Machine learning assisted first-principles calculation of multicomponent solid solutions: estimation of interface energy in Ni-based superalloys

Abstract

A disordered configuration of atoms in a multicomponent solid solution presents a computational challenge for first-principles calculations using density functional theory (DFT). The challenge is in identifying the few probable (low energy) configurations from a large configurational space before DFT calculation can be performed. The search for these probable configurations is possible if the configurational energy E(sigma) can be calculated accurately and rapidly (with a negligibly small computational cost). In this paper, we demonstrate such a possibility by constructing a machine learning (ML) model for E(sigma) trained with DFT-calculated energies. The feature vector for the ML model is formed by concatenating histograms of pair and triplet (only equilateral triangle) correlation functions, g((2))(r) and g((3))(r, r, r), respectively. These functions are a quantitative 'fingerprint' of the spatial arrangement of atoms, familiar in the field of amorphous materials and liquids. The ML model is used to generate an accurate distribution P(E(sigma)) by rapidly spanning a large number of configurations. The P (E) contains full configurational information of the solid solution and can be selectively sampled to choose a few configurations for targeted DFT calculations. This new framework is employed to estimate (100) interface energy (sigma(IE)) between gamma and gamma' at 700 degrees C in Alloy 617, a Ni-based superalloy, with composition reduced to five components. The estimated sigma(IE) approximate to 25.95 mJ m(-2) is in good agreement with the value inferred by the precipitation model fit to experimental data. The proposed new ML-based ab initio framework can be applied to calculate the parameters and properties of alloys with any number of components, thus widening the reach of first-principles calculation to realistic compositions of industrially relevant materials and alloys.