Hofmeister AM
Department of Earth and Planetary Science, Washington University, St. Louis, MO 63130, USA. E-mail:
Science. 1999 Mar 12;283(5408):1699-706. doi: 10.1126/science.283.5408.1699.
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.
基于从红外反射率获得的声子寿命的热导率κ模型，能够复制环境条件下的实验数据。输运性质的压力和绝对温度依赖性可通过格鲁涅森参数γTh、体积模量KT和热膨胀系数α精确得出：晶格贡献κlat等于κ298(298/T)a exp[-(4γTh + 1/3)∫298Tα(θ)dθ]，对于硅酸盐，a = 0.33（对于MgO，a = 0.9），且∂[ln(κlat)]/∂P = (1/3 + 4γTh)/KT。如果存在Fe2+，较小的、与压力无关的辐射贡献κrad等于0.0175 - 0.0001037T + (2.245T2/10(7)) - (3.407T3/10(11))，单位为瓦每米开尔文。由此产生的岩石圈地热梯度很陡。因此，如果低速带无水，地幔地热就高，但如果含水则冷。
