This thesis consists of two completely separate parts. In Part I, we look at disorder in fastionic conductors, and in Part II we examine the pseudoquadrupole effect in ordered magnets. Part I looks at two aspects of the disordered state in fastionics, where the disorder is due to ions moving off their regular sites to positions close to other regular sites, a feature especially characteristic of the fluorites. The first aspect is how Coulomb interactions could be responsible for the co-operative behaviour of defects which causes the transition to fastionic behaviour. We look at this with a model of charged defects on a lattice, applying techniques involving classical diagrammatic perturbation theory to find the free energy of our model system. Using elementary thermodynamics, we show how this model can predict co-operative behaviour. The second aspect is the nature of the disorder above the fastionic transition. We look at disorder in lead fluoride using a molecular dynamics simulation with an interionic potential that we obtained. We use the simulation to examine the distribution of anions in both real space and k space. Simulations have been made on the other fluorites CaF₂ and SrCl₂ and it is possible that the high dielectric constant of lead fluoride might lead to qualitatively different behaviour. Our results show that this is not the case and we find defect concentrations similar to those obtained from CaF₂ and SrCl₂. Our Is space analysis however gives defect concentrations an order of magnitude larger, in approximate agreement with experiment. In Part II we set up a theory for the pseudoquadrupole effect in cubic ferromagnets and show that it is related to the difference in longitudinal and transverse magnetic susceptibilities. Model calculations are performed for a Heisenberg ferromagnet using molecular field theory near the critical temperature t_c, and spin wave theory at low temperatures; and the itinerant model at absolute zero and t_c. We find that the pseudoquadrupole effect in iron and nickel and at impurities in these metals appears to be very much less than measured quadrupole effects. We also look at the effect in GdAl₂ and show that it can not explain a temperature dependent quadrupole interaction seen experimentally We therefore conclude that the observed quadrupole effects are due to real electric field gradients.

A calorimeter was constructed for the determination of heat capacities of solids from 1.5 to 84 K. Results from this and other calorimeters are discussed, on bis(adiponitrile)copper(I) nitrate and tetramethylammonium trichloromanganate(II) ("TMMC") from 1.5 to 300 K, and on β-modification metal-free, copper(II), and nickel(II) phthalocyanines from under 5 to 80 K. Bis(adiponitrile)copper(I) nitrate has not-very-pronounced heat capacity maxima at 51 and 63 K. The total molar anomalous entropy change is estimated as between 1/2 R1n2 and R1n2. A previous assertion by X-ray crystallographers (Bull.Chem.Soc. Japan, <strong>32</strong>, 1221 (1959)) that the nitrate ions are disordered among four orientations at room temperature is not supported by these results or by consideration of structure factors or of the potential field on the nitrate ions. The TMMC heat capacity results are consistent with those given in Solid State Comm., <strong>15</strong>, 1185 (1974) and Phys.Rev. B, <strong>12</strong>, 5858 (1975). The anomalous molar entropy change associated with the monoclinic-hexagonal transition at 126 K is estimated as R1n2.8, of which 1/3 occurs between 124 and 127 K; it is suggested that the NC₄ tetrahedra undergo twofold disordering and that the H atoms also undergo some disordering. The heat capacities of the copper and nickel phthalocyanines are surprisingly different from each other, especially below 25K, where the former is markedly lower except for two first-order transitions at about 9-13K with a total molar entropy change of not less than approximately R1n4. Magnetic and Schottky anomalies are, apparently, not involved in either material; perhaps the transitions in copper phthalocyanine involve disordering of the copper ions among four positions in the plane of each molecule. Below 8 K, the heat capacities of copper and metal-free (but not nickel) phthalocyanine apparently obey the T³ law.

by Cheung Kei Wai. / Parallel title in Chinese. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1992. / Includes bibliographical references (leaves 119-123). / Acknowledgement --- p.ii / Abstract --- p.iii / List of Abbreviations --- p.vii / List of Figure and Table Captions --- p.viii / List of Publication --- p.xiii / Chapter 1. --- Introduction --- p.1 / Chapter 1.1 --- Normal Diffusion --- p.4 / Chapter 1.2 --- Statistical Origin of Anomalous Diffusion --- p.10 / Chapter 1.3 --- Various Models of Diffusion --- p.15 / Chapter 2. --- Scaling Theory of Hopping Transport in One Dimension --- p.21 / Chapter 2.1 --- "Scaling Exponents, the Models and their Solutions" --- p.22 / Chapter 2.2 --- Numerical Simulations --- p.32 / Chapter 2.3 --- Relations to Diffusion on Fractals and Hierarchical Structures --- p.37 / Chapter 2.4 --- Non-Markovian Nature of Results and Quasi-localization Effect --- p.42 / Chapter 3. --- Renormalization Group (RG) Analysis of the Problem --- p.43 / Chapter 3.1 --- The Length Scale Renormalization (LSR) --- p.45 / Chapter 3.2 --- Application of the LSR to Random Barrier Model --- p.52 / Chapter 3.2.1 --- The distribution of the renormalized coupling constants / Chapter 3.2.2 --- Behaviour of W and V under the LSR transformation / Chapter 3.3.3 --- The scaling exponents from LSR / Chapter 3.3 --- Scaling Form of Diffusion Front --- p.66 / Chapter 4. --- Diffusion in Hierarchical Systems --- p.72 / Chapter 4.1 --- Scaling and Probability Densities --- p.75 / Chapter 4.2 --- Exact Renormalization and Lattice Green Function --- p.82 / Chapter 4.3 --- The Range of Diffusion --- p.89 / Chapter 5. --- Biased Diffusion --- p.95 / Chapter 5.1 --- Scaling Theory --- p.98 / Chapter 5.1.1 --- Linear Response / Chapter 5.1.2 --- Diffusion-Drift Crossover / Chapter 5.2 --- Crossover Behaviour under an Additional Bias --- p.103 / Chapter 6. --- Physical Realizations and Related Problems --- p.108 / Chapter 6.1 --- Physical Realizations --- p.109 / Chapter 6.2 --- Equivalence with Random Resistor Network (RRN) Problems --- p.113 / Chapter 7. --- Discussion and Conclusion --- p.116 / References --- p.119 / Chapter Appendix A --- Derivation of Eq. (1.3.8) --- p.124 / Chapter Appendix B --- Derivation of Eq. (1.3.10) --- p.126 / Chapter Appendix C --- Sampling from a Distribution --- p.129 / Chapter Appendix D --- Scaling Form of P (s) in Ordered System --- p.130 / Chapter Appendix E --- Explicit Form of the Lattice Green Function --- p.132

