Krasnoshlyk N. Mathematical modeling of the motion of interphase boundaries under the condition of interdiffusion in binary systems

The object of the research is the processes of growth/inhibition of intermediate phases during interdiffusion in binary metallic systems. The aim of the thesis is the creation and computer realization of mathematical models of the motion of interphase boundaries under the condition of interdiffusion in binary systems taking into consideration partial molar volumes of components and conducting of a numerical study of competition phases in multiphase metal alloys to predict their properties. In order to solve the tasks methods of mathematical modeling, numerical methods for solving systems of nonlinear equations and partial differential equations and the theory of diffusion in metals and alloys were used. Scientific novelty of the results is: 1. For the first time a two-dimensional mesoscopic model of diffusion competition phases taking into consideration partial molar volumes of the components is developed, in which phases have the appearance of inclusions of arbitrary shape, that allowed to conduct a computer simulation of the process of manufacturing a superconductor by bronze technique to determine the factors that contribute to the growth of needed phase. 2. One-dimensional mathematical models of the interdiffusion in binary multiphase metal systems were improved by taking into account the difference of the partial molar volumes of components, making it possible to predict the phase composition of alloys more accurately in the presence of thermal effects during their processing or exploitation. 3. The method of modeling the evolution of the interfaces boundary in the two-dimensional region through the construction of two-dimensional problem to a set of one-dimensional problems with moving boundaries has been further developed, which allowed to extend the class of tasks and build quasi-model of diffusion interaction in binary metallic systems for numerical study of the movement of the interfaces boundary of complex form when a metal coating applied on a solid substrate. The practical significance of the results of the research is to develop computational algorithms for the implementation of the proposed models which are used to create software for simulation of growth/inhibition of intermediate phases in arbitrary metallic systems during their thermal or thermochemical treatment and it is confirmed by the acts of introduction. The results can be used to solve a wide range of problems to determine the optimal composition and to predict properties of metallic alloys, which will become the basis for system management and control of technological processes of their obtaining.