Patel, Atul; (1992) The analysis of the lattice dynamics and thermodynamics of major Earth-forming silicates. Doctoral thesis (Ph.D), UCL (University College London).

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Abstract

There is a great demand for accurate data of structural, elastic and thermodynamic properties of the Earth-forming silicates. Experiments to simulate the conditions of the mantle and core are obviously difficult. Therefore, theoretical models which can predict the required geophysical data at such conditions are of immediate importance. This work is a theoretical investigation into the lattice dynamics and thermodynamics of the major Earth-forming silicates. We use an atomistic approach based on the Born model of solids. This work is a rigorous test of the methodology and reliability of the lattice dynamics model at extreme geological conditions, i.e. high pressures and temperatures. We chose the modelling of oxygen isotope fractionation between geologically relevant silicates as a stringent test for our approach. The model works very well, although the calculated fractionation factors are not yet sufficiently accurate to be practically useful. We have compared calculations based on the quasi-harmonic approximation with corresponding molecular dynamics results for the geophysically important minerals periclase (MgO) and MgSiO3 perovskite. It has been clearly shown that the quasi-harmonic approximation breaks down at high temperatures and low pressures but this deviation is reduced when the external pressure is increased. Therefore, it is necessary to use the molecular dynamics technique for upper mantle conditions and the lattice dynamics model is limited to the lower mantle although inclusion of intrinsic anharmonicity into the model will remove such restrictions. All electron Hartree-Fock calculations were performed for the geologically relevant cubic MgSiO3 perovskite (an idealised structure). Successful geometry optimisations and reasonable bulk moduli were obtained. Subsequently, potentials obtained by fitting to such an ab initio energy surface can be incorporated into the lattice dynamics code, thus eliminating the problem of empirically determined potentials. The inclusion of the above considerations into the lattice dynamics code will yield a reliable theoretical technique for studying minerals at any geological condition. With such a powerful tool, coupled with the growing experimental techniques to probe such levels, the models of the Earth's interior can be clarified to give an overall consistent picture.

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