Abstract
Diffusion couple technique in combination with the Boltzmann-Matano method is the widely used approach to evaluate the interdiffusion coefficients in the target systems. However, the quality of the evaluated interdiffusion coefficients due to the Boltzmann-Matano method strongly depends on the fitting degree of the utilized continuous function to the discrete experimental composition profiles. In this paper, the application of different types of distribution functions is proposed to solve this problem. For the simple D-c relations, the normal, pseudo-normal, skew normal, pseudo-skew normal distributions can be employed, while for the complex D-c relations, the superposed distributions should be used. Even for the cases with uphill diffusion, the combined superposition of distributions may be chosen. Through validation in several benchmarks and real alloy systems, accurate diffusion coefficients are proved to be successfully obtained by using the distribution functions. It is anticipated that the Boltzmann-Matano method together with the distribution functions may serve as the general solution for determining the accurate interdiffusion coefficients in different materials.
Highlights
Diffusion plays an important role in a variety of disciplines[1,2,3,4]
In order to utilize the Boltzmann-Matano method for calculation of the interdiffusion coefficients, the discrete experimental composition-distance (c-x) data should be always fitted by a continuous curve firstly[19], from which the interdiffusion flux and slope of composition curve can be evaluated
Though the distribution functions have been widely investigated by many mathematical researchers[26,27,28,29,30,31], they focused on the profiles of the probability distribution functions (PDFs)
Summary
Diffusion plays an important role in a variety of disciplines[1,2,3,4]. Accurate diffusion coefficient, as one of the basic physical properties, is the prerequisite for quantitative description and comprehensive understanding of various phase transformation processes[5,6,7]. The mostly used experimental technique for interdiffusivity measurement is the semi-infinite single-phase diffusion couple together with some calculation approaches, like the traditional famous Boltzmann-Matano (B-M) method and its variants[15,16,17,18,19]. In order to utilize the Boltzmann-Matano method for calculation of the interdiffusion coefficients, the discrete experimental composition-distance (c-x) data should be always fitted by a continuous curve firstly[19], from which the interdiffusion flux and slope of composition curve can be evaluated. In order to evaluate the accurate interdiffusion coefficients via the Boltzmann-Matano method based on the discrete experimental data, the best fitting function should be chosen. Because a variety of CDFs, including the classic normal distribution, skew normal distribution, and more complex ones, like pseudo-normal distribution and pseudo-skew normal distribution, are available for choices, the much more
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