Interdiffusivity at Unstable Compositions

Because composition is a locally-conserved order parameter, it cannot change in one location without affecting its neighborhood—fluxes are required to change a composition field. For example, in a binary alloy, the concentration field cb is re- 

Kinetics of Materials. By Robert W. Balluffi, Samuel M. Allen, and W. Craig Carter. 433 Copyright 2005 John Wiley Sons, Inc. 

If D 0, Eq. 18.2 implies that a system with a uniform composition Xb(x) = (Q dgnst would not evolve. However, if D 0, small composition fluctuations would grow without bound a system described by Eq. 18.2 would develop into many unphysical and finely spaced large fluctuations in composition. 

To show how the sign of D is related to the sign of d2F fdX, consider chemical diffusion in a substitutional A-B crystalline material, as described in Section 3.1.3. The fluxes JA and Jg in the C-frame are given by Eq. 3.7 and can be written in the forms 

For simplicity, we assume in this chapter that the atomic volumes of A and B are equal and constant (i.e., lA = constant).2 Then, using Eqs. 3.21, 18.4, 

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