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.

Using the new Picker flow calorimeter, the excess heat capacity (C(,p)('E)) has been measured for systems containing normal, branched and cyclic alkanes. The results indicate two unusual effects: (1) a large negative contribution due to the destruction of orientational order in a pure n-alkane component, and (2) a positive contribution attributed to the "condensation" of a more freely-moving molecule or segment on a sterically-hindered branched alkane, resulting in a restriction of rotational movement, i.e. creation of order in the solution. Mixtures of cycloalkanes and their methyl derivatives also show unexpected positive effects in the excess heat capacity. Thus the plate-like cyclopentane molecule gives positive C(,p)('E) values when mixed with other plate-like methyl derivatives of cyclohexane suggesting a hindering of its molecular rotation. / Cyclohexane mixed with globular branched and cyclic alkanes shows S-shaped C(,p)('E) curves, negative at low concentration of cyclohexane but positive at high, indicating the possibility of a restriction of cyclohexane motion. / Effects of order are also apparent in the equation of state of a liquid. The thermal pressure coefficient for systems containing n-hexadecane has been found to be anomalous and is explained by a lowering of the internal energy of n-hexadecane by orientational order. / Excess volume (V('E)) has been studied for systems of branched and normal alkanes by investigating different effects contributing to the total V('E), particularly an important effect of a difference in thermal pressure coefficients of the two components.

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.

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A method was found for creating ordered nanoparticles whose size and theoretical order-disorder temperature are ideal for study in the TEM. Specifically FePt, NiPt, FeNiPt and AuCu nanoparticles were studied. We were able to show how a nanoparticle's size affects its order-disorder temperature (Tod). When the particles were around 6 nm in diameter there was a shift downward of the Tod of 10-15 percent compared to the bulk. While particles around 10 nm in diameter experienced a downward shift of 0-6 percent compared to the bulk. One can approximate that particles less than 10-15 nm in diameter would show significant decreases in order-disorder temperature. We confirmed that alumina prevents copper losses, compositions were well within percent error. In addition we showed that when the alumina used is thin enough the images are not adversely affected and charging is not an issue.

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Multiferroics are currently intensely investigated because the coexistence and coupling of ferroic arrangements brings about new physical effects and, for the few room-temperature examples, interesting prospects for applications in various fields. This interest is illustrated by the recent publication of several articles on multiferroics in high impact reviews over the last five years. The main goal of the thesis was to look for new multiferroics by exploiting overlooked and original polar and magnetic arrangements. We more precisely investigated compounds based on lead iron tungsten PbFe2/3W1/3O3 (PFW) and lead zirconate PbZrO3 (PZO) oxides. PFW displays long- and short-range both polar and magnetic orders (ferroelectric-relaxor and antiferromagnetic-spin-glass) while PZO is antiferroelectric with antiferrodistorsivity (oxygen tilts) and existence of ferroelectric instabilities. Combining various techniques from synthesis to electric, magnetic and structural characterizations, we demonstrated that it is possible to get a multiferroic compound (50%PFW-50%PZO) with coexistence of multiple ferroic and structural arrangements with room temperature properties of practical interest. This work opens new prospects in this rich field of multiferroics in peculiar by using antiferroelectrics.