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 three dimensions. A criterion for the critical spacing below which no stable array growth can exist is derived from analysis of individual tip shapes. Constricted solute diffusion in the array leads to a deformation of the dendrite tip shape that competes with the deformation due to surface tension anisotropy. At the critical spacing both effects balance and a stable growth solution is destroyed. This mechanism is identified to determine the critical spacing of a dendritic array and leads to a dependence of the spacing on the anisotropy of the solid–liquid interface energy in a similar way as for the dendrite tip radius.