Graphene, a sheet of carbon atoms organized in a honeycomb lattice, is a two dimensional crystal. Even though the material has been known for a long time, only recently has it stimulated considerable interest across different research areas. Graphene is interesting not only as a platform to study fundamental physics in two dimensions, but it also has great potential for post-silicon microelectronics owing to its exceptional electronic properties. Of the several methods known to produce graphene, epitaxial growth of graphene by sublimation of silicon carbide is probably the most promising for practical applications. This thesis is a theoretical study of the growth kinetics of epitaxial graphene on SiC(0001). We propose a step-flow growth model using coarse-grained kinetic Monte Carlo (KMC) simulations and mean-field rate equations to study graphene growth on both vicinal and nano-faceted SiC surfaces. Our models are consistent with experimental observations and provide quantitative results which will allow experimenters to interpret the growth morphology and extract energy barriers from experiments. Recently, it has been shown that graphene grown epitaxially on metal surfaces may lead to potential applications such as large area transparent electrodes. To study deposition-type epitaxial growth, we investigate a new theoretical approach to this problem called the phase field method. Compared to other methods this method could be less computationally intensive, and easier to implement at large spatial scales for complicated epitaxial growth situations.

With respect to the principles of biomineralization, it is of interest to study the crystallization of calcium oxalates under various experimental conditions. Calcium oxalates play decisive roles as biominerals in plants and as pathological “urinary/kidney stones” in vertebrates. Calcium oxalate exists in three different hydration states; calcium oxalate monohydrate (COM, monoclinic, a = 6.290(1)Å, b = 14.583(1)Å, c = 10.116(1)Å, β = 109.46°, P21/c), calcium oxalate dihydrate (COD, tetragonal, a = b = 12.371(3)Å, c = 7.357(2)Å, α = β = γ = 90°, I4/m) and calcium oxalate trihydrate (COT, triclinic, a = 6.11(1)Å, b = 7.167(2)Å, c = 8.457(2)Å, α = 76.5(2)°, β = 70.35(2)°, γ = 70.62(2)°, P ). Monoclinic COM and tetragonal COD are the most common phyto-crystals and the main constituents of kidney and urinary stones. The occurrence of calcium oxalates in plants represents a useful biogenesis (protection against herbivores) unlike the devastating occurrence in renal tubules. Therefore, biomineralization can be physiological or pathological. A systematic investigation of the morphological evolution of calcium oxalates in the presence of organic components is essential for understanding the mechanism of “pathological biomineralization”. In order to understand the pathological biomineralization of uroliths, it is necessary grow calcium oxalates comparable in morphology under similar growth conditions. The formation of calcium oxalate stones within a gelatinous state of proteins, polysaccharides, lipids and other biomacromolecules under a flow of supersaturated urine supports the fact that an “organic” gel model can simulate the process of urinary stone formation under in vitro conditions. Furthermore, synthetic polymers with precisely known functions and solution behaviours are better choices to understand the interaction of acidic proteins with calcium oxalates. Therefore, as a first step to unravel the complex pathology of uro/nephro lithiasis, we started to examine the structure and morphology of calcium oxalates crystallized in the presence of organic additives such as the sodium salt of polyacrylic acid (PAA) as well as agar gel. The influence of initial calcium oxalate concentration, pH and concentration of the additives on the formation of hydration states of calcium oxalates have been investigated along with the stated general methods. Apart from the three hydrated forms, calcium oxalate exists also in the anhydrous form (COA). Although three modifications of COA (α, β and γ) are reported in the literatures, the crystal structures and phase transformations were controversially discussed. We have been able to reveal the crystal structure of the β-modification of the anhydrous calcium oxalate by a combination of atomistic simulations and Rietveld refinements on the basis of powder X-ray diffraction pattern. β-COA belongs to the monoclinic system with unit cell parameters, a = 6.1644(3)Å, b = 7.3623(2)Å, c = 9.5371(5)Å, β = 90.24(2)°, P2/m (No. 10). The dehydration of COM was mimicked in silico to receive an initial model of the crystal structure of anhydrous calcium oxalate. This general approach may also be accessible for other decomposition processes ending up with crystalline powders of unknown crystal structure. No evidence for transformations from or to the α- or γ- modifications was found during our investigations. The growth pattern of COD crystals precipitated from aqueous solutions in the presence of PAA is clearly dependent on the concentration of PAA. By increasing the concentration of PAA, the shape of COD has been found to change from tetragonal bi-pyramids with dominant (101) pyramidal faces to tetragonal prisms with dominant (100) prism faces and finally to dumbbells. At still higher PAA concentrations, the morphology is reverted back to rod-like tetragonal prisms. Apart from these experiments, the interaction of PAA with (100) and (101) crystal faces of COD was explored with the aid of atomistic simulations. The simulation confirmed that during the development of the aggregates, strong interactions of PAA with the (100) faces take over control of morphologies. Our investigations show that the inner architecture of all the morphological varieties of COD was found to be dominated by an inner “core” consisting of thin elongated crystallites together with incorporated PAA and an outer “shell” formed as a consequence of secondary nucleation processes. We propose that for all types of COD aggregates, relative proportion of calcium oxalate and PAA dictates the shape and formation of nanometer sized crystallites which then aggregate and align to form the core. Such cores enriched with PAA may act as the sites for secondary nucleation events of calcium oxalate crystallites which then cover the core like a shell. In vitro experimental models for the growth of calcium oxalates can give valuable information on the growth and aggregation of urinary stones. Therefore, the “double diffusion technique” in agar gel matrix has been used for the biomimetic growth of calcium oxalate (COM) stones. A great variety of morphological forms of COM are produced in agar gel matrices (2 wt.-% agar gel of pH 8.5) ranging from platy crystallites to dumbbells and spherulites. The COM dumbbells and spherulites are assumed to be formed by the aggregation of smaller crystallites as a consequence of increased supersaturation inside the gel. Moreover, an increase of the pH value of the agar gel has been found to suppress the growth of COM and favours the growth of COD. The morphology of COD crystals grown in 2 wt.-% agar gel of pH 11.5 includes tetragonal prisms and dumbbells. The system calcium oxalate/ PAA/ H2O is a suitable model system for the investigation of principles of biomineral growth (shape development) in general. Our results demonstrate that the double diffusion technique in agar gel is a convenient route to grow calcium oxalate aggregates showing close resemblance to biogenic calculi and to study their ontogeny.

