Strain through-space term

At this point, we have adapted the concept of chemical potential so as to apply it in situations where the stress field is nonhydrostatic as well as nonuniform through space. We have related a material s strain rate or change-of-dimension behavior to its chemical-potential field. But so far we have discussed only problems of continuum mechanics type—the same problems that we were able to discuss effectively in terms of stress. We have used chemical potential in describing continuum-mechanics behavior, the left-hand two boxes in Figure 17.1 but we have not yet used chemical potential in describing change of concentration of an atomic species, which is of course one of the concept s most natural and powerful uses. 

A binary material s behavior can be described by giving a velocity field for the joint behavior of both components plus a velocity field for the exchange of one for the other. In many circumstances this effectively separates questions of mechanics from questions of chemistry in particular, nonhydrostatic stress affects only the joint field, while gradients of composition through space affect only the exchange process. In such circumstances, boxes (i) and (ii) in Figure 19.1 are empty and eqn. (12.8) relating the strain rate to the potential is exactly equivalent to eqn. (12.7) in terms of the stress 0. 

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