This thesis presents neutron and x-ray scattering measurements on quasi-two-dimensional honeycomb antiferromagnets A2IrO₃ (A=Na, Li) and the solid-solution intermediate material (Na_1-xLi_x)₂IrO₃. The aim is to study the magnetic order and excitations of 5d Ir⁴⁺ ions in a honeycomb lattice, where unusual magnetic properties have been theoretically predicted to be stabilised by the combinations of strong spin-orbit coupling and honeycomb lattice geometry with 90 degree Ir-O-Ir bonding. By using an optimised setup to minimise the strong neutron absorption by Ir nuclei, inelastic neutron scattering measurements on powder sample of Na₂IrO₃ observed dispersive excitations below 5meV with a dispersion that can be accounted for by including substantial further-neighbor exchanges that stabilize zigzag magnetic order. The onset of long-range magnetic order was confirmed by the observation of oscillations in zero-field muon-spin rotation experiments. Higher-resolution inelastic neutron data found features consistent with a spin gap of 1.8meV and the data was parameterised by including Ising-type exchange anisotropy. Combining single-crystal diffraction and density functional calculations, a revised crystal structure model with significant departures from the ideal 90 degree Ir-O-Ir bonds required for dominant Kitaev exchange was proposed. Various "idealised'' crystal structures were constructed to emphasize the departures between the actual structure and structures with cubic IrO₆ octahedra. The magnetic excitations from the isostructural Li₂IrO₃ revealed strongly dispersive magnetic excitations, qualitatively different from Na₂IrO₃. Elastic neutron diffraction detected a magnetic Bragg peak with a wavevector consistent with spiral orders. To explain the observed neutron data, the spiral H2 phase in the Heisenberg J₁-J₂-J₃ model was proposed, and a full calculation was performed with strong in-plane anisotropic interaction. A further measurement for improving the lower-energy excitation found no clear evidence for a spin gap down to E=0.7meV. Lastly, the crystal structure of (Na_1-xLi_x)₂IrO₃ was investigated with single-crystal x-ray diffraction, revealing a site-mixing of Ir and Na ions in the honeycomb lattice and insensitivity of the refinement to the Li positions. Ab initio calculations suggested that up to x=0.25 Li ions replaced Na in the honeycomb centre and phase separation occurred beyond that, which is consistent with the evolution of observed lattice parameters.

This thesis studies parameters influencing both the performance and stability of solid state sensitized solar cells (ssSSCs). ssSSCs benefit from their low materials and manufacturing processing costs, a consequence of using solution processed materials. However, solution processed materials are often structurally and electronically disordered. By characterizing fully operational ssSSCs and their charge transport properties, this thesis elucidates the factors limiting charge transport and proposes routes towards both improved photovoltaic conversion efficiency and long-term stability. Chapter 2 provides an explanation of the operation of ssSSCs, while Chapter 3 discusses the basic methods used in this thesis. Having set this background, Chapter 4 explores the interaction between atmospheric oxygen and charge doping mechanisms in the organic semiconductors used in ssSSCs. To understand the implications of the findings presented in Chapter 4, a new technique, “transient mobility spectroscopy”, was developed to understand the evolution of balanced charge transport behaviour of disordered semiconductors at different operating conditions in ssSSCs. This technique is presented in full in Chapter 5. The understanding gained in Chapters 4 and 5 suggest that alternative light absorbers with higher extinction coefficients may be beneficial to improving the performance of ssSSCs. Chapter 6 discusses the use of an organometal trihalide perovskite, as light absorber in ssSSCs. Using time resolved techniques, the charge transport and recombination mechanisms in various device architectures are explored, allowing suggestions to be made towards future improvements. Chapter 7 uses the technique presented in Chapter 5 to understand a rapid degradation mechanism of working ssSSCs. Particular focus is placed on the titanium dioxide charge-transporting layer. Building on this newfound understanding, two methods for attaining stable photovoltaic performance are provided, a great step forward for this technology.

