Topology-symmetry analysis and structure prediction in nonlinear optical AB4O6F (A = Na, K, Rb, Cs, NH4) and AAlB3O6F (A = K, Rb, Cs) polytypes

Abstract

Topology-symmetry analysis based on order-disorder (OD) theory for polytypic structures is a useful tool for understanding structure-property relationships, and it could serve as a basis for structure predictions and materials design. This approach systematically characterizes structural fragments and their stacking sequences through partial symmetry operations. Here, the nonlinear optical (NLO) fluorooxoborate family AB₄O₆F (A = Na, K, Rb, Cs, NH₄) and the alkali-aluminum borate fluorides AAlB₃O₆F (A = K, Rb, Cs) are investigated within OD theory framework and described via symmetry groupoids. By enumerating admissible stacking operations, we derive several hypothetical maximum degree of order (MDO) polytypes for NaB₄O₆F, RbB₄O₆F, CsB₄O₆F, CsKB₈O₁₂F₂, CsAlB₃O₆F and RbAlB₃O₆F. New noncentrosymmetric (NCS) polytype of RbB₄O₆F (sp.gr. Pnn2) and centrosymmetric (CS) polytype of RbAlB₃O₆F (sp.gr. P2₁/с) are predicted. Furthermore, we discuss the influence of layer symmetry and stacking topology on optical properties. The results demonstrate that the competition between different stacking manifolds provides a plausible explanation for the occurrence of stacking faults in this family of materials.