Analytical description of nanowires III: regular cross sections for wurtzite structures

Setting out from König & Smith [ Acta Cryst. (2019), B75, 788–802; Acta Cryst. (2021), B77, 861], we present an analytic description of nominal wurtzite-struc­ture nanowire (NWire) cross sections, focusing on the underlying geo­metric–crystallographic description and on the associated number theory. For NWires with diameter d (Wire)[i], we predict the number of NWire atoms N (Wire)[i], the bonds between these N (bnd)[i] and NWire interface bonds N (IF)[i] for a slab of unit-cell length, along with basic geometric variables, such as the specific length of interface facets, as well as widths, heights and total area of the cross section. These areas, the ratios of internal bonds per NWire atom, of internal-to-interface bonds and of interface bonds per NWire atom present fundamental tools to interpret any spectroscopic data which depend on the diameter and cross section shape of NWires. Our work paves the way for a fourth publication which – in analogy to König & Smith [ Acta Cryst. (2022). B78, 643–664] – will provide adaptive number series to allow for arbitrary morphing of nominal w-structure NWire cross sections treated herein.