The chemical and physical properties of organic molecular crystals depend on both the molecular and crystal structure. The systematic approach to understanding and controlling crystal structure lies in the field of "crystal engineering". One strategy to emerge within crystal engineering has been the utilisation of specific interactions or couplings / synthons to predictably build supramolecular arrays such as tapes, ribbons or sheets. These arrays form a subset of the crystal structure. While many couplings take the form of cyclic motifs in which component interactions are of comparable strength, a cyclic coupling consisting of an O-- H<SUP>...</SUP>N and a C-H<SUP>...</SUP>O interaction was noted as having a potential use in designing supramolecular arrays. This type of strong / weak coupling is possible upon the interaction of an N-heterocycle with a carboxyl group. The following research describes the co-crystallisation of various N-heterocyclic bases with a number of olefinic and aliphatic dicarboxylic acids. The crystal structures of various complexes of phenazine, 1,10-phenanthroline and quinoxaline were solved from single-crystal X-ray diffraction data and are discussed. Two distinct strong / weak couplings were identified within the three sets of co-crystals. A comparison of the relative stabilities of the two couplings was made using the quinoxaline system. Supramolecular tapes were observed in all of the phenazine co-crystals and in three of the four quinoxaline co-crystals. (The stoichiometry of the phenazine co-crystals may be related to the position of the carboxyl groups on the participating acid.) The packing of the tapes is discussed with particular reference to tape topography and inter-tape C-H<SUP>...</SUP>O interactions. Proton transfer occurred in four of the five co-crystals of 1,10-phenanthroline. Co-crystals were prepared via two methods: by growth from a solution and by grinding of a physical mixture of the starting components. Solid-state grinding was found to be a viable method for the preparation of co-crystals. Complexes of 1,10-phenanthroline prepared via the two routes were analysed using solid-state <SUP>13</SUP>C MAS NMR and the effects of protonation on certain carbon resonances is discussed.

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Mathematically triply periodic minimal surfaces (TPMS) are easy to define but extremely hard to calculate. We have described the exact computation of three surfaces most commonly found in nature, designated P, D and G. We give analytical equations for their coordinates in terms of special functions, as well as for their metric properties such as surface to volume ratios. Nodal surfaces are simply surfaces over which any function f(x, y, z) = 0, for example Cos(x) + Cos(y) + Cos(z) = 0. We have obtained extremely accurate and far more practicable models for TPMS by fitting exact surfaces to a Fourier expansion in non-orthogonal basis sets of the nodal surfaces of crystallographic structure factor expressions. These have been compared with existing models in the literature by a novel technique of colouring their surface curvatures, and found to be far superior. The contours of zero electrostatic potential within an arrangement of positive and negative electric charges in ionic crystals, as for example in the lattice of CsCl, can be plotted as a surface which separates space into domains of positive and negative potential. These surfaces correspond topologically to TPMS. We give new analytical expressions for 11 zero equipotential surfaces (ZEPS) in terms of Jacobi theta functions. The numerical integration of these now standard expressions is extremely slow, taking several hours to obtain a surface. We give nodal expressions for the most important electrostatic surfaces reducing the computation time to mere seconds. Using this technique we have analysed the scalar curvature and vector field properties for a large range of crystal structures, producing the most comprehensive quantitative comparison of triply periodic surfaces to date. By considering the purely classical motion of a charged particle over the zero equipotential surfaces of CsCl, we have proved that quantization of field and energy is solely a function of the metric defined by charge, and not a function of scale. We have further proved that triply periodic minimal surfaces define this metric. This work shows the importance and relevance of TPMS as potential universal descriptors of all charge and matter.

The erosion rate of CVD diamond was ascertained using various sized erodents, impacting at different velocities. The relative sizes of the contact area and the size of the grains affected the erosion rate. Since the contact area increased with erodent size and impact velocity, both the sand size exponent and the velocity exponent were dependent upon the size of the grains. This result confirms that the ratio of the contact area to the microstructure is important. CVD diamonds often exhibit small fractures near to grain boundaries. These fractures usually contain graphitic or amorphous carbon that has become trapped during growth. These "micro-features" are discussed in Chapter 4, and the erosion rate of CVD diamond was obtained at regions of different micro-feature densities. The change in erosion rate caused by different micro-feature densities was small, much smaller than that caused by different grain sizes. This was because there were few micro-features, and even fewer that were close enough to the surface to have an affect. They are shown to contribute to fracture progress on the growth side, but have limited effect on the nucleation side. The erosion rate of the nucleation side is dominated by the more numerous grain boundaries. The erosion rate of mechanical grade CVD diamond is experimentally determined to be lower than optical grade CVD diamond. The main difference between the two grades is a higher concentration of dislocations in the mechanical grade. However, the erosion erosion rates of CVD diamonds with very different dislocation densities are shown to be similar. A four-point bend test is used to determine the fracture toughness of mechanical grade CVD diamond, and it is shown that this parameter is higher for the mechanical grade CVD diamond. The low erosion rate of mechanical grade CVD diamond results from higher fracture toughness, but the reason for this is yet to be understood. It is suggested that micro-features may play a significant part in the lower fracture toughness of optical grade CVD diamond. However, Raman spectroscopy has been used to show that non-diamond carbon is present in both grades of CVD diamond.

