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This thesis covers three topics related to the field of crystal engineering. Three different approaches to improving the understanding of hydrogen bonding are covered; analysis of a family of related molecules, investigations of specific functional groups and a systematic, data-driven study of intramolecular hydrogen bonding patterns. Chapters 2 to 4 and chapter 11 cover the background theory to the different methods used to obtain the data discussed in the remainder of the thesis. X-ray and neutron diffraction techniques are discussed, along with sections describing the Cambridge Structural Database, which was used as a data source throughout this work, and a brief section on intermolecular forces. Crystal structure analyses of seventeen gem-alkynol molecules are given in chapters 5 to 10. The gem-alkynol functionality is particularly interesting for a study of intermolecular interactions as it is a combination of both a strong and weak hydrogen bonding group. The group of molecules was investigated with the aim of locating robust supramolecular motifs. The group is subdivided into sections containing molecules with similar structures and their packing patterns are discussed. The second experimental section, chapters 12 and 13, comprises statistical studies into the function of the azido and cyano functional groups as hydrogen bond acceptors. The technique used was to use the Cambridge Structural Database as a data source for the main analysis, then complement the results with simple theoretical calculations. The remaining chapter, 14, describes a systematic analysis of intermolecular hydrogen bonded motifs. A data-driven approach was designed which allows direct comparison of motifs by means of a probability ordered list.

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Pressure and temperature are two environmental variables that are increasingly being exploited by solid-state researchers probing structure-property relationships in the crystalline state. Modern high-pressure apparatus is capable of generating many billions of Pascals in the laboratory, and therefore can produce significantly greater alterations to crystalline materials than changes in temperature, which can typically be varied by only a few thousand Kelvin. Many systems such as single-molecule magnets exhibit interesting properties under low-temperature regimes that can be substantially altered with pressure. The desire by investigators to perform analogous single-crystal X-ray diffraction studies has driven the development of new high-pressure apparatus and techniques designed to accommodate low-temperature environments. [Ni(en)3][NO3]2 undergoes a displacive phase transition from P6322 at ambient pressure to a lower symmetry P6122/P6522 structure between 0.82 and 0.87 GPa, which is characterized by a tripling of the unit cell c axis and the number of molecules per unit cell. The same transition has been previously observed at 108 K. The application of pressure leads to a general shortening of O···H hydrogen bonding interactions in the structure, with the greatest contraction (24%) occurring diagonally between stacks of Ni cation moieties and nitrate anions. A novel Turnbuckle Diamond Anvil Cell designed for high-pressure low-temperature single-crystal X-ray experiments on an open-flow cryostat has been calibrated using the previously reported phase transitions of five compounds: NH4H2PO4 (148 K), ferrocene (164 K), barbituric acid dihydrate (216 K), ammonium bromide (235 K), and potassium nitrite (264 K). From the observed thermal differentials between the reported and observed transition temperatures a linear calibration curve has been constructed that is applicable between ambient-temperature and 148 K. Low-temperature measurements using a thermocouple have been shown to vary significantly depending on the experimental setup for the insertion wire, whilst also adding undesirable thermal energy into the sample chamber which was largely independent of attachment configuration. High-pressure low-temperature single-crystal X-ray diffraction data of [Mn12O12(O2CMe)16(H2O)4] (known as Mn12OAc) reveals a pressure-induced expulsion of the crystallized acetic acid from the crystal structure and resolution of the Jahn-Teller axes disorder between ambient pressure and 0.87 GPa. These structural changes have been correlated with high-pressure magnetic data indicating the elimination of a slow-relaxing isomer over this pressure range. Further application of pressure to 2.02 GPa leads to the expansion of these Jahn-Teller axes, resulting in an enhancement of the slow-relaxing magnetic anisotropy as observed in the literature. Relaxation of pressure leads to a resolvation of the crystal structure and re-disordering of the Jahn-Teller axes, demonstrating that this structural-magnetic phenomenon is fully reversible with respect to pressure. The space group of the Prussian blue analogue Mn3[Cr(CN)6].15H2O has been re-evaluated as R-3m between ambient pressure and 2.07 GPa using high-pressure single-crystal X-ray and high-pressure neutron powder data. Reductions in metal-metal distances and gradual distortions of the Mn octahedral geometry have been correlated with previously reported increases in Tc and declines in ferrimagnetic moment in the same pressure range. Increasing the applied pressure to 2.97 GPa leads to partial amorphization and results in a loss of long-range magnetic order as shown by the literature. The application of pressure (1.8 GPa) to the structure of K2[Pt(CN)4]Br0.24.3.24H2O (KCP(Br)) causes a reduction in the Pt intra-chain and inter-chain distances, and results in an enhancement of the overall conductivity under these conditions as demonstrated in the literature. Almost no changes occur to the high-pressure crystal structure upon cooling to 4 K, except in the Pt-Pt intra-chain distances which converge and suppress the Peierls distortion known to occur at 4 K, resulting in a comparatively greater electrical conductivity under these conditions.

