A general approach to quantify the uncertainty of interdiffusion coefficients in binary, ternary and multicomponent systems evaluated using Matano-based methods

Abstract

In this paper, we developed a general approach to quantify the uncertainties of interdiffusion coefficients in binary, ternary and multicomponent systems evaluated using the Boltzmann-Matano and related other methods together with the distribution functions. Various sources of errors from both experimental and calculation procedures and their propagation were fully considered and quantified in the finally obtained interdiffusion coefficients. Benchmark tests in hypothetical binary systems with three types of the preset D-c relations and three noise levels were utilized to validate the presently proposed approach, which was then successfully applied in the practical binary, ternary and high-entropy alloys. The comprehensive comparison between the presently calculated interdiffusivities in different alloys with the literature data indicated that the integration of Matano-based methods, the distribution function and the present approach represents a general ensemble solution for evaluation of the reliable interdiffusion coefficients and their uncertainties. Further discussion indicates that the accurate interdiffusion coefficients with reliable uncertainty are the “cornerstone” for the subsequent analysis on diffusion properties, i.e., the sluggish diffusion in high-entropy alloys, and the development of high-quality atomic mobility databases, and the impurity diffusion coefficients with uncertainties can be directly retrieved from the evaluated composition-dependent binary interdiffusion coefficients.