Selection of doublet cellular patterns in directional solidification through spatially periodic perturbations

Abstract

Pattern formation at the solid-liquid interface of a growing crystal was studied in directional solidification using a perturbation technique. We analyzed both experimentally and numerically the stability range and dynamical selection of cellular arrays of ''doublets'' with asymmetric tip shapes, separated by alternate deep and shallow grooves. Applying an initial periodic perturbation of arbitrary wavelength to the unstable planar interface allowed us to force the interface to evolve into doublet states that would not otherwise be dynamically accessible from a planar interface. We determined systematically the ranges of wavelength corresponding to stable singlets, stable doublets, and transient unstable patterns. Experimentally, this was accomplished by applying a brief UV light pulse of a desired spatial periodicity to the planar interface during the planar-cellular transient using the model alloy Succinonitrile-Coumarin 152. Numerical simulations of the nonlinear evolution of the interface were performed starting from a small sinusoidal perturbation of the steady-state planar interface. These simulations were carried out using a computationally efficient phase-field symmetric model of directional solidification with recently reformulated asymptotics and vanishing kinetics ͓A. Karma and W.-J. Rappel, Phys. Rev. E 53 R3017 ͑1996͒; Phys. Rev. Lett. 77, 4050 ͑1996͒; Phys. Rev. E 57, 4323 ͑1998͔͒, which allowed us to simulate spatially extended arrays that can be meaningfully compared to experiments. Simulations and experiments show remarkable qualitative agreement in the dynamic evolution, steady-state structure, and instability mechanisms of doublet cellular arrays.

Experimental observation of oscillatory cellular patterns in three-dimensional directional solidification

“…Beyond the oscillatory modes described here, those experiments provided a large variety of results, covering a large number of topics. Ongoing investigations include the formation of multiplets, another secondary instability of the cellular pattern, previously predicted by numerical simulation and described in thin samples [49][50][51][52]; as well as the dynamical selection of the primary spacing. Furthermore, 3D experiments were found to introduce additional unavoidable deviations from ideal models of solidification, which are negligible or controllable in thin samples, and which affect the microstructure characteristics and dynamics.…”

Groove oscillation of the doublon structure in the phase-field model

“…They confirmed that doublon patterns appear in experimental conditions of the low anisotropy and the high supercooling. Losert et al investigated the stability of doublon structures, changing the strength of fluctuations in an experiment of the directional solidification and a numerical simulation of the phase-field model [3]. The doublon patterns were also found in an experiment of a drying water film [4].…”

“…The groove oscillation does not decay in a very narrow parameter range. Different types of groove oscillations were found in numerical simulations of a directional solidification [3] and eutectic alloys [16]. In this paper, we investigate the groove oscillation more in detail, changing the anisotropy parameter.…”

Phase-field model for multicomponent alloy solidification

“…By using the singular perturbation method [6], Caginalp [7] proved that the phase-field model could be reduced to the Stefan problem in the limit that the thickness of the interface approaches zero and Kobayashi [8] studied the dendritic growth of a pure melt by using the phase-field model for pure materials. The models which were proposed for simulating dendritic growth in pure undercooled melt [8][9][10][11][12][13] have been extended to modeling of binary alloy solidification [14][15][16][17][18][19][20][21][22][23] and recently multicomponent alloy solidification [24].…”