Anisotropy and anelasticity of HCP metals: a key to the dynamics of Earth's inner email@example.com
The solid iron inner core is the most remote and inaccessible part of our planet but its structure and composition may provide a key record needed to untangle the geological history of the surface environment. Information encoded in the inner core during its solidification could reveal the timing and nature of the onset of Earth’s protective magnetic field generated by convection in the liquid outer core or even of changes in the way the mantle convects and drives surface dynamics. Key to developing our understanding of the inner core is our ability to use seismic observations to constrain its structure on all scales. Seismic wave velocities are mostly sensitive to the atomic scale crystal structure, temperature and composition. On a larger scale the microstructure of the inner core, reflecting its deformation and crystallization history, can be probed by seismic studies of elastic anisotropy (variation of wave velocity with direction) and anelasticity (responsible for the time lag between the deformation associated with the passage of seismic energy and recovery to the pre-strained state leading observable to seismic signals). Seismic observations in principle allow us to infer the inner core’s history of growth and deformation, but require information on the material properties of hexagonal close packed (HCP) iron – the high-pressure phase of iron expected to form the inner core. The overall aim of this project is to make use of atomic scale simulations to provide this information. In particular, you will seek to understand the origin of anisotropy and analesticity in the inner core and use this understanding to decode the information hidden in the center of the Earth.
Figure 1: cartoon showing the dynamics of the Earth’s interior. Convection in the mantle drives plate tectonics at the surface and cools the outer core to drive the generation of the magnetic field. Growth of the inner core provides additional power for magnetic field generation and its crystallization leaves evidence of Earth’s history at the center of the planet (such as the green ‘inner inner core’ or textured anisotropic material forming much of the inner core in this image). From Ed Garnero (http://garnero.asu.edu/).
The deformation mode of solids is dependent on the time scale and magnitude of stress as well as the temperature, pressure and microstructure. On the shortest time scales and well below the melting point small stresses result in elastic strains where stored energy is immediately returned once the stress is removed. On much longer time scales and typically at higher temperature stress can cause the motion of imperfections in the crystal structure (such as point defects, dislocations and grain boundaries) leading to irrecoverable plastic deformation. Between these extremes, stress applied at seismic frequencies leads to strain by the realignment of crystal imperfections. When the stress is removed the strain disappears after a delay time that is characteristic of the deformation mechanism. This anelasticity leads to frequency dependent moduli and loss of energy from the mechanical system. These processes are seismically observed in the core [1,2] and known to seismologists as dispersion and intrinsic attenuation. They link seismology and the nature of the imperfections within crystals that are the inevitable result of deformation or growth. Therefore, seismic observation of dispersion and attenuation of the inner core provides key information on its growth and dynamics. These observations are now being made, including new study of normal modes (where large earthquakes make the planet 'ring like a bell'), but in order to interpret them experimental data on the controls of anelasticity in core materials are needed [3,4]. However, the most recent study of the anelasticity of iron  is now over a decade old and is limited to low pressure where iron adopts the body centered cubic (BCC) or face centered cubic (FCC) structure. It is now widely, although not universally, accepted that iron in the core adopts the HCP structure. There are no results that reveal the anelasticity of this core-forming phase.
Advances in atomic scale simulation techniques, where the properties of Earth materials are predicted by considering the behaviour of the electrons, and improvement in the power and availability of high performance computing, allows the properties of materials at extreme pressure and temperature to be predicted without recourse to experiment. These methods allow the nature of crystal imperfections to be examined and this, in turn, allows us to study the viscosity and anelasticity of the inner core. Use of these methods lies at the center of this project.
In order to provide the information needed to understand the origin and evolution of the inner core, you will undertake atomic scale simulations of point defects and dislocations in HCP iron. The project will evolve in a number of distinct steps as you develop a mastery of atomic scale simulation techniques. In particular, you will:
Simulate the structure, mobility and vibrational properties of point defects (atomic impurities) in order to test and quantify the idea that the motion of point defects is responsible for attenuation in the inner core .
Study the nature of dislocations (line defects)  in HCP iron, to provide constraints on the viscosity of the core, explore the mechanism leading to anisotropy, and probe the possibility of dislocation damping as the origin of anelasticity.
Construct combined models of the viscosity and anelasticity of HCP iron under the conditions found in the core, and link these to models of inner core growth and deformation.
With these results in hand, you will examine the possibility of deformation of the growing inner core as the origin of seismic anisotropy and how the anelastic and anisotropic structure can be used to reveal the growth history of the inner core.
You will receive training in skills tailored to the project but also useful to help secure a future career as a research scientist in academia or elsewhere. To allow you to complete the project you will learn to use a wide range of atomic scale simulation methods and, in particular, the application of density functional theory to defects in solids. You will need to master the application of lattice dynamics and molecular dynamics, and become skilled in the analysis of the results of atomic scale simulation. These advanced methods have great utility across a wide range of science and industry. Some examples from beyond the Earth sciences include use in drug discovery and development, advanced materials design and optimisation for engineering applications, and the development of green solar and fuel cell energy technologies. You will also learn how to confidently develop software for the analysis of results and to use large-scale high performance computing resources. Alongside the transferable skills in communication and management this can open a wide range of career pathways. These skills will be developed by a mixture of hands on experience, attending external training courses, and by participating in the Leeds – York NERC doctoral training partnership programme
Figure 2: University of Leeds hosted tier 2 high performance computing facility of the N8 HPC consortium (http://n8.hpc.org.uk), one of the supercomputers that can be used in this project.
You will have a good first degree in the physical sciences (e.g. physics, chemistry or geology) that included modules in mineralogy, crystallography or other subjects including components of condensed matter physics. The ideal candidate will also have experience of basic scientific programming and computation possibly derived from the completion of an undergraduate research project.
References and further reading
 I. Sumita and M. I. Bergman (2007) Inner-core dynamics. Core Dynamics: Treatise on Geophysics volume 8 (P. Olson, ed.). Elsevier, Amsterdam.
 D. J. Doornbos (1974) The anelasticity of the inner core. Geophysical Journal of the Royal Astronomical Society 38:397-415
 A. M. Makinen and A. Deuss (2013) Normal mode splitting function measurements of anelasticity and attenuation in Earth’s inner core. Geophysical Journal International 194:401-416.
 A. M. Makinen, A. Deussn and S. A. T. Redfern (2014) Anisotropy of Earth’s inner core intrinsic attenuation from seismic normal mode models. Earth and Planetary Science Letters 404:354-364.
 I. Jackson, J. D. Fitz Gerald and H. Kokkonen (2000) High-temperature viscoelastic relaxation in iron and its implication for the shear modulus and attenuation of the Earth’s inner core. Journal of Geophysical Research 105:23605-23634.
 A. M. Walker, P. Carrez, and P. Cordier (2010) Atomic-scale models of dislocation cores in minerals: progress and prospects. Mineralogical Magazine, 74:381-413.
Related undergraduate subjects:
- Computer science
- Materials science