The rough or faceted morphology of the solid-liquid interface during solidification of multicrystalline silicon is discussed in terms of classical crystallographic, energetic and kinetic considerations. This allows establishing diagrams of the interface structure as a function of process parameters. It is shown that the grain-grain-liquid triple phase line structures determine quantitatively the direction of growth of the grain boundaries, then opening the door to the numerical modeling of the grain structure of photovoltaic silicon ingots as a function of growth conditions. (C) 2012 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved