Biradical states of oxygen-vacancy defects in -quartz R. I. Mashkovtsev* Institute of Geology and Mineralogy, SB RAS, 630090 Novosibirsk, Russia D. F. Howarth and J. A. Weil Department of Chemistry, University of Saskatchewan, Saskatoon, Saskatchewan, Canada S7N 5C9 Received 31 July 2007; revised manuscript received 16 October 2007; published 21 December 2007 Several radiation defects with effective electron spin S = 1 have been observed in synthetic -quartz, using room-temperature RTelectron paramagnetic resonance EPRspectroscopy. It turns out that these defects had better be considered as biradicals, i.e., pairs of S =1 / 2 species. The parameter matrices g 1 , g 2 , D as well as matrices A describing the hyperfine interactions with two slightly inequivalent 29 Si nuclei have been deter- mined for the most intense but RT unstablesuch defect, which herein is labeled E 1 . The triplet-state approach and the biradical approach are compared. Inter-electron distances have been estimated using magnetic dipole concepts. A structure for center E 1 is proposed, suggesting an oxygen O 0 vacancy with two unpaired elec- trons holesexisting at silicon cations on opposite sides of the cavity, and the model is compared with the observed data and with published results for related single-unpaired electron species. Firm correlations be- tween spin-Hamiltonian parameter matrix principal axes EPR dataand crystallographic directions x-ray diffraction datahave been attained. DOI: 10.1103/PhysRevB.76.214114 PACS numbers: 61.72.Hh, 76.30.Mi, 42.70.Ce I. INTRODUCTION Silicon dioxide in its various forms is among the most extensively used materials. Since many of its interesting properties persist in its different varieties, SiO 2 is used in many forms and for various purposes. The importance of oxygen-deficient defects in SiO 2 arises mostly from the wide application of the material in a variety of electronic and op- tical devices. In all of these applications, the nature and num- ber of defects are crucial to the reliability. On the more eso- teric side, SiO 2 is the material which recently has permitted the first single electron spin detection. 1 The pointlike centers in -quartz have been studied ex- tensively over the past 50 years, both experimentally and theoretically for reviews, see Refs. 25. For instance, the detailed analysis of a biradical center in -quartz investi- gated by electron paramagnetic resonance EPRspectros- copy has been published, but is not yet well understood. 6 The well-known paramagnetic E' defects, each with a single un- paired electron spin S =1 / 2, and thought to be associated with an oxygen vacancy, are quite abundant and can be eas- ily generated in SiO 2 . Experimental results for center E 1 ' Refs. 79have caused lengthy discussions about the model of this center. The substantial spin density observed in one Si sp 3 nonbond- ing orbital is not in accord with the presence of a single oxygen vacancy. An agreement with the experimental result is possible provided a sufficiently large asymmetric relax- ation of the two Si atoms facing the vacancy is involved. In -quartz, the asymmetry for a positively charged oxygen va- cancy, VO + , was originally proposed by Feigl et al. 10 in 1974. Further theoretical efforts have improved this assumption. 1113 The positive charge state yields a minimum- energy configuration with large relaxation of the silicon Si1 Fig. 1on the long-bond side of the vacancy. This silicon is thought to move through its basal oxygen plane and to bond with an oxygen atom, making that O atom threefold coordi- nated, and the spin is localized on the other silicon Si0, moved toward the oxygen vacancy e.g., OIin Fig. 1. In 1997, Boero et al. 14 offered an accurate theoretical estimate of the 29 Si hyperfine HFcoupling parameters for E 1 ' in -quartz and the equivalent center E ' in vitreous silica a-quartz, one that turns out to be in rather good agreement with the experimental result, 9 and thus, a general consensus about a microscopic model has nearly been reached. How- ever, alternative models have been proposed, involving a FIG. 1. Portrait of a fragment of the crystalline structure of -quartz showing a Si 2 O 7 unit including the neighboring silicon atoms see Ref. 19. Here, the three axes a i are the piezoelectric axes, and axis z not shown, plane of the paper, at the originis the crystal optic axis c. The oxygen anions are labeled with Roman numerals. PHYSICAL REVIEW B 76, 214114 2007 1098-0121/2007/7621/21411411©2007 The American Physical Society 214114-1