Optimum Cross‐Sections for Wurtzite‐Structure Nanowires From Analytic Thermodynamic and Crystallographic Arguments

Crystalline nanowire (NWire) cross‐section shapes are known to vary considerably in experiment; an accurate analytic evaluation of NWire cross‐sections from a thermodynamic perspective is still missing. Building on previous work, analytic descriptions are given for wurtzite (w) NWire cross‐section morphing to arbitrary convex hexagonal shapes in order to evaluate the crystallographic‐structural stability of experimental NWire cross‐sections. The maximum of the ratio of NWire‐internal bonds per NWire atom describes the most stable crystallographic and thermodynamic shape of the NWire as far as internal forces are concerned. This maximum occurs when the first derivative of the above ratio , with presenting respective optimum morphing indices to obtain . The stability evaluation is then carried out by comparing derived from the experimental image over the complete morphing range of the NWire cross‐section represented by . This user‐friendly analytic approach allows to calculate the optimum morphing indices and thus all follow‐on parameters, such as , , the number of interface bonds and the NWire cross‐section area . The normalization of analytic results enables a direct comparison of cross‐sections with different shape, size, and even material. General results of the analytic decriptions explain the preferred growth of w‐NWires with growth vector and six facets by their highest ratio for the same cross‐section area of all three NWire types considered. Examples with experimental data demonstrate the versatility and detailed insight the stability evaluation provides to any w‐lattice NWire cross‐section.