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The proposed model for center E 1 Љ . Figure modified after 

The proposed model for center E 1 Љ . Figure modified after 

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Several radiation defects with effective electron spin S=1 have been observed in synthetic alpha-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 desc...

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... The former contains a proton near the oxygen vacancy, wheras the latter with diagnostic 27 Al superhyperfine structures provide experimental proof for the hypothesis that Al impurity plays an important role in the formation of E ′ centres (Jani et al., 1983;Mashkovtsev and Pan, 2018;Mashkovtsev et al., 2019). In addition, various E ′′ centres arising from interactions between two neighbouring E ′ centres have been discovered and characterised with the triplet-state model in recent years (Table S2; Mashkovtsev et al., 2007;Mashkovtsev and Pan, 2011, 2012a, 2012b. ...
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Quartz (trigonal, low-temperature α-quartz) is the most important polymorph of the silica (SiO2) group and one of the purest minerals in the Earth crust. The mineralogy and mineral chemistry of quartz are mainly determined by its defect structure. Certain point defects, dislocations and micro-inclusions can be incorporated into quartz during crystallization under various thermodynamic conditions and by secondary processes such as alteration, irradiation, diagenesis or metamorphism. The resulting real structure is a fingerprint of the specific physicochemical environment of quartz formation and also determines the quality and applications of SiO2 raw materials. Point defects in quartz can be related to imperfections associated with silicon or oxygen vacancies (intrinsic defects), to different types of displaced atoms, and/or to the incorporation of foreign ions in lattice sites and interstitial positions (extrinsic defects). Due to mismatch in charges and ionic radii only a limited number of ions can substitute for Si⁴⁺ in the crystal lattice or can be incorporated in interstitial positions. Therefore, most impurity elements in quartz are present at concentrations below 1 ppm. The structural incorporation in a regular Si⁴⁺ lattice position was proved for Al³⁺, Ga³⁺, Fe³⁺, B³⁺,Ge⁴⁺, Ti⁴⁺, P⁵⁺ and H⁺, of which Al³⁺ is by far the most frequent and often the most abundant. Unambiguous detection and characterization of defect structures in quartz are a technical challenge and can only be successfully realized by a combination of advanced analytical methods such as electron paramagnetic resonance (EPR) spectroscopy, cathodoluminescence (CL) microscopy and spectroscopy as well as spatially resolved trace-element analysis (e.g., LA-ICP-MS, SIMS). The present paper presents a review of the state-of-the-art knowledge concerning the mineralogy and mineral-chemistry of quartz and provides important geological implications of quartz properties.
... Moreover, the Al analog of the E 1 center has never been found in quartz or other SiO 2 forms. Indeed, all but one previously reported E and E centers in quartz and silica do not have any evidence of 27 Al hyperfine or super-hyperfine interactions (SHFI) [9][10][11][12][19][20][21][22][23][24][25][26]. The only exception is E 11 that features an incompletely resolved multiplet in single-crystal EPR spectra measured at X-band frequencies (∼9.3 GHz), which was tentatively interpreted to arise from 27 Al SHFI but did not allow quantitative angular dependence analysis to determine its 27 Al hyperfine parameters [27]. ...
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Two new paramagnetic defects ( and ) have been revealed in neutron-irradiated natural -quartz by using electron paramagnetic resonance (EPR) spectroscopy. The EPR spectra of the center as well as a previously reported but incompletely characterized center demonstrate that their super-hyperfine structures arise from interaction with ²⁷Al, the first-ever examples of Al-associated centers in crystalline quartz. The matrices g and , of , g and of the center, have been determined.
... EPR-NMR spectral fitting using an effective spin S = 5 for the ten strongest satellites flanking the central peak of the dominant Gd 3+ center (Lin et al., 2013a), and (2) EasySpin (Stoll and Schweiger, 2006) simulations for several spectra using a spin Hamiltonian for exchange interaction between two identical Gd 3+ ions equivalent to the dominant Gd 3+ center. The first approach, which is unable to determine the isotropic exchange coupling constant (Mashkovtsev et al., 2007;Lin et al., 2013a), is valid in the strong exchange limit, where the dipolar coupling is the leading term of the Hamiltonian (Bencini and Gatteschi, 1990). This approach yielded an effective dipolar coupling constant D e /g e b e = À30.8 ...
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... Triplet states of E centers are the result of interactions between two neighboring E centers. Several E centers are well studied [8,[15][16][17][18]. The E centers are characterized by HFIs with two 29 Si nuclei and their hyperfine (HF) values may be either about half or full integer of those for the E 1 centers depending on the exchange interaction between the two centers [8,17]. ...
... In all cases radiation damage is dependent on the doses from the point defect creation (E centers and oxygen hole centers or OHC) to the formation of continous trails of amorphous SiO 2 [30]. In this contribution we present EPR investigations of defects in neutron-irradiated quartz up to doses of 10 20 n/cm 2 , with emphasis on the discovery of three new defects (E [13][14][15] ) that have similar spin Hamiltonian parameters and thermal properties to other E centers. ...
