Quantitative mapping of strain and displacement fields over HR-TEM and HR-STEM images of crystals with reference to a...

A method for the reciprocal space treatment of high-resolution transmission electron microscopy (HR-TEM) and high-resolution scanning transmission electron microscopy (HR-STEM) images has been developed. Named "Absolute strain" (AbStrain), it allows for quantification and mapping of interplanar distances and angles, displacement fields and strain tensor components with reference to a user-defined Bravais lattice and with their corrections from the image distortions specific to HR-TEM and HR-STEM imaging. We provide the corresponding mathematical formalism. AbStrain goes beyond the restriction of the existing method known as geometric phase analysis by enabling direct analysis of the area of interest without the need for reference lattice fringes of a similar crystal structure on the same field of view. In addition, for the case of a crystal composed of two or more types of atoms, each with its own sub-structure constraint, we developed a method named "Relative displacement" for extracting sub-lattice fringes associated to one type of atom and measuring atomic columns displacements associated to each sub-structure with reference to a Bravais lattice or to another sub-structure. The successful application of AbStrain and Relative displacement to HR-STEM images of functional oxide ferroelectric heterostructures is demonstrated.