Chemical potentials in non-hydrostatically stressed anisotropic phases

Robert Myhill 

Chemical potentials are 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 nonhydrostatic conditions, they also depend on a “chemical ex-
pansivity tensor” - a second-order tensor with unit trace that characterises how the elastic
network 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.