Systematic global structure search of bismuth-based binary systems under pressure using machine learning potentials

TL;DR

The paper develops and validates polynomial machine-learning potentials to accelerate global structure searches across 11 Bi-based binary systems under 0–20 GPa. By integrating RSS with MLPs and selective DFT refinements, it demonstrates accurate reconstruction of known Bi–binary structures while uncovering numerous previously unreported stable phases. The approach enables high-throughput exploration of vast configurational spaces with billions of energy/force evaluations, yielding pressure-dependent phase diagrams and new design opportunities for Bi-rich materials. The work highlights the reliability and utility of MLP-driven global structure searches for materials discovery under ambient and high-pressure conditions.

Abstract

Machine learning potentials (MLPs) have significantly advanced global crystal structure prediction by enabling efficient and accurate property evaluations. In this study, global structure searches are performed for 11 bismuth-based binary systems, including Na-Bi, Ca-Bi, and Eu-Bi, under pressures ranging from 0 to 20 GPa, employing polynomial MLPs developed specifically for these systems. The searches reveal numerous compounds not previously reported in the literature and identify all experimentally known compounds that are representable within the explored configurational space. These results highlight the robustness and reliability of the current MLP-based structure search. The study provides valuable insights into the discovery and design of novel bismuth-based materials under both ambient and high-pressure conditions.

Figures (13)

• Figure 1: Distributions of cohesive energy values for the DFT datasets in 11 Bi-based binary systems. These values are predicted using both DFT and the updated MLPs. The orange dots indicate the local minimum structures obtained through RSS during the second iteration of the MLP update process. The numerical values enclosed in squares represent the RMSEs of energy, expressed in meV/atom, estimated using the local minima shown as orange dots.
• Figure 2: (a) Formation enthalpies predicted using the MLP for local minimum structures generated with MLP-based RSS in the Na–Bi system, shown in the upper panel. The lower panel presents the formation enthalpies of a subset of local minima with $\Delta H_\text{ch}$ values below 20 meV/atom. (b) Formation enthalpies calculated using DFT for the subset of structures shown in the lower panel of (a). These structures were fully optimized using DFT.
• Figure 3: Crystal structures of the globally stable compounds in the Na--Bi system. Yellow and purple spheres represent Na and Bi atoms, respectively. These structures are visualized using VESTA Momma:db5098.
• Figure 4: Formation enthalpies of local minimum structures in the K--Bi system, calculated using DFT. The black dashed lines and solid orange lines represent the convex hulls constructed using the MLP and DFT, respectively.
• Figure 5: Formation enthalpies of local minimum structures in the Mg--Bi system, calculated using DFT. The black dashed lines and solid orange lines represent the convex hulls constructed using the MLP and DFT, respectively.