Phase field methods have become an extremely popular and powerful tool for the simulation of microstructure formation in materials. Applications range from very fundamental studies to simulation of phase transformations in rather complex alloys. The vast amount of phase field methods make use of the local equilibrium assumption to describe the conditions prevailing at the moving interface, which relates conditions at the moving interface to the phase diagram of the alloy, implying equal chemical potentials of all species on both sides of the interface. This required knowledge of the so-called working tie-line, which is straightforwardly identified in binary systems, but for three and more chemical elements this can pose a stiff challenge and imposes a significant constraints.

The present paper presents a version of the phase field method which removes the constraints imposed by the local equilibrium assumption. The equations of motion of the interface are derived from principles laid out by the absolute reaction rate theory. Using the chemical potentials of all chemical elements as input, the rate of motion of the interface is calculated from the flux balance of atoms across the interface. It is shown that for stationary and sufficiently slow moving interfaces, local equilibrium is obtained as a limiting case. The nature of the method also allows for straightforward extension from binary to multicomponent systems. Unlike known Gibbs energy dissipation phase field models, no new or unknown coefficients are introduced.