Numerical Simulations of Locked Lamellar Eutectic Growth Patterns

Abstract

We present two-dimensional numerical simulations of tilted lamellar growth patterns during directional solidification of nonfaceted binary eutectic alloys in the presence of an anisotropy of the free energy γ of the interphase boundaries in the solid. We used a dynamic boundary-integral (BI) method. The physical parameters were those of the transparent eutectic CBr 4 -C 2 Cl 6 alloy. As in Ghosh et al. [Phys. Rev. E 91, 022407 (2015)], the anisotropy of γ was described by a model function with tunable parameters. The lamellarlocking effect in the vicinity of a deep minimum of the interfacial energy was reproduced. For a weak anisotropy, the lamellar tilt angle θ t was shown to depend on the growth conditions. We systematically studied the influence of usual control parameters (pulling velocity, temperature gradient, lamellar spacing, alloy concentration) on the tilted-lamellar pattern. We identified experimentally accessible conditions under which θ t falls close to the theoretical prediction based on the so-called symmetric-pattern approximation. We finally simulated locked and weakly locked lamellar patterns and found empirically a good morphological matching with experimental observations during directional solidification of thin CBr 4 -C 2 Cl 6 samples.

Gabriel Faivre: his legacy on eutectic solidification

“…The contribution of Gabriel Faivre to this analysis was determining. The qualitative relevance of the sp-approximation was confirmed numerically [48] (also see [49] and refs. therein).…”

Asymptotic Solutions of Steady Lamellar Eutectic Growth in Directional Solidification for Small Tangent Values of the Contact Angles

“…The evolution of eutectic solid-liquid interfacial morphology and its growth stability have become important topics of concern for researchers. Among these theories, many results have been presented using numerical calculation methods [9][10][11][12][13][14][15][16][17][18][19][20]. Liu et al [9] showed that the steady growth of lamellar eutectics had a limited range of spacings by using the boundary element method and an iterative technique.…”

“…Tu et al [16] studied the lamellar growth with solid-solid boundary anisotropy in directional solidification calculated using the phase-field method. Akamatsu et al [17] presented twodimensional numerical simulations of tilted lamellar growth in directional solidification of nonfaceted binary eutectic alloys by using a dynamic boundary-integral method. Ogawa et al [18] developed a multiphase cellular automaton model for eutectic solidification.…”

Global Instability of Rod Eutectic Growth in Directional Solidification

“…Generally, regular eutectic mainly includes a lamellar eutectic and a rod eutectic. Most of the theories and experiments on eutectic growth are focused on the two-dimensional lamellar eutectic growth [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19], while there are few reports on the three-dimensional rod eutectic [20][21][22][23][24][25][26][27][28][29][30][31][32][33]. For the growth of the three-dimensional rod eutectic, three-dimensional dimensions such as rod cross-sectional morphology (round, oval, peanut, etc.)…”