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 RT electron paramagnetic resonance EPR spectroscopy. 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 unstable such 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 holes existing 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 data and crystallographic directions x-ray
diffraction data have 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. 2–5. For instance, the
detailed analysis of a biradical center in -quartz investi-
gated by electron paramagnetic resonance EPR spectros-
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. 7–9 have
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.
11–13
The positive charge state yields a minimum-
energy configuration with large relaxation of the silicon Si1
Fig. 1 on 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., OI in Fig. 1. In
1997, Boero et al.
14
offered an accurate theoretical estimate
of the
29
Si hyperfine HF coupling 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 origin is
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