Thesis (Ph. D.)--McMaster University (Canada), 1990. / Source: Dissertation Abstracts International, Volume: 53-01, Section: B, page: 0310. Supervisor: J.E. Greedan.

Thesis (Ph.D)--Electrical and Computer Engineering, Georgia Institute of Technology, 2010. / Committee Chair: Thomas K. Gaylord; Committee Member: Donald D. Davis; Committee Member: Gee-Kung Chang; Committee Member: Muhannad S. Bakir; Committee Member: Phillip N. First. Part of the SMARTech Electronic Thesis and Dissertation Collection.

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Ph.D. (Theoretical Physics) / In this thesis the thermodynamic and magnetic properties of the non-degenerate Hubbard model are investigated. The underlying lattice is the bcc-lattice. The results obtained will therefore be especially applicable to systems with a single, narrow conduction band. As a check the thermodynamic properties of the model system are first calculated in two limiting cases, namely the free electron 'gas and the strong coupling limit. In this process, use is made of results related to Wick's Theorem, which are developed in an appendix. Another check is provided by the calculation of the ground state spectrum of a finite, fourpoint system. These results are obtained using standard group theory techniques. The ground state for the non-degenerate Hubbard model is solved approximatively by a variational method. Once again the necessary version of Wick's theorem is developed in an appendix. The ,results for the neutral case (i.e. a half-filled band) is in agreement with other studies on AB-lattices: It is found that the system is anti ferromagnetic for all values of the coupling constant. The quarter and three-quarter filled cases, hitherto not studied because of numerical complexity, yield a completely different picture. For increasing values of the coupling constant second order phase transitions are found, first from the para- to the ferromagnetic phase and then from the ferro- to the anti ferromagnetic phase. The only results available in the literature related to this case were obtained for an almost half-filled band in the strong-coupling limit and qualitatively support the findings of the present study. It is proposed that the simple theory used in this study be extended for use in physical systems such as Cr.

The mean quadratic elongation, < A >, is used to measure the distortions of close packed arrays of anions in crystals. It is also used to trace how such distortions vary with temperature (T) and pressure (P). A calculation of < ..\ > for arrays of anions in materials that adopt the rutile and olivine structure-types shows that the arrays exhibit increased distortions with increasing P whereas those in materials that adopt the dolomite structure-type exhibit a decrease in distortion. On the other hand, the close packed arrays in the dolomite and calcite structure-types become more distorted with increasing T. The array of oxide anions in rutile show an increased distortion while those in stishovite show a decreased distortion with increasing T. An analysis of apparent bulk moduli and linear thermal expansion coefficients calculated for the constituent polyhedra shows that the distortion of a material with a close packed structure is governed by its unoccupied as well as its occupied polyhedra. It also indicates that the rearrangement of the anions in such materials induced by an increase in P is governed by the apparent bulk moduli of its constituent polyhedra rather than by a tendency of the anions to adopt a more perfect close packed array. / Master of Science

Thesis: Sc. D., Massachusetts Institute of Technology, Department of Materials Science and Engineering, 1978 / Vita. / Includes bibliographical references. / Sc. D. / Sc. D. Massachusetts Institute of Technology, Department of Materials Science and Engineering

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