Critical Role of Configurational Disorder in Stabilizing Chemically Unfavorable Coordination in Complex Compounds

The crystal structure of a material is essentially determined by the nature of its chemical bonding. Consequently, the atomic coordination intimately correlates with the degree of ionicity or covalency of the material. Based on this principle, materials with similar chemical compositions can be successfully categorized into different coordination groups. However, counterexamples have recently emerged in complex ternary compounds. For instance, covalent IB-IIIA-VIA₂ compounds, such as AgInS₂, prefer a tetrahedrally coordinated structure (TCS), while ionic IA-VA-VIA₂ compounds, such as NaBiS₂, would favor an octahedrally coordinated structure (OCS). One naturally expects that IB-VA-VIA₂ compounds with intermediate ionicity or covalency, such as AgBiS₂, should then have a mix-coordinated structure (MCS) consisting of covalent AgS₄ tetrahedra and ionic BiS₆ octahedra. Surprisingly, only the experimental presence of the OCS was observed for AgBiS₂. To resolve this puzzle, we perform first-principles studies of the phase stabilities of ternary compounds at finite temperatures. We find that AgBiS₂ indeed prefers MCS at the ground state, in agreement with the typical expectation, but under experimental synthesis conditions, disordered OCS becomes energetically more favorable because of its low mixing energy and high configurational entropy. Our work elucidates the critical role of configurational disorder in stabilizing chemically unfavorable coordination, providing a rigorous rationale for the anomalous coordination preference in IB-VA-VIA₂ compounds.