The dissolution forms of single crystal spheres

Lacmann, R.; Heimann, Robert B.; Franke, W.

doi:10.1016/0022-0248(74)90208-5

Cited by 58 publications

(7 citation statements)

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“…Our aim in this paper is to present a satisfactory description of the experimental results by considering that disordering of 2D condensed organic films at the electrochemical interface proceeds from line defects. In an early attempt 5 based on the work of Lacmann et al, , we had assumed that the patches constituting the condensed film are squares with sizes randomly distributed according to a Poisson distribution. However, the two parameters used in this model could be linked only qualitatively to the kinetics of the condensation process.…”

Section: Introductionmentioning

confidence: 99%

Kinetics of Disordering of Two-Dimensional Organic Phases at the Electrochemical Interface

1999

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A mathematical model has been developed to describe the disordering kinetics of a condensed monolayer adsorbed at the electrochemical interface. It is assumed that the disordering process is linked to the presence of defects in the condensed film. In the case of a perfectly smooth electrode, like a mercury drop, the only defects present in the film orginate from its formation by a 2D nucleation and growth process, so that the film can be viewed as an arrangement of linear and point defects. The model is restricted to the case where the disordering starts from lines and corresponds to the progressive shrinkage of patches having the same size. The rate of disorder propagation is considered as time dependent, this dependence being expressed as a function of the surface energy and the line tension. The expression for the surface coverage of the disordered film as a function of time is modulated by two parameters. The validation of the model is based on experimental results obtained by chronocoulometry for the disordering of a coumarin monolayer at the mercury/electrolyte interface.

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Section: Introductionmentioning

confidence: 99%

Kinetics of Disordering of Two-Dimensional Organic Phases at the Electrochemical Interface

1999

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“…For inorganic and organic materials, dissolution not only affects the crystal shape but also plays a vital role in polymorphic phase transformations. The possible end-shapes in crystal dissolution have been discussed in many contexts. – For example, Moore suggested that vertices on growth shapes would end up as faces on dissolution shapes, and Gibbs suggested that shapes in dissolution will differ from the equilibrium form in a direction “opposite” to that of growth . Despite these qualitative descriptions, a model that can quantitatively predict the evolution of crystal shapes during dissolution has only recently been developed .…”

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confidence: 99%

The Evolution of Crystal Shape During Dissolution: Predictions and Experiments

Snyder

Veesler

Doherty

2008

Crystal Growth & Design

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ࠗ w This paper contains enhanced objects available on the Internet at http://pubs.acs.org/crystal. ABSTRACT: A comparison between a priori model predictions and experimental results for crystal shapes of succinic acid crystals dissolving in aqueous solution is presented. The model is the simplest possible model which neglects all effects other than a determination of which faces to include on the crystal habit and their perpendicular growth rates. The experiments are carried out in a thermostatted peltier cell and are imaged in situ using a microscope with digital imaging capabilities. The predicted and experimentally measured crystal shapes are very similar throughout the dissolution process. Thus, the experiments provide support for the model's predictive power.The change in crystal shape as a result of dissolution is a topic of interest for a wide range of materials including organics such as pharmaceuticals, proteins and specialty chemicals as well as inorganics in geology and semiconductors. For inorganic and organic materials, dissolution not only affects the crystal shape but also plays a vital role in polymorphic phase transformations. The possible end-shapes in crystal dissolution have been discussed in many contexts. 1-4 For example, Moore suggested that vertices on growth shapes would end up as faces on dissolution shapes, 2 and Gibbs suggested that shapes in dissolution will differ from the equilibrium form in a direction "opposite" to that of growth. 3 Despite these qualitative descriptions, a model that can quantitatively predict the evolution of crystal shapes during dissolution has only recently been developed. 5 This communication presents recently produced in situ experimental confirmation of the model's predictions for the dynamics of dissolving crystal shapes, along with the related modeling information necessary for comparison.We have chosen -succinic acid crystals dissolving in water as the system to demonstrate the effective predictions of the model. The crystallization and subsequent dissolution and visualization were performed in a thermostatted peltier cell equipped with a Nikon microscope and digital imaging capabilities, and has been previously described in detail. 6 A saturated solution of -succinic acid 7 in 2 mL of water was prepared at a saturation temperature of 36°C. Nucleation was induced at a lower temperature (25°C). Once a crystal could be observed in the solution, the temperature was raised to within a degree of saturation, and the crystal was allowed to grow to a size suitable for dissolution visualization (∼100 µm). Then, the temperature was increased to one degree above saturation, leading to dissolution during which the crystal shape evolution was recorded. Since the mass of the dissolving crystal is very small (∼0.001 mg compared to the 2 mL volume of the crystallizer) the undersaturation is approximately constant throughout the dissolution process.The model for shape evolution can predict and track each of the faces of a fully three-dimensional crystal during growth an...

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“…Thus the Zn-Se pair incorporation energy of the {001} surface steps may be essentially higher than that of the {110} surface ledges. Under the assumption that the spreading velocity of a surface step is proportional to the Zn-Se pair incorporation energy, it follows the observed {110} growth form, when the normal growth rates fulfill the condition [1,17].…”

Section: Zn-se Pair Incorporation Energies For Ledges On (111) (111) ...mentioning

confidence: 58%

Estimation of incorporation energies of Zn-Se and Si-S pairs in different surface steps of ZnSe crystals with a semi-empirical finite-size cluster approach

Herman¹,

Schönherr²

2000

Modelling Simul. Mater. Sci. Eng.

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The dissolution forms of single crystal spheres

Cited by 58 publications

References 10 publications

Kinetics of Disordering of Two-Dimensional Organic Phases at the Electrochemical Interface

Kinetics of Disordering of Two-Dimensional Organic Phases at the Electrochemical Interface

The Evolution of Crystal Shape During Dissolution: Predictions and Experiments

Estimation of incorporation energies of Zn-Se and Si-S pairs in different surface steps of ZnSe crystals with a semi-empirical finite-size cluster approach

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