Atomic bonding in equilibrium single-component melts. The cases of arsenic, antimony and bismuth

TL;DR

The study addresses how quasi-stable structures form in equilibrium melts of arsenic, antimony, and bismuth and how their bonding can be quantified from first principles. It uses ab-initio molecular dynamics with VASP to generate configurations near the melting point and analyzes bonding with projected crystal orbital Hamilton population methods, producing $IpCOHP$ as a bonding metric. Findings show that bonding is governed by $p$-orbital interactions, while $s$-orbital contributions are negligible; the magnitude of $|IpCOHP|$ decreases with the number of atoms in a quasi-stable unit, following a power-law, yielding maximum stable sizes of about 6–8 atoms that increase with atomic number. These results connect local electronic structure to observed structural anomalies in $g(r)$ and $S(k)$ and offer a first-principles framework for understanding quasi-stable structures and potential liquid-liquid transitions in polyvalent melts.

Abstract

In liquid pnictogens, quasi-stable structures can be formed near melting temperature. The nature of their stability does not have the unified point of view. In the present work, the task of determining the degree of atomic bonding in these structures is solved using the Crystal Orbital Hamilton Population (COHP) method. The original results of ab-initio simulation of arsenic, antimony and bismuth melts near their melting temperatures are used. It is shown that the features of the electron interaction at the level of $p$-orbitals determine the characteristic bond lengths and angles between atoms. It has been established that the stability of structures decreases according to a power law with an increase in the atomic mass of a chemical element and the number of atoms in the structure. The obtained results clarify the understanding the mechanisms of formation of quasi-stable structures in pnictogen melts from first principles.

Figures (6)

• Figure 1: Schematic representation of quasi-stable structural formations that can exist in the melts of pure pnictogens. The radial distribution function of atoms for a simple liquid without an "anomalous" structure and for a liquid with quasi-stable structures. The curves are schematic and presented for clarity.
• Figure 2: Dependence of the total energy on the simulation time for As, Sb and Bi melts. The energy fluctuates around a constant value, which confirms that the melts are in a thermodynamic equilibrium state.
• Figure 3: (a) Radial distribution function of atoms g(r) and (b) statical structure factor S(k) for As, Sb and Bi melts. The markers indicate experimental X-ray diffraction data taken from Hafner_liquid_as_1989 (for As) and Waseda_1980 (for Sb, Bi). The solid green lines show the obtained ab-initio simulation (AIMD) results. In top panels, the functions g(r) and S(k) for liquid argon at the temperature 85 K are presented Yarnell_1973_liquid_ar. The g(r) and S(k) curves were obtained under identical thermodynamic conditions at their phase diagrams. Characteristic lengths for dimers and triplets are shown by arrows. In figure, $\sigma$ is the effective diameter of an atom (2.55 Å for As, 3.3 $\AA$ for Sb and 3.4 $\AA$ for Bi), $k_m$ is the position of first maximum in the function S(k) (2.32 $\AA^{-1}$ for As, 2.15 $\AA^{-1}$ for Sb and 2.15 $\AA^{-1}$ for Bi).
• Figure 4: Snapshots of charge density distribution for As, Sb and Bi. In the case of As and Sb, the simulation cell is rhombohedral, while the Bi atoms are located in a rectangular cell. This explains the difference in the shape of the resulting snapshots. The color indicates the change in charge density. The maximum density, which has the value $0.005e$, corresponds to red. The minimum charge density with the value $0.0001e$ corresponds to dark blue color.
• Figure 5: The projected crystal orbital Hamilton populations (pCOHP) for dimers (a)--(c) and triplets (d)--(f) obtained for As, Sb and Bi melts near melting temperatures. Energies are presented relative to the Fermi energy $E_f$ and shifted to zero. Negative (i.e., bonding) contributions are plotted on the right and shaded blue, while positive (i.e., antibonding) contributions are plotted on the left and shaded red. Green zone shows results for calculation of pCOHP with $s$-orbital. Its intergral (IpCOHP) is equal to zero.