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The application of Martin's ideas about ballistic elementary events (jumping inside a crystal or atoms detachment from a crystal) to decomposition, to limited solubility, as well as to the growth of strongly anisotropic structures in strongly nonequilibrium systems under the influence of intense external factors is considered. The essence of these ideas is that external influences on the system force atoms to make jumps and exchange places in the sites of the crystal lattice. The frequency of such "ballistic" jumps (as the antithesis to "thermal" jumps that are associated with thermal fluctuations at a given temperature) doesn`t depend on temperature, but depends on the intensity of external action (say, the radiation flux density and energy of particles). These ideas had been first introduced for irradiated systems, but later applied to ball milling, to severe plastic deformation, of course, taking into account the grinding of grains. In this paper, we consider the application of Martin's ideas to two phenomena:
(1) nucleation, growth and ripening of nanofibers and nanobands of metal oxides in aqueous solutions under the action of intensive stirring,
(2) formation- of solid solutions and intermediate phases of metals in the contact zone by pulsed action.
The time evolution of an ensemble of three-dimensional parallelepipeds is being considered in the first part of the present article. For this purpose, we derived a system of differential equations for the rate of change of each size, taking into account the balance of attachment and detachment fluxes. Based on the solutions of these equations, the asymptotic values of the growth rates of average sizes can be predicted. Graphs of dependences of average sizes on time for different intensities of mixing for a symmetric case are presented.
The application of the idea of ballistic jumps to phase formation with impulse action on diffusion pairs is being briefly considered in the second part. The influence of external action on the solubility of components for the simplest (mathematically) case is analyzed.
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