<p>The aim of the present investigation is to increase theunderstanding of the role played by the solvent in inhibitingor enhancing crystal growth. Drowning-out crystallizationexperiments has been performed by the controlled addition ofwater or ethanol water mixtures to a saturated solution ofbenzoic acid in ethanol-water mixtures. Crystal habitcontrolling factors have been identified.Seededcrystallization experiments have been carried out to evaluatethe effect of solvent composition on crystal habit at constantsupersaturation. The solubility of benzoic acid inethanol-water mixtures at the working temperatures has beendetermined.</p><p>Electro-zone sensing determinations and microscopicmeasurements are used to characterize the final crystallineproduct. It has been found that the shape of the benzoic acidcrystals grown from ethanol-water solutions ranges from needlesto platelets. Platy particles possess a predominant basal plane(001), bound by (010) and (100) faces, while needles aredeveloped along the b-axis. Long needle-shaped particles havebeen produced at low initial bulk concentration and highethanol concentration in the feed. Small platelets are obtainedat high initial bulk concentrations and high waterconcentration in the feed.</p><p>The effect of solvent composition on the growth rate hasbeen evaluated at constant supersaturation. Seed crystals arecharacterized by image analysis measurement both before andafter each experiment. Length and width dimensions have beenmeasured on the particle silhouette. The growth rate, thesolid-liquid interfacial energy and the surface entropy factorfor the (010) faces (length dimension) and (100) faces (widthdimension) have been estimated. The interfacial energy andsurface entropy factor decreases in the direction of increasingethanol concentration due to increasing solubility.</p><p>The results suggest that at low ethanol concentration(xEtOH<60%) growth proceeds by screw dislocation mechanism,and adsorption of ethanol molecules may reduce the growth rate.As the ethanol concentration increases above a critical value(xEtOH ≥60%), the growth mechanism shifts to surfacenucleation and the growth rate increases with increasingethanol concentration. It has been suggested that the observedeffect of the solvent composition on crystal habit is theresult of two conflicting effects here referred as the kineticand interfacial energy effects. High interactions of the pairethanol-benzoic acid seem to be responsible of the growthretardation (kinetic effect) exerted by the solvent. On theother hand, increased ethanol concentration leads to reduceinterfacial energy and increasing surface nucleation whichmight contribute to enhance growth kinetics.</p><p><b>Keywords:</b>drowning-out crystallisation, solventcomposition, benzoic acid, solubility, crystal growth,interfacial energy, surface entropy factor, growth mechanism,crystal shape distribution.</p>

Thesis (Ph. D.)--University of Washington, 2001. / Vita. Includes bibliographical references (p. 129-136).