Thesis (M. Phil.)--Hong Kong University of Science and Technology, 2004. / Includes bibliographical references (leaves 52). Also available in electronic version. Access restricted to campus users.

Thesis (Ph. D.)--University of Oregon, 2002. / Typescript. Includes vita and abstract. Includes bibliographical references (leaves 223-225). Also available for download via the World Wide Web; free to University of Oregon users.

Thesis (Ph. D.)--University of Oregon, 2000. / Typescript. Includes vita and abstract. Includes bibliographical references (leaves 199-204). Also available for download via the World Wide Web; free to UO users.

Calculations are presented for a series of interrelated problems in the theory of disordered solids. The simple mean field theory of tricriticality in the layered Ising metamagnet is modified by inclusion of the Bethe-Peierls equation of state for the planar interactions. The approximation allows for a model of dilution with a finite percolation concentration for the layers. The calculated behaviour as a function of dilution for anisotropic coupling strengths allows comparison with experimental results on dilute ferrous chloride. Estimation is made of the effects of treating fluctuations by theories with mean field singularities. A discussion is given of first order phase transitions in disordered systems. A mean field theory of the implications of introducing quenched disorder to a system undergoing a transition of first order is effected by reformulating the problem in terms of a translationally invariant one via the replica method. The conclusions are examined in terms of a simple scaling theory and criteria derived for smearing of the singularities. Dynamic and thermodynamic properties of diluted magnetic insulators near the percolation concentration are considered in terms of simple geometric models of the percolating cluster as introduced by de Gennes. New scaling relations for the spin wave stiffness and conductivity exponents are derived and differences from previous relations interpreted geometrically. The scaling models of the percolating cluster so found, in which correlations propagate locally via effectively one-dimensional paths, are applied to the determination of the mobility edge for spin wave excitations in a dilute Heisenberg magnet near the percolation threshold. A prediction for the functional form of the mobility edge is made by means of results known for the Anderson model and a localisation length derived from an exact solution of a random problem by Dyson.

Thesis (M. Phil.)--Hong Kong University of Science and Technology, 2002. / Includes bibliographical references (leaves 58-59). Also available in electronic version. Access restricted to campus users.

Thesis (Ph. D.)--Ohio State University, 2009. / Title from first page of PDF file. Includes vita. Includes bibliographical references (p. 152-162).

A cubic lattice with random parameters is reduced to a linear chain by the means of the projection technique. The continued fraction expansion (c.f.e.) approach is herein applied to the density of states. Coefficients of the c.f.e. are obtained numerically by the recursion procedure. Properties of the non-stationary second moments (correlations and dispersions) of their distribution are studied in a connection with the other evidences of transport in a one-dimensional Mori chain. The second moments and the spectral density are computed for the various degrees of disorder in the prototype lattice. The possible directions of the further development are outlined. The physical problem that is addressed in the dissertation is the possibility of the existence of a non-Anderson disorder of a specific type. More precisely, this type of a disorder in the one-dimensional case would result in a positive localization threshold. A specific type of such non-Anderson disorder was obtained by adopting a transformation procedure which assigns to the matrix expressing the physics of the multidimensional crystal a tridiagonal Hamiltonian. This Hamiltonian is then assigned to an equivalent one-dimensional tight-binding model. One of the benefits of this approach is that we are guaranteed to obtain a linear crystal with a positive localization threshold. The reason for this is the existence of a threshold in a prototype sample. The resulting linear model is found to be characterized by a correlated and a nonstationary disorder. The existence of such special disorder is associated with the absence of Anderson localization in specially constructed one-dimensional lattices, when the noise intensity is below the non-zero critical value. This work is an important step towards isolating the general properties of a non-Anderson noise. This gives a basis for understanding of the insulator to metal transition in a linear crystal with a subcritical noise.