Chemical potentials in non-hydrostatically stressed anisotropic phases

Chemical potentials are defined as the partial derivatives of the Helmholtz energy withrespect to moles of chemical components under conditions of zero domain strain andfixed temperature. Under hydrostatic conditions, chemical potentials are dependent onlyon state properties. Under nonhydrostatic conditions, they also depend on a “chemical ex-pansivity tensor” - a second-order tensor with unit trace that characterises how the elasticnetwork 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. Animportant group within this class are the “uniaxial chemical potentials”, which quantifythe Helmholtz energy change when new material is incorporated via compression along asingle axis. Chemical and mechanical equilibrium is achieved when all uniaxial chemicalpotentials remain constant along their respective axes.The derived expressions apply to both crystalline and amorphous materials. Their utilityis demonstrated through solutions to classic phase-equilibrium problems.