Journal ArticleDOI
Effect of surface tension anisotropy on cellular morphologies
TLDR
In this paper, a weakly nonlinear analysis for conditions near the onset of instability at the crystal-melt interface was carried out to second order, taking into account the effects of latent heat generation and surface-tension anisotropy of the crystal melt interface; particular consideration was given to the growth of a cubic crystal in the 001-, 011-, and 111-line directions.About:
This article is published in Journal of Crystal Growth.The article was published on 1988-08-01. It has received 34 citations till now. The article focuses on the topics: Anisotropy & Instability.read more
Citations
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A convective Cahn-Hilliard model for the formation of facets and corners in crystal growth
TL;DR: In this article, the authors consider solidification into a hypercooled melt in which kinetic undercooling and anisotropic surface energy are present, and track the unstable evolution of an initially planar front to a facetted front.
Journal ArticleDOI
Equilibrium and growth shapes of crystals: how do they differ and why should we care?
TL;DR: In this article, the Czochralski shape of a crystal is defined as minimizing its anisotropic surface free energy under the constraint of constant volume; it is given by the classical Wulff construction but can also be represented by an analytical formula based on the ξ-vector formalism of Hoffman and Cahn.
Journal ArticleDOI
How does the flow within the boundary layer influence morphological stability of a vicinal face
TL;DR: In this article, the effect of solution flow within the boundary layer on the stability is considered for the first time, and the analytical solution found describes the drift of diffusion clouds (enriched or improverished regions of solution) surrounding spontaneously appearing slight step bunches.
Journal ArticleDOI
Role of instabilities in determination of the shapes of growing crystals
TL;DR: In this paper, the shape of growing crystals is determined by an interplay of complex processes that include transport of energy and matter through bulk phases, capillarity-related processes that determine local equilibrium conditions at the crystal-nutrient interface, and non-equilibrium kinetic processes that take place locally to that interface.
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In situ and real-time observation of the formation and dynamics of a cellular interface in a succinonitrile-0.5 wt% acetone alloy directionally solidified in a cylinder
TL;DR: In this article, a microstructure gradient was observed at the interface of a solid-liquid interface during upward Bridgman growth of succinonitrile-0.5 wt% acetone in a cylinder.
References
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Journal ArticleDOI
Instabilities and pattern formation in crystal growth
TL;DR: In this article, the authors examined several common modes of crystal growth and identified a few new theoretical ideas and a larger number of outstanding problems, including sidebranching and tip-splitting instabilities.
Journal ArticleDOI
A Method for Obtaining Electronic Eigenfunctions and Eigenvalues in Solids with An Application to Sodium
Journal ArticleDOI
A nonlinear stability analysis of the freezing of a dilute binary alloy
David J. Wollkind,L. A. Segel +1 more
TL;DR: In this paper, a nonlinear model is used to describe an experimental situation in which solidification is controlled so that the mean position of the interface moves with constant speed, and it is found that the interface can be unstable to finite amplitude disturbances even when linear stability theory predicts stability to infinitesimal disturbances.
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Houston's Method and Its Application to the Calculation of Characteristic Temperatures of Cubic Crystals
TL;DR: In this article, approximate formulas are given for the integral in terms of the values of $I(ensuremath{\theta, \enuremath{-})$ along three and any or all of the (210), (211), and (221) directions.
Journal ArticleDOI
The development of cells during the solidification of a dilute Pb-Sb alloy
L.R. Morris,W. C. Winegard +1 more
TL;DR: In this paper, the development of a cellular solid-liquid interface from a planar interface is outlined in some detail for a dilute binary alloy of Sb in zone-refined Pb.
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A nonlinear stability analysis of the freezing of a dilute binary alloy
David J. Wollkind,L. A. Segel +1 more