| Sammanfattning: | <p>This thesis studies the phase behaviour of a variety of complex solid structures. The principal approach taken is to develop a suitable coarse graining of the degrees of freedom in order to allow a representation in terms of interaction models.</p>
<p>Chapter 3 concerns the polytypism of layered AB2 compounds. We develop a simple interaction model that has at its ground states many of the key experimentally determined structural phases. At phase boundaries we identify complex disordered states that we show sometimes provide a more convincing descriptor of the polytypism than established models. These results allow us to question the existence of previously characterised phases and new undocumented phases are put forward as perhaps more chemically sensible alternatives.</p>
<p>Continuing on the theme of layered materials, Chapter 4 maps the stacking disorder present in the layered inorganic material Ni(CN)2 onto a model containing continuous degrees of freedom. Moreover, the model can also take the form of the Heisenberg XXZ model used to describe interacting chains of quantum spins, and as such, we have identified a system realising the classical analogue of a 1D quantum chain.</p>
<p>Chapter 5 maps complex magnetic phases onto structural degrees of freedom by focusing on topological defects within chiral magnets. Here we show that these degrees of freedom can be related to quadrupolar orientations of molecules within a chiral framework, and can create analogous topological defects in chiral MOFs. This result expands the field of data storage by highlighting potential materials not normally associated with emergent phenomena.</p>
<p>This thesis ends with two appendices containing experimental work carried out during the DPhil, which had to be put on hold due to constraints set up by the ongoing COVID-19 pandemic. Both these studies tie into the theme of statistical mechanical models and structural disorder, with the first centring on the extent to which ice like disorder manifests in the compositionally disordered cyanospinel KRb[Zn(CN)<sub>4</sub>]. The second study focuses on the stacking disorder present in the solid solution K[Ag<sub>x</sub>Au<sub>1-x</sub>(CN)<sub>2</sub>] which varies as a function of composition and temperature. The larger aim of both these studies is to see how correlated disorder may selectively effect the phononic properties of materials.</p>
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