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 conditi ons. The pressure and absolute temperature dependences of transport propert ies are accurately obtained from the Gruneisen parameter gamma(Th), bulk mo dulus K-T, and thermal expansivity alpha: The Lattice contribution kappa(la t) equals kappa(298)(298/T)(a) exp[-(4 gamma(Th) + 1/3) integral(298)(T)alp ha(theta)d theta] with a = 0.33 for silicates (or 0.9 for MgO), and partial derivative[ln(kappa(lat))]/partial derivative P = (1/3 + 4 gamma(Th))/K-T. The smaller, pressure-independent radiative contribution kappa(rad) equals 0.0175 - 0.0001037T + (2.245T(2)/10(7)) - (3.407T(3)/10(11)), in units of watts per meter-kelvin, if Fe2+ is present. The resulting Lithospheric geot herm is steep. Consequently, the mantle geotherm is hot if the Low-velocity zone is anhydrous, but cold if hydrated.