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<I>Ab initio</I> electronic structure calculations within the density functional formalism have been performed to study the behaviour of various types of bonding under pressure. Primarily covalent bonding is studied in the III-V semiconductor materials GaAs and InSb by studying their sequence of phase transitions under pressure. The stability of a new phase of GaAs is reported. Calculations on the more ionic copper halides have also been performed. The effect of directional bonding on the ease with which the lowest energy structure is found can then studied by comparison of the two systems. Simulations of the layered material TiS<SUB>2</SUB> under pressure show good agreement with experiment and the calculated band structures show a semiconductor to semi-metal transition at approximately the same pressure as experiment. Some of the motivation for studying materials under pressure comes from effects caused by lattice mis-match in semiconductor heterojunctions. The last chapter concerns whether the macroscopic theory of elasticity can be applied to heterojunctions where there are just a few inserted layers. While theory holds for the stoichiometric InAs in GaAs it is shown to fail in the case of AlAs in Si.

Prediction of the conditions required for the transformation of one phase of a mineral into another has long been a goal of condensed matter physics. This is especially desirable for phase transitions which are believed to be involved in geological processes, but for which the conditions of temperature or pressure are hard to reproduce experimentally. This thesis examines a number of structural phase transitions including those of MgSiO<SUB>3</SUB> perovskite, which is thought to form the largest part of the Earth's mantle and of ZrO<SUB>2</SUB> which plays an important role in inhibiting crack formation in ceramics. These phase transitions, in which an alternative phase may be reached by continuous distortions of the structure on an atomic level, are examined primarily through the use of first principles electronic structure calculations. Existing first principles techniques were extended to facilitate determination of the equilibrium structure by relaxation of the unit cell and the calculation of the lattice dynamics of complex phases. The distortion involved in most of the phase transitions studied is found to reflect the normal vibrational modes of one or both phases. The phase transitions of MgSiO<SUB>3</SUB> are found to be well described by only a few normal modes of the highest-symmetry cubic phase, dominated by two modes involving tilting of the SiO<SUB>6</SUB> octahedra. These modes resemble rigid unit modes, in which SiO<SUB>6</SUB> octahedra are assumed to remain perfectly rigid but may rotate with respect to other octahedra, whilst preserving linkages between them. The extent to which such simple modes are an accurate description of the dynamics of MgSiO<SUB>3</SUB>, BaZrO<SUB>3</SUB> and SiO<SUB>2</SUB> is investigated by way of structural analysis and lattice dynamics of both stable and metastable phases. Both simple models deduced from the lattice dynamical analysis and molecular dynamics using forces calculated from first principles are used to estimate transition temperatures for thermally induced phase transitions in MgSiO<SUB>3</SUB>.

Mixtures of thermotropic liquid crystal (5CB) and colloid (polymethylmethacrylate) particles have been studied. When these composites are cooled through the isotropic-nematic (IN) phase transition an optically switchable material is formed with an unusually high storage modulus. Previous studies have shown that the particles form into an interconnected network. In this thesis the mechanism of network formation, and the morphological and mechanical properties of the network are explored. Time-resolved laser scanning confocal microscopy (LSCM) is used to achieve near-single-particle resolution and observe the kinetics of the network formation upon cooling from the initial isotropic dispersion. As the mixture is cooled below the IN transition temperature (<i>T_IN</i>), the particles are expelled by growing droplets of nematic liquid crystal to form the walls of a three dimensional network. This process takes the order of 30 seconds (dependent upon cooling rate), but the IN transition of the pure liquid crystal is much quicker. The presence of impurities adsorbed onto the particles before they are dispersed in liquid crystal could be responsible for this. These impurities open up a biphasic region in the phase diagram and slow down interface movement. Calorimetric data are consistent with this interpretation. Microscopy observations show that upon heating above <i>T_IN</i> single particles become free and exhibit Brownian motion. As the sample is heated deep into the isotropic phase the network is broken up but clusters of particles remain. Sedimentation of these clusters causes a density gradient of particles to form across the sample with varying height and upon cooling a new network of particles or ‘clusters of particles’ is formed.