This thesis considers the theory and calculations of image formation mechanisms for various modes of three-dimensional imaging in aberration-corrected scanning transmission electron microscopy. Discrete tomography is used to determine and refine the three-dimensional structure of molecular nanowire bundles. The structure determination is expedited by the use of annular dark-field imaging, an incoherent imaging mode which provides directly interpretable images. The development of spherical aberration correctors and the subsequent reduction in probe sizes, including the depth of field, has made optical depth sectioning a feasible technique. The localisation in three dimensions of substitutional impurity atoms in zone-axis imaging is discussed. Both the channelling of the probe and the pre-focussing effect of the atomic column play an important role in determining the depth response of the impurity atom. Interband scattering within a sample is shown to be influential in imaging crystals containing dislocations and optical depth sectioning is explored as a possible option for overcoming surface relaxation effects in the imaging of screw dislocations end-on. The possibility of extending the optical depth sectioning approach using aberration-corrected scanning confocal electron microscopy is discussed. The coherent and incoherent imaging modes, involving elastically and inelastically scattered electrons respectively, are investigated.

In this thesis, we consider two problems in the Q-tensor theory of nematic liquid crystals. The first concerns eigenvalue constraints on the Q-tensor order parameter. In particular, by employing a singular potential constructed by Ball and Majumdar, we consider the existence, regularity and "strict physicality" of weak solutions to the Beris-Edwards equations of nemato-hydrodynamics. In the second part of the thesis, we consider a gradient flow of the well-studied Landau-de Gennes energy. We prove some rigorous results on the average long-time statistical behaviour of its solutions, which are in agreement with experimental observations in the condensed matter physics literature.

This thesis describes neutron scattering experiments on strongly correlated systems exhibiting a range of emergent phenomena: antiferromagnetism, charge order, superconductivity and multiferroicity. I have examined the La_{2}CoO_{4} compound which is a Mott insulator and orders antiferromagnetically near room temperature. The La_{2}CoO_{4} sample was studied using spherical neutron polarimetry and I present magnetic structure models to describe the two antiferromagnetic phases of the compound. Furthermore, the magnetic fluctuations have been investigated using neutron time-of-flight technique. This has allowed us to extract the dominant exchange interactions in the system. More interestingly, the work on La_{2}CoO_{4} presented in this thesis provides a basis for the experimental evidence of an hourglass dispersion in La_{5/3}Sr_{1/3}CoO_{4}, previously only observed in the copper oxide based superconductors. This dispersion has been understood in terms of a stripe ordered magnetic phase and was found to be well described by a linear spin-wave model. Neutron scattering experiments were also carried out on the new iron-based high-temperature superconductors, FeSe_{x}Te_{1−x}. A range of compositions were studied, including both antiferromagnetically ordered and superconducting. Below the superconducting phase transition temperature, a spin resonance mode was found centred on the antiferromagnetic wavevector. This is an important feature shared by many unconventional superconductors. The spin resonance intensity was found to reflect the order parameter of the superconducting state. Polarised inelastic neutron scattering experiments have revealed a small anisotropy between the in-plane and out-of-plane magnetic fluctuations at the resonance. This anisotropy cannot be readily explained by the usual anisotropic terms in the Hamiltonian. This could be evidence of new physics in the FeSe_{x}Te_{1−x} superconductors. Finally, I have studied CuO – a high-temperature multiferroic. Analysis of polarised neutron diffraction experiments shows that the magnetic domain population can be varied using an externally applied electric field. This unambiguously demonstrates coupling between the magnetic and ferroelectric degrees of freedom. Using representation analysis I derive the incommensurate magnetic structure in the multiferroic phase. The origin of the magnetoelectric coupling is consistent with models based on the inverse Dzyaloshinskii-Moriya interaction.

