The elastic contribution to ledge growth on coherent interfaces in the system of a cube-shaped γ′ precipitate in nickel alloys. Part II: The elastic energy

The elastic energy of ordered arrays of ledges on the coherent planar face of a γ́ precipitate in nickel alloys was calculated as a function of the lateral growth of the ledges. This energy is separated into three components: the self energy of the ledges, the interaction among ledges and the interaction of the ledges with the underlying cube-shaped precipitate. The interaction between the cube and the ledges is always repulsive. The self energy of the ledges and the interaction among ledges decreases with a decrease in their height to width ratio. In the interplay between these two energies, the interaction energies may greatly reduce the elastic energy of the system, overwhelming the increase in the self energy. Hence the interaction among ledges generates a tendency for ordering of the ledges, favoring the formation of high and densely spaced ledges. Too dense arrays are prohibited, however, by the self energy of the ledges and an optimum spacing between ledges exists.