Thesis (Ph.D.)--City University of Hong Kong, 2009. / "Submitted to Department of Physics and Material Sciences in partial fulfillment of the requirements for the degree of Doctor of Philosophy." Includes bibliographical references (leaves 140-167)

Thesis (Ph. D.)--University of Washington, 2003. / Vita. Includes bibliographical references (p. 232-243).

Thesis (Ph. D.)--University of Chicago, Department of Physics, December 2003. / CD-ROM includes PDF files of figures 2.1-4.7. Includes bibliographical references. Also available on the Internet.

Thesis (Ph. D.) in Physics--University of Maine, 2001. / Includes vita. Includes bibliographical references (leaves 96-102).

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This thesis numerically solves the tensor order parameter continuum theory equations for nematic liquid crystals to investigate liquid crystal texturing mechanisms during an isotropic to nematic phase transition in a bulk unstable isotropic phase and next to solid surfaces. The Time Dependent Ginsburg Landau equation with a Landau de Gennes Helmholtz free energy density description is used to predict the shapes, textures and defect mechanisms that occur in the expanding droplets and films of a 4'-pentyl-4-cyanobiphenyl (5CB) nematic phase immediately after their nucleation from an unstable isotropic phase, due to a temperature quench. To create a robust simulation method able to tackle high curvature, defect nucleation, heterogeneous substrates and phase ordering interfaces, particular attention was paid to adapting the mathematical model and computational methods to what was previously known about the nucleation and growth events that occur experimentally during a bulk 5CB isotropic to nematic phase transition and next to decorated solid surfaces. The numerical simulations provide detailed predictions about (i) growth rates for different temperature quenches, (ii) structure of the isotropic-nematic interface, (iii) shapes of expanding nano and submicron nematic droplets, (iv) texturing within growing nano and submicron nematic droplets, (v) a new defect formation mechanism called "interfacial defect shedding", and (vi) the effect of contact angle and interface curvature next to a solid surface with anchoring switches. The main contributions of this thesis are its detailed predictions that emerge from the liquid crystal simulation results, the careful adaptation of the mathematical model and numerical method to what is currently known about early stage growth in a nematic liquid crystal phase, and the validation of new theory by the simulation results.

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This thesis describes a diversity of scattering experiments on a number of different systems. Using time-of-flight neutron scattering, a study of polycrystalline sodium in the highmomentum limit known as the impulse approximation has been performed. The purpose of this study was to look for anharmonic effects in the neutron recoil scattering of sodium as the temperature was increased from 30K to 300K. No such effects were detected and the results agreed with an isotropic harmonic solid to an accuracy of about 4%. Two experiments were carried out on antiferromagnetic systems using triple-axis neutron scattering techniques to measure the spin-wave dispersion relations. The first was on CuO to verify its description as a spin 1/2 one-dimensional antiferromagnet. The dispersion relation was measured along the chain direction up to an energy transfer of 8OmeV. This was done above and below the Néel temperature (T_N =240K). However, no evidence was seen to justify the description of CuO as a one-dimensional antiferromagnet, with the spin waves behaving like those in a classical three-dimensional system. The other spin-wave study examined the two-dimensional antiferromagnet KFeF₄ . The measurement of the spin-wave dispersion relation at two temperatures (50K and 100K) below the Néel temperature (T_N =136.75±0.25K), confirmed the description of KFeF₄ as a two-dimensional Heisenberg antiferromagnet with small Ising anisotropy. Studies of the magnetic phase transition in KFeF₄ revealed that below the Néel temperature, the critical behaviour is described by two-dimensional Ising models, and above a crossover to Heisenberg behaviour is seen. This crossover was detected by measuring the order parameter below T_N, and the static and dynamic susceptibilities above T_N using neutron scattering techniques. The results were compared to power-law behaviour and also to theories for the classical Heisenberg antiferromagnet and the more recent quantum Heisenberg antiferromagnetic model. The final study of KFeF₄ involved an x-ray experiment on the structural phase transition around 400K. It has been suggested that there is a second-order transition at 410K to an incommensurate phase, which then undergoes a first-order lock-in transition at 400K to the low-temperature structure. This single crystal x-ray scattering study confirms the existence of the first-order phase transition, but shows no evidence for a higher temperature second-order transition or for the incommensurate phase.