The binding of liquid crystal molecules to surfaces in liquid crystal cells is a difficult interaction to characterise as the environment which surrounds the liquid crystal molecules makes the systems inaccessible to experimental and theoretical studies. However, insight may be gained from an examination of simplified systems which represent specific aspects of this interaction. First principles electronic structures calculations based on planewave density functional theory allow the adsorption of an isolated molecule on an extended surface to be examined and compared with studies on complex molecules. One possible binding interaction between a liquid crystal molecule and a metallic surface may be represented by the interaction of a conjugated p system with a metal. In order to characterise this interaction, this thesis examines the interaction of ethylene with aluminium and copper, and benzene with copper. The electronic interaction which occurs between the species can be rationalised by an identification of criteria which are important for the formation of a chemical bond in a complex molecule and an examination of whether these criteria can be met on adsorption of the hydrocarbon on an extended surface. It is found that ethylene is physisorbed on the s-p metal aluminium surface, but can be chemisorbed on the transition metal copper surface. Benzene can also be chemisorbed on a copper surface at certain sties. These results are explained by an examination of the Al(C₂H₄), Cu(C₂H₄) and Cu(C₆H₆) complexes.

X-ray diffraction techniques have been employed in the solution of the crystal structures of two alkoxides of beryllium and of an oxime complex of indium. The structures were determined by the heavy atom method, and refined by the method of least squares using three dimensional data. The

This thesis is mainly concerned with structural studies of some hydrogen-bonded phosphate compounds (all monoclinic) - namely T1H2P04, CsH2PO4, NaH2PO4 and PbHP04. All these compounds, except NaH2PO4, have a ferroelectric transition. Structural studies of the above compounds have been undertaken for the following primary purposes (i) to contribute accurate structural information to the understanding of the transition mechanism, (ii) to contribute experimental information about hydrogen bond dimensions. Full three-dimensional X-ray and neutron diffraction data from single crystals of T1HZP04 and CsH2PO4 were collected at room temperature on four-circle diffractometers. Full three-dimensional neutron-diffraction data were also collected from a single crystal of NaH2P04 at room temperature. The previously unknown structure of T1H2P04 has been solved from a Patterson map with the X-ray data followed by Fourier difference-syntheses with the neutron data. Accurate positional parameters of the hydrogen atoms in all the above compounds have been determined from the neutron data. The symmetry-restricted hydrogen bonds of the T1H2P04 and CsH2PO4 structures have been found to be disordered. All the other hydrogen bonds, including those of NaH2PO4, have been found to be asymmetric. The crystal structures of T1H2P04 and CsH2PO4 are closely similar: the P04 groups are linked by hydrogen bonds into puckered sheets perpendicular to the long axis of the cell. By contrast, the P04 groups are H-bonded into a continuous network in NaH2P04, rather like monoclinic 021,04. The most extensive study of crystal structure in relation to a structural phase transition has been performed in PbHPO4. Three-dimensional neutron-diffraction data were collected at six different temperatures from well below to just above the transition. The crystal structure (previously uncertain) in the high-temperature, paraelectric phase, has been determined. It has been shown that the hydrogen atoms are disordered in this phase. Then the onset of order of the proton system in the ferroelectric phase, and accompanying heavy ion displacements, have been shown to vary with temperature very much like the onset of the spontaneous polarization.

An in-depth analysis of neutron powder-diffraction data from a sample of ice VII is presented. This study involved an attempt to extract information about the detailed nature of atomic disorder present in the water molecule, information only accessible via neutron techniques. The resulting difficulties lead to an exploration of the fundamental limits of powder-diffraction. This investigation highlighted a need to extend the maximum accessible pressure for single-crystal techniques that, for structural neutron-diffraction, is currently limited to 25kbars. The majority of the work constituting this thesis was devoted to increasing this limit. In order to realise this advance, two different techniques were developed in parallel. The first of these centred on the use of the Paris-Edinburgh (PE) cell to compress single-crystal samples. The new instrumentation, experimental methodologies and software developed by the author included modifications to both the cell and diffractometer and are presented here. These successfully facilitated a significant increase in accessible pressure up-to at least 70kbars. This new capability was used in a comparative powder and single-crystal study of the structure of potassium di-hydrogen phosphate (KDP). The results of this study challenged the previously published structure. They also facilitated a detailed comparison of the relative capabilities of powder and single-crystal measurements confirming the significant advantages of the latter in the measurement of low d-spacing intensities. The second technique to be developed by the author used a new large-volume diamond-anvil cell (DAC). This device provides optical access to the sample and thus the possibility of the in-situ growth of high-pressure phases. This property combined with large apertures for the diffracted beam gives the DAC a significant advantage over the PE cell. The techniques developed to perform neutron diffraction with the cell are presented as are the techniques of crystal growth. It was found that the DAC was currently limited in maximum pressure by the size of available anvils. However, this was sufficient to enable a investigation of D₂-D₂O clathrate, a compound only formed under high pressure. The results of this first neutron study are discussed in comparison with the previous published structure determined by <i>x-ray</i> diffraction, which was unable to resolve the hydrogen atoms.

