Structure and properties of states containing strongly-correlated disorder

Understanding of material properties has traditionally emerged from an appreciation of the ordered atomic structure. As such, the development of functional materials has focussed on crystalline systems. Correspondingly, structural disorder is often considered as a motif to avoid, as any desired physical response is believed to be diminished by its presence. The work presented in this thesis aims to challenge this paradigm by showing that, in the presence of particular types of strongly-correlated disorder, useful characteristics are accessible that are not possible in their ordered counterparts.
Here, a new class of disorder, the procrystalline state, is introduced. These disordered phases are derived from a generalisation of ice-rules, wherein a combination of a high-symmetry topological template and low-symmetry building unit produces aperiodic configurations. Indeed, there are numerous types of procrystalline phases—i.e. where different topological templates and building units have been considered. Subsequently, many well-known examples of disordered systems from a wide-variety of scientific fields, beyond those associated with ice, are shown to map onto procrystalline configurations including dimer states, polyhedral tilings, the triangular Ising antiferromagnet and the inaugural ferroelectric, BaTiO3. Furthermore, it is demonstrated that procrystalline disorder can be characterised using common experimental methods such as microscopy, pair distribution function data and diffuse scattering signatures in powder and single crystal diffraction patterns.
Initially, the work in this thesis is focussed on understanding the changes in the vibrational spectra due to procrystalline disorder. These systems lack the translational symmetry that is axiomatic to conventional lattice dynamical methods, so here, the supercell lattice dynamical (SCLD) method is developed. This approach enables the explicit effect of disorder on the phonon dispersion curves to be determined. Subsequently, the SCLD method is applied to a variety of procrystalline models, revealing that in the presence of certain types of correlated disorder, phononic band gaps emerge. Importantly, these features are not present in the vibrational spectra of either a randomly disordered state, or the associated average structure (virtual crystal approximation). Moreover, procrystalline models are also shown to ‘break the rules’ of conventional lattice dynamical theory, as a disordered decoration with an average structure containing a single atom in the parent unit cell generates an unconventional and unexpected band gap. Analogous effects are also demonstrated to occur in both the electronic and photonic band structure of procrystalline states, where the opening of band gaps is directly correlated with the electronic conductivity and optical properties of these materials. Finally, the effect of disorder on the mechanical properties of one-dimensional fibre packings is investigated, which somewhat surprisingly concludes that the introduction of topological disorder has the potential to increase the swelling response of these structures.

Keywords: Material properties
Disorder
Crystallography
Advisor: Goodwin, A
Chater, P
Tucker, M