The first part of this thesis contains an account of the asymptotic theory, for small source Knudsen number, of spherical expansions of monatomic gases into vacuo. It is shown how a near equilibrium solution of Boltzmann's equation breaks down,:and how this breakdown leads to a scaled Boltzmann equation valid in the outer non-equilibrium region. This scaled equation gives rise to a closed set of moment equations for this region, and in particular a study is made of the third and fourth moments. Numerical solutions of the fourth moment equations have been obtained, and these results yield some information on the nature Of the distribution function itself. In addition the asymptotic theory has been extended to derive equations for the higher order terms of the second and third moments. Limiting solutions of these equations are presented and it is shown how these provide second order terms for heat transfer and temperature. The second part of this thesis deals with conditions near the surface of a Langmuir probe. Continuum theories depend on the boundary condition that the particle densities are zero at the wall. This is the continuum limit obtained as the teen-free-path (A) of charged to neutral particles tends to zero. It has been shown that the field has a second order effect near the wall, and an asymptotic analysis has been made of the effect of this perturbing field on the diffusion dominated region near the wall.

The magnetic susceptibility of some dilute alloys has been measured between 2 and 300°K by a force method. The investigation has been concerned mainly with solid solutions of I at.% or less of the elements of the second half of the rare-earth series in silver or gold, in order to study local moments on the impurity ions. The observed departures of the susceptibility from a Curie-Weiss behaviour can be understood and fitted primarily in terms of crystal , field effects. In some of the more concentrated alloys the effects of inter impurity interactions can be seen. Measurements have also been made on Pd and Pd based alloys, in particular on some PdNi alloys in view of the recent theoretical and experimental interest in this system.

The physical and mechanical properties of the thin oxide films, which form on many metals, determine the rate at which metallic oxidation and corrosion may proceed. A survey of the literature showed that very few measurements, particularly of the mechanical properties of films ,had previously been made. In this work, measurements were made of the deformability of oxide films, their electrical conductivity, and the stresses due to growth, as these should enable a clearer understanding to be obtained of the mechanism of oxidation and corrosion processes. The measurements of stresses showed that both tensile and compressive stresses could occur, and in the case of oxide films on aluminium, the origin of the two types is discussed in terms of the growth rates, and the influence of ionic diffusion. Measurements of the mechanical properties showed that the elastic deformation which may be tolerated by the thin oxide films on aluminium and several other metals and alloys, was considerably greater than that observed for the corresponding bulk oxides. In the absence of an ionic diffusion flux, the Young's Modulus of separated aluminium oxide films was found to be an order of magnitude less than that for bulk alumina. In addition, some evidence was obtained that at room temperature, oxide films on aluminium could deform plastically if 'the ionic diffusion flux was sufficient. Studies of the electrical properties showed that hydrogen could increase the electrical conductivity of thin oxide films, and a 'similar effect was observed in single crystals of rutile. Possible relations between the electrical and mechanical properties of oxide films are discussed.

The Egerton-Powling burner has been suitably modified and adapted for studying flames quenched by cold surfaces. The necessary instrumentation for measuring gas flows and their initial temperatures has been set up and successful efforts have been made to obtain flames which are reproducible and perfectly steady for long periods. Schlieren photography and particle track techniques have been tried for establishing the location of the flame front and for burning velocity measurements. The region of interaction of a cooled metallic heat sink with a premixed lean flat ethylene/air flame has been investigated. The detailed distribution of burning velocity has been measured, by means of a refinement of the particle track method. Two dimensional distributions of temperature and composition in this region have been obtained from thermocouples and microprobe sampling, followed by gas-chromatographic analysis. The burning velocity-heat loss relation has been found to depend on the orientation of the flame front to the heat sink. Heat release rates deduced by substituting temperature and flow data into conservation equations revealed some unexpected features close to the heat sink; in particular the zone of heat release becomes narrower and the maximum rate of heat release does not decrease appreciably towards the heat sink, in spite of a considerable reduction in temperature. These features have been interpreted in terms of the composition pattern, which suggests that the narrowing is due to quenching of the second stage of the reaction, while the reaction rate effect is caused by diffusion of hydrogen atoms to the surface, which acts as a sink for them. It has been shown that a reaction such as H + 02 Surface → HO2 would account for all the features observed; conclusions are drawn regarding the status of quenching theory and the role of flame-surface interactions in flame structure studies.

