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.