Mechanism of Local Lattice Distortion Effects on Vacancy Migration Barriers in FCC Alloys

Abstract

Accurate prediction of vacancy migration energy barriers, $\Delta E_a$, in multi-component alloys is extremely challenging yet critical for the development of diffusional transformation kinetics needed to model alloy behavior in many technological applications. Here, results from $\Delta E_a$ and the energy driving force $\Delta E$ of many (>1000) vacancy migration events calculated using density functional theory and nudged elastic band method show large changes (~1eV) of $\Delta E_a$ in different local chemical environments of the model face-centered cubic Al-Mg-Zn alloys. Due to local lattice distortion effects induced by solute atoms (such as Mg) with different sizes than the matrix element (Al), the changes of $\Delta E_a$ for one type of migrating atoms originate primarily from fluctuations of $\Delta e_a\equiv \Delta E_a - \frac{1}{2}\Delta E$. To understand the fluctuations, a quartic function is shown to accurately describe the energy landscape of the minimum energy path (MEP) for each vacancy migration event. Analyses of the quartic function show that $\Delta e_a$ can be approximated with $\Delta e_a \approx \alpha k_fD^2$, where $\alpha\sim 0.022$ is a constant of all types of migrating atoms. Here $D$ is the distance of a migrating atom between two adjacent equilibrium positions and $k_f$ is the average vibration spring constant of this atom at these two equilibrium positions. $k_f$ and $D$ quantitatively describe the lattice distortion effects on the curvatures and locations of the MEP at its initial and final states in different local chemical environments. We also used the local lattice occupations as inputs to train surrogate models to predict coefficients of the quartic function, which accurately and efficiently output both $\Delta E_a$ and $\Delta E$ as the necessary inputs for the mesoscale studies of diffusional transformation in Al-Mg-Zn alloys.