Mantle values of thermal conductivity and the geotherm from phonon lifetimes

A model for thermal conductivity kappa, based on phonon lifetimes obtained from infrared reflectivity, replicates experimental data at ambient conditions. The pressure and absolute temperature dependences of transport properties are accurately obtained from the Gruneisen parameter gammaTh, bulk modulus KT, and thermal expansivity alpha: The lattice contribution kappalat equals kappa298(298/T)a exp[-(4gammaTh + 1/3) integral298Talpha(theta)dtheta] with a = 0.33 for silicates (or 0.9 for MgO), and partial differential[ln(kappalat)]/ partial differentialP = (1/3 + 4gammaTh)/KT. The smaller, pressure-independent radiative contribution kapparad equals 0.0175 - 0.0001037T + (2.245T2/10(7)) - (3.407T3/10(11)), in units of watts per meter-kelvin, if Fe2+ is present. The resulting lithospheric geotherm is steep. Consequently, the mantle geotherm is hot if the low-velocity zone is anhydrous, but cold if hydrated.