This thesis presents three investigations of the magnetic and electronic proper- ties of manganese oxide materials. The investigations are performed using a variety of neutron scattering and x-ray scattering techniques. The electronic ground-state of Pr(Sr_0.1 Ca_0.9)₂ Mn₂O₇ an antiferromagnet with CE-type ordering, is determined using neutron spectroscopy, as opposed to the more usual approach of using diffraction. The Zener polaron model of the elec- tronic ground state of the CE-type magnetic phase is shown to be unsuitable for this material. The ground-state is shown to agree well with the electronic ground state proposed by Goodenough in the 1950’s, but without significant Mn^3+/Mn^4+ disproportionation. The distribution of the magnetisation density within the unit cell of the CE-type antiferromagnet La_0.5Sr_1.5MnO₄ is determined from a polarised neutron diffraction experiment by analysing the results with the maximum entropy method. The majority of the magnetisation density is found to be located at the Mn site. The investigation shows tentative evidence of a small magnetic moment on the in-plane O site. However, a larger moment is observed at both the La/Sr site and the out-of-plane O site. The magnetic structure of the magnetoelectric multiferroic DyMn₂O₅ is inves- tigated using resonant magnetic x-ray scattering. The magnetic structure is shown to be similar to other members of the RMn₂O₅ series of multiferroics, but with the key difference that the magnetic moments are closely aligned parallel with the crystallographic b-axis, in contrast to the usual observation of the moments being close to parallel with the a-axis. This study also shows evidence that the electrical polarisation has a significant contribution from the valence electrons of the O ions, agreeing with previous work.

KirBac channels are prokaryotic homologs of eukaryotic inwardly-rectifying potassium channels, which have served as models for gaining insight into the structure of eukaryotic channels. This thesis focuses on the structure-function relationship in these channels. The first part of this study concerns a novel KirBac channel, KirBac9.2, which contains a unique amino acid sequence in the place of the canonical GYG selectivity filter. Although expressed and purified in a stable and functional form, the protein did not form well-diffracting crystals. Functional studies suggest that KirBac9.2 is non-selective for monovalent cations and a random mutagenesis screen identified a number of activatory mutants in the cytoplasmic domains of the channel. A full electrophysiological investigation of KirBac9.2 channel function is beyond the scope of this study. However, initial studies suggest that it is possible to record currents from KirBac9.2 channels reconstituted into lipid bilayers. The second part of this thesis investigates KirBac3.1, which is a classical KirBac channel containing the consensus GYG sequence for potassium selectivity. Five high resolution structures of a mutant channel are reported, which suggest a new feature in the gating mechanism of KirBac3.1 where a rotation of the cytoplasmic domains is linked to a change in the electrostatic environment of the cytoplasmic cavity. In addition, a functional study of the KirBac3.1 showed that the channel is highly pH sensitive.

In this thesis, two-dimensional materials such as graphene are tested for their suitability for opto-electronic applications using terahertz time domain spectroscopy (THz-TDS). This ultrafast all-optical technique can probe the response of novel materials to photoexcitation, and yield information about the dynamics of the material systems. Graphene grown by chemical vapour deposition (CVD) is studied using optical-pump THz-probe time domain spectroscopy in a variety of gaseous environments in Chapter 4. The photoconductivity response of graphene grown by CVD is found to vary dramatically depending on which atmospheric gases are present. Adsorption of these gases can open a local bandgap in the material, allowing stimulated emission of THz radiation across the gap. Semiconducting equivalents to graphene, molybdenum disulphide (MoS₂) and tungsten diselenide (WSe₂), grown by CVD, are investigated in Chapter 5. These members of the transition metal dichalcogenide family show sub-picosecond responses to photoexcitation, suggesting promise for use in high-speed THz devices. In Chapter 6, an alternative production route to CVD is studied. Liquid-phase exfoliation offers fast, easy production of few-layer materials. THz spectroscopy reveals that the dynamics of these materials after photoexcitation are remarkably similar to those in CVD-grown materials, offering the potential of cheaper materials for future devices. Finally in Chapter 7, it is shown that carbon nanotubes can be used to make ultrafast THz devices. Unaligned, semiconducting single walled carbon nanotubes can be photoexcited to produce an ultrafast, dynamic THz polariser. The work in this thesis demonstrates the potential for these novel materials in future opto-electronic applications. THz spectroscopy is shown to be an important tool for the characterisation of new materials, providing information that can be used to understand the dynamics of materials, and improve production methods.

