APPLICATION OF THE CONCEPT OF BALLISTIC JUMPS TO MODELING OF ELONGATED NANOSTRUCTURES

Abstract

This paper proposes and theoretically substantiates a generalized approach to describing the processes of nucleation, formation, and structural evolution of anisotropic nanostructures in strongly nonequilibrium physicochemical systems. The concept is based on the idea of ballistic (non-thermal) atomic jumps arising under intense external воздействия. Two types of elementary events are distinguished: intracrystalline jumps leading to local lattice rearrangement, and forced detachment of atoms from surface layers of a crystal under external driving forces.

The model establishes a quantitative relationship between macroscopic system parameters and microscopic mechanisms governing the decomposition of supersaturated solutions, limited phase solubility, and the growth kinetics of elongated nano-objects. Under conditions of strong mechanical perturbation, anisotropic erosion of crystallographic facets becomes the dominant mechanism. This results in different detachment rates of structural units from various facets and, consequently, in the formation of high-aspect-ratio structures such as nanoribbons and nanobelts.

Within the developed phenomenological framework, a closed system of differential equations is formulated that accounts for the superposition of ballistic and thermal processes for each crystallographic facet. This makes it possible to model not only the evolution of average particle sizes but also the dynamics of their anisotropy and the transition from isotropic to directed growth.

The numerical integration scheme was improved by replacing the Euler method with the fourth-order Runge–Kutta method, which significantly enhanced computational accuracy and stability. The obtained results adequately describe the kinetics of particle growth, supersaturation dynamics, and asymptotic power-law behavior. The simulation results are in good agreement with experimental data: the formation of highly elongated nanobelts is confirmed, and an almost linear dependence of their average length on the stirring intensity of the medium is established. The proposed approach can be effectively applied to the theoretical analysis and optimization of synthesis conditions for anisotropic nanostructures.