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Semiconductor nanowires (NWires) experience stress and charge transfer bytheir environment and impurity atoms. In return, the environment of NWiresexperiences a NWire stress response which may lead to propagated strain andchange in shape and size of NWire cross sections. We deduce geometrical numberseries for zinc-blende- (zb-) and diamond-lattice NWires of diameter$d_{\mathrm{Wire}}$ to obtain the number of NWire atoms$N_{\mathrm{Wire}}(d_{\mathrm{Wire}}[i])$, bonds between NWire atoms$N\mathrm{_{bnd}}(d_{\mathrm{Wire}}[i])$ and interface bonds$N\mathrm{_{IF}}(d_{\mathrm{Wire}}[i])$ for six high symmetry zb NWires withlow-index faceting frequently ocurring in bottom-up and top-down approaches ofNWire processing. Along with these primary parameters, we present specificlength of interface facets, cross section widths and heights as well as thecross section area. The fundamental insights into NWire structures revealedhere offer a universal gauge and thus enable major advancements in datainterpretation and understanding of all zb- and diamond-lattice based NWires.We underpin this statement with results from the literature on cross-sectionimages from III-V core-shell NWire growth and on Si-NWires undergoingself-limiting oxidation and etching. The massive breakdown of impurity dopingdue to self-purification is shown to occur for both, Si NWires and Sinanocrystals (NCs) for a ratio of$N\mathrm{_{bnd}}/N_{\mathrm{Wire}}=1.94\pm0.01$ using published experimentaldata.

Analytic Description of Cross Sections for Regular Forms of Zincblende- and Diamond-Lattice Nanowires