Unlocks Photoluminescence Quantum Efficiency Enhancement in Eu²⁺-Doped Phosphors via Bond Angle Variance Index

Rational design of inorganic luminescent materials with high photoluminescence quantum yield (PLQY) has long been constrained by the absence of precise structural descriptors. Here, we realizes a giant 15.7-fold PLQY enhancement in apatite-type La_{9- x}Lu_xBi(SiO₄)₆O₃:Eu²⁺ phosphors and demonstrates that bond angle variance (Bav, δ²) can be used as a universal crystallochemical metric. By decoupling the contributions from structural rigidity, thermal quenching (TQ), and cation disorder, we identify isovalent Lu³⁺ substitution-driven Bav engineering, and further establish a predictive Bav-PLQY linear relationship (R² > 0.95) via a generalized distortion quantification model for irregular polyhedra (CN = 7). Local structure characterization and bond valence sum (Bvs) analyses reveal that δ² modulation optimizes the coordination environments for Eu²⁺ incorporation while enhancing radiative transitions. This work bridges lattice distortion to PLQY via the Bav descriptor, offering a predictive route toward designing inorganic phosphor and advancing material design from trial-and-error to database approaches.