Evaporated carbon has been used for graphitization studies in the heat treatment range 1000 — 2400°C, using the techniques of electron diffraction and electron microscopy for characterisation. It has been established that the material is graphitizing, and the results indicate that even for relatively low heat treatment temperatures, (1000°C — 1640°C), there exist at least two stages in the crystal growth process. A value of approximately 2 eV, (46 kcal/ mole), has been obtained for the activation energy corresponding to the first of these stages. The causes of the scatter in results have been investigated, but it is indicated that the elimination of these effects requires more sophisticated equipment than that used in the present study. The nature of the scatter, together with results from the electron microscopy studies suggest that the techniques used may be more revealing than the more common X—ray technique in graphitization studies. The discovery that anisotropic layer plane growth may sometimes occur is an illustration of this point. The detection of the influence of specimen composition or heat treatment atmosphere was hampered by the presence of the large scatter in the data, and no positive result was found, although a catalytic action of iron seems probable. Electron microscopy of specimens heat treated at the higher temperatures, (1640°C - 2400°C), has allowed the identification of crystallite boundaries, both in bright field and dark field conditions. The orientation of the crystallites revealed by moire patterns in the dark field image obtained from the basal plane reflection, relative to the local film direction, has been established, and shown to coincide with the expected condition of preferred orientation.

In the broadest sense, the focus of this thesis concerns the role of entropy in macroscopic systems related to liquid crystals in equilibrium. We be- gin by defining a broad generalisation of the Ball-Majumdar potential, applicable to a wide variety of order parameter models relevant to liquid crystals. First we provide a geometric characterisation of the set of ad- missible order parameters for general systems. We demonstrate the key properties of convexity, regularity, and blow up at the boundary of the singular potential. This is then followed by a discussion of applications to Onsager type models and enforcing physicality constraints in Landau expansion-type models. Next we consider the recently proposed Onsager-type model of Zheng, Taylor and Palffy-Muhoray. Unlike Onsager's free energy density, the non-trivial solutions to the new model all have non-trivial support, implying two-sided variations cannot find solutions. In order to overcome this issue, we apply similar heuristics to the previous chapter to split the minimisation into two steps, a strictly convex minimisation problem with linear constraints and a finite dimensional, C1 minimisation problem, the latter of which provides an Euler-Lagrange-type equation satisfied by all Lp -local minimisers. We also perform a more direct analysis on the model to obtain the qualitative features of its phase behaviour. Finally, we consider an extension of the Kuhn-Grün model of polymer elasticity, adapted for use in the modelling of main-chain nematic elas- tomers. This is a particular case of the generalised singular potential, where the anisotropy of the polymer network is included as a further parameter in the energy. This shows the expected energetic coupling between the anisotropy of the system and the extension of a single chain. Furthermore, the polymer chain is finitely extensible, with the energy blowing up as the chain reaches the taut-chain limit, and an implicit force/extension relationship is provided. We conclude with a discussion of network theo-ries for describing macroscopic deformations, with particular focus on the rigidity properties that arise from the growth rate of the chain energy.

No description available.

