A New Finding About Conditions for More Than One Kirkendall Marker Plane in Binary Single Phase Diffusion Couples

摘要

It is now well known that there are experimental results of bifurcate, trifurcate or more Kirkendall marker planes (K-plane) in a multiple phase diffusion couple (M-couple). In the case of Au-Zn binary alloy system, for example, even in a beta'/beta' single phase diffusion couple (S-couple) there is a possibility of the bifurcate K-planes because the ratio R = D (Zn)/D (Au) of the intrinsic diffusion coefficients in the beta' phase is smaller than 1 in the Au rich side and larger than 1 in the Zn rich side. It has been reported that the positions of the K-planes in a diffusion zone can be found graphically as intersections between the plot of marker moving distance versus X (k) and the plot of a straight line versus X (k). Here, is the marker velocity with respect to the volume fixed frame of reference (V-frame) defined by, and is that determined experimentally by the following equation, In this work, we studied the alignments of multiple markers (M-Ms) after diffusion anneal embedded in a S-couple for widely different constant values of ratio of intrinsic diffusion coefficients, R = D (B) /D (A), with respect to the mole fixed frame of reference (N-frame) by our numerical technique taking the change in molar volume into account. For this purpose, new two plots to know the K-plane(s) for the N-flame were derived. A possibility was indicated that Kirkendall markers can locate not only at the intersection(s) between these new two plots but also at an unexpected place where the intersection cannot be found.