Lithium-ion mobility in solid-state systems is an important field with significance for a range of technological interests, especially in the field of energy materials. The binary lithium compounds Li2O and Li3N have been studied using modern computational techniques to elucidate their diffusion properties. The macroscopic diffusion coefficients have been calculated and the underlying microscopic diffusion processes elucidated using molecular-dynamics-based techniques. In both systems studied the diffusion has been modelled over a wider temperature range than previously attempted. The agreement between the calculated diffusion coefficients and the best available experimental data surpasses previous computational studies. The level of agreement achieved is due to the use of force-field non-equilibrium molecular dynamics (FF-NEMD). This method, which has only recently been applied to solid-state diffusion, allows rates of diffusion that are typically too low to be studied with equilibrium molecular dynamics to be modelled. NEMD uses a fictitious external field to increase the frequency of the rare diffusion events in a predictable manner without changing the nature of the diffusion mechanisms. In the case of Li2O the transition from the non-superionic to the superionic regime has been modelled. The dominant mechanism in each regime has been determined: in the non-superionic regime a concerted mechanism dominates and in the superionic regime an interstitial-mediated mechanism dominates. For Li3N the anisotropic nature of the lithium diffusion coefficient has been modelled. The diffusion mechanisms dominant for different directions have also been elucidated. The rapid diffusion in the (001) plane of the hexagonal structure has been explained by the presence of vacancies on the in-plane Li sites, both in this thesis and in previous works. Previous studies have explained this by the presence of contaminants leading to non-stoichiometric Li3N. However, in this thesis the under occupation of these sites has been explained by the formation of Li2 dumbbells, or site sharing, largely about the interlayer Li sites, but also about the in-plane Li sites. The existence of these dumbbells explains the experimental diffusion coefficients of stoichiometric Li3N.

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In this thesis I present experimental measurements on a number of different quasi-one and quasi-two-dimensional metallic crystal systems susceptible to density-wave formation. I outline the discovery of a density-wave superstructure found via X-ray diffraction measurements in the quasi-two-dimensional Na2Ti2As2O and Na2Ti2Sb2O compounds. Na2Ti2Sb2O and Na2Ti2As2O are members of the Ti-based oxy-pnictides a group of compounds which exhibit complex phase diagrams and share structural similarities with the high temperature superconductors. Temperature-dependent X-ray diffraction measurements confirmed the superstructure in both materials to be concomitant with transitions seen in resistivity and magnetic data. The observation of the superstructure combined with results from other experimental techniques demonstrated the transition to be a charge-density-wave. I also present results on a series of intercalated charge-density-wave compounds NixZrTe3. NixZrTe3 was measured using X-ray diffraction and ARPES to investigate the effects of chemical pressure on charge-density-wave formation. The transition temperature for density-wave formation in this series of compounds had been previously shown to vary as a result of Ni-content. X-ray diffraction measurements on the series revealed no changes in the wavevector of the associated superstructure modulation across the series. However ARPES measurements on NixZrTe3 showed subtle changes in the binding energy of the one-dimensional band associated with the charge-density-wave thought to be a result of the Ni-intercalation. Through a combination of XPS, EDX and ARPES measurements the Ni-content in these crystals was deduced to be much lower than growth parameters suggested. Finally I describe the construction and testing of a straining device designed specifically for use with X-ray synchrotron type measurements. The straining device was successfully tested at the I16 beamline at the Diamond Light Source and shown to induce dynamic strain in a test sample of M2Mo6Se6. Further testing at the ID28 beamline at the ESRF revealed that the strain induced in a M2Mo6Se6 was significant and resulted in a change in the lattice dynamics of the material.

