Development of a finite element model for calculating concentration dependent interdiffusion coefficient
Understanding the mechanism of microstructural changes caused by isothermal phase transformation reactions in materials plays a vital role in driving the development and effective performance of materials in elevated temperature applications. The kinetics of the phase changes in the microstructure of materials which affect their properties, are often diffusion controlled and a key parameter that is used in the prediction and analysis of diffusion effects is concentration-dependent interdiffusion coefficient, D(C). Existing standard analytical methods of extracting D(C) from experimental concentration profiles such as the Boltzmann-Matano, Sauer-Freise, Wagner, and Hall methods have some flaws, which is a major concern for accuracy and reliability. One of the limitations common to these traditional analytical methods is the assumption on which they are formulated which states that the initial composition profile is a step-function in space. In this study, a new numerical diffusion model, which eliminates non - trivial common assumptions in the literature that degrade accuracy, including the assumption of initial composition profile being a step-function in space, is developed. The new model uses finite element and Galerkin weighted residual methods combined with the Dufort Frankel/Leap Frog explicit scheme and one-dimensional Murray-Landau transformation. The model is successfully validated with previously reported experimental data in the literature and the results obtained show excellent agreement between the model predicted results and experimental data, which confirms the reliability of the new model. The model, which incorporates variable diffusion coefficients and coupled with a recently reported forward simulation technique, can be used to extract the D(C) operative between any two isothermal diffusion times, which is crucial for studying the effect of time on D(C). This is an achievement that is not possible by conventional analytical methods such as the Boltzmann-Matano, Sauer-Freise, Wagner, and Hall methods.
finite element model, concentration-dependent, interdiffusion, numerical simulation, model development