K6Mo8PO29OH·H2O and K6Mo5P2O23·7H2O: strongly distorted [MoO6] octahedral groups effectively enhance birefringence

Two examples of molybdate phosphates, K6Mo8PO29OH·H2O and K6Mo5P2O23·7H2O, were designed and synthesized using a hydrothermal method, introducing strongly distorted [MoO6] octahedral groups. K6Mo8PO29OH·H2O crystallizes in the centrosymmetric space group Cmcm, where each [PO4] combines [Mo4O15] and [Mo4O14(OH)] groups to form a unique [Mo8PO29(OH)] cluster. K6Mo5P2O23·7H2O crystallizes in the non-centrosymmetric space group P212121, where two [PO4] link [Mo5O21] groups to form a closed hollow ellipsoidal [Mo5P2O23] cluster. They possess wide experimental band gaps of 3.57 and 3.34 eV, respectively. Compared to K3PO4, the introduction of strongly distorted [MoO6] octahedral groups enhances their birefringence from 0.006 to 0.127 and 0.077@1064 nm (about 21 × and 11 × K3PO4), with the source of the birefringence being dominated by the contribution of strongly distorted [MoO6] octahedral groups. The relationship between its structure and optical properties is analyzed based on first-principles calculations. This work effectively enhances the birefringence properties of phosphate crystals by introducing highly distorted [MoO6] groups, providing insights for designing and synthesizing ultraviolet optical crystal materials with superior performance.