Composition, Temperature, and Pressure Dependence of the Phonon (Thermal) Conductivity of Silicate Geoliquids

The study of geoliquids and their transport properties is a burgeoning field that sheds light on many critical geological problems. One such property, the thermal conductivity, measures the heat conduction capacity of a material and plays an important role in mantle and crust dynamics. Previous research has suggested that an increased insulation factor in rocks of the crust, regulated by relatively small values of the thermal conductivity, promotes anatexis and alleviates radiogenic heating requirements for the inducement of dehydration-triggered partial melting (Whittington et al., 2009). At greater depths, the proposed existence of melt patches along and immediately above the Core-Mantle Boundary (CMB) at ~2900 km depth could explain the discrete rather than graduated thermal gradient seen across the CMB (Murakami and Bass, 2011). This thesis describes the use of Molecular Dynamics (MD) simulations to compute thermal conductivity for three liquid silicates: CaMgSi2O6, NaAlSi3 O8 and MgSi2O4. The motivation for this study was to examine the temperature, pressure and compositional dependencies of thermal conductivity approximating conditions in the upper mantle (0-30 GPa, 2000-4500 K) for a few end member geosilicate liquids of natural importance. Results at low pressure and temperature show good agreement with recent laboratory measurements on CaMgSi2O6 and NaAlSi3O8 suggesting that MD simulation can provide realistic values at elevated pressure and temperature, conditions not readily accessible without great expense and time in the laboratory. For example, simulation results for molten diopside at 1763±13 K and 0.36±0.017 GPa provide a thermal conductivity value of k=1.186±0.019 W/m K while laser-flash data from Hofmeister et al. (2009) provides a value of k=1.178 ±0.06 W/m K, agreement to within a percent. Further, a positive correlation between atomic structure and thermal conductivity is confirmed. At low pressure, the polymeric liquid NaAlSi3O8, in which each oxygen atom is surrounded by two nearest neighbors of either Si or Al, is expected to possess a longer phonon mean free path, and thus higher conductivity, than the less polymerized liquid CaMgSi2O6, in which each oxygen atom, on average, is surrounded by only 4/3 nearest neighbors of Si. Simulation results for diopside melt at 2059±12 K and 0.04±0.14 GPa and albite melt at 2090±20 K and 0.20±0.23 GPa give values of k=1.143±0.004 W/m K and k=1.498±0.147 W/m K, respectively. Thus, this expectation based on empirical results has been faithfully captured by MD simulation. A modified Arrhenian expression was found to fit all liquids over the temperature and pressure range of the simulations (2000-4500 K and 0-30 GPa) reasonably well (correlation coefficient R2 ≈ 0.9). Activation energies are around 20 kJ/mol and activation volume is of order a few cm3/mol. A good correlation between the coordination numbers (CN) of Ca, Mg, Na, Al and Si around oxygen and by oxygen around the cations and thermal conductivity may be used semi-quantitatively to predict thermal conductivity in multi-component silicate liquids.