Journal ArticleDOI
Interdendritic Spacing: Part I. Experimental Studies
TLDR
In this article, a scaling law is shown to exist between the secondary dendrite arm spacing, λ2, near the tip and the Dendrite tip radius, p, which is λ 2/ρ = 2.2 ± 0.3.Abstract:
Directional solidification experiments have been carried out in a succinonitrile-5.5 mol pct acetone system to characterize dendrite tip radius and interdendrite spacings as functions of growth rate and temperature gradient in the liquid. A maximum in primary dendrite spacing as a function of growth rate is observed, and this maximum is found to occur at the dendrite-cellular transition velocity. A scaling law is shown to exist between the secondary dendrite arm spacing, λ2, near the tip and the dendrite tip radius, p, which is λ2/ρ = 2.2 ± 0.3. Experimental results on ρ have been found to agree with the theoretical model based on the marginal stability criterion.read more
Citations
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Book ChapterDOI
Theory of Microstructural Development during Rapid Solidification
Rohit Trivedi,Wilfried Kurz +1 more
TL;DR: In this article, some of the fundamental factors which play important roles in determining microstructures under rapid solidification condition are described, and it is shown that the interface stability analysis needs to be extended to include the possibility of high thermal as well as high solute undercoolings.
Journal ArticleDOI
Pattern selection in fingered growth phenomena
TL;DR: In this article, the authors survey recent theoretical work which elucidates how such systems arrive at their observed patterns, focusing on dendritic solidification, simple local models thereof, and the Saffman-Taylor finger in 2D fluid flow.
Journal ArticleDOI
Solidification microstructures: recent developments, future directions
William J. Boettinger,Sam R. Coriell,A.L. Greer,Alain Karma,Wilfried Kurz,Michel Rappaz,Rohit Trivedi +6 more
TL;DR: The status of solidification science is critically evaluated and future directions of research in this technologically important area are proposed in this paper, where the most important advances in solidification sciences and technology of the last decade are discussed: interface dynamics, phase selection, microstructure selection, peritectic growth, convection effects, multicomponent alloys, and numerical techniques.
Journal ArticleDOI
Numerical modeling of cellular/dendritic array growth: spacing and structure predictions
J.D. Hunt,Shu-Zu Lu +1 more
TL;DR: A numerical model has been developed that can predict cellular and dendritic spacings, undercoolings, and the transition between structures, and fully self-consistent solutions are produced for axisymmetric interface shapes.
Journal ArticleDOI
Interdendritic Spacing: Part II. A Comparison of Theory and Experiment
TL;DR: In this article, a theoretical model based on the Hunt model is developed, and it is found that the theory adequately explains the variation in primary spacing, λ 1, with the growth rate,V.
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
Dendrite growth at the limit of stability: tip radius and spacing
Wilfried Kurz,D.J. Fisher +1 more
TL;DR: In this article, a general framework is proposed to relate tip radius, interface undercooling and primary arm spacing in alloy dendrite growth, and all the growth morphologies developed between the limiting morphology at low and at high velocity are described to a first approximation, using an ellipsoid of revolution.
Journal ArticleDOI
Theory of dendritic growth—i. elements of a stability analysis
J.S. Langer,H. Müller-Krumbhaar +1 more
TL;DR: In this paper, the maximum velocity principle was replaced by a stability criterion of the form υρ 2 = constant, where υ is the growth rate and ρ the tip radius of a dendrite.
Journal ArticleDOI
Overview 12: Fundamentals of dendritic solidification—I. Steady-state tip growth
S.-C. Huang,Martin E. Glicksman +1 more
TL;DR: In this article, the dendritic stability criterion measured is 2 αd 0 / VR 2 = 0.0195, where V is the growth velocity, R is the dandritic tip radius, a is the liquid thermal diffusivity, and d 0 is a capillary length defined in the text.
Journal ArticleDOI
Cellular and dendritic growth. I
M.H. Burden,J.D. Hunt +1 more
TL;DR: In this article, a theoretical model was developed to explain the variation in cellular or dendritic tip temperatures with velocity and temperature gradient, and it was shown that the undercooling can be considered to arise as a result of build up of average solute concentration ahead of the growth front depending mainly on the imposed temperature gradient.