Thesis (Ph. D.)--University of Missouri-Columbia, 1997. / Typescript. Vita. Includes bibliographical references (leaves 107-110). Also available on the Internet.

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This thesis describes the development of an empirical model of focus beam reflectance measurements (FBRM) and the application of the model to monitoring batch cooling crystallization and extracting information on crystallization kinetics. Batch crystallization is widely used in the fine chemical and pharmaceutical industries to purify and separate solid products. The crystal size distribution (CSD) of the final product greatly influences the product characteristics, such as purity, stability, and bioavailability. It also has a great effect on downstream processing. To achieve a desired CSD of the final product, batch crystallization processes need to be monitored, understood, and controlled. FBRM is a promising technique for in situ determination of the CSD. It is based on scattering of laser light and provides a chord-length distribution (CLD), which is a complex function of crystal geometry. In this thesis, an empirical correlation between CSDs and CLDs is established and applied in place of existing first-principles FBRM models. Built from experimental data, the empirical mapping of CSD and CLD is advantageous in representing some effects that are difficult to quantify by mathematical and physical expressions. The developed model enables computation of the CSD from measured CLDs, which can be followed during the evolution of the crystal population during batch cooling crystallization processes. Paracetamol, a common drug product also known as acetaminophen, is selected as the model compound in this thesis study. The empirical model was first established and verified in a paracetamol-nonsolvent (toluene) slurry, and later applied to the paracetamol-ethanol crystallization system. Complementary to the FBRM measurements, solute concentrations in the liquid phase were determined by in situ infrared spectra, and they were jointly implemented to monitor the crystallization process. The framework of measuring the CSD and the solute concentration allows the estimation of crystallization kinetics, including those for primary nucleation, secondary nucleation, and crystal growth. These parameters were determined simultaneously by fitting the full population balance model to process measurements obtained from multiple unseeded paracetamol-ethanol crystallization runs. The major contributions of this thesis study are (1) providing a novel methodology for using FBRM measurements to estimate CSD; (2) development of an experimental protocol that provided data sets rich in information on crystal growth and primary and secondary nucleation; (3) interpretation of kinetics so that appropriate model parameters could be extracted from fitting population balances to experimental data; (4) identification of the potential importance of secondary nucleation relative to primary nucleation. The protocol and methods developed in this study can be applied to other systems for evaluating and improving batch crystallization processes.

In this paper we will discuss the first successful molecular simulation studies exploring the statesteady crystal growth of sI and sII methane hydrates. Since the molecular modeling of the crystal growth of gas hydrates has proven in the past to be very challenging, we will provide a brief overview of the simulation framework we have utilized to achieve heterogeneous growth within timescales accessible to simulation. We will probe key issues concerning the nature of the solid/liquid interface for a variety of methane hydrate systems and will make important comparisons between various properties. For example, the interface demonstrates a strong affinity for methane molecules and we find a strong tendency for water molecules to organize into cages around methane at the growing interface. The dynamical nature of the interface and its microfaceted features will be shown to be crucial in the characterization of the interface. In addition to the small and large cages characteristic of sI and sII hydrates, water cages with a 51263 arrangement were identified during the heterogeneous growth of both sI and sII methane hydrate and their potential role in cross-nucleation of methane hydrate structures will be discussed. We will describe a previously unidentified structure of methane hydrates, designate structure sK, consisting of only 51263 and 512 cages, and will also show that a polycrystalline hydrate structure consisting of sequences of sI, sII and sK elements can be obtained. In this paper we will also detail a variety of host defects observed within the grown crystals. These defects include vacant cages, multiple methane molecules trapped in large cages, as well as one or more water molecules trapped in small and large cages. Finally, preliminary results obtains for THF and CO2 hydrates will be presented and their behaviour contrasted to that of methane hydrate.

