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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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For 11 crystals of the amblygonite-montebrasite series LiAlPO₄(F,OH) ranging in composition from 4.0 to 91.8 mole percent fluorine with only two containing significant sodium, 2V and principal refractive indices were determined to 0.5° and 0.0005, respectively, by spindle-stage methods. If F < 60 mole percent, as is true for the vast majority of natural specimens, fluorine can usually be estimated to within 2 mole percent from the equation F = -66.3 + 1.08 * 2V_Z as well as from similar regression equations involving the refractive indices α, β, and γ. Above 60 mole percent F, the optical properties are less sensitively (and non-linearly) related to fluorine content. Estimates of F proved feasible despite significant substitution of Na for Li. By contrast, this substitution may introduce significant errors when estimating F by methods involving lattice parameters. Progressive substitution of (OH), a natural dipole involving a covalent bond, for the relatively non-polarizable F anion caused all three principal refractive indices to increase; γ increases more than α or ß because its corresponding principal vibration direction Z becomes sub-parallel to the O···H vector in the structure as (OH) content increases. / Master of Science / incomplete_metadata

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Silicon carbide as a representative wide band-gap semiconductor has recently received wide attention due to its excellent physical, thermal and especially electrical properties. It becomes a promising material for electronic and optoelectronic device under high-temperature, high-power and high-frequency and intense radiation conditions. During the Silicon Carbide crystal grown by the physical vapor transport process, the temperature gradients induce thermal stresses which is a major cause of the dislocations multiplication. Although large dimension crystal with low dislocation density is required for satisfying the fast development of electronic and optoelectronic device, high dislocation densities always appear in large dimension crystal. Therefore, reducing dislocation density is one of the primary tasks of process optimization. This dissertation aims at developing a transient finite element model based on the Alexander-Haasen model for computing the dislocation densities in a crystal during its growing process. Different key growth parameters such as temperature gradient, crystal size will be used to investigate their influence on dislocation multiplications. The acceptable and optimal crystal diameter and temperature gradient to produce the lowest dislocation density in SiC crystal can be obtained through a thorough numerical investigation using this developed finite element model. The results reveal that the dislocation density multiplication in SiC crystal are easily affected by the crystal diameter and the temperature gradient. Generally, during the iterative calculation for SiC growth, the dislocation density multiples very rapidly in the early growth phase and then turns to a relatively slow multiplication or no multiplication at all. The results also show that larger size and higher temperature gradient causes the dislocation density enters rapid multiplication phase sooner and the final dislocation density in the crystal is higher. / Includes bibliography. / Dissertation (Ph.D.)--Florida Atlantic University, 2015. / FAU Electronic Theses and Dissertations Collection