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The vacancy mechanism is simulated by means of Monte Carlo (MC) method. In this model, the impurity diffusion occurs by migration of substitutional atoms B via the exchange with vacancies whose frequencies near a solute atom differ from a free vacancy. Whenever a defect leaves the lattice, periodic boundary conditions are made to bring it into the lattice. The solute concentration profiles are given using a technique developed by Murch which has been shown to be equivalent to a finite source. The fit of these profiles allows the comparison between our results and analytical solutions. The parameters extracted from a Gaussian function fit which agrees well with numerical profiles are in very good quantitative agreement with theoretical predictions.

Within the limits of the uniform approach with the assistance of the vacancy mechanism the description of melting and surface roughening of both free nanoparticles and nanoparticles deposited on the surface of solid body under conditions of thermodynamic equilibrium is offered. Surface roughening of a spherical particle is represented as a phase transition in vacancy subsystem, in which supersaturation is formed by reducing the particle size. It is shown that interaction between vacancies result in to the unification of vacancies on a surface in vacancy clusters, that can be regarded as the appearance of a surface roughness of nanoparticles. It is shown that increasing concentration of vacancies caused by the modification of effective vacancy formation energy with decreasing sizes of nanoparticles result into a modification of shear modulus of material. By vanishing the shear modulus (Born criteria of melting) the dependence of temperature of fusion of nanoparticles of different metals on radius was determined.