⁷³Ge, ¹⁷O and ²⁹Si hyperfine interactions of the Ge E'₁ center in crystalline SiO₂

E' centers as fundamental radiation-induced defects in amorphous and crystalline SiO2 have been thought to be related to oxygen vacancies for >50years. However, direct proof for oxygen vacancies from experimental (17)O hyperfine data has never been provided. In this contribution, we report on the most complete set of spin Hamiltonian parameter matrices g, A((73)Ge), P((73)Ge), A((17)O), and A((29)Si) for the Ge analog of the classic E1(') center (denoted GeE1(')), determined from single-crystal electron paramagnetic resonance (EPR) analyses of two fast-electron-irradiated, Ge-doped α-quartz samples, including one grown from (17)O-enriched water. These experimental data, particularly the three distinct matrices A((17)O), not only confirm the GeE1(') center to represent spin trapping on a substitutional Ge atom coordinated to three nonequivalent nearest-neighbor O atoms (i.e., the GeO moiety involving an oxygen vacancy) and two next-nearest-neighbor Si atoms but also permit determination of the spin population on all of these atoms. These EPR data also have been evaluated by periodic density functional theory (DFT) calculations to demonstrate that the widely popular single-oxygen-vacancy V(O)(+) model for the GeE1(') center cannot account for A((17)O) arising from three nonequivalent nearest-neighbor oxygen atoms. A new tri-vacancy with an Al impurity model V(SiO2)(Al), on the other hand, reproduces all the EPR experimental hyperfine matrices A((73)Ge), A((17)O), and A((29)Si) and explains the common associations of the E' centers with both Al related defects and superoxide/peroxy radicals in quartz and amorphous silica.