The main focus of this thesis is the experimental muon-spin relaxation technique (μ+SR) and its application to study novel and unconventional magnetic behaviour. I present a range of experimental measurements which I supplement with theoretical calculations to remove the two main limitations inherent to μ+SR and thereby improve the understanding of the experimentally observed behaviour. Additionally, I investigate the potential effects of demagnetising fields on highfield μ+SR measurements. μ+SR employs positively charged muons as sensitive local magnetic probes but has the essential drawback that there is normally a lack of knowledge about where the muons implant in a given sample and the extent of subsequent local distortions. In some cases this nescience makes interpretation of μ+SR data very challenging and severely limits the conclusions that can be drawn. Two research projects presented in this thesis are centred around utilising ab initio structural calculations based on density functional theory in order to remove these two inherent limitations of μ+SR and gain insights into the stopping sites of the muons and their local environments. In the case of the Pr based pyrochlores Pr2B2O7 (B=Sn, Hf, Zr, Ir) I combine such ab initio computations of the muon sites with calculations of the crystalfield levels of the Pr3+ ions. I demonstrate that the non-Kramers doublet ground state of the Pr ions is split due to the presence of the muons and that this consequently results in a hyperfine enhancement of the Pr nuclear moments. By showing the theoretically calculated values of the ground state splittings to be in fair agreement with those obtained from fits to the experimental data, I demonstrate that the μ+SR measurements of Pr2B2O7 re ect muon induced effects rather than intrinsic behaviour. I subsequently investigate the conceptually very similar spin ices A2Ti2O7 (A= Dy, Ho) using the same methodology and confirm that in this case the muons act as passive probes. A second project presented in this thesis concerns the compound a-RuCl3, in which Ru ions form nearly perfect two-dimensional honeycomb layers. The experimental μ+SR data reveal two magnetic phase transitions, the origins of which I study by combining calculations of the potential muon sites with computations of the dipolar fields experienced by the muons at these sites for different magnetic structures. I show that the experimental observations are only fully explained through a temperature regime between the two measured transitions in which the Ru spins share significant correlations within the honeycomb layers but not between the separate layers. A final research aspect I present is a study of the potential effects of demagnetising fields in high field μ+SR measurements. I derive an analytical solution for the demagnetising tensor of a uniformly magnetised finite cylinder and use it to show that edge regions of a sample suffer the most from demagnetising effects. I subsequently discuss the resulting experimental signatures and methods to identify and reduce them.

The nucleation and structural details of evaporated layers of the compound semiconductors InSb and PbTe have been studied. To evaluate the electrical behaviour of these polycrystalline films as grown on amorphous substrates both resistivity and Hall voltage have been measured both as a function of deposition conditions and of temperature. Dynamic measurement of the high frequency differential capacitance associated with the surface space charge region on these materials when in contact with anodically formed A1203 has enabled the trapping behaviour of the surface region of these semiconductors to be determined across essentially the entire band gap. When combined with the results of field effect measurements a measure of the specularity to current carriers of these interfaces has also been obtained. Theoretical analysis of the surface measurements has required, for these narrow band gap materials, the use of degenerate statistics and in the case of InSb the inclusion of terms to account for the large non-paraboli - city of its conduction band. Because of the complexity of the resulting expressions their evaluation has been carried out on an IBM 7090 computer. Correlation between the surface and Hall results has been obtained and in the case of PbTe, as a result of its inordinately large value of permittivity, it is believed that the apparent intrinsic behaviour results from compensation of the bulk dopant by surface states. Thin film field-effect transistors have been fabricated from both InSb and PbTe. Both materials have proved reasonably successful in this respect but in the case of PbTe its large temperature sensitivity has indicated the inapplicability of its commercial exploitation. Dielectric trapping, the degrading effects of high resistance channel contacts and minority carrier conduction have been studied, the last apparently setting a fundamental limit on the device application of InSb.

This thesis is concerned with translational non—equilibrium effects in certain two dimensional expanding flows. These flows, involving monatomic gases, are characterized by initial continuum conditions, and the corresponding Knudsen Number is assumed to be small. The two problems considered are shown to have similar mathematical formulations. Firstly, the unsteady expansion of a cylindrically symmetric mass of a monatomic gas is examined and secondly the problem of the steady axisymmetric jet, expanding from continuum reservoir condition; is considered in a similar manner In both cases a near equilibrium perturbation solution of Boltzmann's equation, for Maxwell molecules, valid near the initial continuum region, is shown to breakdown in the far field of the flow. In order to account for this non—uniformity, Boltzmann's equation is resealed and an outer asymptotic expansion procedure is derived. The zeroth order enter solution for the thermodynamic variables is found and matched to the inner equilibrium solution in the appropriate limit, collectively determining the core of the flow. The core solution, found in this manner, is shown to be invalid near the front predicted by the continuum solution. The physical reason for this behaviour is indicated and a further resealing of the Boltzmann equation is made to account for it. Unfortunately the simplifications which are present in the core of the flow, notably in the velocity and density distributions, do not occur in the front region and a solution of both problems in this region is not attempted.