Local Order Average-Atom Interatomic Potentials

TL;DR

The paper tackles local ordering in random alloys by extending the average-atom framework to LOAA, which incorporates short-range order through partial RDFs. It constructs an effective LOAA potential $V_{eff}(r,R)$ with RDF-derived weights $G_{XY}(R)$, enabling accurate predictions across deformations and temperatures while remaining computationally efficient. Validation on a 2D LJ binary crystal and 3D FeNiCr and NiAl alloys shows LOAA outperforms the traditional AA approach in LO scenarios, capturing ground-state energies, elastic constants, lattice constants, and phase transformations with fewer resources. This method promises practical benefits for simulating complex materials, including high-entropy alloys, by reducing system size requirements without sacrificing LO accuracy.

Abstract

This article describes an extension to the effective Average Atom (AA) method for random alloys to account for local ordering (short-range order) effects by utilizing information from partial radial distribution functions. The new Local-Order Average Atom (LOAA) method is rigorously derived based on statistical mechanics arguments and validated for non-stoichiometric binary 2D hexagonal crystals and 3D FeNiCr and NiAl alloys whose ground state is obtained through Monte Carlo sampling. Material properties for these alloys, and phase transformations for the NiAl system, computed from static and dynamic atomistic simulations using standard interatomic potentials (IPs) exhibit a strong dependence on local ordering that is captured by simulations with effective LOAA IPs, but not the original AA method. The advantage of LOAA is that it requires smaller system sizes to achieve statistically converged results and therefore enables the simulation of complex materials, such as high-entropy alloys, at a fraction of the computational cost of standard IPs.

Figures (15)

• Figure 1: Distinct LO patterns for (a) $N_B=2$, and (b) $N_B=3$.
• Figure 2: Phase diagram and associated simulation results using different $\epsilon$ values. (Left) phase diagram with the green region corresponding to phase separation (PS), the orange region corresponding to a homogeneous solid solution (SS), and the black line corresponding to a random alloy; (middle) LO patterns; (right) MC simulation results for a 288 atom system with concentrations $c_A = 0.8$ and $c_B = 0.2$. Visualization using OVITO ovito.
• Figure 3: TS cohesive energy contours over $\epsilon$-space. The no-LO line is shown in red.
• Figure 4: Difference in the cohesive energy between the (a) AA method, and (b) LOAA method, and the exact TS results plotted across $\epsilon$-space. The no-LO line is shown in red.
• Figure 5: (a) $\text{C}_{11}$ and (b) $\text{C}_{12}$ as a function of perpendicular distance from the no-LO line, $t$, computed using the TS, AA, and LOAA methods. Standard deviation error bars are plotted for TS.