Two-dimensional simulations and experiments of homogenization and Kirkendall effect in single-phase diffusion triples

Abstract

A fully discrete local discontinuous Galerkin (LDG) method has been successfully adopted to simulate two-dimensional (2D) homogenization in single-phase diffusion triples controlled by diffusion process. Two Co-Ni and Co-Fe-Ni diffusion triples were prepared and analyzed to verify the simulation results at 1473 K. In areas far away from the triple conjunction of a diffusion triple, there exists composition gradient in only one direction, which can be efficiently predicted by one-dimensional (1D) sharp-interface diffusion simulations (for example, DICTRA: DIffusion-Controlled TRAnsformation simulation software). It has been extensively adopted in the study of diffusional phase transformations readily supported by multi-component multi-phase thermodynamics and full diffusion matrix establishing an integrated thermodynamics-kinetics simulation platform for engineering materials and industrial applications. However, there are composition gradients in two independent directions in the vicinity of triple conjunction (i.e. triple diffusion zone), which cannot be handled on this platform. In the present work, the LDG method combining with alloy thermodynamics and diffusion kinetics was demonstrated to tackle this 2D homogenization problem very well and the effectiveness of this method has been proved from the aspect of numerical analysis by realizing it with a standalone C++ code. In addition to the composition and flux evolutions during 2D homogenization processes, one can reasonably simulate the shift of the Kirkendall plane in the 2D single-phase diffusion zone. This standalone code serves as a solid basis to further consider 2D diffusional multi-phase transformations assuming sharp interfaces in between.