Atomic-scale evidence for continuous surface dislocations in crystalline interfaces

Abstract

In interfacial dislocation theory, misfit dislocations are conventionally perceived only as discrete arrays, derivable from the quantized Frank-Bilby equation (FBE), largely because experiments and atomistic simulations can usually resolve only well-separated, discrete dislocations. Consequently, Bilby’s surface dislocations, i.e., continuous misfit-dislocation distributions, have long been considered purely mathematical constructs, rather than a physically identifiable defect state. Here, we combine atomistic simulations with a high-resolution Nye-tensor-based analysis to examine misfit accommodation in twist grain boundaries over a broad range of twist angles. Two FBE-compliant misfit dislocation arrays are tracked simultaneously. With increasing twist angle, the smaller-spacing array gradually loses atomic resolvability and evolves into a continuous distribution, whereas the larger-spacing array remains discrete. At the critical transition, the resolvable array still obeys the FBE, and the grain boundary remains free of long-range stress, implying that the unresolved component must persist as a continuous dislocation distribution. The grain boundary energy and sliding resistance vary smoothly across the transition, indicating that this continuous distribution is thermodynamically stable and mechanically active. These results provide strong atomic-scale support for Bilby’s surface-dislocation concept, establish the physical significance of continuous interfacial dislocation distributions, and unify discrete and continuous descriptions of crystalline interfaces within a single Frank-Bilby framework.