Thesis (Ph. D.)--Princeton University, 1931.

Thesis (PH. D.)--Princeton University, 1931.

Thesis--Wisconsin. / Vita. Includes bibliographical references.

Thesis (Ph. D.)--Catholic University of America, 1929. / Biography.

by David H. Douglass, Jr. and M.W.P. Strandberg. / "September 1, 1961." "Reprinted from Physica, vol. 27, pp. 1-17, 1961." / Bibliography: p. 17. / Army Signal Corps Contract No. W-36-039-sc-78108. Dept. of the Army Task 3-99-20-001 and Project 3-99-00-000. Army Signal Corps Contract DA36-039-sc-87376.

Inelastic neutron scattering measurements by Okazaki, Tuberfield, and Stevenson (1964) of the antiferromagnetic spin wave energy, spectrum in manganese fluoride crystal at low temperatures, agree with the results predicted by a dispersion relation introduced without proof in their paper. In this thesis the question is considered in detail to what extent this dispersion relation is justified. The interaction between the manganese ions is described by the Heisenberg exchange Hamiltonian. Following Holstein and Primakoff's formalism the spin deviation operators are introduced and the part of the Hamiltonian ℋ[superscript B] containing all the terms up to those bilinear in the spin deviation operators is diagonalised by means of the Anderson transformation. A correction is next obtained by retaining the diagonal part of those terms which are quadrilinear in the spin deviation operators. Under certain conditions it is shown that ℋ[superscript B] together with the correction term give rise to, a dispersion relation which is identical with that used by Okazaki et al. (1964). Finally the validity of the approximations is also discussed. / Science, Faculty of / Physics and Astronomy, Department of / Graduate

Thesis (MSc. (Physics)) -- University of Limpopo, 2016 / Nanostructured materials are attractive candidates for efficient electrochemical energy storage devices because of their unique physicochemical properties. Introducing nanotube systems as electrode materials represents one of the most attractive strategies that could dramatically enhance the battery performance. Nanostructured manganese based oxides are considered as ideal electrode materials for energy storage devices such as high energy and high power lithium-ion batteries. In this study, computer simulation strategies were used to generate various structures of MnO2 and spinel LiMn2O4 nanotubes; where Miller index, diameter and symmetry are considered as variables. The effect of these variables on nanotube generation was investigated. MnO2 and spinel LiMn2O4 nanotubes were generated using MedeA® software. Lower Miller indices, namely; {001}, {100}, {110} and {111} with diameter ranging from 5Å30Å were investigated for both systems. There are two ways that a nanotube structures could be wrapped along different directions, i.e., a_around_b or b_around_a. It was observed that wrapping direction has an effect on the geometrical structure of the nanotube. MnO2 nanotube generated from {110} revealed that nanotube wrapped along b_around_a gave a close-packed structure compared to its counterpart nanotube wrapped a_around_b. Diameter represents an important structural parameter of nanotubes; however, precise control of nanotube diameter over a wide range of materials is yet to be demonstrated. In this study, it was found that as the diameter of the nanotube is changed, parameters such as cross-sectional area and bond length change as well. The average bond distance of the nanotubes is less than that of MnO2 and LiMn2O4 bulk structure. Molecular dynamics simulation is further used to investigate the structure of MnO2 and LiMn2O4 nanotubes and the effect of temperature on the generated systems. Molecular graphical images used for the atomic positions for the nanotubes were investigated. The nanotube structures are described using radial distribution functions and XRD patterns. The calculated XRD patterns are in good agreement with the experiments, thus validating the generated structural models for the nanotubes. The resulting models conform to pyrolusite polymorph of MnO2 and LiMn2O4, featuring octahedrally coordinated manganese atoms. It was established that the variables have a direct control on nanotube morphology and the stability of generated nanotube model depends on surface morphology and termination. / National Research Foundation (NRF) and Centre for High Performance Computing (CHPC) of CSIR