Interphase boundary segregation and precipitate coarsening resistance in ternary alloys: An analytic phase-field model describing chemical effects

Many experimental and first principles studies on precipitation hardening alloys show that segregation of elemental species to the matrix-precipitate interphase boundary (IB) reduces the boundary's energy. This segregation mechanism can thermally stabilize the microstructure against precipitate coarsening processes and allow for higher operating temperatures in structural applications. In this paper, we develop a phase-field modeling framework to describe IB solute segregation in ternary alloys. The interfacial thermodynamics is effectively described by defining an IB phase with a characteristic free energy-concentration dependence. Equilibrium for the IB phase is established via the parallel tangent plane construction, analogous to classical treatments for segregation to free surfaces and grain boundaries. Analytic steady-steady solutions elucidating the dependence of IB properties on bulk phase composition, temperature and model parameters are derived for a one-dimensional system. Analytic relations for the classical thermodynamic quantities--IB energy and relative solute excess--are derived and the Gibbs adsorption equation is shown to hold; therefore, predictions of the model can be compared with experiments and atomistic simulations. An application of the model is demonstrated for Zn segregation to Mg/Mg2Sn using representative IB parameters. A two-particle coarsening simulation of IB segregation is performed; the result demonstrates enhanced coarsening resistance of the ternary alloy relative to the binary alloy.