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-VIA compounds, such as AgInS, prefer a tetrahedrally coordinated structure (TCS), while ionic IA-VA-VIA compounds, such as NaBiS, would favor an octahedrally coordinated structure (OCS). One naturally expects that IB-VA-VIA compounds with intermediate ionicity or covalency, such as AgBiS, should then have a mix-coordinated structure (MCS) consisting of covalent AgS tetrahedra and ionic BiS octahedra. Surprisingly, only the experimental presence of the OCS was observed for AgBiS. To resolve this puzzle, we perform first-principles studies of the phase stabilities of ternary compounds at finite temperatures. We find that AgBiS 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-VIA compounds.