The Core Composition of Terrestrial Planets
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The Core Composition of Terrestrial Planets: A Study of the Ternary Fe-Ni-Si System Elizabeth Wann UCL A thesis submitted to University College London for the degree of Doctor of Philosophy. August 2015 2 I, Elizabeth Wann, confirm that the work presented in this thesis is my own. Where information has been derived from other sources, I confirm that this has been indicated in the thesis. 3 Abstract The exact composition of the cores of terrestrial planets is not known, but it is gen- erally agreed that they are composed of iron alloyed with a fraction of nickel plus a small percentage of a light element, likely Si, S, O, C or H. Silicon has long been a popular choice and is still regarded as a very likely candidate, based on density deficit and cosmochemical arguments. Although much work has been carried out on the Fe-Si system, studies on the Fe-Ni-Si system have only recently been carried out. The major- ity of studies have concentrated on specific candidate core compositions, based on core formation models or matching the observed density deficit. This can be problematic when core formation models depend on core composition. In this thesis, the Fe-Ni-Si system is investigated as a whole, starting with the end-member binary systems, FeSi and NiSi. This provides a more methodical approach to solving the core composition problem. Both ab initio calculations and high-pressure, high-temperature experiments have been used in this work. Ab initio calculations at 0 K were used to find the transition pressure of the "-FeSi to CsCl-FeSi phase transition, and also to test the stability of newly discovered NiSi-structured phases in FeSi. Lattice dynamics calculations at high temperatures and pressures have been carried out to determine the Clapeyron slope of the "-FeSi to CsCl transition, in both FeSi and NiSi systems. Laser-heated diamond anvil cell experiments were used to measure the melting curves of NiSi and the Fe-FeSi eutectic, and in-situ neutron di↵raction experiments were used to determine the equation of state of MnP-structured NiSi at high-pressure and high-temperature. Finally, X-ray di↵raction experiments were used to measure the thermal expansion of a range of (Fe,Ni)Si alloys. 4 Acknowledgements This PhD would not have been possible without the support and advice of my super- visors, Prof. Lidunka Voˇcadlo and Prof. Ian Wood. Their help and expertise were invaluable and I feel extremely grateful to have had such excellent supervisors. I am particularly grateful to Lidunka for her kindness and patience and whose encourage- ment pushed me forward to accomplishing this work. I would also like to thank Dr. Oliver Lord, for all his guidance with the diamond anvil cell experiments, and Dr. Benjam´ıMartorell for his helpful advice with VASP. Thank you also to Prof. John Brodholt, Prof. David Dobson and Prof. Dario Alf´e,as well as Dr. Simon Hunt and Dr. Alex Lindsay-Scott for their help and input during my PhD. Finally, my thanks go to my friends and family for their support and encouragement. To Becky, Adam, Jo and Amanda for sharing the highs and lows of my PhD and to Amy for making each conference more fun and enjoyable. To my family, for their words of encouragement and for always having faith in me. And lastly to Stephen, for being a constant source of support and for being there for me always. This PhD was funded by the Science & Technology Facilities Council, and made use of the facilities of HECToR and ARCHER (http://www.archer.ac.uk), the UK’s national high-performance computing service, which was provided by UoE HPCx Ltd at the University of Edinburgh, Cray Inc and NAG Ltd, and funded by the Office of Science and Technology through EPSRC’s High End Computing Programme. 