  Our quest to design materials often envisions as a first step the conceptual
decomposition of a material into meaningful atomic scale neighborhoods. The
performance of the monolithic material is then seen to arise from the combined
properties of these much simpler regions. It is the nearsightedness of
electronic matter (NEM) principle that provides the rigorous justification for
this "divide and conquer" approach. NEM asserts that a material property may be
significantly affected by a perturbation, no matter how large, only over a
neighborhood of size $R$. Though NEM posits the existence of meaningful atomic
scale neighborhoods, for the most part these regions are identified
empirically. In this paper we propose a methodology to divide real materials
into meaningful neighborhoods determined by the topology of the charge density.
We generalize this approach by applying the same to determine neighborhoods
representative of elemental crystalline materials and then use these
neighborhoods to model the embrittling effects of bismuth atoms segregated to
copper grain boundaries. We show that embrittlement is the result of impurity
atom-induced enhancements of copper nearsightedness. We further suggest that
just as nearsightedness plays an overlooked role mediating embrittlement, it
may also be an important factor affecting a broad range of unresolved problems
as apparently diverse as energy focussing phenomena and enzyme kinetics.
