Chemical potentials in non-hydrostatically stressed anisotropic phases

Chemical potentials can be defined as the partial derivatives of the Helmholtz energy with respect to moles of chemical components under conditions of zero domain strain and fixed temperature. Under hydrostatic conditions, chemical potentials are dependent only on state properties. Under non-hydrostatic conditions, they also depend on a ‘chemical expansivity tensor’—a second-order tensor with unit trace that characterizes how the elastic network of the phase is compressed to accommodate new material within the local domain element. The five degrees of freedom of this tensor generate a class of chemical potentials. An important group within this class are the ‘uniaxial chemical potentials’, which quantify the Helmholtz energy change when new material is incorporated via compression along a single axis. Chemical and mechanical equilibrium is achieved when all uniaxial chemical potentials remain constant along their respective axes.The derived expressions apply to both crystalline and amorphous materials. Their utility is demonstrated through solutions to classic phase-equilibrium problems.