Bifurcations in a sidebranch surface of a free-growing dendrite

Galenko, Peter; Krivilyov, M. D.; Buzilov, S. V.

doi:10.1103/physreve.55.611

Cited by 13 publications

(17 citation statements)

References 24 publications

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“…Galenko et al note that dendrite formation in material growth is a trademark of nonequilibrium. 9 However, despite the predictions by Galenko et al, we do not observe secondary and continuing branch bifurcations along the dendrites as predicted by many prevailing dendrite growth models, such as the models by Feigenbaum, Galenko, and Zhuravlev, or Hopf. However, this may be due to the resolution restrictions of the FESEM rather than an actual absence of such structures.…”

Section: Resultscontrasting

confidence: 49%

Dendritic-pattern formation in anodic aluminum oxide templates

Friedman

Menon

2007

Journal of Applied Physics

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Formation of disordered and ordered pore patterns in two dimensions have been reported in pore growth in nanoporous alumina templates. This is explained in terms of instability in the pattern formation. Here, we report our observation of instability in the pattern formation in three dimensions, that is, along the cylindrical axis of the pores. The instability is revealed in the form of dendrites in the pore pattern under certain fabrication conditions. We examine the conditions under which two- and three-dimensional instability occurs and compare our observations of the two dimensional case with existing models in the literature.

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Section: Resultscontrasting

confidence: 49%

Dendritic-pattern formation in anodic aluminum oxide templates

Friedman

Menon

2007

Journal of Applied Physics

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“…We also note that the period of the final, well developed side-branches is almost exactly double the period of the initial perturbation in all cases. In this respect there are interesting parallels with the model of [13], in which a period doubling of the initial side-branching instability was also identified. Moreover, for anisotropies of   0.030 (to the left of the minimum in Fig.…”

Section: Figurementioning

confidence: 74%

“…Although it is well established that secondary arm coarsening proceeds by the dissolution of unfavourable branches from the tip back towards the trunk [28,29], this appears not to be the case here, as the branches never fully develop. Instead, these appear to be remnants indicative of a period doubling instability as described by [13]. …”

Section: Figurementioning

confidence: 99%

“…However, models of deterministic side-branching have been proposed, such as that by [13], in which the dendrite experience repeated period doubling of an initially high frequency sidebranching instability at the tip. Recently, based upon a re-evaluation of the IDGE data, Glicksman [14,15] has proposed that dendrites may undergo deterministic side-branching.…”

Section: Introductionmentioning

confidence: 99%

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Spontaneous deterministic side-branching behavior in phase-field simulations of equiaxed dendritic growth

Mullis

2015

Journal of Applied Physics

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The accepted view on dendritic side-branching is that side-branches grow as the result of selective amplification of thermal noise and that in the absence of such noise dendrites would grow without the development of side-arms. However, recently there has been renewed speculation about dendrites displaying deterministic side-branching [see e.g. ME Glicksman, Metall. Mater. Trans A 43 (2012) 391]. Generally, numerical models of dendritic growth, such as phase-field simulation, have tended to display behaviour which is commensurate with the former view, in that simulated dendrites do not develop side-branches unless noise is introduced into the simulation. However, here we present simulations that show that under certain conditions deterministic side-branching may occur. We use a model formulated in the thin interface limit and a range of advanced numerical techniques to minimise the numerical noise introduced into the solution, including a multigrid solver. Spontaneous side-branching seems to be favoured by high undercoolings and by intermediate values of the capillary anisotropy, with the most branched structures being obtained for an anisotropy strength of 0.03. From an analysis of the tangential thermal gradients on the solid-liquid interface, the mechanism for side-branching appears to have some similarities with the deterministic model proposed by Glicksman.

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“…The 1D system under study was not the only example of period doubling effect during coarsening after discontinuous transformation. Numerical simulations of dendritic growth showed that the coarsening process of the sidebranch structure during growth stage also exhibits mechanism of period doubling [34,35], which was substantiated by direct experimental observations of growing dendrites of succinonitrile [36] and ammonium bromide [37]. When the volume fraction of coarsening domains is rather high the coarsening process is a result of strong longrange interaction between them through the temperature field.…”

Section: Coarsening: Approach To Equilibriummentioning

confidence: 90%

Thermal effects of phase transformations: A review

Umantsev

2007

Physica D: Nonlinear Phenomena

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All the stages of phase transformations in materials, nucleation, growth, and coarsening, are subject to thermal effects that stem from the redistribution of energy in the system, like release of latent heat, and heat conduction. The thermal effects change the rate and outcome of the transformation and may result in the appearance of unusual states or phases, in particular in nanosystems. This review will cover the attempts of researchers to build a comprehensive theory of thermal effects in different phase transformations. Although the dynamical Ginzburg-Landau (continuum) approach will be used for the analysis of the effects, they are robust and conceivably independent of the theoretical method employed. On general physical grounds a possibility of an oscillatory regime in nucleation is considered and evolution equations for the interfacial motion are derived. The equations show that there are two distinctly different sets of thermal effects of interface motion: one set originates from the existence of the Gibbs-Duhem thermodynamic force on the interface, which has opposite directions compared to the velocity of the interface in the cases of continuous and discontinuous transitions, resulting in a heat trapping effect for the latter and a drag effect for the former. The other set of thermal effects stems from the existence of the surface internal energy and the necessity to carry it over together with the moving interface. As a result, temperature double layers accompany moving domain boundaries after a continuous transition or the surface creation and dissipation effect appear after a discontinuous one. An unusual, novel phase that may appear in isolated nanosystems (adiabatic nanophase) is described. Several experiments are suggested for the verification of the thermal effects in different material systems.

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Bifurcations in a sidebranch surface of a free-growing dendrite

Cited by 13 publications

References 24 publications

Dendritic-pattern formation in anodic aluminum oxide templates

Dendritic-pattern formation in anodic aluminum oxide templates

Spontaneous deterministic side-branching behavior in phase-field simulations of equiaxed dendritic growth

Thermal effects of phase transformations: A review

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