  Analysis of nanoscale short-range chemical and/or structural order via
(scanning) transmission electron microscopy (S/TEM) imaging is fundamentally
limited by projection of the three dimensional sample, which averages
informational along the beam direction. Extracting statistically significant
spatial correlations between the structure and chemistry determined from these
two-dimensional datasets thus remains challenging. Here, we apply methods
commonly used in Geographic Information Systems (GIS) to determine the spatial
correlation between measures of local chemistry and structure from
atomic-resolution STEM imaging of a compositionally complex relaxor,
Pb(Mg$_{1/3}$Nb$_{2/3}$)O$_{3}$ (PMN). The approach is used to determine the
type of ordering present and to quantify the spatial variation of chemical
order, oxygen octahedral distortions, and oxygen octahedral tilts. The extent
of autocorrelation and inter-feature correlation among these short-range
ordered regions are then evaluated through a spatial covariance analysis,
showing correlation as a function of distance. The results demonstrate that
integrating GIS tools for analyzing microscopy datasets can serve to unravel
subtle relationships among chemical and structural features in complex
materials that can be hidden when ignoring their spatial distributions.
