Progress in high-resolution electron and probe based, real space imaging techniques like (Scanning) Transmission Electron Microscopy (STEM) and Scanning Probe Microscopy (SPM) has consistently delivered imaging of atomic columns and surface atomic structures with ever growing precision. As the instruments evolve, the basic data processing principle - analysis of structure factor, or essentially a two point correlation function averaged over probing volume ï¿½ remains invariant since the days of Bragg. We propose a multivariate statistics based approach to analyze the coordination spheres of individual atoms to reveal preferential structures and symmetries.
The underlying mechanism is that for each atom, i, on the lattice site with indices (l, m), we construct a near coordination sphere vector , where is the radius-vector to j/2-th nearest neighbor. Once the set of Ni vectors is assembled, it is analyzed though cluster analysis and other multivariate methods to reveal and extract regions of symmetry, distortions, different phases, boundaries, defects, etc., that can be back projected on the atomically mapped surface. Results are presented on various model and real material systems including La0.7Sr0.3MnO3, BiFeO3, LaCoO3 and discussed in light of physical parameter extraction.
Research for (AB, QH, AB, SJ, SVK) was supported by the US Department of Energy, Basic Energy Sciences, Materials Sciences and Engineering Division. Research was conducted at the Institute for Functional Imaging of Materials and Center for Nanophase Materials Sciences, which is sponsored at Oak Ridge National Laboratory by the Scientific User Facilities Division, Office of Basic Energy Sciences, US Department of Energy.