Robert Myhill 

This paper presents expressions for chemical potentials in non-hydrostatically stressed anisotropic phases. Chemical potentials are here defined as the change in Helmholtz energy on adding a single chemical component to a material while locally preserving total volume, temperature and the shape of the domain. The paper demonstrates that an entire class of chemical potentials can be defined given different boundary conditions. Total derivatives of the Helmholtz free energies use a chemical potential defined by imposing isotropic compression of existing material, while crystal growth and dissolution is governed by interfacial chemical potentials, defined by imposing uniaxial compression of existing material normal to the crystal surface. A chemical equivalent of the conservation of linear momentum (Cauchy's first law) is provided that encapsulates the concept of chemical equilibrium under non-hydrostatically stressed states. The derived chemical potentials are valid for all phases; both solid and liquid, crystalline and amorphous, and do not depend on rheology. They are discussed in the context of previous results, resolving several points of controversy in the literature.