Hyperfine splitting arising from "0 for the Ge'+ (S = -') uncompensated [Ge04], "aswell as chargecompensated [Ge04/Li]z c centers has been measured in an isotopically enriched a-quartz crystal. The EPR results indicate that the Ge04 tetrahedron is distorted for [Ge04], and [Ge04/Li]c so that no two oxygen ions are symmetry equivalent. In contrast, for [Ge04],, and [Ge04/Li]0"the expected local symmetry (C2) is present and only two types of oxygen atoms are observed. Inclusion of the oxygenic contribution brings the total measured spin population to 100go (within the margin of probable errors).Analysis of the ' 0 hyperfine matrices revealed that the majority of the oxygenic spin density is found on only two of the four oxygen atoms, in 2p orbitals. For each center studied, the unique principal direction of the 0 hyperfine matrix of the high-spin-density oxygen atoms lies along the O-O interatomic direction of these two oxygen atoms. The unique principal direction of the Ge hyperfine matrix lies along the bisector of angle 0-Ge-0 for these same oxygen atoms. Comparison of the various "0 hyperfine splitting patterns furnishes conclusive proof of an isomorphic relationship between centers [Ge04], and [Ge04/Li]c and also between [Ge04]tt and [GeO~/Li]". We conclude that the compensated centers basically have the same electronic structure as the corresponding uncompensated centers, with the compensating Li+ causing only a minor perturbation. The EPR data are consistent with a qualitative model which suggests that the MO of the unpaired electrons in electron-rich paramagnetic defects resembles the LUMO of a Si(OSi&&4)4 cluster model for quartz.
Ab-initio self-consistent-field molecular-orbital (SCF MO) Hartree-Fock (HF) calculations using the STO-3G, 6-31G, and 6-31G' basis sets, were performed to model quasi-tetrahedral silicon species in silicon dioxide.Mostly nine-atom clusters, [Si(OH),]9t, with charge number qt = 0 or + 1, were studied. The positions of the Si and 0 atoms were varied to achieve minimum total energies, while the protons were held fixed in the 0-(neighboring)Si direction to simulate the rigid crystal surroundings. The aquartz-type local symmetry GL was found to be retained for the neutral cluster, but not for the ionic one. The unrestricted HF calculations indicate that the latter paramagnetic centre, (qt = + l), has its spin population almost entirely on one short-bonded oxygen ion bonded weakly to its neighboring Si, and is quite high in energy (9.55 eV with 6-31G) compared to the diamagnetic centre (qt = 0). The ionization energy is much higher than the self-trapping potential of the polaronic hole, a fact which may account for the failure so far to observe a [SiO,]
Ab initio SCF-MO Hartree-Fock calculations were performed using the STO-3G, 6-31G, and 6-31G* basis sets to model hypothetical substitutional carbon impurities in silicon dioxide. We utilized nine-atom clusters, [C(OH),]qt, with charge number qt = 0 and + 1. The positions of the C and 0 atoms were varied to achieve minimum total energies, while the fured protons served to simulate the rigid crystal surroundings. In the optimized configuration of the neutral cluster, the C-0 bond lengths are appreciably longer than typical C-0 bonds, indicating relatively weak bonds for a carbon impurity at a sipcon site. For comparison, the relative positions of all nine atoms in the [C(OH),]O model were allowed to vary. This unconstrained model yielded more normal bond lengths and was lower in energy than the fured-proton model by 6.80 eV with the 6-31G* basis set. The free-H model compared favorably with the x-ray diffraction data for an analogous orthocarbonate. Our results are in concert with the lack of reports of any substitutional carbon impurity in a-quartz. In the fured-H models, the twofold local symmetry was found to be retained when qt is 0 but not when qt is + 1. For the latter ion, the unrestricted H-F calculations indicate that this paramagnetic center has its spin population almost entirely on one oxygen ion and is high in energy (5.31 eV with 631G) compared to the diamagnetic neutral one. Conclusions reached with the nine-atom clusters were confirmed by a series of calculations on the extended model [C(0SiH3)Jo.
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