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 θ_t with respect to the temperature gradient axis. θ_t 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, θ_t 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.