Periodicity at crystalline interfaces

Abstract

When two parts O and S of a crystal do not match at an interface, due either to slip or to lattice misfit, periodic interfacial forces—a major topic of this essay—come into play to act on interfacial atoms. Their displacement is opposed by the half crystals hosting them. The following non-inclusive aspects of such interfaces are briefly reviewed: (i) A reciprocal space construction of appropriate Fourier representations (including struc-ture factors) to model the periodicity, (ii) proximity modified elastic constants of ultrathin films to model the resistance to atomic displacements, (iii) predictions of the governing equations involving these competing forces in epitaxy, dynamics of, and phase transitions in adsorbed layers, and the formation of new phases in certain low concentration alloys, some with irrational boundaries. A meaningful assessment of the consequences requires quan-tification of optimum Fourier coefficients and proximity modified elastic constants. An epitaxy criterion based on interfacial energy minimization by in-plane and edge-to-edge row matching is summarized, as are critical misfits and thicknesses for sustaining epilayer coherency, and interfacial energies that favour layer-by-layer growth, both strongly driven by large Fourier coefficients (i.e. deep potential valleys), and their impact on technology. Predictions of the Peierls (-Nabarro) model of dislocations in macroscopic crystals are noted; as are predictions in which Nabarro was a major role player, e.g. in estimating the Peierls force; an important resistive force to dislocation motion and nucleation; and an extension of the model to describe interfaces at interphase boundaries, as well as twist and tilt boundaries in bulk crystals.