Multiscale Modeling and Simulation of Stepped Crystal Surfaces

A primary goal of this dissertation is to understand the links between mathematical models that describe crystal surfaces at three fundamental length scales: The scale of individual atoms, the scale of collections of atoms forming crystal defects, and macroscopic scale. Characterizing connections between different classes of models is a critical task for gaining insight into the physics they describe, a long-standing objective in applied analysis, and also highly relevant in engineering applications. The key concept I use in each problem addressed in this thesis is coarse graining, which is a strategy for connecting fine representations or models with coarser representations. Often this idea is invoked to reduce a large discrete system to an appropriate continuum description, e.g. individual particles are represented by a continuous density. While there is no general theory of coarse graining, one closely related mathematical approach is asymptotic analysis, i.e. the description of limiting behavior as some parameter becomes very large or very small. In the case of crystalline solids, it is natural to consider cases where the number of particles is large or where the lattice spacing is small. Limits such as these often make explicit the nature of links between models capturing different scales, and, once established, provide a means of improving our understanding, or the models themselves. Finding appropriate variables whose limits illustrate the important connections between models is no easy task, however. This is one area where computer simulation is extremely helpful, as it allows us to see the results of complex dynamics and gather clues regarding the roles of different physical quantities. On the other hand, connections between models enable the development of novel multiscale computational schemes, so understanding can assist computation and vice versa. Some of these ideas are demonstrated in this thesis. The important outcomes of this thesis include: (1) a systematic derivation of the step-flow model of Burton, Cabrera, and Frank, with corrections, from an atomistic solid-on-solid-type models in 1+1 dimensions; (2) the inclusion of an atomistically motivated transport mechanism in an island dynamics model allowing for a more detailed account of mound evolution; and (3) the development of a hybrid discrete-continuum scheme for simulating the relaxation of a faceted crystal mound. Central to all of these modeling and simulation efforts is the presence of steps composed of individual layers of atoms on vicinal crystal surfaces. Consequently, a recurring theme in this research is the observation that mesoscale defects play a crucial role in crystal morphological evolution.

Correlation among Growth Conditions, Morphology, and Optical Properties of Nanocolumnar InGaN/GaN Heterostructures Selectively Grown by Molecular Beam Epitaxy

This work reports on the selective area growth mechanism of green-emitting InGaN/GaN nanocolumns. The evolution of the morphology of the InGaN segment is found to depend critically on the nominal III/V ratio as well as the diameter of the GaN section. In addition, the In distribution inside the InGaN segment is found to depend on the local III/V and In/Ga ratios.

Life Cycle of Deccan Trap Magma Chambers: A Crystal Scale Elemental and Strontium Isotopic Investigation

The Deccan Trap basalts are the remnants of a massive series of lava flows that erupted at the K/T boundary and covered 1-2 million km2 of west-central India. This eruptive event is of global interest because of its possible link to the major mass extinction event, and there is much debate about the duration of this massive volcanic event. In contrast to isotopic or paleomagnetic dating methods, I explore an alternative approach to determine the lifecycle of the magma chambers that supplied the lavas, and extend the concept to obtain a tighter constraint on Deccan’s duration. My method relies on extracting time information from elemental and isotopic diffusion across zone boundary in an individual crystal. I determined elemental and Sr-isotopic variations across abnormally large (2-5 cm) plagioclase crystals from the Thalghat and Kashele “Giant Plagioclase Basalts” from the lowermost Jawhar and Igatpuri Formations respectively in the thickest Western Ghats section near Mumbai. I also obtained bulk rock major, trace and rare earth element chemistry of each lava flow from the two formations. Thalghat flows contain only 12% zoned crystals, with 87Sr/86Sr ratios of 0.7096 in the core and 0.7106 in the rim, separated by a sharp boundary. In contrast, all Kashele crystals have a wider range of 87Sr/86Sr values, with multiple zones. Geochemical modeling of the data suggests that the two types of crystals grew in distinct magmatic environments. Modeling intracrystalline diffusive equilibration between the core and rim of Thalghat crystals led me to obtain a crystal growth rate of 2.03x10-10 cm/s and a residence time of 780 years for the crystals in the magma chamber(s). Employing some assumptions based on field and geochronologic evidence, I extrapolated this residence time to the entire Western Ghats and obtained an estimate of 25,000 – 35,000 years for the duration of Western Ghats volcanism. This gave an eruptive rate of 30 – 40 km3/yr, which is much higher than any presently erupting volcano. This result will remain speculative until a similarly detailed analytical-modeling study is performed for the rest of the Western Ghats formations.

