of this layer against convection largely depends on the concentration of Fe ions in the silicate and oxide phases. Incorporation of metal particles similarly increases opacity, making radiative transfer less efficient, and convection more vigorous and time dependent