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Effect of interface anisotropy on spacing selection in constrained dendrite growth
The selection of spacing in directional dendritic solidiﬁcation is investigated numerically using the phase-ﬁeld method in two and t dimensions. A criterion for the critical spacing below which no stable array growth can exist is derived from analysis of individual shapes. Constricted solute diffusion in the array leads to a deformation of the dendrite tip shape that competes with the deformation to surface tension anisotropy. At the critical spacing both eﬀects balance and a stable growth solution is destroyed. This mechanism identified to determine the critical spacing of a dendritic array and leads to a dependence of the spacing on the anisotropy of the so liquid interface energy in a similar way as for the dendrite tip radius.