Occupancy-Weighted Global Instability Index: A Pragmatic Metric for Disordered Crystal Structures

The Global Instability Index was developed to aggregate bond valence sum deviations into a single structural quality metric, but its standard formulation weights all species at all crystallographic sites equally regardless of fractional occupancy. For disordered structures, minority species at mixed-occupancy sites contribute disproportionately, systematically inflating apparent instability in well-refined phases. Here, a Weighted-Average Global Instability Index (WAGII) is proposed that weights each deviation by its site occupancy, requiring no new parameters and reducing identically to standard GII for ordered structures. Validation across 363 rock salt and 36 spinel structures confirms that the correction scales with occupancy asymmetry, reaching 66% at minority fractions below 0.05 and diminishing toward zero as occupancies approach parity. In 27% of mixed-occupancy rock salts, WAGII exceeds GII, identifying majority-species strain that standard GII obscures. WAGII addresses previously reported occupancy-dependent limitations of GII at the structural level and is proposed for routine structural analyses and validation of disordered phases. WAGII is implemented in Eir v1.7.2, and the methodology is easily adaptable for other crystallographic software developers.