Vocadlo, Nicole Ludmila; (1993) The role of lattice dynamics in determining the Grunesien parameter and diffusion processes in minerals and their analogues. Doctoral thesis (Ph.D), UCL (University College London).

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Abstract

The determination of the structural and rheological properties of the Earth's deep interior is severely hindered by its inaccessibility and the limitations on experimental techniques. With continuing progress being made in the development of increasingly powerful supercomputers, it is now possible to probe the Earth's interior via predictions based upon the atomistic simulation of Earth forming minerals. It is this consolidation between the microscopic and macroscopic nature of matter that is the essence of these computer simulations, and as such make computer modelling an extremely powerful tool with which to explore the innermost parts of our planet. This thesis uses such simulation techniques to investigate the Grüneisen parameter and diffusion processes in Earth forming structures. The Grüneisen parameter relates relevant thermodynamic properties and has an approximately constant, dimensionless value for most minerals over the entire pressure-temperature range for the deep interior. Its original definition is in terms of the vibrational spectrum which makes it an ideal quantity to investigate through lattice dynamics. It is this link between microscopic and macroscopic definitions of the Grüneisen parameter that is investigated in this thesis. Dynamical processes within the Earth are governed by the transport of energy in the form of physical quantities such as matter, momentum and heat; these in turn depend upon the conductivities and diffusivities of Earth materials. The diffusion of matter is poorly understood. Presently, there is great disparity in the experimental data where the components of the diffusion equation are not precisely defined. Phenomenological approaches to the determination of the diffusion coefficient are based upon limited theories which include many assumptions; these in turn lead to approximate results containing considerable uncertainty. Computer calculations based upon lattice dynamics enable us to predict an absolute diffusion coefficient by studying the mechanisms governing the diffusion process thereby calculating values for activation energies and pre-exponential factors. This thesis illustrates the importance of computer simulation as a valuable technique in determining some important quantities relevant to the interior Earth. Following an introduction, chapter two gives an outline to the theory of lattice dynamics and the computer code. In chapter three, the problem concerning the Grüneisen parameter is addressed, followed by calculations on a simple monatomic cubic lattice to provide a microscopic underpinning to current theoretical relations, and then on MgO, to determine its applicability to real materials. Chapter four elucidates the shortcomings of the phenomenological approach to determining the diffusion coefficient, whilst chapter five focuses upon an accurate determination of the absolute diffusion coefficient in MgO. Finally, in chapter six, the implications of this research to current theories is discussed with a view to gaining a deeper understanding of the processes occurring in the Earth's deep interior.

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