Two Remarks on Wagner Integrated Diffusion Coefficient

Abstract

Integrated interdiffusion coefficient, introduced by Carl Wagner in 1969, is revisited. First, it is applied for the whole diffusion zone, consisting of solid solutions and/or layers of intermediate compounds. We demonstrate, for the first time, that the Wagner coefficient satisfies the simple additive rule: the total squared inter-penetration width is proportional just to the sum of all Wagner coefficients of all intermediate phases of the system. Second, we check the applicability of Wagner coefficients in the atomistic-scale modelling of reactive diffusion. Checking is done for the growth of intermediate compound AB with BCC lattice.

Diffusion Laws and Modified Pascal’s Triangles

“…Convex shape of the diffusion profile along grain boundary or (OX) axis near the wedge "nose" top involving outflow into the bulk was predicted in [15]. Such convex shape of the diffusion profile was confirmed by atomically-resolved electron microscopy in [1] (Fig.…”

“…A model of an intermediate phase growth with a narrow concentration range of homogeneity between low-soluble components during diffusion along grain boundaries involving outflow into bulk was suggested in [15]. The model was based on following assumptions: 1) an intermediate phase forms at first on the base of the grain boundary (GB) due to diffusion of the substance B atoms; the boundary A-A transforms to the boundary 1-1 and remains of thickness δ ≈ 1 nm since easy influx with a diffusion coefficient DGB (i.e., the GB is not overgrown with forming phase and does not bifurcate); 2) formed phase 1 broadens normally to the GB due to volume diffusion with a diffusion coefficient D << DGB; 3) at all points of the formed 1-A phase boundary between the broadening phase 1 and the matrix A the concentration of the component B is C1 on the side of phase 1 and is zero on the side of substance A (solubility of B in A is ignored); 4) outflow from the GB is the same at all GB points; 5) the flow into the volume of the phase wedge normal to the GB is approximately constant along (OY) axis to be perpendicular to (OX) axis.…”

“…We can assume a linear concentration profile along the dislocation line instead of assumption "outflow from the dislocation line is the same at all dislocation points" like it was done for grain-boundary diffusion in [15]:…”

Li+ intercalation current generation in amorphous and crystalline MoS2: Experiment and theory

“…Semi-infinite non-ideal diffusion is described by a partial differential equation and is closely related to the change in the thermodynamic characteristics of intercalate phases. It closely links the physical nature of the transformation of this diffusion (to the ideal diffusion), but only in a layer of limited (in relation to the sinusoidal signal) thickness, to the change in the Wagner factor [28], which includes E(t) from Eq. ( 1).…”