Σ3{111} coherent twin boundary (CTB) in face-centered-cubic (FCC) metals and alloys have been regarded as an efficient way to simultaneously increase strength and ductility at the nanoscale. Extensive study of dislocation-CTB interaction has been carried out by a combination of computer simulations, experiments and continuum theory. Most of them, however, are based on the perfect CTB assumption. A recent study [Wang YM, Sansoz F, LaGrange T, et al. Defective twin boundaries in nanotwinned metals. Nat Mater. 2013;12(8):697-702.] has revealed the existence of intrinsic kink-like defects in CTBs of nanotwinned copper through nanodiffraction mapping technique, and has confirmed the effect of these defects on deformation mechanisms and mechanical behavior. One of the deformation mechanisms proposed therein, i.e. general hard dislocation slip intersecting with kink line is studied here in detail by molecular dynamics (MD) simulation. Simulations are performed using copper bicrystal models with a particular focus on the interaction of a screw dislocation with 0 degree and 60 degree kinked CTBs. It is found that kink-like defects have a profound impact on screw dislocation - CTB interaction mechanisms, resulting in significant strengthening or softening effects.

Small molecule organic semiconductors such as phthalocyanines and their derivatives represent a very interesting alternative to inorganic semiconductor materials for the development of flexible electronic devices such as organic thin field effect transistors, organic Light Emitting Diodes and photo-voltaic cells. Phthalocyanine molecules can easily accommodate a variety of metal atoms as well in the central core of the molecule, resulting in wide range of magnetic properties. Exploration of optical properties of organic crystalline semiconductors thin films is challenging due to sub-micron grain sizes and the presence of numerous structural defects, disorder and grain boundaries. However, this can be overcome by fabricating macroscopically ordered semiconductor films by solution processing. Presence of fewer grain boundaries and defects while modifying the pi orbital overlap by controlling the molecular stacking by forming macroscopic long range ordered grains, was essential in understanding the delocalization and diffusion length and its role in magnetic exchange mechanisms in this system. The origins of magnetic exchange mechanism between delocalized ligand electrons and spins in organic semiconductors has been of key interest as it underlies many complex optical and transport properties and is investigated in this thesis. The interaction between magnetic ions in organic magnetic semiconductors is quite challenging to interpret due to competing exchange mechanisms present in crystalline thin films. Better understanding of these exchange mechanisms is essential for tuning of magnetic exchange interaction to suit the need of practical magnetic storage and spintronic devices. Optical techniques such as linear dichroism, magnetic circular dichroism and magneto-photoluminescence are used and provided key understanding about the relation between excitons, spin exchange mechanisms and collective magnetic behavior of delocalized electrons in organic semiconductors. An enhancement in the collective magnetization of the crystalline thin films with strong exchange coupling between the delocalized ligand electrons and d-electrons is observed. The electronic states responsible for magnetic exchange are identified utilizing magnetic field and temperature dependent studies. Furthermore, soluble organics allowed engineering of organic analogues to diluted magnetic semiconductors (DMS) by creation of metal/metal-free Pc alloys. Optical studies provided crucial information about delocalization and diffusion lengths in these systems allowing fine tuning of this delocalization length scale and metal-metal distance. The exploration of magnetic behavior in metal/metal-free Pc alloys opens an avenue for tuning magnetic properties through an exchange similar to Ruderman-Kittel-Kasuya Yosida (RKKY) type interaction in organic magnetic semiconductors.