Finding Stable Zintl Phases using an Upper-Bound Energy Minimization Approach

Thermodynamic phase stability is a prerequisite in the search for novel functional materials. Density functional theory (DFT) has been the workhorse for phase stability predictions but is computationally expensive for large search spaces. In this context, machine learning models have become powerful in predicting phase stability and material properties. In particular, graph neural networks (GNNs) have outperformed more traditional ML models in phase stability predictions. In GNNs, the periodic crystal structures are converted into graphs with atom positions represented by nodes and bonds with edges connecting the nodes. In materials searches, often, hypothetical structures are created either by chemical substitutions in prototype structures or other strategies. The resulting hypothetical structure needs to be relaxed before it can be used as an input to a GNN for predicting stability. Such relaxation requires expensive DFT calculations or is achieved with machine-learned interatomic potentials. To address this challenge, we have recently proposed an upper-bound energy minimization approach (UBEM) that finds very stable structures that lie deep in the convex hull, without having to perform structural relaxations [1]. We demonstrate the efficacy of this approach by discovering novel Zintl phases that possess complex structures, and are located between saltlike compounds and intermetallic phases with a combination of ionic and covalent bonding. Although Zintl phases represent a chemically and structurally diverse family of materials, only a limited number of such phases are currently known. The potential for discovering new Zintl phases remains largely untapped and traditional experimental approaches are resource-intensive and slow. We performed a search over ~100,000 hypothetical Zintl phases using UBEM and discovered 2,140 stable Zintl phases. We have validated these predictions with DFT. Furthermore, we compared our predictions with M3GNet, which utilizes machine-learned interatomic potentials to explicitly perform structural relaxations and predict phase stability[2]. Further investigation of the thermoelectric performance of the predicted stable phases and experimental validation are currently underway.<br/><br/>[1] Law et al., <i>JACS Au </i>3, 113 (2023). [2] Chen et al., <i>Nature Comp. Sci. </i>2, 718 (2022).