The crystal structure of L-serine has been determined at room-temperature at pressures between 0.3 and 4.8 GPa. Compression of this phase is facilitated through the closing-up of voids in the middle of ring motifs and compression of a long OH…OH interaction. Above 4.8 GPa the structure undergoes a phase transition to a previously uncharacterized polymorph, which we designate L-serine-II. This transition occurs via a change from a <i>gauche </i>to <i>anti</i> conformation of the OH group, and a change in the NC<i>_a</i>CO torsion angle. In a separate high-pressure powder neutron diffraction experiment, compression of deuterated L-serine-I was found to be analogous to that observed previously in our single crystal study. On increasing pressure further to 8.1 GPa the structure undergoes another transition to a second previously unobserved phase of L-serine (L-serine-III). The crystal structure of hexagonal L-cystine has been determined at room temperature at pressures between 0.4 and 3.7 GPa; unit cell dimensions were measured up to 6.4 GPa. The structure consists of H-bonded layers which are connected on one side by the disulfide bridges within the cystine molecules, and on the other by NH….OH-bonds to other layers. Application of pressure pushes the layers closer together occurring approximately equally in the regions of the interlayer H-bonds and the disulfide bridges. The crystal structure of L-cysteine (hereafter L-cysteine-I) was compressed to 1.8 GPa, where the main effect of compression was to contract voids in the middle of ring motifs. On increasing pressure further, a transition occurs to a new phase of L-cysteine, L-cysteine-III. The phase transition is accompanied by a change in the NCCS torsion angle and small positional displacements, but with no major changes in the orientations of the molecules. L-cysteine-III was found to be stable to at least 4.2 GPa. On decompression to 1.7 GPa, another phase transition formed another previously uncharacterised phase, L-cysteine-IV. This phase is <i>not </i>observed on increasing pressure. Further decompression to ambient pressure generates L-cysteine-1. The crystal structure of <i>a</i>-glycylglycine (<i>a</i>-GLYGLY) has been determined at room temperature at pressures between 1.4 and 4.7 GPa; unit cell dimensions were measured up to 5.4 GPa. The structure can be considered to consist of layers of glycylglycine molecules which stack perpendicular to the (1 0 -1) direction. The arrangement of glycylglycine molecules within each layer resembles that of an anti-parallel β-sheet motif observed in protein structures.

The problems associated with refining a molecular structure using gas-phase electron diffraction (GED) data alone are well known. In particular, similar interatomic distances may be strongly correlated, and the positions of light atoms (particularly hydrogen) are poorly determined due to their low electron scattering ability. These problems make it necessary to fix some geometric parameters at assumed values. This is undesirable for two reasons, which are closely related. First, because this parameter is tacitly assumed to be correct, its effect on other refining parameters cannot be gauged; second, fixing parameters can result in unrealistically low estimated standard deviations for correlated parameters. It has been found that the inadequacies of GED data can, to some extent, be overcome by combining the data with those obtained by other structural techniques, particularly rotational spectroscopy and/or liquid crystal NMR (LCNMR) spectroscopy. This is the ideal approach, as the resulting structure is based entirely on experiment. However, sufficient experimental data are often not available. Work undertaken for this thesis concerned the development of a new technique to complete GED structural refinements using data obtained from <I>ab initio</I> molecular orbital calculations. The new method (called SARACEN - Structure Analysis Restrained by <I>Ab initio </I>Calculations for Electron diffractioN) is fully described in this thesis and illustrated with examples from two different classes of compounds. The first series of compounds are small chlorinated aromatic ring systems which serve as model compounds for larger biological systems. The second series is an extensive array of compounds based on the <I>arachno</I> boron hydride, tetraborane(10), with general formulas H<SUB>2</SUB>MB<SUB>3</SUB>H<SUB>8</SUB> and (CH<SUB>3</SUB>)<SUB>2</SUB>MB<SUB>3</SUB>H<SUB>8</SUB>, where 'M' represents a Group 13 element B, Al, Ga and In. Wherever possible gas-phase structures obtained are compared to solid-phase structures (either already known or derived as a part of this work).