Roughening transition and universality of single step growth models in (2+1)-dimensions

Abstract

We study (2+1)-dimensional single step model for crystal growth including both deposition and evaporation processes parametrized by a single control parameter p. Using extensive numerical simulations with a relatively high statistics, we estimate various interface exponents such as roughness, growth and dynamic exponents as well as various geometric and distribution exponents of height clusters and their boundaries (or iso-height lines) as function of p. We find that, in contrary to the general belief, there exists a critical value p 0.25 c » at which the model undergoes a roughening transition from a rough phase with p p c < in the Kardar-Parisi-Zhang universality to a smooth phase with p p c > , asymptotically in the Edwards-Wilkinson class. We validate our conclusion by estimating the effective roughness exponents and their extrapolation to the infinite-size limit.

Roughening transition as a driving factor in the formation of self-ordered one-dimensional nanostructures

“…the possibility of breakup into single nanoclusters with a total surface energy that is finally less than the initial energy of the nanowire. In our study, the abovementioned modification of the surface morphology of a quasi-one-dimensional nanosystem before breakup is associated with the development of roughening transition, which is known for two-dimensional systems [56][57][58][59][60][61][62][63][64][65][66].…”

Restructuring and breakup of nanowires with the diamond cubic crystal structure into nanoparticles

“…3d)notches created by the facets of [100]-types. The appearance of such surface modulations -the effects of surface roughening [41][42][43][44][45][46]65,69] -absolutely does not correspond to the classical model [39] for the instability under consideration. These notches may result in the nanowire breakup at high temperatures ( ~2.4), which is presented and discussed in the Supplementary Information (Figs.…”

“…The demonstrated dependence of the breakup scenarios on temperature shows the important role of the vapor of free atoms at all the stages of nanowire dynamics. The formation of short-wave modulations of the nanowire cross-section is due to the well-known effect of roughening transition [41][42][43][44][45][46] . The sign of this phenomenon is that the morphology of the flat interface of a crystal that is in equilibrium with its vapor dramatically transforms at a particular temperature, , followed by the appearance of steps, terraces, pits, and other structures.…”

“…Under such conditions, we associate the short-wavelength perturbations of the surface of considerable amplitude ( Fig. 1) with the well-known effect of the roughening transition [41][42][43][44][45][46][47] .…”

Universality and crossover behavior of single-step growth models in $1+1$ and $2+1$ dimensions

“…[16,17,[34][35][36]. However, some authors [18,37] found that there exists a critical value p c around which for p > p c the model consistently resembles p = 0.5…”