  Based on the Monte Carlo kinetic method, we investigated the formation
mechanisms of periodical modulations arising along the length of
one-dimensional structures. The evolution of initially cylindrical
nanowires/slabs at temperatures lower than their respective melting
temperatures can result either in breakup into single nanoclusters or in the
formation of stable states with pronounced modulations of cross section. Such
configurations, observed in a number of experiments, are excited at wavelengths
that are below the critical value for the development of classical Rayleigh
instability. We show that the modulation excited in the subcritical mode
corresponds to the appearance of roughening transition on the
quasi-one-dimensional surface of nanowires/slabs. Since the arise of roughening
transition is possible only on certain facets of metals with a given crystal
structure, the short-wavelength modulations of one-dimensional systems, as
shown in our work, can be realized (i) with the proper orientation of the
nanowire/slab axis providing spontaneous appearance of roughening transition on
its lateral surface, (ii) by the method of activating the surface diffusion of
atoms by external impact (irradiation with an electron beam or contact with a
cold plasma), which stimulates roughening transition without significant
heating of the nanowire. The results obtained for the cases of BCC and FCC
lattices can be used in the controlled synthesis of ordered one-dimensional
structures for use in optoelectronics and in ultra-large-scale integrated
circuits.
