Grand-potential-based phase-field model for multiple phases, grains, and chemical components

Abstract

Grand-potential-based phase-field model for multiple phases, grains, and chemical components is derived from a grand-potential functional. Due to the grand-potential formulation, the chemical energy does not contribute to the interfacial energy between phases, simplifying parametrization and decoupling interface thickness from interfacial energy, which can potentially allow increased interface thicknesses and therefore improved computational efficiency. Two-phase interfaces are stable with respect to the formation of additional phases, simplifying implementation and allowing the variational form of the evolution equations to be used. Additionally, we show that grand-potential-based phase-field models are capable of simulating phase separation, and we derive conditions under which this is possible.

Grand-potential based phase-field model for systems with interstitial sites

“…However, considering that the contribution of the interstitial vacancy to the corresponding chemical potential is relatively negligible, Comparing Eqs. (27) and 28, it is evident that, while the diffusion potential of the regular-lattice element ( µ � sub:i ) considers the difference in the chemical potentials, the corresponding conjugate pair of the interstitial component, µ �…”

“…Having distinguished the diffusion potentials of components occupying regular and interstitial site respectively through Eqs. (27) and (28), the quasi-equilibrium condition, which is assumed across the diffuse interface, is separately written as Correspondingly, the bulk driving-force of a system with regular and interstitial lattice, in this framework, is expressed as where the number of independent variables amounts to m − 1 . Despite distinguishing the components of the system based on their lattice position, the fictitious phase-dependent concentrations continue to remain the fundamental variable of the bulk driving-force, in Eq.…”

“…7, and are written as where each entries, depending on the lattice position of the component, adhere to the description rendered by Eqs. (27) or (28). When viewed in relation to Eq.…”

“…The change in the fundamental variables from concentration to diffusion potential is achieved by the Legendre transformation of the free-energy density. Considering that the Legendre transformation of the free-energy density yields the grand-chemical potential of phases, this technique is referred to 'grand-potential' model 19,26,27 . The fundamental variables of grand-potential technique are expressed as where the diffusion potential represented as a tuple of m − 1 entities that read…”

Report on plasma jet printer for sensor fabrication with process parameters optimized by simulation input

“…A grand-potential based phase field model is used to simulate sintering of the metallic nanoparticles on an alumina substrate. This phase-filed formulation is presented in Aagesen et al [6] and is implemented in the MOOSE framework. The particle diameters in the following simulations were set at 20 nm which is within the 10 to 100 nm range seen in transmission electron microscopic (TEM) images like Fig.…”