Matano plane

FIGURE 2.3-10 Matano-Boltzmann analysis of tree-diffusion experiment. Matano plane (2 = 0) Located by area ABC — area CDE. 

The meaning of the right-hand-side of eq. (7-26) now becomes clear. Finally, it may be noted from eq. (7-26) that d jdt becomes equal to zero when the diffusion currentsin the a- and j5-phases at the phase boundary x = ( are equal at all times. The Matano interface is then coincident with the phase boundary. In all other cases, the phase boundary moves away from the Matano plane with velocity /21 as has just been calculated. 

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. 

Consider the Boltzmann-Matano analysis leading to Eq. 4.51. Explain why the condition imposed by Eq. 4.50 determines the location of the x = 0 plane (i.e., the position of the original interface). 

Figure 2.3-10 illustrates the integral and derivative that are to be computed from the experimental curve to calculate the diffusion coefficient. The r = 0 plane is known as the Matano mierface2 77 7 and must he. located on the profile by applying the condition... 

M. Hasegawa, T. Matano, Y. Shindo, and T. Sugimura, Spontaneous molecular orientation of polyimides induced by thermal imidization. 2. In-plane orientation, Macrorrwlecules, 29, 7897-7909 (1996). 

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