On the Analysis of Composition Profiles in Binary Single-Phase Diffusion Couples: Systems with a Strong Compositional Dependence of the Interdiffusion Coefficient
Abstract:Diffusion couple technique is an efficient tool for the estimating the chemical diffusion coefficients. Typical experimental uncertainties of the composition profile measurements complicate a correct determination of the interdiffusion coefficients via the standard Boltzmann-Matano, Sauer-Freise or the den Broeder methods, especially for systems with a strong compositional dependence of the interdiffusion coefficient. A new approach for reliable fitting of the experimental profiles with an improved behavior at… Show more
“…The goodnesses of fit for the method in ref. 49 and the present method are 1–5.9836 × 10 −6 ; and 1-4.3276 × 10 −8 respectively. (b) Calculated D using the two methods, compared with the pre-set D-c relation.…”
Section: Discussionmentioning
confidence: 68%
“… Figure 10 Calculated results for the case ideal D2 using the method in ref. 49 and the present method. (a) Fitting c-x profiles.…”
Section: Discussionmentioning
confidence: 83%
“…9 . Figure 9 Fitting c-x profiles of Cu and Sn in Cu-Ag-Sn ternary system 48 at 1073 K, compared with the experimental data 49 . The profiles of Sn and Cu are fitted by skew normal distribution function and combined superposition method respectively, R 2 = 0.9943 and 0.9323 for Sn and Cu profiles.…”
Section: Resultsmentioning
confidence: 99%
“…( iii ) Very recently, Kavakbasi et al . 49 proposed a method to calculate the interdiffusion coefficient based on the error function. The idea of their work is to adjust the error function by changing the denominator term while the idea of this work is to adjust the normal CDFs by multiplying terms.…”
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.
“…The goodnesses of fit for the method in ref. 49 and the present method are 1–5.9836 × 10 −6 ; and 1-4.3276 × 10 −8 respectively. (b) Calculated D using the two methods, compared with the pre-set D-c relation.…”
Section: Discussionmentioning
confidence: 68%
“… Figure 10 Calculated results for the case ideal D2 using the method in ref. 49 and the present method. (a) Fitting c-x profiles.…”
Section: Discussionmentioning
confidence: 83%
“…9 . Figure 9 Fitting c-x profiles of Cu and Sn in Cu-Ag-Sn ternary system 48 at 1073 K, compared with the experimental data 49 . The profiles of Sn and Cu are fitted by skew normal distribution function and combined superposition method respectively, R 2 = 0.9943 and 0.9323 for Sn and Cu profiles.…”
Section: Resultsmentioning
confidence: 99%
“…( iii ) Very recently, Kavakbasi et al . 49 proposed a method to calculate the interdiffusion coefficient based on the error function. The idea of their work is to adjust the error function by changing the denominator term while the idea of this work is to adjust the normal CDFs by multiplying terms.…”
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.
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