Hall Effect and transient surface photovoltage (SPV) study of Cu3BiS3 thin films

Se presentan las propiedades eléctricas del compuesto Cu3BiS3 depositado por co-evaporación. Este es un nuevo compuesto que puede tener propiedades adecuadas para ser utilizado como capa absorbente en celdas solares. Las muestras fueron caracterizadas a través de medidas de efecto Hall y fotovoltaje superficial transiente (SPV). A través de medidas de efecto Hall se encontró que la concentración de portadores de carga n es del orden de 1016 cm-3 independiente de la relación de masas de Cu/Bi. También se encontró que la movilidad de este compuesto (μ del orden de 4 cm2V -1s-1) varía de acuerdo con los mecanismos de transporte que la gobiernan en dependencia con la temperatura. A partir de las medidas de SPV se encontró alta densidad de defectos superficiales, defectos que son pasivados al superponer una capa buffer sobre el compuesto Cu3BiS3.

Synthesis and characterization of boehmite nanofibers

Boehmite nanofibers of high quality were synthesized through a wet-gel conversion process without the use of a surfactant. The long nanofibers of boehmite with clear-cut edges were obtained by steaming the wet-gel precipitate at 170 ºC for 2 days under a pH 5. Hydrothermal treatment of the boehmite gels enabled self-assembly through directed crystal growth. Detailed characterization using X-ray diffraction (XRD), Scanning Electron Microscopy (SEM), Infrared Emission Spectroscopy (IES) and Raman Spectroscopy is presented.

Numerical study of two ill-posed one-phase Stefan problems

We treat two related moving boundary problems. The first is the ill-posed Stefan problem for melting a superheated solid in one Cartesian coordinate. Mathematically, this is the same problem as that for freezing a supercooled liquid, with applications to crystal growth. By applying a front-fixing technique with finite differences, we reproduce existing numerical results in the literature, concentrating on solutions that break down in finite time. This sort of finite-time blow-up is characterised by the speed of the moving boundary becoming unbounded in the blow-up limit. The second problem, which is an extension of the first, is proposed to simulate aspects of a particular two-phase Stefan problem with surface tension. We study this novel moving boundary problem numerically, and provide results that support the hypothesis that it exhibits a similar type of finite-time blow-up as the more complicated two-phase problem. The results are unusual in the sense that it appears the addition of surface tension transforms a well-posed problem into an ill-posed one.

Fabrication of macro-mesoporous zirconia-alumina materials with a 1D hierarchical structure

A series of one dimensional (1D) zirconia/alumina nanocomposites were prepared by the deposition of zirconium species onto the 3D framework of boehmite nanofibres formed by dispersing boehmite nanofibres into butanol solution. The materials were calcined at 773K and characterized by X-ray diffraction (XRD), scanning electron microscopy (SEM), transmission electron microscope (TEM), N2 adsorption/desorption, infrared emission spectroscopy (IES). The results demonstrated that when the molar percentage X=100*Zr/(Al+Zr) was > 30 %, extremely long ZrO2/Al2O3 composite nanorods with evenly distributed ZrO2 nanocrystals on the surface were formed. The stacking of such nanorods gave rise to a new kind of macroporous material without the use of any organic space filler\template or other specific technologies. The mechanism for the formation of long ZrO2/Al2O3 composite nanorods was proposed in this work.