This thesis is about the growth of ZnO thin films for optoelectronic applications. ZnO thin films were grown using plasma assisted molecular beam epitaxy and were studied using various conventional and novel characterisation techniques. The significance of different growth variables on growth efficiency was investigated. The growth rate of ZnO films was found to be linearly dependent on the Zn flux under O-rich growth conditions. Under Zn-rich conditions, the growth rate was dependent on both atomic and molecular oxygen flux. By characterising the oxygen plasma generated using different RF power and aperture plate designs and correlating the results with the growth rates observed, it was found that atomic oxygen was the dominant growth species under all conditions. Molecular oxygen also participated in the growth process, with its importance dependent on the aperture plate design. In addition, an increase in growth temperature was found to monotonically decrease the growth rate. A growth rate of 1.4 Å/s was achieved at a growth temperature of 650 ℃ by using an oxygen flow rate of 1.6 standard cubic centimetres utilising a plasma source with a 276 hole plate operating at 400 W, and a Zn flux 1.4✕10¹⁵ atoms/cm²⋅s. Characterisation of the MBE grown thin films revealed that the qualities of ZnO thin films were dependent on the growth conditions. Experimental evidence suggested that a maximum adatom diffusion rate can be achieved under Zn-rich conditions, giving samples with the best structural quality. O-rich conditions in general led to statistical roughening which resulted in rough and irregular film surfaces. Experimental results also suggested that by increasing the atomic oxygen content and decreasing the ion content of the plasma, the excitonic emission of the ZnO thin films can possibly be improved. It was also found that the conductivity of the films can possibly be reduced by increasing the plasma ion content. By investigating the evolution of the buffer layer surface during the early stages of growth, dislocation nucleation and surface roughening were found to be important strain relief mechanisms in MBE grown ZnO thin films that affected the crystal quality. The usage of LT-buffer layers was found to improve substrate wetting, and was shown to significantly reduce dislocation propagation. Further strain reduction was achieved via the application of a 1 nm MgO buffer layer, and a significant reduction of carrier concentration and improvement in optical quality was subsequently observed. A carrier concentration of <1✕10¹⁶ cm⁻³ and a near band emission full width half maximum of 2 meV was observed for the best sample. The study of electrical characteristics using the variable magnetic field Hall effect confirmed the existence of a degenerate carrier and a bulk carrier in most MBE grown ZnO thin films. The bulk carrier mobility was measured to be ~120 - 150 cm²/Vs for most as-grown samples, comparable to the best reported value. A typical bulk carrier concentration of ~1✕10¹⁶ - 1✕10¹⁸ cm⁻³ was observed for as-grown samples. Annealing was found to increase the mobility of the bulk carrier to ~120 - 225 cm²/Vs and decrease the bulk carrier concentration by two orders of magnitude. Using time resolved photoluminescence, it was found that the radiative recombination in MBE grown ZnO thin films was dominated by excitonic processes, and followed a T³⁄² trend with temperature. A maximum radiative lifetime of 10 ns was observed for as-grown samples. The non-radiative lifetime in ZnO thin films was dominated by the Shockley-Read-Hall recombination processes. The modelling of the temperature dependence of the non-radiative lifetime suggested that an electron trap at ~0.065 eV and a hole trap at ~0.1 eV may be present in these samples. The application of time resolved photoluminescence also allowed the direct observation of carrier freeze-out in these ZnO films at low temperature.

SixGe1-x is a promising alloy semiconductor material that is gaining importance in the semiconductor industry primarily due to the fact that silicon and germanium form a binary isomorphous system and hence its properties can be adapted to suit the needs of a particular application. Liquid phase diffusion (LPD) is a solution growth technique which has been successfully used to grow single crystals of SixGe1-x. The first part of this thesis discusses the development of a fixed grid solver to simulate the LPD growth under zero gravity condition. Initial melting is modeled in order to compute the shape of the initial growth interface along with temperature and concentration distribution. This information is then used by the solidification solver which in turn predicts the onset of solidification, evolution of the growth interface, and temperature and concentration fields as the solidification proceeds. The results are compared with the previous numerical study conducted using the dynamic grid approach as well as with the earth based experimental results. The predicted results are found to be in good qualitative agreement although certain noticeable differences are also observed owing to the absence of convective effects in the fixed grid model. The second part investigates the effects of crucible translation on the LPD technique using the dynamic grid approach. The case of constant pulling is examined first and compared with the available experimental results. Then a dynamic pulling profile obtained as a part of simulation process is used to achieve the goal of nearly uniform composition crystal. The effect of crucible translation on the interface shape, growth rate, and on the transport process is investigated. Finally, the effect of magnetic field on the LPD growth is examined. / Graduate