This thesis will introduce the study of methane as a mineral. Along with ammonia and water, methane is one of the main planetary-forming materials in the outer solar system. The topic of `new mineralogy of the outer solar system' is outlined and introduced, and previous studies in the area are discussed. This review identities a lack of highpressure structural knowledge on methane when compared to ammonia and water. The significance of this knowledge for the study of the planets Neptune and Uranus is discussed. The crystal structures of methane above 5.2 GPa were, prior to this thesis, unknown. To tackle this long-standing problem an integrated approach of high-pressure diffraction techniques had to be used. The dominance of hydrogen within the structures of methane necessitated the use of neutron diffraction. The difficulties and limitations of highpressure neutron powder diffraction are presented. It will be shown that the complexity of the subsequent structures required the use of single-crystal x-ray diffraction. Using a combination of x-ray and neutron diffraction the structures of methane phase A (5.2 - 10 GPa) and B (10 - 25 GPa) were solved. The structure of phase A, was shown to conform to an indexing from literature [Nakahata 99] of a rhombohedral unit cell with α ≈ 89.3° and a ≈ 8.6 Å. Powder data were insufficient to determine atomic positions for this phase, and a single-crystal xray diffraction study was undertaken. The process of growing samples for this study is described as well as data collection. As a result of these studies the carbon atoms were located within methane phase A, and the density of the structure confined. The heavy atom structure, of phase A, was refined against neutron powder diffraction data, enabling positions of hydrogen atoms to be found. Preliminary powder diffraction studies of methane phase B found that the structure did not conform to the unit cell described within the literature. The phase was instead assigned to a cubic unit cell with a ≈ 11.73 Å. Similarly to the studies of phase A, a single-crystal x-ray diffraction study was undertaken. This was complicated by the presence of a contaminant within the sample area. This contaminant was shown to have no effect on the structural results. From a single-crystal study the heavy atom structure of phase B was found. The thesis charts the attempt, but ultimate failure, to obtain neutron powder diffraction on this phase. Comparisons of phase B with the higher pressure phase HP (25 GPa +) led to the conclusion that there would still be some disorder within the hydrogen atoms of phase B. Other studies have been carried out on the methane phase diagram. A Raman spectroscopy study, in the literature, on the low-temperature and high-pressure region of the phase diagrams (20 K up to 30 GPa) had suggested the existence of 3 additional phases of methane. A low-temperature, high-pressure neutron diffraction experiment was undertaken to try and characterise these phases. It was found that the phase A structure persisted under all conditions (to 20 K and 5 GPa) throwing the original results into question. During the growth of single-crystals for the above studies on phase A and B, a high-temperature solid-solid phase transition was observed. This transition line was mapped out and the phase resulting from it characterised with high-temperature single-crystal x-ray diffraction.

