Abstract: Bismuthene is a heavy 2D material whose strong spin-orbit coupling and recently observed single-element ferroelectricity have intensified interest in its structural, vibrational, and transport properties. Accurate modeling of these behaviors requires a short-range interatomic potential that can reproduce the underlying bonding physics at a fraction of the computational cost of first-principles methods. However, such a potential is currently unavailable. In this work, we construct a Tersoff bond-order potential for β-bismuthene using a reinforcement-learning framework that integrates a continuous Monte Carlo Tree Search with a simplex-based local optimizer. The optimized parameter sets reproduce first-principles lattice constants, cohesive energy, the equation of state, elastic constants, and phonon dispersion. We validate the models by performing thermal-conductivity calculations and uniaxial fracture simulations- our findings confirm the reliability of the resulting models across multiple thermomechanical regimes. Comparison of the three best solutions reveals how differences in pairwise interactions, angular terms, and bond-order behavior govern phonon features and mechanical responses. We demonstrate an interpretable and computationally efficient potential for bismuthene and demonstrate a general reinforcement-learning strategy for developing bond-order models in emerging 2D materials.

Abstract: A semi-empirical interatomic potential for the post-transition metal, bismuth, is developed based on the second nearest-neighbor modified embedded-atom method (MEAM). The potential reproduces a range of physical properties, such as the lattice constant, cohesive energy, elastic constants, vacancy formation energy, surface energy, and the melting point of pure bismuth. The calculations are done for the rhombohedral ground state of Bi. The results show good agreement with density functional theory and experimental data. The developed MEAM potential for bismuth is useful for material and mechanical behavior studies of the pure material at different conditions and sets the stage for the development of interatomic potentials for bismuth alloys or other bismuth compounds.

Abstract: The embedded atom model (EAM) potentials of liquid gallium, lead, and bismuth calculated by the author using the Schommers algorithm were refined and written in a unified analytic form more convenient for applications. Pair contributions to EAM potentials are described by piecewise continuous functions. The form of EAM potentials admits the transition to a high-density state characteristic of shock compression. Series of models of these liquid metals were constructed by the molecular dynamics method at temperatures up to 1500 (Zn), 3000 (Ga, Pb), and 1800 K (Bi). For all the metals, close agreement with experiment was obtained over the whole temperature range for density, structure, bulk compression modulus, and self-diffusion coefficient. The standard deviations of model pair correlation functions (PCF) from the diffraction PCFs of gallium and lead were on the order of 0.01. As distinct from alkali metals, the calculated energy of gallium and lead models was close to actual energy over the whole temperature range, and excess electronic heat conductivity was almost unobservable. With bismuth, agreement with experiment for energy and structural characteristics was noticeably worse, which shows that the embedded atom model is less applicable to bismuth.

Abstract: Liquid metal embrittlement during hot rolling of recycled steels, caused by tramp elements accumulated through repeated scrap recycling, represents a critical challenge for sustainable steel production. Here we develop interatomic potentials for Fe-Cu-X (X = Sn, Sb, As, Pb, and Bi) ternary systems and employ molecular dynamics simulations to elucidate atomistic mechanisms governing grain boundary penetration of liquid metals. Systematic investigation of binary Fe-X and Cu-X systems establishes that penetration is controlled by wetting thermodynamics depending on both the mixing enthalpy and the solute concentration dissolved in the liquid phase. Extension to ternary systems reveals three distinct penetration regimes determined by the disparity in mixing enthalpies between binary pairs relative to entropic stabilization: (i) Sn and Sb promote cooperative penetration where tramp elements lead Cu into grain boundaries, with penetration efficiency increasing systematically with tramp element concentration in the liquid; (ii) Pb and Bi suppress penetration as their unfavorable Fe interactions exclude them from the solid-liquid interface, maintaining baseline Fe-Cu behavior; and (iii) As exhibits decoupled penetration where its extreme Fe affinity induces liquid phase separation, suppressing Cu penetration despite independent As infiltration. These findings establish a thermodynamic framework based on the difference between binary mixing enthalpies that enables prediction of tramp element effects on grain boundary penetration and provides guidance for prioritization of elements for industrial control.