Graph Convolutional Neural Networks for Fast and Accurate Predictions of Formation Energy and Mechanical Properties of Solid Solution Alloys with Multiple Crystal Structures

Accomplishment:  A GCNN model was trained to predict the formation energy and bulk modulus of solid solution alloys with different crystal lattice structures, element composition, and atomic disorder. By allowing a rapid screening of atomic information in large material search spaces, the inexpensive but still accurate GCNN predictions of material properties have the potential to significantly reduce the computational effort compared to computationally expensive ab initio calculations, e.g., density functional theory (DFT) simulations. The model will allow material scientists to overcome the data scarcity challenge in material science and efficiently use sparse data in a high dimensional space, for efficient prediction and design of desired formation energy and mechanical properties of solid solution alloys.

Since atomic data is expensive to generate from ab initio calculations, GCNNs are well suited surrogate models for atomic modeling because they attain comparable accuracy to ab initio data. Specifically, the graph convolutional layers of the GCNN model capture local short-range interactions between atoms and transfer the learnt interactions from one local neighborhood to another, thereby reducing the data requirement and alleviating the computational burden of training, compared to some other deep learning (DL) models [1]. 

As an illustration, we trained a GCNN model on a dataset for the binary nickel-niobium (NiNb) alloy generated by using the EAM potential for various crystal structures. General irregular structures were obtained by geometry optimization, starting from initial regular face-centered cubic (FCC), body-centered cubic (BCC), and hexagonal close-packed (HCP) structures that spanned the possible compositional range, with randomly sampled disordered atomic configurations for each composition. Atomic and bond descriptors were used to help the GCNN model distinguish between different crystal structures, atomic arrangements, and lattice parameters.

Numerical results show that the GCNN model learns the dependency of the formation energy and mechanical properties of the solid solution alloy on the crystal structure, atomic disorder, and lattice parameters, producing accurate predictions for unseen atomic structure within a less than 1% error for the formation energy and less than 5% error for the bulk modulus from EAM model. Since previous work that uses graph-based models in this field focused only on alloys consisting of a single crystalline phase, our accomplishment represents a significant generalization as it extends the results to alloys with different crystal structures.