Todd, Benjamin John
(2019)
*Simulating the lattice thermal conductivity of iron-bearing bridgmanite with implications on core-mantle boundary heat flux.*
PhD thesis, University of Leeds.

## Abstract

In this thesis, I calculate the thermal conductivity of bridgmanite across a range of lower mantle conditions, with particular focus on the core-mantle boundary (CMB). Thermal conductivity of the lowermost mantle has direct implications on the heat flux from the core. Heat flux, and its lateral variations, control dynamic processes on both sides of the CMB, affecting the core geodynamo, the mantle convective cycle, and plate tectonics at the surface. Thermal conductivity is difficult to determine at the high pressures and temperatures of the CMB using experimental methods, but computational approaches are able to reproduce these physical conditions. The thermal conductivity of bridgmanite has previously been modelled under limited conditions, but here, I model the full range of CMB conditions including temperatures from 1000-5000 K, and the effects of adding Fe2+ impurities (i.e., the full suite of MgSiO3 to FeSiO3-endmember composition). I compare two different molecular dynamic approaches to determine thermal conductivity: the direct method and the Green-Kubo method, previously not compared in application to bridgmanite at CMB conditions. In atomic-scale simulations, finite system sizes can misrepresent the properties of the bulk material, leading to inaccurate estimates of thermal conductivity in the case of this study. Finite-size effects in the Green-Kubo method are easily addressed, and the Green-Kubo results can then be used to evaluate finite-size effects in direct method simulations. I present a comprehensive analysis of finite-size effects at 1000 K and 4000 K, and 136 GPa, identifying where simulations from existing literature may be incorrect. I also suggest minimum direct method system sizes (2 by 2 at 4000 K, lengths of 8-24 unit cells) for computing the thermal conductivity of bridgmanite at the CMB, which could be implemented in density functional theory calculations. It is possible to use the direct method to calculate thermal conductivity at lower mantle conditions, but care must be taken to avoid finite-size effects. I conclude that accurate results are more easily obtained using the Green-Kubo method. Using the Green-Kubo method, I investigate the effects of iron impurities across a wide range of temperatures (1000-5000 K) at a CMB pressure of 136 GPa. At a CMB pressure and temperature (4000 K), I calculate lattice thermal conductivity to be 7.07+/-0.06 W/m.K for bridgmanite, 5.30+/-0.05 W/m.K for the FeSiO3 endmember, and 5.46+/-0.05 W/m.K for the 50% (Mg,Fe)SiO3 solid solution. I find that adding impurities (introducing phonon-defect scattering) causes conductivity to decrease, but the rate of the decrease decays with impurity concentration. The conductivity reduction due to temperature (increased phonon-phonon scattering) is more significant than the conductivity reduction due to impurities. I identify saturation in thermal conductivity as phonon-phonon and defect scattering increase, where the relative significance of these scattering mechanisms determines the reduction in conductivity as a function of temperature and composition. I combine the temperature and compositional-dependence of thermal conductivity to create a new combined model. I use this model with a simple representation of the large-scale structure of the lower mantle to investigate CMB heat flux. The results from thermochemical LLSVP models show that in order to reproduce LLSVP shear velocity anomaly and heat flux across the CMB, the values of lateral thermal boundary layer temperature range and LLSVP Fe content range from 100 K and 10% Fe, to 1000 K and 4% Fe. For simplified models of large low shear velocity provinces (LLSVPs), where the seismic anomaly is caused by lateral variation in mantle temperature, I find larger lateral variation in CMB heat flux than for models where the equivalent seismic anomaly is caused by lateral variations in the Fe2+ content. However, absolute values of the integrated CMB heat flux and its variability depend on the temperature at the CMB as well as the origin of LLSVPs, and will be sensitive to other phases and impurities found in the lower mantle. It is only by investigating the effect of finite system size on atomic-scale modelling that it is possible to obtain reliable conductivity estimates. By determining a comprehensive suite of thermal conductivity values across a range of temperature and composition, I produce a new combined model and show how this can be used to inform on dynamic processes both sides of the CMB.

## Metadata

Keywords: | bridgmanite thermal conductivity finite size effects lower mantle molecular dynamics green kubo direct method large low shear velocity provinces LLSVP magnesium silicate perovskite iron mg fe endmember solid solution impurities impurity content composition compositional model core mantle boundary lateral variation heat flux classical potential oganov LAMMPS molecular computational modelling atomic scale simulation temperature gradient auto correlation function phonon defect boundary scattering high pressure temperature composition saturation thermal thermochemical seismic anomaly |
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Awarding institution: | University of Leeds |

Academic Units: | The University of Leeds > Faculty of Environment (Leeds) The University of Leeds > Faculty of Environment (Leeds) > School of Earth and Environment (Leeds) The University of Leeds > Faculty of Environment (Leeds) > School of Earth and Environment (Leeds) > Institute of Geophysics and Tectonics (Leeds) |

Identification Number/EthosID (e.g. uk.bl.ethos.123456): | uk.bl.ethos.797994 |

Depositing User: | Dr. Ben Todd |

Date Deposited: | 29 Jan 2020 13:03 |

Last Modified: | 11 Feb 2022 10:53 |

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