... The absence of any "weak" 29 Si SHFS for the E 2 center in quartz and for E γ in amorphous silica is explained by puckering relaxation [35]. For the triplet E 1 center we invoked such a puckering relaxation to explain the calculated quadrupole parameter D and the absence of the observed "weak" 29 Si SHFS [15]. It is amazing that the unique principal g 1 and A 1 ( 29 Si) directions of the E 13 center (table 1) are very similar to those of the center E 9 [11], although the latter has slightly smaller absolute A principal values. ...
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Electron paramagnetic resonance (EPR) of defects in neutron-irradiated natural α-quartz exposed to doses from 10^16 to 10^20 n/cm2 has been studied. New E' centers and other defects have been revealed. The intensities of hole-like defects, including a novel triplet-state H''1 center, and E'-type centers in relation to neutron fluencies and post-irradiation annealing temperature have been investigated. For the new E'13center the primary spin Hamiltonian parameter matrices g and A(29Si) (hyperfine interaction for 29Si) as well as the radiation dose dependence and thermal stability have been determined.
... The absence of a particle-induced CL in pink quartz can arise from either ''self quenching'' or a homogeneous distribution of a particle-induced damage/defects. The former scenario is unlikely because our EPR spectra show that all paramagnetic radiation-induced defects are discrete without evidence for dipolar interactions (Mashkovtsev et al. 2007. The latter explanation is favored on the basis of our previous study of similar drusy quartz crystals at the McArthur River deposit, where partial HF dissolution experiments demonstrated that a particleinduced defects are distributed homogeneously in such FIG. ...
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... The E″ Centers Three oxygen-vacancy defects in triplet states (i.e., the E″ centers) have long been observed in irradiated quartz [32,57,58] but their spin Hamiltonian parameters have quantitatively been determined only recently [59][60][61]. After a synthetic quartz subjected to electron irradiation (3 MeV and a fluence of 10 17 cm −2 ) at room temperature, the E″ 1-7 centers were observed. ...
... After a synthetic quartz subjected to electron irradiation (3 MeV and a fluence of 10 17 cm −2 ) at room temperature, the E″ 1-7 centers were observed. The intensities of the E″ 1-5 centers diminish but those of the E″ 6,7 centers remain unchanged after the sample was kept at room temperature for about half year [59,60]. Mashkovtsev and Pan [61] studied another piece of this crystal using isochronal annealing treatments (5 min each step) immediately after electron irradiation at room temperature. ...
... The biradical state ( S = 1) of two similar defects is characterized by one-half hyperfine value in comparison to the single defect state ( S = 1/2) when the exchange energy is far greater than the hyperfine constant [62]. Therefore, the E″ 1,9 centers are two interacting E′ defects forming biradicals with large exchange terms that centers as well as the E′ 4 center [61] cannot be determined directly from the EPR spectra [59]. With the increase of distance between interacting E′ centers the exchange term decreases and becomes comparable with the strong 29 Si hyperfine values, resulting in hyperfine lines shift to the normal magnetic field positions (i.e. the splitting between the pair of lines at ~40 mT) of the usual E′ centers [61]. ...
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Continuous-wave electron paramagnetic resonance (EPR) spectroscopy has been the technique of choice for the studies of radiation-induced defects in silica (SiO2) for 60 years, and has recently been expanded to include more sophisticated techniques such as high-frequency EPR, pulse electron nuclear double resonance (ENDOR), and pulse electron spin echo envelope modulation (ESEEM) spectroscopy. Structural models of radiation-induced defects obtained from single-crystal EPR analyses of crystalline SiO2 (α-quartz) are often applicable to their respective analogues in amorphous silica (a-SiO2), although significant differences are common.
... The related defects in triplet states (E centers) are less known and, although, we observed a dozen of such centers the microscopic model for them is only tentative [13][14][15]. The only theoretical work for possible models of E defects [16] was based on then incompleted experimental data. ...
... Results and discussion. -A sample with the dimensions of 3 × 6 × 6.5 mm 3 in the X, Y , and Z directions, respectively, was cut for EPR investigations from the same bar of right-handed quartz without any artificial dopant as described in [13]. The sample was irradiated with fast electrons (3 MeV, a fluence of 10 17 cm −2 ). ...
... The explanation for this relatively large RMSD may lie in the triplet-state and biradical-state models used for spin Hamiltonian analyses. For other E centers the two strong 29 Si HF structures are better optimized by one of these approximations [13][14][15]. Probably for the E 9 center we meet the marginal case that both models are not sufficiently good. ...
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The paramagnetic center in triplet state occurring in electron-irradiated, synthetic α-quartz has been investigated by using electron paramagnetic resonance (EPR) spectroscopy. The primary spin Hamiltonian parameter matrices g, D and A (hyperfine interactions for five 29Si nuclei) have now been determined. The principal values and principal directions of D and A matrices allow us to suggest the structural model for this stable triplet defect. The center involves the two unpaired electrons located in the orbitals of two silicon atoms next to one oxygen vacancy each. Firm correlations between the spin Hamiltonian matrix principal axes and crystallographic directions have been attained.
