Finite Difference Solution of the Diffusion Equation and Calculation of the Interdiffusion Coefficient using the Sauer-Freise and Hall Methods in Binary Systems

Abstract

The study of concentration dependent diffusion is important in the field of alloys and semiconductors. It is a key issue to calculate accurate interdiffusion coefficients using experimentally obtained concentration profiles. The Boltzmann-Matano (BM) method is often used for determining diffusion coefficients. But this technique has some shortcomings in calculating an accurate interdiffusion coefficient. Because of this, the Sauer and Freise (SF) method (which is a clever modification of the BM method) is more useful for calculating the interdiffusion coefficient. The Hall Method (HM) was specifically designed for determining the interdiffusion coefficient at the low and high concentration limits. In the present study, concentration profiles have been numerically generated as a solution to the interdiffusion problem in a binary system when the interdiffusion coefficient is dependent on concentration. This has been done using an explicit finite difference method. A comparative study of the HM, BM and SF methods has been performed using the generated concentration profiles. This allows for a direct comparison between the SF, BM and HM techniques. Present results clearly indicate that the HM technique can only be applicable when the interdiffusion coefficient is constant (independent of concentration) or almost constant at the low concentration regions. In all other cases the SF method gives the best agreement with the input interdiffusion function.

Experimental Diffusion Research on BCC Ti-Mn Binary and Ti-Al‐Mn Ternary Alloys

“…The Sauer-Freise (S-F) [20] and Whittle-Green (W-G) [21] methods were employed respectively to extract the interdiffusion coefficients of Ti-Mn binary and Ti-Al-Mn ternary BCC alloys from the ERFEX-processed profiles. Compared with the conventional Boltzmann-Matano method [22] in binary and Matano-Kirkaldy (M-K) method [23] in ternary, the S-F and W-G methods allow to extract the interdiffusion coefficients from diffusion profiles more accurately without suffering from the error of positioning the Matano plane. [22,24] In the S-F and W-G methods, a normalized composition variable Y ¼ xÀx L…”

Investigation of water diffusion dynamics in corneal phantoms using terahertz time-domain spectroscopy

“…Because there is no analytical solution to the variable thickness model, it was numerically solved using the Finite-Difference Time-Domain (FDTD) method. The FDTD version of the Fick's equation [29] is given by,…”

Compartmental modeling of skin transport

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