Abstract
The link between changes in the material crystal structure and its mechanical, electronic, magnetic, and optical functionalities – known as the structure-property relationship – is the cornerstone of the contemporary materials science research. The recent advances in scanning transmission electron and scanning probe microscopies (STEM and SPM) have opened an unprecedented path towards examining the materials structure–property relationships on the single-impurity and atomic-configuration levels. Lacking, however, are the statistics-based approaches for cross-correlation of structure and property variables obtained in different information channels of the STEM and SPM experiments. Here we have designed an approach based on a combination of sliding window Fast Fourier Transform, Pearson correlation matrix, linear and kernel canonical correlation, to study a relationship between lattice distortions and electron scattering from the SPM data on graphene with defects. Our analysis revealed that the strength of coupling to strain is altered between different scattering channels which can explain coexistence of several quasiparticle interference patterns in the nanoscale regions of interest. In addition, the application of the kernel functions allowed us extracting a non-linear component of the relationship between the lattice strain and scattering intensity in graphene. The outlined approach can be further utilized to analyzing correlations in various multi-modal imaging techniques where the information of interest is spatially distributed and has usually a complex multidimensional nature.
