Properties of the Earth's deep interior studied using ab initio modelling techniques
This thesis describes first-principles simulation work undertaken by the author to understand the thermodynamic and elastic properties of iron at the high temperatures and pressures of the Earth's inner core, and how these properties inform our understanding of the inner core, as observed by seismic measurements. In particular, I address the observation that compressional elastic waves travelling parallel to the polar axis traverse the inner core some 3-4% more quickly than waves travelling in the equatorial plane. The Earth's inner core is a solid ball of iron, alloyed with small amounts of nickel and light elements. The temperature at the boundary with the liquid outer core is approximately 5600 K, and the pressure 330 GPa. The high-pressure, high-temperature phase digram of iron is complex however it is widely believed that iron has either a bcc or an hep structure in the core. Here I focus on hep iron. I first investigate and repeat a number of previous calculations of the thermodynamics and elasticity of hep iron made using density functional theory and an approximate particle-in-cell model. It is concluded that the calculations do not correctly describe the high-pressure, high-temperature elasticity of hep Fe, and that more rigorous calculations are required to gain an understanding of these properties. I then go on to perform ab initio molecular-dynamics and harmonic calculations of the temperature dependence of the axial ratio of hep iron at inner-core pressures, and using this information, perform similar calculations of the elastic constants at inner-core temperatures and pressures. Using these data, I compute compressional wave velocities and their anisotropy in hep Fe, and draw conclusions about the polycrystalline texturing of the inner core.