This grant explores quantitative approaches to the analysis of small regions less than one nanometer in the scanning transmission electron microscope. In this renewal of the research the investigators continue their quantitative interpretation of microdiffraction data combined with recent advances in scanning transmission electron microscope. Nanocrystals, layered materials, and particle/network structures are subject to analysis by scanning transmission electron microscope techniques. Improved instrumentation and techniques for characterizing small particles and thin films should result as well as advancing understanding of the nature of catalysts.