On the thermodynamics of non-hydrostatically stressed solids

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Abstract
A recent review (Paterson 1973) has drawn together the literature on nonhydrostatic thermodynamics. When assembled together, the various approaches display certain inconsistencies which require attention and which point the way to new understanding. It is shown here that the chemical potential, μ, of the various components in a solid under non-hydrostatic stress can be specified for every point within the body as well as on its surface. For situations in which a true thermodynamic equilibrium can be attained, the equilibrating species unmix, producing a heterogeneous composition, even when the stress is homogenous. For situations in which equilibrium cannot be attained, a steady state or pseudo-steady state develops in which μ varies such that ▽2μ=0. In all cases involving non-hydrostatic stress, crystal size and shape become thermodynamic parameters. The non-hydrostatic stress problem is the inverse of the osmotic pressure problem.

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