Noise-induced sidebranching in the three-dimensional nonaxisymmetric dendritic growth

Brener, Efim A.; Temkin, D. E.

doi:10.1103/physreve.51.351

Cited by 119 publications

(107 citation statements)

References 13 publications

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“…Models for this process, in the framework of microscopic solvability theory, have been put forward by Langer [7,8] and by Brener & Tempkin [9]. Such models appear to be supported by a number of phase-field simulations, in which it has been observed that dendrites grow without side-branches unless noise is introduced at the solid-liquid interface [10].…”

Section: Introductionmentioning

confidence: 75%

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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Section: Introductionmentioning

confidence: 75%

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

Mullis

2015

Journal of Applied Physics

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“…Thermal noise is more difficult to analyze because it involves a wide range of frequencies and is spatially distributed. Consequently, current estimates of the sidebranching amplitude [10,11] involve some overall prefactor which is only known approximately. Secondly, the predicted sidebranching amplitude depends sensitively on the non-axisymmetric tip shape which seems to vary from system to system.…”

Section: Introductionmentioning

confidence: 99%

“…The second goal is to use this approach to carry out a quantitative study of sidebranching in order to test the predictions of the linear WKB theory of noise amplification [10,11]. Here, simulations are restricted to two dimensions in order to carry out this comparison in the simplest non-trivial test case.…”

Section: Introductionmentioning

confidence: 99%

Phase-field model of dendritic sidebranching with thermal noise

1999

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We investigate dendritic sidebranching during crystal growth in an undercooled melt by simulation of a phase-field model which incorporates thermal noise of microscopic origin. As a non-trivial quantitative test of this model, we first show that the simulated fluctuation spectrum of a onedimensional interface in thermal equilibrium agrees with the exact sharp-interface spectrum up to an irrelevant short-wavelength cutoff comparable to the interface thickness. Simulations of dendritic growth are then carried out in two dimensions to compute sidebranching characteristics (root-meansquare amplitude and mean spacing between sidebranches) as a function of distance behind the tip. These quantities are found to be in good overall quantitative agreement with the predictions of the existing linear WKB theory of noise amplification. The extension of this study to three dimensions remains needed to determine the origin of noise in experiments.

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“…The result shows that the fitted parameter b equals 1.665, which is close to the theoretical value 5/3 predicted by the microsolvability approach for nonaxisymmetric dendritic growth. 32,33) As shown in Fig. 4, the power law fit is more accurate than the fourth-order polynomial fit.…”

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confidence: 92%

Numerical Simulation of Microstructure Evolution During Alloy Solidification by Using Cellular Automaton Method

et al. 2010

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This paper presents two and three dimensional cellular automaton (CA) based models and derived coupling models to simulate micro-scale microstructure evolution during alloy solidification. The models adopt a local solutal equilibrium approach to calculate the kinetics of the solid/liquid (SL) interface evolution, which allows the reasonable calculation of crystal growth from the initial unstable stage to the steady-state stage without the need of a kinetic parameter. Dendrite morphologies with various crystallographic orientations and well developed side branches in two and three dimensions can be successfully simulated by the proposed models. In conjunction with the lattice Boltzmann method (LBM), adopted for numerically solving fluid flow and solutal transport, a coupling model was derived to simulate the solutal dendrite growth in the presence of melt convection. The 2D model was extended to the multiphase system for the simulation of divorced eutectic solidification of spheroidal graphite (SG) cast iron. The quantitative capabilities of the models are addressed by comparing simulations to analytical predictions and experimental data.KEY WORDS: solidification; microstructure simulation; cellular automaton; lattice Boltzmann method. 1851© 2010 ISIJ Review and trapping rules for new interface cells. The quantitative capabilities of the model were well addressed by validation of the simulation results with experimental data and the Lipton-Glicksman-Kurz (LGK) theory.Lee and co-workers 14,15) developed a CA-FD model in which the growth velocity is also determined by solving the solute conservation equation subject to the boundary conditions at the SL interface. The model adopts a modified decentered-square growth algorithm to generate various crystallographic orientations. Recently, the model was further developed by incorporating the solution of the NavierStokes equations to simulate the dendritic solidification under natural and forced convection in two and three dimensions.16)The diffusion-controlled CA models [10][11][12][13][14][15][16] with the assumption of solute conservation at the moving SL interface mentioned above have the merit of allowing the simulation of dendrite growth without the need of introducing a kinetic coefficient. Since the condition of solute conservation is only satisfied for steady-state growth, those CA models fail to reasonably calculate the growth velocity of the interface points undergoing unstable growth.Building on an earlier meso-scale CA model, Zhu and Hong developed a micro-scale modified CA (MCA) model by incorporating the effects of the solute and the curvature undercoolings on the equilibrium temperature at the SL interface. The model was applied to simulate single and multi-dendritic growth in two and three dimensions, 17,18) non-dendritic and globular microstructures formed in semisolid process, 19) dendritic growth in the presence of forced melt convection, 20,21) and microstructure formation in regular and irregular eutectic alloys. 22,23) The model was also extended t...

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Noise-induced sidebranching in the three-dimensional nonaxisymmetric dendritic growth

Cited by 119 publications

References 13 publications

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

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

Phase-field model of dendritic sidebranching with thermal noise

Numerical Simulation of Microstructure Evolution During Alloy Solidification by Using Cellular Automaton Method

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