Growth Rates Of Individual Faces Research Articles

Effect of seed loading and cooling rate on crystal size and shape distributions in protein crystallization—A study using morphological population balance simulation

A morphological population balance model is applied to crystallization of hen-egg white lysozyme for investigation of the effect of seed loading and cooling rate on supersaturation, and crystal size and shape distributions. Growth rates of individual faces and final crystal size and shape distributions were examined under varied seeding and cooling conditions. It was found that for growth only crystallization, desired crystal size and shape can be obtained by coordinative manipulation of the seed loading and cooling rate: low seed loading and high cooling rate lead to large crystals of low aspect ratio, but care has to be taken to avoid nucleation and major shape change such as width becoming larger than the length. The interesting results not only demonstrate the effectiveness of morphological population balance simulation for protein crystallization but also provide useful knowledge for process optimization and control.

Mechanisms of Dye Incorporation into Potassium Sulfate: Computational and Experimental Studies

Potassium sulfate crystals orient and overgrow 2-aminobenzenesulfonate (OSA), and many other sulfonated aromatic compounds, on particular facets during growth from solution. The energetics associated with adsorption of OSA and benzenesulfonate (BS) were calculated using both molecular mechanical and density functional methods, in order to assess the surface binding effectiveness of these compounds on various faces of potassium sulfate. It was found that both theoretical techniques predicted that OSA and BS bind to potassium sulfate to a similar extent. The surface binding capacities were also assessed experimentally by studying the growth rates of individual faces of K2SO4, with results showing similar findings to those from the computational studies.

Multi-dimensional population balance modeling of the growth of rod-like L-glutamic acid crystals using growth rates estimated from in-process imaging

Abstract —Traditionally, population balance (PB) modeling of crystal growthin crystallizers has been based on a single scalar parameter for particle size, typically the volume equivalent diameter. This misses important information about particle shape, especially for crystals of high aspect ratios. In recent years attempts have been made to extend PB to two or more size dimensions by taking into consideration of the crystal shape. A key step in multi-dimensional PB (M-PB) modeling is the estimation of the growth rates of individual faces as a function of temporal operating conditions, e.g. the supersaturation. In this paper, we propose to carry out M-PB modeling based on real-time experimentally derived growth rates for different faces using in-process imaging and image analysis. Results are presented for the seeded cooling crystallisation of rod-like β-form L-glutamic acid in a 0.5-l batch reactor.

Growth of Gallium Orthophosphate Single Crystals under Hydrothermal Conditions

Gallium orthophosphate (GAPO4) single crystals have been grown from phosphoric acid solutions under hydrothermal conditions. The crystals have been studied in terms of twinning because of the strong effect of this structural defect on the piezoelectric properties. The growth rates of individual faces have been compared to each other by considering the dipyramidal habit of the grown crystals.

Theoretical analysis of changes in habit of growing crystals in response to variable growth rates of individual faces

The subject of this paper is research and analysis of the kinetic conditions corresponding to changes in habits of growing crystals. In particular, the formula to evaluate the rate of changes in length of any edge in any three-dimensional crystal is presented. This formula is the basis for the analysis of changes in habits depending on growth rates of individual faces which may be described by any time-dependent or time-independent function. The theoretical predictions are verified by computer modeling performed for crystal grown in nature – wulfenite. On the example of this crystal it is shown that the presented formulae may be used as a tool to describe the evolution of crystal morphologies and to predict the habits of growing crystals at given growth rates of individual faces.

A guide to quantitative morphology of accessory zircon

Traditionally, the morphological evolution of zircon crystals is presented as paths connecting morphological types arranged in rectangular grids. The present guide introduces an alternative approach overcoming the major deficiencies of the typological methods. The growth rates of individual crystal faces are normalized to a {011}-reference face and plotted as functions of the reference face's central distance. Thus, the morphological evolution of a crystal can be constrained by a set of normalized growth rate functions. The information necessary for determining these functions is obtained from the measurement of central distances and growth steps in crystallographically oriented sections, viewed with cathodoluminescence techniques. The data for individual crystals are generally not representative, but they can be joined in diagrams plotting normalized growth rates vs. central distance for a large population of crystals. In a case study, this procedure is applied to a calc-alkaline granodiorite. The normalized growth rates of the {010}-prism faces show a negative correlation with the central distance of the {011}-reference faces. This is related to the global change of a still unknown factor in the magma body. The new quantitative method should encourage further detailed correlations between morphological characteristics and petrogenetic environments. This procedure is transferable to crystals of other minerals, provided that oriented sections can be obtained and growth bands can be revealed. As a major advantage over traditional typological methods, the new method considers growth rates of individual faces which are immediately controlled by interface kinetics.

XXIX. The growth of ice crystals from the vapour

Summary The growth and evaporation of single ice crystals have been studied in relation to the temperature and supersaturation of the environment. The sequence of crystal forms which occurs in clouds as the temperature falls from 0°c to - 40°c has been reproduced in these experiments. Measurements of the growth rates of individual faces of crystals growing under fixed environmental conditions reveal that dR2 /dt=const. where R is a linear crystal dimension, but the growth rates of basal and prism faces are different to a degree depending mainly on the temperature. At constant temperature, dR2 /dt varied as the square of the supersaturation σ over the range of σ studied. A critical supersaturation for growth was found which varied in an apparently random manner from face to face, there being no systematic difference between the values for the prism and basal faces. The crystal habit, denned by limiting values of the axis/diameter ratio, was found to be controlled very largely by the temperature, the supers...