Abstract

Over the years, geometric phase analysis of HR(S)TEM images has become a widely used technique for strain mapping. Whilst successful, the approach is not without limitations. An internal reference of undisturbed crystal must be present within the field of view and the regions of crystal to be analysed must have common, or closely related, reciprocal lattice vectors. Even in the presence of an internal reference, elastic strains should be determined relative to the relaxed crystal structure, which is not necessarily the same as the reference used for the analysis. Here, we present a major extension of GPA that addresses these problems. It allows the study of strain in nanocrystals, where no reference region is generally present, in epitaxial heterostructures, where the materials can be very different from the substrate, and across grain boundaries, where no common lattice planes in general exist. The new theory is based on adding crystallographic information to the analysis. In so doing, the reference problem, large lattice rotations and global optical distortions can be dealt with. It is little known, for example, that a global shear applied to an image will cause errors to conventional strain analysis. We apply the method to some representative examples and highlight the implications for other strain mapping techniques based on images or diffraction.