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

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 $E\left(\sigma \right)$ 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 $E\left(\sigma \right)$ 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, $g^{\left(2\right)}\left(r\right)$ and $g^{\left(3\right)}(r,r,r),$ 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 $P\left(E\right(\sigma \left)\right)$ by rapidly spanning a large number of configurations. The $P\left(E\right)$ 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 $\left({\sigma }_{IE}\right)$ between $\gamma$ and ${\gamma }^{\prime }$ at 700 °C in Alloy 617, a Ni-based superalloy, with composition reduced to five components. The estimated ${\sigma }_{IE}\approx$ 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. (paper)