Interdiffusion, apparent coefficient

Charge balance requires that the outward flux of cations from the silicate be balanced by the inward flux of hydrogen ions. For example, the apparent sodium diffusion coefficient in equation 5 is therefore really the interdiffusion coefficient, +,... 

The Kirkendall effect is a well-known phenomenon resulting from the difference in intrinsic diffusivities of chemical constituents of substitution solid solutions (non-reciprocal diffusion). Many textbooks provide a detailed and quantitative treatment of this important phenomenon (Philibert, 1991) schematized in Fig. 2.2 for a homogeneous diffusion couple of constituents A and B forming a continuous substitutional solid solution. In Fig. 2.2a, the initial position of the contact surface is marked by fixed inert markers that define the origin, also named the Matano plane (M), of the reference frame centred on the mass or the number of moles this reference frame is conunonly used to define interdiffusion processes and the unique interdiffusion coefficient that permits the characterization of the transport of A and B. Moving inert markers determine the actual position of the initial contact surface (Fig. 2.2b) and therefore visualize the drift of lattice planes within the diffusion zone. They mark the origin, also named the Kirkendall plane, of the lattice-fixed frame of reference that permits the definition of the different intrinsic diffusion coefficients of the A and B constituents. Relative to the Matano plane, this drift of lattice planes is equivalent to a translation of the diffusion couple without apparent deformation and without the action of any externally applied stress or, in other words, to a rigid body translation of the phase lattice. 

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