<p>This thesis is based on a study of five distinct intermetallic systems with the aim of expanding the general knowledge of aperiodically modulated crystal structures. Families of compounds that contain a variety of superstructures together with incommensurately modulated structures have been investigated mainly by means of single crystal X-ray diffraction and higher dimensional structure models.</p><p>A uniform (3+1)-dimensional structure for Bi-Se phases was developed with the composition as a single variable. The structure description is based on a cubic NaCl type structure with homoatomic layer stackings. It is shown by computational modelling that the formation energies of bismuth selenides with more than 40 at. % Bi are close to zero, a result that supports the idea of a continuous series of stackings corresponding to an ordered solid solution of Bi in Bi₂Se₃.</p><p>The Nowotny chimney-ladder structures are described with a (3+1)-dimensional composite structure, valid for all such compounds regardless of the included elements, the composition or the valence electron concentration. A new member is added to this family by the ZrBi_1.62 compound. The modulation is believed to arise as a secondary effect of the criteria of a fixed electron count.</p><p>A symmetry analysis is presented for the <i>RE</i>_1+ε(MB)₄ (<i>RE</i> = rare earth elements, M = iron metal elements) family of compounds and a uniform (3+1)-dimensional composite structure description has been developed. The modulation may be due to the presence of unusually short contacts between the <i>RE</i> channel atoms, giving rise to a rotational modulation of the (MB)₄ tetraederstern chains.</p><p>A (3+1)-dimensional incommensurate structure has been determined for the novel δ₁ – CoZn compound. The structure displays a unique assembly of fused icosahedra and the modulation is induced by geometric strain.</p><p>The structure of the K(PtSi)₄ compound was re-determined. Despite a close kinship with the <i>RE</i>_1+ε(MB)₄ compounds, this structure is not modulated.</p>

This thesis is based on a study of five distinct intermetallic systems with the aim of expanding the general knowledge of aperiodically modulated crystal structures. Families of compounds that contain a variety of superstructures together with incommensurately modulated structures have been investigated mainly by means of single crystal X-ray diffraction and higher dimensional structure models. A uniform (3+1)-dimensional structure for Bi-Se phases was developed with the composition as a single variable. The structure description is based on a cubic NaCl type structure with homoatomic layer stackings. It is shown by computational modelling that the formation energies of bismuth selenides with more than 40 at. % Bi are close to zero, a result that supports the idea of a continuous series of stackings corresponding to an ordered solid solution of Bi in Bi2Se3. The Nowotny chimney-ladder structures are described with a (3+1)-dimensional composite structure, valid for all such compounds regardless of the included elements, the composition or the valence electron concentration. A new member is added to this family by the ZrBi1.62 compound. The modulation is believed to arise as a secondary effect of the criteria of a fixed electron count. A symmetry analysis is presented for the RE1+ε(MB)4 (RE = rare earth elements, M = iron metal elements) family of compounds and a uniform (3+1)-dimensional composite structure description has been developed. The modulation may be due to the presence of unusually short contacts between the RE channel atoms, giving rise to a rotational modulation of the (MB)4 tetraederstern chains. A (3+1)-dimensional incommensurate structure has been determined for the novel δ1 – CoZn compound. The structure displays a unique assembly of fused icosahedra and the modulation is induced by geometric strain. The structure of the K(PtSi)4 compound was re-determined. Despite a close kinship with the RE1+ε(MB)4 compounds, this structure is not modulated.

Natural and synthetic common-rock forming minerals were examined using single-crystal X-ray diffraction (SXRD) and electron microprobe (EMP) analyses. The influences of common defect features, such as inclusions in spinel and oxygen positional disorder and twinning in kalsilite, were reported on the respective structures. The case studies show that these defect features could lead to a misinterpretation of X-ray intensity data. The structural interpretations obtained from these XSRD analyses could be significantly different when physical properties of the crystals are considered.In the second part of my dissertation, comparative crystal chemical studies on mantle-derived minerals such as spinel, clinopyroxene, and olivine are reported. These studies were carried out to examine temperature, pressure, and compositional effects on the structures of these phases. In particular, packing arrangements of oxygen atoms were examined in detail to investigate how the packing affects element partitioning among upper-mantle minerals. At ambient conditions, oxygen packing is more distorted in the order of spinel < olivine < clinopyroxene. The packing of oxygen atoms in olivine might have a significant control on element substitutions at high pressure. Because elements whose radius is larger than that of Mg distort the packing of mantle olivine (Fo~89), olivine might limit the amount of those elements, such as Fe2+, entering the structure. In contrast, substitutions of smaller cations in C2/c clinopyroxenes increase packing distortion. For clinopyroxenes enclosed in peridotite and eclogite, higher equilibration pressures are associated with more distorted, less efficiently packed structures. Unlike many minerals reported in Thompson and Downs (2001), spinel becomes more packed with rising temperature when intracrystalline cation exchange reactions are possible. Despite wide chemical variations, spinel samples from one geological environment display a constant packing distortion, which might suggest that spinel is capable of achieving an optimal packing configuration at a given P and T.