Heat flow in the laser-heated diamond anvil cell and the thermal conductivity of iron-bearing oxides and silicates at lower mantle pressures and temperatures

The thermal conductivity of minerals in the lowermost mantle controls the total heat flow across the core-mantle boundary and is critical for the thermal evolution of the Earth. However, lower mantle thermal conductivity values and their pressure, temperature, and compositional dependencies are not well known. Here we present our recent progress combining 3D models of heat flow in the laser-heated diamond cell (LHDAC) with laboratory measurements of hotspot temperature distributions to assess the thermal conductivity of lower mantle minerals as a function of pressure and temperature. Using our numerical model of heat flow in the LHDAC, central hotspot temperature and radial and axial temperature gradients are calculated as a function of laser power, sample thermal conductivity, and sample geometry. For a given geometry, the relationship between peak sample temperature and laser power depends on the sample thermal conductivity. However, quantifying the experimental parameters sufficiently to precisely determine an absolute value of sample thermal conductivity is difficult. But relative differences in thermal conductivity are easily inferred by comparing the slopes of differing temperature vs. laser power curves measured on the same system. This technique can be used to measure the pressure dependence of thermal conductivity for minerals at lower mantle conditions. We confirm the effectiveness of this approach by measuring the pressure slope of thermal conductivity for MgO between 10 and 30 GPa. MgO retains the B1 phase throughout the experimental pressure range, and existing experimental measurements and theoretical calculations are in good agreement on the pressure- and temperature- dependence of the thermal conductivity of MgO. We also use this technique to measure the relative thermal conductivity of high pressure assemblages created from San Carlos olivine starting material. Both MgO and (Mg,Fe)2SiO4 materials show a shallower temperature vs. laser power slope as a function of pressure as expected for increasing thermal conductivity. In addition, olivine undergoes a series of phase transformations which changes its thermal behavior at upper mantle conditions (10-20 GPa) where olivine and wadsleyite are stable compared with lower mantle (25-30 GPa) conditions where the olivine transforms to a perovskite + oxide assemblage.