Paramagnetic Spectra ofE2′Centers in Crystalline Quartz

The electron spin resonance spectra of the ${E_2}^{\prime }$ center, a defect of the quartz structure, are in agreement with a phenomenological Hamiltonian for a spin state $S=\frac{1}{2}$. The Hamiltonian is $\mathcal{H}=\frac{1}{6}N\Sigma {i=1\mathrm{}}^{}{}_{}{}^6{}_{}{}^{}(\beta \mathrm{H}·{\mathrm{g}}_i·\mathrm{S}+\mathrm{S}·{\mathrm{A}}_{\mathrm{ki}}·{\mathrm{I}}_{\mathrm{ki}})$. The $i$ subscript refers to the symmetry operations of the quartz crystal and indicates that a defect at an arbitrary point in the unit cell has an equal probability of being at five other equivalent sites which are related by the symmetry operations of the crystal. The $k$ subscript identifies the nuclear sites with which a defect at the $i\mathrm{th}$ site may interact. The $k=1\mathrm{}$ site is occupied by a proton for nearly all of the ${E_2}^{\prime }$ centers. $k=2, 3, 4, 5$ are Si sites. Of these sites, 4.7% are occupied by ${\mathrm{Si}}^{29}$ ($I=\frac{1}{2}$). The occupancy of the $k=1\mathrm{}$ site by a proton was confirmed by substituting a deuteron for the proton. The hyperfine interaction with the proton is less than the magnitude of the interaction with the field $H$ at the proton, i.e., $\left|\gamma \right(\mathrm{H}\left){\beta }_{n}H\right|>\mathrm{}\left|A\right|, \mathrm{}\left|B\right|\mathrm{}$ where $A$ and $B$ are the principal values of the hyperfine interaction tensor. The angular variation of the splitting agrees with the values calculated on this basis. The hyperfine interactions with ${\mathrm{Si}}^{29}$ were not of this form. A model is proposed which is in agreement with the observations. The principal feature of the model is a Si-O vacancy with an electron trapped on the defect Si from which the O ion is missing. The proton is trapped nearby. The data for the ${\mathrm{E}}_2$′ center are compared with the data for the ${E_1}^{\prime }$ center.