Application of distribution functions in accurate determination of interdiffusion coefficients

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.

Determination of interdiffusion coefficients of Si and Al in Ti3SiC2–Ti3AlC2 diffusion couple at 1373‐1673 K

“…In other words, the accuracy of the calculated interdiffusion coefficients is dependent on the fitting function used as well. In this work, to minimize the fitting errors, the c ‐ x profiles obtained experimentally by EPMA analysis were fitted using a Boltzmann function and cumulative distribution function (CDF), respectively . The expressions of these two adopted functions are given as follows:…”

“…In the expression of either B-M method or S-F method (Equation 1 or 4), the concentration gradient dc/dx should be determined accurately prior to the calculation of diffusion coefficient. Therefore, the discrete experimental data of c-x profile (commonly obtained by EPMA) is always fitted as a continuous curve firstly, 33 from which the interdiffusion flux and concentration gradient of diffusion components can be readily determined. In other words, the accuracy of the calculated interdiffusion coefficients is dependent on the fitting function used as well.…”

“…In this work, to minimize the fitting errors, the c-x profiles obtained experimentally by EPMA analysis were fitted using a Boltzmann function and cumulative distribution function (CDF), respectively. 33,34 The expressions of these two adopted functions are given as follows:…”

An Effective Approach to Acquire the Impurity Diffusion Coefficients in Binary Alloys with Quantified Uncertainties

“…The schematic diagram of the presently proposed approach to acquire the impurity diffusion coefficients and related uncertainties in binary alloys is illustrated in Figure 1b, and its general framework is given in Figure 2. The first step is to evaluate the interdiffusion coefficients from the measured composition profiles fitted by the distribution function library [22]. The uncertainties, noted as µ, of the evaluated interdiffusion coefficients are then quantified following the recently developed uncertainty quantification approach [18].…”

“…Moreover, the presently evaluated impurity diffusion coefficient with quantified uncertainties are compared with the true values, as displayed in Figure 3b-f. As can be Following our previous work [18], the Boltzmann-Matano method together with the distribution functions [22] were employed to retrieve the composition-dependent interdiffusion coefficients and their uncertainties. The evaluated interdiffusion coefficients and uncertainties are given in the Supporting Information in order to save the space here because some similar results have been given in our previous publication [18].…”