5 6 Table of Contents Abstract 4 Acknowledgements 5 Table of Contents 7 List of Figures 13 List of Tables 19 1 Introduction 21 1.1 Introduction . 21 1.2 The Earth’s Inner Core . 23 1.3 Seismology . 25 1.3.1 Anisotropy and Layering of the Inner Core . 26 1.4 The Terrestrial Planets . 28 1.4.1 The Moon . 28 1.4.2 Mars . 29 1.4.3 Mercury . 33 1.4.4 Venus . 37 1.4.5 Summary of Terrestrial Planetary Cores . 38 1.5 The Case For Silicon . 38 1.5.1 Silicon in the Earth’s Inner Core . 39 1.5.2 Seismological Evidence for Silicon . 40 1.5.3 The E↵ect of Si on the Structure of Iron . 41 1.6 E↵ect of Nickel . 45 1.7 Investigations on the Fe-Ni-Si System . 47 2 Computational Methods 49 2.1 Ab initio .................................... 49 2.1.1 The Schr¨odinger Equation . 50 2.1.2 The Born-Oppenheimer Approximation . 50 7 2.1.3 The Many Electron Problem . 51 2.1.4 Independent Electrons . 51 2.1.5 Indistinguishable Electrons . 52 2.1.6 Self-Consistency . 53 2.1.7 The Hartree Method . 54 2.1.8 Hartree-Fock Theory . 55 2.2 Density Functional Theory (DFT) . 56 2.2.1 Hohenberg-Kohn Theorems . 56 2.2.2 Kohn-Sham Electrons . 57 2.2.3 LDA and GGA . 58 2.3 Plane Waves and Basis Sets . 58 2.4 k-point Sampling . 60 2.5 Pseudopotentials . 60 2.6 Projector Augmented Wave Method . 61 2.7 Ab initio Packages . 62 2.8 Static Calculations . 63 2.8.1 Geometry Optimisations . 63 2.8.2 Birch-Murnaghan Equation of State . 65 2.9 High Temperature Calculations . 66 2.9.1 Molecular Dynamics . 66 2.9.2 Lattice Dynamics . 67 2.9.3 Gibbs Free Energy . 68 2.9.4 Phase Diagram . 71 2.10 Summary . 72 3 Experimental Methods 73 3.1 High Pressure Experiments . 73 3.1.1 Shock Experiments . 74 3.1.2 Compression Experiments . 74 3.1.3 The Multi-Anvil Press (MAP) . 75 8 3.1.4 The Diamond Anvil Cell (DAC) . 77 3.2 O✏ine DAC Melting Experiments . 78 3.2.1 Sample Preparation . 79 3.2.2 Pressure Determination . 82 3.2.3 Heating the Cell . 83 3.3 X-Ray and Neutron Di↵raction . 85 3.3.1 Bragg’s Law . 86 3.3.2 Di↵use Scattering . 88 3.3.3 Analysis of Powder Di↵raction Data . 89 3.3.3.1 Rietveld Method . 89 3.3.3.2 Le Bail Method . 90 3.3.3.3 GSAS . 91 3.4 Thermal Expansion . 91 3.5 Synchrotron Experiments . 92 3.5.1 Introduction . 92 3.5.2 In situ Experiments . 93 3.5.3 ESRF DAC Experiments . 94 3.5.4 NSLS MAP Melting Experiments . 95 3.5.5 ISIS Equation of State Measurements . 95 3.6 Summary . 97 4 The Calculated FeSi Phase Diagram 99 4.1 Introduction . 99 4.2 The FeSi Phase Transition at 0 K . 100 4.3 Static FeSi Calculations . 102 4.3.1 VASP Calculations . 103 4.3.2 CASTEP Calculations . 104 4.3.3 Abinit Calculations . 104 4.4 Di↵erences in Transition Pressure . 105 4.5 The FeSi Phase Transition at High Temperatures . 107 9 4.6 Experiments on the FeSi Phase Transition . 107 4.7 Lattice Dynamics Calculations of FeSi . 109 4.8 FeSi Phase Diagram . 113 4.9 Conclusions . 115 4.10 Further Work . 115 5 Calculated Stabilities of NiSi-structured Phases in FeSi 117 5.1 Introduction . 117 5.2 NiSi Phases . 119 5.2.1 The MnP Phase . 119 5.2.2 The ‘anti-MnP’ Phase . 120 5.2.3 The Pbma-I Phase . 120 5.2.4 The WC Structure . 121 5.2.5 The Pmmn Phase . 121 5.3 VASP Calculations . 122 5.4 Conclusions . 124 6 The Calculated "-FeSi CsCl Phase Transition in NiSi 127 ! 6.1 Introduction . 127 6.2 The "-FeSi CsCl Phase Transition . 127 ! 6.3 Lattice Dynamics Calculations . 129 6.4 Conclusions . 134 7 NiSi Melting 137 7.1 Introduction . 137 7.2 Methods . 137 7.2.1 O↵-line LH-DAC Melting Experiments . 138 7.2.2 In situ LH-DAC Melting Experiments . 138 7.2.3 In situ MAP Experiment . ..