Is Crystal Growth under Low Supersaturations Influenced by a Tendency to a Minimum of the Surface-Free Energy?
The long-standing problem of face morphology is discussed. Special emphasis is put on macroscopically flat faces, whose growth, under low supersaturations, is driven by dislocations possessing some screw component. The most general case, where the crystal face is pierced by more than one screw dislocation, is considered.If performed under sufficiently low supersaturation, the growth leads to the formation of the face morphology corresponding to the minimum of the surface-free energy. The thermodynamic driving force for face flattening is the difference in the surface-free energy of the vicinal faces of the hillocks (emanating from screw dislocations) and that of a singular face, which can truncate the valley between the growth hillocks. The hillock slope gives the quantitative relation between energetics and kinetics. The result of the considerations is that the lower the supersaturation, the more important is the role of the surface-free energy in face flattening. Another factor, particularly under sufficiently low supersaturations, is the effective increase in the local supersaturation at the valley separating two growth hillocks. The reason is that the dislocation strain energy vanishes there. (This is most evident when two dislocations of opposite sign are considered.) Besides, the valley floors are concave regions on the crystal surface, where the building blocks are bound more strongly. Thus, the kinetic reason for face flattening is the relative preference for incorporation of atoms, arriving from the ambient phase, at the valley floor. Note that accelerated step annihilation in the valley floor should be a universal factor, which favors face flattening under any supersaturation. The amount of flattening in the growth situation is determined by the interplay between supersaturation and thermodynamics
growth of a flat crystal face surface energy reasons kinetically determined stabilization factors