Reference planes for binary diffusion with variable molar volume

Present-day treatments of diffusion in metallic solid solutions require an accurate, convenient analysis that takes account of the actual variations of atomic size with concentration. Recent research by the author has produced such an analysis, which employs ordinary Cartesian coordinates. The first and second Fick equations are essentially the same as the usual forms (for constant, equal atomic size), differing only in the addition of the factor ¯V, the total molar volume of the solid solution. The prevalent erroneous concept of an “invariant” for diffusion demonstrates the need for a clearer understanding of the role of reference planes in treatments of diffusion. Reference systems of two types are dicussed: conventional reference systems (Fick and molecular), and the lattice (Kirkendall) reference system. The diffusion velocity,v, of a given component is used as the basis for defining the diffusion flux. Absolute values ofv can be determined from data on the Kirkendall shift, but only relative values (v−Ω) can be employed if only a conventional reference system is used in the analysis.