From phase analysis to phase tracking: a robust approach to atomic-scale strain mapping

Abstract

Atomic-scale strain governs the electronic, ferroic and mechanical properties of materials, and atomic-resolution microscopy measures it most directly. Geometric phase analysis (GPA) is the standard tool, but it fails when a Bragg reflection moves outside its fixed Fourier aperture under large strain or rotation, or in misoriented grains. Here we introduce geometric phase tracking analysis (GPTA), whose Fourier aperture tracks the Bragg reflection at each pixel in real space. A narrow aperture can therefore reject noise without losing a displaced reflection. On 13,795 simulated and experimental atomic-resolution images under various imaging conditions, GPTA reduces GPA's failure rate from 27% to 11.5% with up to 335 times better accuracy. It also gives strain and dislocation maps across grains, resistance to dynamical-scattering extinction, and a confidence map, capabilities that GPA lacks. Tracking the aperture combines reciprocal-space dose efficiency with real-space spatial resolution and extends atomic-scale strain metrology to beam-sensitive materials and challenging imaging conditions.