Non-equilibrium thermodynamics model for calculating diffusion fluxes under phase transformations in alloy steels

The phase transformations in alloyed iron-carbon alloys is largely related to diffusion of components, foremost to the carbon. For the analysis of diffusive processes in alloy steels, it is possible to use the mathematical methods of non-equilibrium thermodynamics. The equation for the diffusive fluxes of the system contains unknown in general case of coefficients activity of elements and vacancies, and their derivatives for to the concentrations, that extraordinarily makes it difficult being of values of cross coefficients. In the article a non-equilibrium thermodynamics methodology of calculation of diffusive fluxes at presence of two phases in alloy steels is described. It allows one to calculate both direct- and cross coefficients in the Onsager equations. Formulas for calculation of thermodynamics forces in the alloy steel – for iron, alloying element of substitution – chrome, of element of introduction – carbon and vacancies, are presented. Common expressions are suggested for calculation of cross-factors, motive forces and fluxes in the Onsager’s equations for a multicomponent thermodynamic system. The example of using the developed model to find changes in concentrations and diffusion fluxes over time is given. For the model system used, it was established that at the stage of predominant diffusion of carbon in the alloy steel, cementite inclusions with a size of about 18 nm are formed rather quickly (within ~ 200 s). The technique developed in the article allows one to perform diffusion kinetics calculations in multicomponent thermodynamic systems, which are also iron-carbon alloys and to control the size of the phases formed, for example, of carbide nanoparticles.