This thesis reports a pure and applied study on non-thermal plasmas (NTPs) produced using Dielectric Barrier Discharge (DBD) generators of various forms. The main aim of the pure aspect of the study was to obtain a better understanding of the chemistry taking place within the NTP in an air-fed DBD and to what extent the plasma output varies from the glow to the downstream regions under various operational conditions. Thus, a DBD plasma jet generator was designed and employed for the investigations of these regions. The analyses of the plasma glow region and the downstream exhaust were carried out using Fourier Transform InfraRed (FTIR) and UV–Vis absorption spectroscopies. The applied studies focussed on the development of a novel, dielectric barrier discharge-packed bed reactor (DBD-PBR) for effective ozone generation from oxygen or air, and its application to the remediation of Cu(II)-EDTA and Fe(III)-EDTA containing water in combination with an oscillatory baffled reactor (OBR) and a UV irradiation reactor (UVR). In-situ analysis of the plasma glow region of the plasma jet identified: O3, N2O5, N2O, NO2 HNO3, CO2, CO and, for the first time, a vibrationally excited form of CO2 (i.e. CO2*(v)), while O3, N2O5, HNO3 and N2O were detected in the downstream exhaust. The behaviour of these species was monitored as a function of a range of experimental conditions including: input power, gas flow rate, relative humidity, gas temperature and feed gas composition, and mechanisms postulated based on literature precedent. It is clear from this work that the feed gas composition, input power, gas temperature and relative humidity have a significant effect upon the NTP chemistry in the glow and post glow regions. Unexpectedly, the spectroscopic analyses of O3, NO2 and N2O in the plasma glow region and in the downstream exhaust suggested the occurrence of chemical reactions in the afterglow region rather than simple diffusion. This behaviour rules out the general assumption that reactive chemistry is confined to the glow region. The DBD-PBR was designed, fabricated, characterized and optimized for ozone generation from oxygen and air. The effects of reactor arrangement, feed gas flow rate, coolant temperature, input power and dielectric material on ozone generation were investigated. The highest ozone concentration of 152 g m-3 was obtained using 2.0 mm glass beads and an oxygen feed at 5 oC, and 0.06 dm3 min-1, while the highest ozone yield efficiency was 210 g kW-1 h-1 at an oxygen feed rate of 15 dm3 min-1 this compares to 173 g kW-1h-1 reported in the literature. The highest ozone concentration produced from air was 15.5 g m-3 at flow rate Preface v of 0.06 dm3 min-1 with Al2O3 beads as the dielectric. It was found that the dielectric employed in the DBD-PBR had a significant effect upon the selectivity towards ozone at low feed gas flow rates. Different NOx by-products were formed along with ozone when the DBD-PBR was fed with air depending on the coolant temperature and the dielectric material. The efficiency of ozone generation via DBR-PBRs was significantly enhanced reducing the discharge current during the generation of NTP by decreasing the capacitance of the dielectric and by effective heat removal. Finally, a MnO2-based catalyst (CARULIT 200) tested for DBD-PBR exhaust control, and was found to be effective for simultaneous ozone and NOx removal at room temperature. The DBD-PBR was coupled to an OBR to intensify ozone-to-water mass transfer. The OBR was operated as a semi-batch and as a co-current, up-flow continuous reactor. The effect of input ozone concentration, input gas & water flow rates, and oscillation amplitude and frequency on gas hold up, volumetric mass transfer coefficient and mass transfer efficiency were determined. The same reactor was operated as a bubble column (i.e. without baffles or oscillation) and as a baffled column (without oscillation) to assess the effect of the reactor arrangement on the mass transfer. The results show that the OBR was 5 and 3 times more efficient for ozone-water mass transfer than the baffled and bubble columns, respectively. The enhancement obtained with the OBR over the baffled column reactor was found to decrease with gas flow rate due to changes in bubble flow pattern from homogenous to heterogeneous. Under continuous flow conditions, the performance of the baffled reactor and the OBR were found to be twice as efficient for ozone-water mass transfer than when operating under semi-batch conditions. The mass transfer efficiency (MTE, %) was found to increase from 57 % using the baffled reactor to 92 % with OBR under continuous flow at water and gas superficial velocities of 0.3 and 3.4 cm s-1, respectively. From these results it is clear that the OBR and baffled reactor are promising approaches for enhancing ozone-water mass transfer and its application in water treatment. One of the targeted fields of the DBD-PBR/OBR/UVR system is in water treatment, and hence it was important to evaluate its performance in such application. Therefore, the system was employed for the treatment of water samples contaminated with Cu(II)-EDTA and Fe(III)-EDTA. These compounds were chosen because they are difficult to remove from water using conventional methods. The effects of reactor arrangement, ozonation time and ozonation plus UV irradiation on remediation of the complexes were investigated under Preface vi continuous flow conditions. The results suggest that Cu(II)-EDTA was decomposed completely by ozonation within 17 minutes using the OBR, with no significant enhancement by UV irradiation. However, the Fe(III)-EDTA was converted to other stable complexes (i.e. Fe(III)-ED3A and Fe(III)-IDA) by ozonation, and hence following the ozonation by UV irradiation was essential to ensure complete degradation. The total organic carbon (TOC) of the Fe(III)-EDTA and Cu(II)-EDTA solutions was reduced by 50% after 17 minutes of O3/UV treatment using the OBR. Some of the final products were identified using Ion Chromatography and included: oxalic acid, formic acid, acetic acid, glycolic acid, nitrate and nitrite ions. From these results, it is clear that the enhancement in ozone-water mass transfer using the OBR or the baffled reactor was essential for reducing the treatment time and ozone dosage required for the remediation of Cu(II)-EDTA and Fe(III)-EDTA over conventional bubble column reactors.

