Packing systematics of the silica polymorphs: The role played by O-O nonbonded interactions in the compression of quartz

Abstract

The anion skeleton of quartz is a distorted body-centered cubic (BCC) arrangement. A hypothetical ideal BCC crystal structure for quartz has been derived and used to locate and describe the unoccupied tetrahedral sites, quantify the distortion of the quartz anion arrangement from ideal BCC, and characterize the role of tetrahedral distortion and O-O interactions in the compression of quartz. Quartz has eight crystallographically nonequivalent tetrahedra, one occupied by silicon and seven unoccupied. These tetrahedra completely fill space, something that cannot be done using only regular tetrahedra. In ideal BCC quartz, the nonequivalent tetrahedra are identical in size and shape with a unique geometry and are referred to as Sommerville tetrahedra. In reality, the unoccupied tetrahedra of quartz are very distorted from both regular and Sommerville tetrahedra. Changes in the unoccupied tetrahedra are responsible for most of the compression in quartz with pressure, as the volume of the Si tetrahedron decreases by <1% over 10.2 GPa, but the volume of the bulk structure decreases by almost 16%. The ideal BCC quartz has been used to quantify the distortion from ideal BCC of the O arrangement in quartz at several pressures up to 10.2 GPa. Distortion decreases by over 60% across this domain. Other parameters have been derived to quantify the distortion of the unoccupied and occupied tetrahedra in quartz from Sommerville tetrahedra, the characteristic tetrahedra of BCC. By all measures, the anion packing in quartz approaches ideal BCC as pressure increases. The compression mechanisms of quartz are compared to those of cristobalite and coesite. Si-O-Si angle-bending controls compression in each of these minerals. The bulk moduli of these minerals are shown to correlate with average nearest intertetrahedral anion distances, consistent with the hypothesis that anion-anion interactions stiffen the Si-O-Si angle as inter-tetrahedral anion distances decrease. The tetrahedral distortion in quartz with pressure is attributed to anion-anion interaction, and is not considered a compression mechanism.

The compression pathway of quartz

“…These facts have spawned a vast literature of experimental and theoretical studies of quartz at ambient and non-ambient conditions. Thompson and Downs (2010) presented a comprehensive review of the literature on the behavior of quartz at high pressure.…”

“…Over this same pressure domain, tetrahedral angle variance (Robinson et al 1971), a traditional measure of tetrahedral distortion, increases from 0.72 to 21.24. Thus, the distortion in the Si tetrahedron is not contributing to the compression of the bulk crystal and the tetrahedron is actually much more resistant to compression than the unoccupied tetrahedral voids around it (Thompson and Downs 2010). Implicit in the above quote (Levien et al 1980) is the idea that an atomic-scale behavior must contribute to the compression of a crystal to be considered a compression mechanism and Thompson and Downs (2010) explicitly adopted this definition.…”

“…Thus, the distortion in the Si tetrahedron is not contributing to the compression of the bulk crystal and the tetrahedron is actually much more resistant to compression than the unoccupied tetrahedral voids around it (Thompson and Downs 2010). Implicit in the above quote (Levien et al 1980) is the idea that an atomic-scale behavior must contribute to the compression of a crystal to be considered a compression mechanism and Thompson and Downs (2010) explicitly adopted this definition. Thompson and Downs (2010) compared observed quartz with a hypothetical high-pressure "endpoint" structure that has a perfectly body-centered cubic (BCC) arrangement of oxygen anions and confirmed the conclusion of Sowa (1988) that quartz becomes more like this structure with pressure.…”

“…Implicit in the above quote (Levien et al 1980) is the idea that an atomic-scale behavior must contribute to the compression of a crystal to be considered a compression mechanism and Thompson and Downs (2010) explicitly adopted this definition. Thompson and Downs (2010) compared observed quartz with a hypothetical high-pressure "endpoint" structure that has a perfectly body-centered cubic (BCC) arrangement of oxygen anions and confirmed the conclusion of Sowa (1988) that quartz becomes more like this structure with pressure. They analyzed the individual responses of the Si tetrahedron and the seven crystallographically non-equivalent unoccupied tetrahedral sites to increases in pressure.…”

“…An important prior result that Thompson and Downs (2010) incorporated into their argument was the Rigid Unit Mode (RUM) theory conclusion that the Si-O-Si angle in quartz can theoretically change without inducing distortion in the silica tetrahedra, implying that the α-quartz structure has no intrinsic geometrical constraint creating the distortion during compression [see Dove et al (1995) for a paper specifically addressing RUM theory and quartz; Ross (2000) for an excellent review of RUM theory applied to silicates with numerous references]. Smith (1963) derived some geometrical constraints that must be satisfied for a quartz structure to contain regular tetrahedra.…”