Transport in Inhomogeneously Stressed Crystals

In this section, we consider the influence of inhomogeneous stress on matter transport. Tb illustrate the problem, let us formulate a simple transport equation diffusion of an interstitial component i in an otherwise immobile solid (e.g., H in Pd). Furthermore, we neglect cross effects. For an electrically neutral species i (i.e., H) we then have 

In Eqn. (14.19), which is the fundamental equation for transport in systems with inhomogeneous stresses, it is assumed that , does not depend on concentration. This is obviously true for our dilute solution of species i in the matrix crystal. Correspondingly, we may also assume that fj is independent of the concentration of i. 

From Eqn. (14.20), one obtains the stress gradient in the direction of transport as 

With the given assumptions, we introduce Eqn. (14.21) into the transport equation (14.18) and obtain 

There is a local (Fickian transport) and a non-local (stress induced) term in this flux equation. In the local term, the stress acts in the same way as an activity coefficient does. It always increases local diffusion since V] is positive and independent of the sign of the partial molar volume of /. 

---