Influence of morphological instability on grain boundary trajectory during directional solidification

The interplay between the diffusion-controlled dynamics of a solidification front and the trajectory of a grain boundary groove at the solid-liquid interface is studied by means of thin-sample directional solidification experiments of a transparent alloy, and by numerical simulations with the phase-field method in two dimensions. We find that low-angle grain boundaries (subboundaries) with an anisotropic interfacial free energy grow tilted at an angle θt with respect to the temperature gradient axis. θt remains essentially equal to its value imposed at equilibrium as long as the solidification velocity V remains low. When V increases and approaches the cellular instability threshold, θt decreases, and eventually vanishes when a steady-state cellular morphology forms. The absence of mobility of the subboundary in the solid is key to this transition. These findings are in good agreement with a recent linear-stability analysis of the problem.