Energetic instability of polygonal micro- and nanowires

Micro- and nanowires are commonly used in biological sciences, micro- and nanoelectronics, and optoelectronics, and their morphological stability needs to be understood and controlled. Previous linear-stability analyses of infinitely-long circular wires have shown that the critical wavelength for instability approaches infinity if the wire surface is facetted. Thus, Rayleigh's instability is suppressed in finite facetted circular wires and possibly in finite facetted polygonal wires. This work studies the energetic stability of long facetted regular-polygonal and rectangular wires that are not in thermodynamic equilibrium. The long wire is assumed to break up into N identical equilibrium crystals with the same cross-sectional shape as the wire. The length of the wire is N lambda and that of the crystal is L. The surface energy of the system is found to decrease after breakup if lambda/L > 9/4 -2/3N + ... for N >> 1. This instability criterion holds for regular-polygonal wires of arbitrary sides and for rectangular wires of arbitrary aspect ratios. The criterion also applies to infinitely long equilibrium wires if N is set to infinity. Previous experimental studies of pore channels in sapphire have revealed that the facetted channels break up not by Rayleigh's instability, but by tip shedding. The observed crystal separation to length ratio agrees with the above instability criterion. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4717709]