Edge-to-edge matching—The fundamentals

The basis of the present authors’ edge-to-edge matching model for understanding the crystallography of partially coherent precipitates is the minimization of the energy of the interface between the two phases. For relatively simple crystal structures, this energy minimization occurs when close-packed, or relatively close-packed, rows of atoms match across the interface. Hence, the fundamental principle behind edge-to-edge matching is that the directions in each phase that correspond to the “edges” of the planes that meet in the interface should be close-packed, or relatively close-packed, rows of atoms. A few of the recently reported examples of what is termed “edge-to-edge matching” appear to ignore this fundamental principle. By comparing theoretical predictions with available experimental data, this article will explore the validity of this critical atom-row coincidence condition, in situations where the two phases have simple crystal structures and in those where the precipitate has a more complex structure.