... In these materials, the neutral oxygen vacancy has only an S = 0 ground state (and no low-lying triplet state) because both of the trapped electrons are distributed symmetrically around the vacancy and shared by all adjacent cations (i.e., a "pair" spin system is not formed because the two trapped electrons are not separately localized on different * cation neighbors). Thus far, the most notable examples of stable triplet (S = 1) ground states of oxygen vacancies are the family of E centers in crystalline SiO 2 , where the two electrons are trapped as Si 3+ ions on opposite sides of the vacancy [24][25][26]. ...
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Electron paramagnetic resonance (EPR) is used to investigate the triplet (S = 1) ground state of the neutral oxygen vacancy in bulk rutile TiO2 crystals. This shallow donor consists of an oxygen vacancy with two nearest-neighbor, exchange-coupled Ti3+ ions located along the [001] direction and equidistant from the vacancy. The spins of the two trapped electrons, one at each Ti3+ ion, align parallel to give the S = 1 state. These neutral oxygen vacancies are formed near 25 K in as-grown oxidized TiO2 crystals by illuminating with sub-band-gap 442 nm laser light. The angular dependence of the EPR spectra provides the principal values and axes for the g and D matrices. Observations of the 47Ti and 49Ti hyperfine lines when the magnetic field is along high-symmetry directions show that the two Ti3+ ions are equivalent; i.e., they have equal hyperfine A matrices. The A matrix for each Ti3+ ion in the neutral S = 1 oxygen vacancy is approximately half of the A matrix reported earlier for the one Ti3+ ion in the singly ionized S = 1/2 oxygen vacancy [Brant et al., J. Appl. Phys. 114, 113702 (2013), 10.1063/1.4819805]. The neutral oxygen vacancies are thermally unstable above 25 K. They release an electron to the conduction band with an activation energy near 63 meV and convert to singly ionized S = 1/2 oxygen vacancies. When undoped TiO2 is sufficiently oxygen deficient (i.e., reduced), this combination of conduction band electrons and singly ionized oxygen vacancies may result in carrier-mediated ferromagnetism at room temperature.
... The two parts in the hyperfine coupling constants for the 73 Ge, 29 Si and 17 O nuclei in the Ge E 0 1 center, isotropic a and anisotropic T i , are calculated as follow [42]: ...
... We note that the substitutional Ge atoms in JC324 are not uniformly distributed among the Si positions in the quartz structure. A pair of EPR lines associated with two of the six GeO 4 tetrahedra (denoted as sites 1 and 1 0 ) is $1.7 times more intense than the 73 Ge HF 5th, 6th and 7th lines, and the main lines close to 333 mT, (b) 17 OI hyperfine lines, (c) 17 OII hyperfine lines, and (d) 17 OIII hyperfine lines. other four lines. ...
... other four lines. This observation helps the site assignments among the main lines and their corresponding 73 Ge and 17 O HF lines. ...
... However, the number of E 0 centers is not restricted to the above-mentioned defects. Several EPR signals in the region of 29 Si hyperfine structures (HFS; i.e., two equalintensity lines with the separation of *40 mT) were observed with the applied magnetic field along the crystallographic c-axis in natural and synthetic quartz (Solntsev et al. 1977; Mashkovtsev et al. 2007), although their spin Hamiltonian matrices have not been determined. Also, a [SiO 4 /Li] 0 center with 29 Si hyperfine (HF) values similar to those for E 0 centers was observed in X-ray-irradiated synthetic (Jani et al. 1986) and natural quartz (Bailey and Weil 1991). ...
... A sample with the dimension of 3 9 6 9 6.5 mm 3 in the X, Y, and Z directions, respectively, was cut for EPR investigations from the same bar of the right-handed synthetic quartz as described in Mashkovtsev et al. (2007). To induce the paramagnetic defects, the sample was irradiated with fast electrons (3 MeV, 10 17 cm -2 ). ...
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Single-crystal electron paramagnetic resonance (EPR) spectra of fast-electron-irradiated quartz, after annealing at 120 and 200°C, reveal five new E′ type centers, herein labeled $ E_{ 5}^{\prime } ,\,E_{ 6}^{\prime } ,\,E_{ 7}^{\prime } ,\,E_{ 8}^{\prime } ,\,{\text{and}}\,E_{ 9}^{\prime } $ . Centers $ E_{ 5}^{\prime } ,\,E_{ 7}^{\prime } ,\,{\text{and}}\,E_{ 9}^{\prime } $ are characterized by the orientations of the unique principal g and A(29Si) axes close to a short Si–O bond direction, hence representing new variants of the well-established $ E_{ 1}^{\prime } $ center. Centers $ E_{ 6}^{\prime } $ and $ E_{ 8}^{\prime } $ have the orientations of the unique principal g and A(29Si) axes approximately along a long Si–O bond direction, similar to the $ E_{ 2}^{\prime } $ centers. Therefore, these new E′ type centers apparently arise from the removal of different oxygen atoms and represent variable local distortions around the oxygen vacancies.