Chemical potential under nonhydrostatic stress

There are obvious parallels between eqn. (10.5) and eqn. (10.2) in fact eqn. (10.5) suggests that continuum mechanics is just one more set of applications of the idea that materials tend to move down gradients of chemical potential. But there is also a conspicuous difference ideas in group A embody the idea that, at any point in space, a material component just has a chemical potential—a single value by contrast, group B embodies the idea that, under nonhydrostatic stress, it is a plane or a direction i that has a chemical potential associated with it, and that the potential associated with one plane can be different from the potential associated with another plane at the same point in space. The objective of this book is to treat situations where deformation and interdiffusion are occurring simultaneously that is to say, we want to combine eqns. (10.2) and (10.5), and hence the question, Is chemical potential single-valued or multi-valued must be faced. 

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