Multi-impurity adsorption model for modeling crystal purity and shape evolution during crystallization processes in impure media

Peer reviewed

A Mineralogical Study of a Dravitic Tourmaline from the Grenville Province

Tourmaline from a gem-quality deposit in the Grenville province has been studied with X-ray diffraction, visible-near infrared spectroscopy, Fourier transform infrared spectroscopy, scanning electron microscopy, electron microprobe and optical measurements. The tourmaline is found within tremolite-rich calc-silicate pods hosted in marble of the Central Metasedimentary Belt. The crystals are greenish-greyish-brown and have yielded facetable material up to 2.09 carats in size. Using the classification of Henry et al. 2011 the tourmaline is classified as a dravite, with a representative formula shown to be (Na0.73Ca0.2380.032)(Mg2+2.913Fe2+0.057Ti4+0.030) (Al3+5.787Fe3+0.017Mg2+0.14)(Si6.013O18)(BO3)3(OH)3((OH,O)0.907F0.093). Rietveld analysis of powder diffraction data gives a = 15.9436(8) Å, c = 7.2126(7) Å and a unit cell volume of 1587.8 Å3. A polished thin section was cut perpendicular to the c-axis of one tourmaline crystal, which showed zoning from a dark brown core into a lighter rim into a thin darker rim and back into lighter zonation. Through the geochemical data, three key stages of crystal growth can be seen within this thin section. The first is the core stage which occurs from the dark core to the first colourless zone; the second is from this colourless zone increasing in brown colour to the outer limit before a sudden absence of colour is noted; the third is a sharp change from the end of the second and is entirely colourless. These events are the result of metamorphism and hydrothermal fluids resulting from nearby felsic intrusive plutons. Scanning electron microscope, and electron microprobe traverses across this cross-section revealed that the green colour is the result of iron present throughout the system while the brown colour is correlated with titanium content. Crystal inclusions in the tourmaline of chlorapatite, and zircon were identified by petrographic analysis and confirmed using scanning electron microscope data and occur within the third stage of formation.

On the microstructure, growth pattern and original porosity of belemnite rostra: insights from calcitic Jurassic belemnites

Calcitic belemnite rostra are usually employed to perform paleoenvironmental studies based on geochemical data. However, several questions, such as their original porosity and microstructure, remain open, despite they are essential to make accurate interpretations based on geochemical analyses.This paper revisits and enlightens some of these questions. Petrographic data demonstrate that calcite crystals of the rostrum solidum of belemnites grow from spherulites that successively develop along the apical line, resulting in a “regular spherulithic prismatic” microstructure. Radially arranged calcite crystals emerge and diverge from the spherulites: towards the apex, crystals grow until a new spherulite is formed; towards the external walls of the rostrum, the crystals become progressively bigger and prismatic. Adjacent crystals slightly vary in their c-axis orientation, resulting in undulose extinction. Concentric growth layering develops at different scales and is superimposed and traversed by a radial pattern, which results in the micro-fibrous texture that is observed in the calcite crystals in the rostra.Petrographic data demonstrate that single calcite crystals in the rostra have a composite nature, which strongly suggests that the belemnite rostra were originally porous. Single crystals consistently comprise two distinct zones or sectors in optical continuity: 1) the inner zone is fluorescent, has relatively low optical relief under transmitted light (TL) microscopy, a dark-grey color under backscatter electron microscopy (BSEM), a commonly triangular shape, a “patchy” appearance and relatively high Mg and Na contents; 2) the outer sector is non-fluorescent, has relatively high optical relief under TL, a light-grey color under BSEM and low Mg and Na contents. The inner and fluorescent sectors are interpreted to have formed first as a product of biologically controlled mineralization during belemnite skeletal growth and the non-fluorescent outer sectors as overgrowths of the former, filling the intra- and inter-crystalline porosity. This question has important implications for making paleoenvironmental and/or paleoclimatic interpretations based on geochemical analyses of belemnite rostra.Finally, the petrographic features of composite calcite crystals in the rostra also suggest the non-classical crystallization of belemnite rostra, as previously suggested by other authors.

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.

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.