In this paper, we studied the macro-morphology and micro-structure of crystal-molt interfaces, which was exposed by rapid separating the growing crystal from the melt. We have determined the indices of the facets revealed on the interface of Czochralski-pulled YAG single crystals with various orientations. The facets have been discovered on the concave interface as well as on convex interface of -oriented grown YAG single crystals. We have observed the micro-structure of vicinal interface, which is composed of sections of singular surface dispersed with steps. The experimental evidence for the step movement as well as the interaction of steps with inclusions on these interfaces is presented.The micro-structure of the interfaces and the correspondence between the facets and the core for concave interface growth are discussed, and it is implied that the macro-shapes of interface influence the micro-mechanism of growth. The growth mechanism for concave and convex interfaces based on these considerations is then developed.