For calculating the properties of solids and molecules, density functional theory (DFT) has become extremely popular because of its inherent computational efficiency. However, despite being in principle exact, an approximation must be introduced into DFT in practice. The accuracy of DFT has been key to its popularity; however, even for some of the simplest systems, using common approximations to the exchange-correlation (xc) functional may give inaccurate results. Therefore, we aim to contribute to the development of improved approximate xc functionals. It is logical to begin by studying the most elementary of systems where the common approximate xc functionals require improvement, as one can model these systems exactly by solving the many-electron Schrödinger equation. By allowing us to study DFT and time-dependent DFT (TDDFT) in the absence of approximations for prototype systems, this approach provides insight into the fundamental principles of the theory, informing the development of new approximations. We show that steps arise in the level of the exact xc potential: steps are known to be important for giving accurate electron and current densities, yet little about their origin is understood. We show that steps form due to a change in the 'local effective ionisation energy' of the electrons: this concept is well defined for strongly localised electrons. We find that the tendency of an electron to exclude others from its vicinity (electron localisation) is surprisingly high in our finite systems; hence, we develop an approximate functional that uses a measure of localisation as an ingredient, with the analytical form of the Kohn-Sham potential in the limit of complete localisation. Our functional, termed the mixed localisation potential, gives accurate electron and current densities for our test systems where local approximations are less valid. The approximation’s success stems in part from its ability to reproduce steps in the xc potential.

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Quantum uids possess amazing properties of which two are particularly striking. Firstly they exhibit super uid ow, with the total absence of viscosity. Secondly, there are no excitations when the uid velocity (relative to some obstacle or surface) is slower than a critical value; above this velocity the ow becomes dissipative and macroscopic excitations are created in the form of quantised vortices with xed circulation proportional to Planck’s constant. In this thesis we numerically study the dynamics of quantum uids in the vicinity of obstacles and surfaces, from the production of a single vortex pair to the complex and chaotic motion of turbulent vortex tangles. This approach provides quantitative predictions for atomic Bose-Einstein condensates (BEC) and qualitative insight for super uid helium. We give detailed descriptions of the numerical schemes and present extensive numerical simulation of the Gross-Pitaevskii equation (GPE) and its variants at zero temperature and beyond, in both two and three dimensions. We study the wake that forms behind obstacles in the presence of a super uid ow, modelling atomic BEC experiments with moving laser-induced potentials, and explore the dependence on obstacle shape and size. We nd that suitable obstacles produce classicallike wakes consisting of clusters of vortices of the same polarity. Remarkably, symmetric wakes resemble those observed in classical viscous ow at low Reynolds number, despite the constrained vorticity. The structures are unstable, forming time-dependent asymmetric wakes similar to a classical Bénard–von Kármán vortex street. Motivated by the recentwork of Kwon et al. (Phys. Rev. A 90, 063627 (2014)), we model an atomic BEC experiment in which a trapped, oblate condensate is translated past a stationary, laser-induced obstacle. The critical velocity is exceeded and so vortices nucleate, forming a state of two-dimensional quantum turbulence. We explore the system at both zero-temperature and with thermal dissipation, modelled through a phenomenological term in the GPE. Our simulations provide insight into early stage evolution, not accessible experimentally, and into the decay of vortices by annihilation or passage out of the condensate. We use classical eld methods to simulate homogeneous Bose gases at nite temperature, from strongly non-equilibrium initial distributions to thermalised equilibrium states. We introduce a moving cylindrical potential and study how the thermal component of the gas a ects vortex nucleation. We have found that the critical velocity decreases with increasing temperature and scales with the speed of sound of the condensate. Above the critical velocity, vortices are nucleated as irregular vortex lines, rings, or vortex tangles. Finally we model the surfaces of walls and moving objects (such as wires, grids, propellers or spheres) in the presence of super uid ow, using a real rough boundary obtained via atomic force microscopy. We nd evidence pointing to the formation of a thin ‘super- uid boundary layer’ consisting of vortex loops and rings. As boundary layers usually arise from viscous forces, this is a surprising and intriguing result.