P-Cristobalite

At approximately 0.5 GPa /I-quartz will transform directly to p -cristobalite. 

The fact that silsesquioxane molecules like 2-7 contain covalently bonded reactive functionalities make them promising monomers for polymerization reactions or for grafting these monomers to polymer chains. In recent years this has been the basis for the development of novel hybrid materials, which offer a variety of useful properties. This area of applied silsesquioxane chemistry has been largely developed by Lichtenhan et al With respect to catalysis research, the chemistry of metallasilsesquioxanes also receives considerable current interest. As mentioned above, incompletely condensed silsesquioxanes of the type R7Si70g(0H)3 (2-7, Scheme 4) share astonishing structural similarities with p-tridymite and p-cristobalite and are thus quite realistic models for the silanol sites on silica surfaces. Metal... 

Silicon itself crystallizes with the same structure as diamond. Its normal oxide, silica, Si02, is polymorphic and in previous sections we have discussed the crystal structure of two of its polymorphs—P-cristobalite (Section 1.5.2) and P-quartz ... 

Many attempts have been made to measure silanol surface density (aon)-Her [7] estimated Ooh to be equal to 8 groups/nm on the basis of the [100] face of P-cristobalite. However, most porous amorphous silicas show surface silanol concentration on the level of 4.6 to 5 groups/nm [6]. 

Its existence at room temperature has been questioned by Geller and Thurmond (1955) who consider the X-ray diffraction pattern, formerly attributed to SiO, to arise from a mixture of P cristobalite and silicon carbide the carbon being derived from the reaction vessel. 

Figure 11. T(r) functions for the high and low temperatures phases of cristobalite obtained from neutron total scattering measurements. The two peaks at low-r correspond to the Si-0 and 0-0 bonds. The dashed lines trace features in T(r) for p-cristobalite that are not seen in the T(r) for a-cristobalite.

Figure 12. Polyhedral representations of the atomic configurations (from RMC) of the high and low temperature phases of cristobalite, viewed down a common direction that corresponds to [1,M] in P-cristobalite.

The nature of the structural disorder in P-cristobalite has been discussed from the perspective of the RUM model (Swainson and Dove 1993, 1995a Hammonds et al. 1996, Dove et al. 1997, 1998, 1999bX The basic idea is that there are whole planes of wave... 

Figure 13. Si-O-Si and Si-Si-Si angular distribution functions for cristobalite at various temperatures, obtained from analysis of the RMC configurations. The two unmarked plots lying between the two labelled plots for p-cristobahte correspond to intermediate temperatures. The plots for a-cristobahte show features not seen in any of the plots for p-cristobalite.

The RUM density of states plots for silica glass and P-cristobalite are shown in Figure 25. The important point, as noted earlier, is that the RUM density of states tends towards a constant value as 0. We do not yet understand the origin of this RUM flexibility. 

Figure 25. RUM density of states of p-cristobalite and silica glass.

Stirling WG (1972) Neutron inelastic scattering study of the lattice dynamics of strontium titanate harmonic models. J Phys C Solid State Physics 5 2711-2730 Swainson IP, Dove MT (1993) Low-frequency floppy modes in p-cristobalite. Phys Rev Letters 71 193-196... 

Swainson IP, Dove MT (1995a) Molecular dynamics simulation of a- and p-cristobalite. J Phys Condensed Matter 7 1771-1788... 

Swainson IP, Dove MT (1995b) On the thermal expansion of p-cristobalite. Phys Chem Minerals 22 61-65 Tantz FS, Heine V, Dove MT, Chen X (1991) Rigid unit modes in the molecular dynamics simulation of qnartz and the incommensurate phase transition. Phys Chem Minerals 18 326-336 Teznka Y, Shin S, Ishigame M (1991) Observation of the silent soft phonon in p-quartz by means of hyper-raman scattering. Phys Rev Lett 66 2356-2359... 

Vallade M, Berge B, Dolino G (1992) Origin of the incommensurate phase of quartz II. Interpretation of inelastic neutron scattering data. J Phys, I. 2 1481-1495 Welberry TR, Hua GL, Withers RL (1989). An optical transform and Monte Carlo study of the disorder in P-cristobalite Si02. Journal of Applied CrysMlogr 22 87-95... 

Withers RL, Thompson JG, Welberry TR (1989) The structure and microstmcture of a-cristobalite and its relationship to P-cristobalite. Phys Chem Minerals 16 517-523 Withers RL, Thompson JG, Xiao Y, Kirkpatrick RJ (1994) An electron diffraction study of the polymorphs of Si02-tridymite. Phys Chem Minerals 21 421 33... 

From its sensitivity to short-range structure and low-frequency dynamics, NMR spectroscopy provides some constraints on the nature of the P-cristobalite structure. For cristobalite, only powder NMR techniques can be applied, because large single crystals do not survive the a-P transition intact. It is helpful to consider also AlP04-cristobalite, because it is similar in essential respects to Si02 and the cubic point symmetry of the Al-position in the average structure of the P-phase provides some additional constraints. 

Figure 6. Local structure and disorder in the oxygen positions of p-cristobalite. Large circles correspond to the cation positions, Si for Si02, A1 at the center and P at the comers for AIPO4 cristobalite. Small circles correspond to oxygen positions for one of the a-like orientational variants.

Figure 8. Variation of Si NMR chemical shifts for Si02 polymorphs with the average Si-O-Si angle. The solid line corresponds to angular dependence predicted by quantum chemical calculations. Dotted line corresponds to 5i measured for p-cristobalite (Fig. 7), from which an average Si-O-Si angle of 152° can be inferred.

Although these NMR data clearly support a dynamical model for disorder in P-cristobalite, they are not sensitive to whether the motions of adjacent oxygens are correlated (as required for a model of re-orienting twin domains), or, whether the motion is continuous or a hopping between discrete positions they indicate only that the path of each oxygen traces a pattern with 3-fold or higher symmetry over times of the order 4.7-10 s. Thus, these results cannot discriminate between models based on RUMs or dynamical twin domains, and place only a lower limit on the timescale of the motions. A tighter restriction... 

A small complication arises from the presence of crystal defects, which at normal concentrations result in a small residual EFG such that the average Cq is not identically 0. Quadrupolar nuclei in all nominally cubic materials experience small EFG s due to charged defects (e.g., Abragam, pp. 237-241) and that observed for AIPO4 P-cristobalite is smaller than typically observed for crystals such as... 

Figure 11. Simulated spectra for the outer [+(3/2,5/2)] satellite transitions for Al in ALPO4 P-cristobalite for a model of re-orienting twin- and anti-phase domains of a-like symmetry. Spectral width for the ordered domains (bottom,...

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