Thesis (Ph. D.)--University of Wisconsin--Madison, 1968. / Vita. Typescript. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references.

Thesis (Ph. D.)--University of Wisconsin--Madison, 1981. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references and footnotes.

Thesis (Ph. D.)--University of Wisconsin--Madison, 1969. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references.

No description available.

The energy of a graph began with German physicist, Erich H¨uckel’s 1931 paper, Quantenttheoretische Beitr¨age zum Benzolproblem. His work developed a method for computing the binding energy of the π-electrons for a certain class of organic molecules. The vertices of the graph represented the carbon atoms while the single edge between each pair of distinct vertices represented the hydrogen bonds between the carbon atoms. In turn, the chemical graphs were represented by an n × n matrix used in solving Schr¨odinger’s eigenvalue/eigenvector equation. The sum of the absolute values of these graph eigenvalues represented the total π-electron energy. The criteria for constructing these chemical graphs and the chemical interpretations of all the quantities involved made up the H¨uckel Molecular Orbital theory or HMO theory. In this paper, we will show how the chemical interpretation of H¨uckel’s graph energy evolved to a mathematical interpretation of graph energy that Ivan Gutman provided for us in his famous 1978 definition of the energy of a graph. Next, we will present Charles Coulson’s 1940 theorem that expresses the energy of a graph as a contour integral and prove some of its corollaries. These corollaries allow us to order the energies of acyclic and bipartite graphs by the coefficients of their characteristic polynomial. Following Coulson’s theorem and its corollaries we will look at McClelland’s first theorem on the bounds for the energy of a graph. In the corollaries that follow McClelland’s 1971 theorem, we will prove the corollaries that show a direct variation between the energy of a graph and the number of its vertices and edges. Finally, we will see how this relationship led to Gutman’s conjecture that the complete graph on n vertices has maximal energy. Although this was disproved by Chris Godsil in 1981, we will provide an independent counterexample with the help of the software, Maple 13

No description available.

Fatigue and electrical degradation including low voltage breakdown of ferroelectric lead zirconate titanate Pb(Zr_xTi_{1 - x})O₃ (i.e. PZT) thin films are the major limitations for commercial memory applications of these films. It is noted that the presence of oxygen vacancies and their entrapment at the electrode-ferroelectric interfaces are the sources of the degradation phenomena. Attempts were made in this study to solve these problems: 1) by minimizing oxygen vacancy entrapment at the interfaces by employing RuO₂ electrodes; 2) by lowering the oxygen vacancy concentration in PZT films using donor doping (e.g. La³⁺ at Pb²⁺ site and Nb⁵⁺ at Ti/Zr⁴⁺ site). For this study, PZT thin films were prepared by a sol-gel method and deposited on both Pt/Ti/SiO₂/Si and RuO₂/SiO₂/Si substrates. The microstructure and electrical properties, such as hysteresis properties, fatigue, leakage current, time dependent dielectric breakdown (TDDB) and retention, were studied with regard to the Zr/Ti ratio, the excess lead, the annealing temperature, the electrode material and the doping amount. Furthermore, the pyrochlore to perovskite phase transformation of PZT on RuO₂ electrodes was also investigated. It was shown that PZT films (Zr/Ti=50/50) with 10 at.% excess lead annealed at 650°C for 30 min possessed the best electrical properties for ferroelectric memory application. In confirmation with earlier theoretical and experimental results, no polarization loss was observed up to 10¹¹ switching cycles for the PZT films deposited on RuO₂ electrodes. However, the low Schottky barrier at the interfaces between RuO₂ and PZT films resulted in a higher leakage current at a high electric fields. Donor doping of PZT films decreased carrier concentrations in PZT films, and thus, decreased the leakage current to acceptable limits. In addition, it was also noted that the pyrochlore to perovskite phase transformation of PZT on RuO₂ was similar to that of PZT on Pt electrodes. It can be concluded that the combination of RuO₂ electrodes and donor doping produced PZT films with high fatigue endurance and low leakage currents which are suitable for memory applications. / Master of Science

The modified electron gas (MEG) model has been used to generate ionic model CaCO₃ crystals in the calcite, aragonite, diopside, and perovskite structure types. For calcite and aragonite, the model predicts shorter CO bonds and larger bulk moduli than observed. Modeling of the thermochemistry of CaCO₃ does not reproduce the observed thermochemistry even qualitatively. The model predicts that the hypothetical diopside structure type is the most stable form CaCO₃ among the four structure types. These discrepancies may illustrate the significance of CO bond covalency in determining the physico-chemical properties of CaCO₃. The MEG model has also been used to generate model alkali halide crystals in the sphalerite, rocksalt, and CsCl types in an exploration of the reliability of the radius ratio rule. The MEG model predicts the correct cation coordination numbers for 13 of 16 alkali halides, whereas the radius ratio rule predicts the correct coordination numbers in at most 9 of the same 16 alkali halides. Analyses of the model crystal structures suggests that energy minimization is more important than packing efficiency in determining the most stable structures for ionic crystals. The molecular orbital (MO) model has been used to determine minimum-energy geometries and electron density distributions in sulfate hydroxyacid molecules. These molecules have been used to model the bonding in sulfate crystals. SO bond lengths calculated for H₂SO₄ and H₂S₂O₇ correlate linearly with fractional s-characters of the bonds, as in sulfate crystals. With increasing S coordination number, the bonded radii of S and O, as determined from electron density maps, increase at the same rate, contrary to the common assumption of constant anion H₂S₂O₇ shows a relatively large change in energy as its SOS angle is deformed from its minimum-energy value (125.6°) to l80°, in conformity with the small variation among observed SOS angles. In contrast, SiOSi and POP angles show relatively wide variations in crystals and molecules. This suggests that polysulfates may be less amenable than polysilicates or polyphosphates to polymorphism or glass formation. Other properties of H₂SO₄ are also calculated and compared with experimental observations and previous calculations. / Ph. D.

Thesis: Ph. D., Massachusetts Institute of Technology, Department of Materials Science and Engineering, 1975 / Vita. / Includes bibliographical references. / Ph. D. / Ph. D. Massachusetts Institute of Technology, Department of Materials Science and Engineering

Extended Hückel methods are known to be a useful tool in understanding surface phenomena. Important quantities about atoms and chemical bonds can be obtained from this computationally simple method, although caution must be exercised in interpreting the results. Application of Extended Hückel calculations to large metal clusters reveals the role of d orbitals in solids. Basic ideas of constructing model compounds have been developed. Several model systems for surface chemisorption processes are constructed in order to understand the surface catalyzed oxidative degradation of polyperfluoroethers. The activation of oxygen molecules can be explained. The Lewis acid character of the iron fluoride surface can be predicted. Based on these results, mechanisms of the degradation processes are discussed.