Nada, Roberto; (1991) Quantum mechanical study of perfect and defective solids. Doctoral thesis (Ph.D), UCL (University College London).

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Abstract

In this thesis we study the ground state properties of perfect and defective materials using quantum mechanical techniques. A number of different approximations are used to investigate the electronic structure of the systems studied. We adopt the Hartree-Fock Hamiltonian for the description of the problem, which we solve ab-initio, i.e. with only knowledge of the atomic number and the geometrical arrangement of the nuclei. The Hartree-Fock equations, that have been applied with great success for many years to the study of molecules, can be reformulated in order to satisfy the periodic boundary conditions that apply in a perfect, translationally invariant lattice. A review of Hartree-Fock theory is given in Chapter 2. In Chapter 3 we discuss the state-of-the-art of Hartree Fock computational schemes in quantum chemistry and we describe the structure of the program CRYSTAL, that adopts the ab-initio periodic Hartree-Fock approach. This program was used to study the electronic properties of silicates (SiO2 quartz and stishovite polymorphs, and of the ilmenite-structured MgSiO3. Results of this study are presented in Chapter 5. The availability of an accurate description of the perfect lattice makes possible the development of techniques to study point defects that locally perturb the host crystal. In Chapter 4 first we review some standard techniques for the study of point defects. Next we discuss an embedding method, where an isolated cluster of atoms, containing the defect, is embedded into the host by means of Green function techniques. We developed a computer program, EMBED, that was thoroughly tested during the work reported in the thesis. The major shortcoming of this approach is the inadequate treatment of long-range polarization effects and of charged defects. We present a technique to interface the quantum mechanical method with a classical description of the polarization potential produced in the relaxed host lattice. We have applied this latter technique to the study of defects in LiF: the bound Schottky pair and the Na substitutional impurity have been considered. Results are presented in Chapter 6, and are compared with classical simulations, where the system is described as a set of point charges interacting via interatomic potentials.

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