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This thesis comprises three related studies of titanium carbide, a refractory material, using atomistic simulations based on the Tight Binding model of cohesion. The first study is a detailed critique of a recently published Tight Binding parameterisation for titanium carbide. In addition to correcting a large number of issues in the original source, the optimisation and suitability of the model were also investigated. In the second study, the same Tight Binding model was applied to the determination of the order structure of TiC<SUB>0.5</SUB>. Owing to a peculiarity of this structure, its unique determination has not been possible using conventional (powder diffraction) techniques. Thus, at least two symmetries have been assigned to TiC<SUB>0.5</SUB> based on experimental work; the results of this thesis allow a distinction to be made on the basis of quantum mechanical calculations. The third and final study is concerned with the deformation processes of TiC<SUB>2</SUB> which displays certain properties that distinguish it from other materials with the same (NaCl) structure. On the basis of a number of simulations, a model for the deformation behaviour is introduced. This model is used to explain the preferred slip system at low temperatures, the origin of the brittle to ductile transition, the expected dislocation dissociation reactions and the origin of the observed change in apparent activation energy of shear stress.

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This thesis studies several electro-optic effects of chiral nematic liquid crystals (N*LCs) for applications in displays and telecommunications. During these studies, an unusual coloured scattering effect of N*LC was observed. Further developing the experiment technique and the use of LC compounds, the reversible colour switching of a polymer stabilised N*LC at an oblique angle has also been demonstrated. In addition, by controlling the processing at different stages we are able to form a new switching mode 10 times faster in response time for a reflective display compared to normal switching modes in N*LC. The flexoelectro-optic effect of the N*LC provides fast switching and when it is aligned in the ULH texture; An in-plane switching of the optic axis that is linear to applied electric field across the sample. These remarkable characteristics give a grey scale capability and provided a potential application in amplitude or phase modulation. In this work, an investigation of the flexoelectro-optic effect of the N*LC in the ULH texture was carried out by examining the LC compounds and a novel LC material with a large tilt angle. Result show the relationship of the pitch length of the N*LC helix, a weak polymer network and an applied frequency to the flexoelectro-optic effect of the N*LC in the ULH texture. In addition, we also show the feasibility of using ferroelectric nanoparticles to optimise the flexoelectro-optic effect. Both a significant improvement in tilt angle and response time was observed.

Chapter 1 gives an introduction to X-ray and neutron powder diffraction and the use of these techniques for crystal structure determination and refinement. The Rietveld structure refinement method is described and examples of different methods of structure determination from powder diffraction data are given. The techniques of EXAFS and Mössbauer spectroscopy, which were used to provide additional structural information, are also introduced. Chapter 2 describes the different radiation sources and experimental techniques used in this work. Chapter 3 describes a structural study of magnetite, Fe<SUB>3</SUB>O<SUB>4</SUB>, below the Verwey phase transition (˜120 K). The P2/c structure of Fe<SUB>3</SUB>O<SUB>4</SUB> at 60 K has been refined with lattice parameters of a = 5.9412(3) Å, b = 5.9290(3) Å, c = 16.789(1) Å and β = 90.196(4). A variable temperature study of the Fe<SUB>3</SUB>O<SUB>4</SUB> lattice parameters between 2-280 K shows this transition is first-order. An EXAFS study between 8-270 K shows that there is no significant change in the average Fe-O distance in Fe<SUB>3</SUB>O<SUB>4</SUB> around the transition. Chapter 4 describes a structural study on a material related to magnetite, Fe<SUB>2</SUB>OBO<SUB>3</SUB>. Two phase transitions have been found for this material. The first of these is due to magnetic ordering and takes place at ˜155 K. The second is due to charge ordering and takes place at 315 K, this is a structural (P2<SUB>1</SUB>/c ↔ Pnma) transition. Chapter 5 describes a resonant scattering experiment done on CsI. Resonant scattering parameters have been refined from synchrotron X-ray powder diffraction data collected at room temperature and at 4 K close to the Cs and I K-edges. The refined f parameters are -6.2(2) e/atom (Cs, λ = 0.3453 Å), -9.0(I) e/atom (I, λ = 0.374105 Å) and -6.2(2) e/atom (I, 4 K, λ = 0.37367 Å). Chapter 6 describes the <I>ab initio </I>structure determination of 4-(2'3'4'-trifluorophenyl)-1235 dithiadiazolyl (C<SUB>7</SUB>S<SUB>2</SUB>N<SUB>2</SUB>F<SUB>3</SUB>H<SUB>2</SUB>; P<SUB>2</SUB>/n, a = 11.543(4) Å, b = 20.666(8) Å, c = 7.045(2) Å and β = 100.35(4) using synchrotron X-ray powder diffraction data. A global optimisation method was used to provide a starting model for Rietveld refinement.