Analyzing Linear Multicomponent Diffusion Phenomena

Abstract

We developed a MatLab c code that implements the multicomponent diffusion approaches outlined by Morral and Thompson [1,2] and by Glicksman and Lupulescu [3]. Zero flux planes (ZFP's), first introduced by Dayananda and Kim [4], occur commonly in ternary and higher-order multicomponent alloys. ZFP's for a component manifest as stationary or symmetrically moving planes disposed about the Matano interface. In contrast to the normal global mixing that occurs in a binary diffusion couple, the presence of a stationary ZFP requires that mixing of the blocked component occurs unilaterally through the release of pairs of coupled depletion-repletion waves that increase the average concentration in the component-poor alloy, but decrease it in the component-rich alloy [3]. We previously analyzed the kinetics of multicomponent diffusion near ZFP's for single-phase couples based on the behavior of diffusion couples between the fixed end-member alloy Cr-10 at.%, Al-10 at.%, Ni-80 at.%, with a series of end-member alloys having a concentration difference vector with a magnitude of 1 at.%. It was demonstrated that the spreading rates of the ternary diffusion zones could be reduced by choosing the orientation of the composition vectors in composition space to be near the Euler angle for the minor eigenvector of the diffusivity matrix. Moreover, a critical Euler angle, ψ * ≈ 29 • , was found in ternary Cr-Al-Ni alloys, near which diffusion couples selected with their composition vectors within ±5 • of ψ * exhibit minimal rates of interdiffusion [3]. The reduced atomic transport predicted in these alloys was associated with the proximity of their Euler angles to that of the ZFP for the major elemental component. Similar analyses performed on ternary couples with the fixed end member alloy Ni-43.5 at.%, Zn-25 at.%, Cu-31.5 at.% and unit composition vectors, show that diffusive spreading is reduced for couples located in composition space close to the ZFP of the minor component.

VisiMat-Software for the Visualization of Multicomponent Diffusion in Two and Three Dimensions

“…[9,10] This software features increased functionality, improved visualization, ability to model couples with many components, and implementation in a modern and portable platform.…”

“…[2] Thus, the condition for the presence of a ZFP is that a composition vector and the maximum interdiffusion rate vector must have a scalar product of zero. As shown graphically [7,9,10] in two dimensions (n = 3), the ZFP composition is located at right angles to the specified maximum flux vector. In two dimensions, there are two compositions that meet the condition for a stationary ZFP.…”

“…VisiMat is a successor to both the Profiler software developed by Brockman and Morral [8] and a MATLAB code with a graphical user interface [9,10] developed at Rensselaer Polytechnic Institute, to implement the equations derived by Glicksman and Lupulescu. [7] VisiMat is written on a more modern platform, which is compatible with many common operating systems.…”

VisiMat^©–Educational Tool for Multicomponent Diffusion in 2 and 3 Dimensions

“…VisiMat ® [10] is a successor to both the Profiler  software developed by Morral and co-workers [3][4][5] and a MatLab ® code with graphical user interface [8,9] developed at Rensselaer Polytechnic Institute, to implement the equations derived by Glicksman and Lupulescu [7]. VisiMat ® software is written on a MatLab ® platform, and is compatible with many common operating systems.…”

“…Here we present VisiMat © , a 2-and 3-d educational code based on the MatLab  computing platform. The new code combines original features available in Profiler  as well as those added by Glicksman and Lupulescu [7] and Lupulescu et al [8,9] to evaluate single phase ternary alloys and to study the kinetics of zero-flux planes (ZFPs). Although VisiMat © [10] could handle numerically any number of components, the 3-d visualizations are not possible for more than four components.…”