Robert Myhill 

This paper presents expressions for chemical potentials in non-hydrostatically stressed anisotropic phases. Chemical potentials are defined here as the derivative of the Helmholtz energy with respect to the addition of a single chemical component to a material while preserving total volume, temperature and shape of the microscopic domain. An entire class of chemical potentials can be defined which differ according to the boundary conditions at the edges of the domain. Total derivatives of the internal energy and Helmholtz energy are most naturally expressed as a function of a chemical potential defined by isotropically compressing existing material. Conversely, crystal growth and dissolution is most naturally described by interfacial chemical potentials that are defined by uniaxially compressing existing material normal to the crystal surface. The derived chemical potentials are valid for all crystalline and amorphous materials including liquids, and do not depend on rheology. The derivations resolve several points of controversy in the literature.