Invited Lecture
Automated Green function calculation of dilute solute diffusivity

While first-principles methods compute activated state energies, upscaling to mesoscale mobilities requires the solution of the master equation. A new automated Green function approach for transport both determines the minimum set of transition states to calculate from symmetry and computes the dilute-limit transport without additional approximations. This approach is both more accurate and efficient that stochastic approaches like kinetic Monte Carlo. It also permits straightforward evaluation of uncertainty quantification and derivatives of transport coefficients. To showcase the new functionality, we focus on magnesium alloys containing Al, Zn, and rare earth elements (Gd, Y, Nd, Ce and La), where current theoretical models to predict diffusivity from atomic jump frequencies make uncontrolled approximations that affect their accuracy. Density-functional theory identifies nine different solute-vacancy configurations from which symmetry analysis determine 17 transitions states corresponding to a 27-frequency model. Our Green function approach computes diffusivity for 14 solutes using the density-functional theory data. We find significant differences for solute drag of Al, Zn, and rare earth solutes, and improved predictions of activation energies for diffusion. The differences with prior predictions can be directly attributed to missing jumps in the 8- and 13-frequency models. The underlying automation also makes the extension of first-principles transport databases significantly more practical and eliminate uncontrolled approximations in the transport model.