Nanoscale waviness of low-angle grain boundaries

Low-angle grain boundaries (LAGBs) are ubiquitous in natural and man-made materials and profoundly affect many of their mechanical, chemical, and electrical properties. The properties of LAGBs are understood in terms of their constituent dislocations that accommodate the small misorientations between grains. Discrete dislocations result in a heterogeneous local structure along the boundary. In this article, we report the lattice rotation across a LAGB in olivine (Mg_1.8Fe_0.2SiO₄) measured at the nanometer scale by using quantitative high-resolution transmission electron microscopy. The analysis reveals a grain boundary that is corrugated. Elastic calculations show that this waviness is independent of the host material and thus a general feature of LAGBs. Based on our observations and analysis, we provide equations for the boundary position, local curvature, and the lattice rotation field for any LAGB. These results provide the basis for a reexamination of grain-boundary properties in materials such as high-temperature superconductors, nanocrystalline materials, and naturally deformed minerals.