Supramolecular selection in molecular alloys

Complexes of the type \[M(phen)3](PF6)2 (M = Ni(II), Fe(II), Ru(II) and phen = 1,10-phenanthroline) were found to co-crystallize to form molecular alloys (solid solutions of molecules) with general formula \[MAxMB1–x(phen)3](PF6)2·0.5H2O in which the relative concentrations of the metal complexes in the crystals closely match those in the crystallizing solution. Consequently, the composition of the co-crystals can be accurately predicted and controlled by modulating the relative concentrations of the metal complexes in the crystallizing solution. Although they are chemically and structurally similar, complexes of the type \[M(bipy)3](PF6)2 (M = Ni(II), Fe(II), Ru(II) and bipy = 2,2′-bipyridine) display markedly different behavior upon co-crystallization. In this case, the resulting co-crystals of general formula \[MAxMB1–x(bipy)3](PF6)2 have relative concentrations of the constituent complexes that are markedly different from the relative concentrations of the complexes initially present in the crystallizing solution. For example, when the nickel and iron complexes are co-crystallized from a solution containing a 50:50 ratio of each, the result is the formation of some crystals with a higher proportion of iron and others with a higher proportion of nickel. The relative concentrations of the metal complexes in the crystals can vary from those in the crystallizing solutions by as much as 15%. This result was observed for a range of combinations of metal complexes (Ni/Fe, Ni/Ru, and Fe/Ru) and a range of starting concentrations in the crystallizing solutions (90:10 through to 10:90 in 10% increments). To explain this remarkable result, we introduce the concept of “supramolecular selection”, which is a process driven by molecular recognition that leads to the partially selective aggregation of like molecules during crystallization.

Experimental transformation of kaolinite to halloysite

A well-characterized kaolinite has been hydrated in order to test the hypothesis that platey kaolinite will roll upon hydration. Kaolinite hydrates are prepared by repeated intercalation of kaolinite with potassium acetate and subsequent washing with water. On hydration, kaolinite plates roll along the major crystallographic directions to form tubes identical to proper tubular halloysite. Most tubes are elongated along the b crystallographic axis, while some are elongated along the a axis. Overall, the tubes exhibit a range of crystallinity. Well-ordered examples show a 2-layer structure, while poorly ordered tubes show little or no 3-dimensional order. Cross-sectional views of the formed tubes show both smoothly curved layers and planar faces. These characteristics of the experimentally formed tubes are shared by natural halloysites. Therefore, it is proposed that planar kaolinite can transform to tubular halloysite.

Microstructural studies of quenched partially-melted Y-123 materials and Y-123 with Y-211, PtO2 and CeO2 additions

The microstructure of YBa2Cu3O7-delta (Y-123) materials partially-melted in air and quenched from the temperature range 900-1100 degrees C, has been characterized using a combination of X-ray diffractometry, optical microscopy, scanning electron microscopy, electron microprobe analyses, transmission electron microscopy and energy and wave dispersive X-ray spectrometries. The microstructural studies reveal significant changes in the character of the quenched partial-melt as a function of temperature and time before quenching. BaCu2O2 and BaCuO2 are found to co-exist in stoichiometric samples quenched from the temperature range 920-960 degrees C. Under suitable cooling conditions, large pockets of melt cristallize as BaCuO2 with an exsolution of BaCu2O2 in the form of thin plates (approximate to 50-100 nm thick) along facets. Y2BaCuO5 (Y-211) additions are associated with the formation of BaCu2O2 at 1100 degrees C. Preliminary results on the effects of PtO2 and CeO2 additions to Y-123 (and Y-123 with Y-211 additions) show that these enhace the formation of BaCu2O2 at the melting temperature of 1100 degrees C. (C) 1998 Elsevier Science S.A. All rights reserved.

Scanning electron microscopy of condensation related minerals : the Bjurbole meteorite

Filamentary single crystals, blades, sheets, euhedral crystals and powders may form by vapor phase condensation depending on the supersauration conditions in the vapor with respect to the condensing species [1]. Filamentary crystal growth requires the operation of an axial screw dislocation [2]. A Vapor-Liquid-Solid (VLS) mechanism may also produce filamentary single crystals, ribbons and blades. The latter two morphologies are typically twinned. Crystals grown by this mechanism do not require the presence of an axial screw dislocation. Impurities may either promote or inhibit crystal growth [3]. The VLS mechanism allows crystals to grow at small supersaturation of the vapor. Thin enstatite blades, ribbons and sheets have been observed in chondritic porous Interplanetary Dust Partics (IDP's) [4, 5]. The requisite screw dislocation for vapor phase condensation [1] has been observed in these enstatite blades [4]. Bradley et al. [4] suggest that these crystals are primary vapor phase condensates which could have formed either in the solar nebula or in presolar environments. These observations [4,5] are significant in that they may provide a demonstrable link to theoretical predictions: viz. that in the primordial solar nebula filamentary condensates could cluster into 'lint balls' and form the predecessors to comets [6].