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The Dependence of the Sio Bond Length on Structural Parameters in Coesite, the Silica Polymorphs, and the Clathrasils

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The Dependence of the Sio Bond Length on Structural Parameters in Coesite, the Silica Polymorphs, and the Clathrasils American Mineralogist, Volume 75, pages 748-754, 1990 The dependence of the SiO bond length on structural parameters in coesite, the silica polymorphs, and the clathrasils M. B. BOISEN, JR. Department of Mathematics, Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061, U.S.A. G. V. GIBBS, R. T. DOWNS Department of Geological Sciences, Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061, U.S.A. PHILIPPE D' ARCO Laboratoire de Geologie, Ecole Normale Superieure, 75230 Paris Cedex OS, France ABSTRACT Stepwise multiple regression analyses of the apparent R(SiO) bond lengths were com- pleted for coesite and for the silica polymorphs together with the clathrasils as a function of the variables};(O), P (pressure), f,(Si), B(O), and B(Si). The analysis of 94 bond-length data recorded for coesite at a variety of pressures and temperatures indicates that all five of these variables make a significant contribution to the regression sum of squares with an R2 value of 0.84. A similar analysis of 245 R(SiO) data recorded for silica polymorphs and clathrasils indicate that only three of the variables (B(O), };(O), and P) make a signif- icant contribution to the regression with an R2 value of 0.90. The distribution of B(O) shows a wide range of values from 0.25 to 10.0 A2 with nearly 80% of the observations clustered between 0.25 and 3.0 A2 and the remaining values spread uniformly between 4.5 and 10.0 A2. A regression analysis carried out for these two populations separately indicates, for the data set with B(O) values less than three, that };(O) B(O), P, and };(Si) are all significant with an R2 value of 0.62. A similar analysis for the remaining data indicates that only B(O) is significant with an R2 value of 0.52. The relationships between these results and those published previously are discussed. INTRODUCTION because data used to construct the correlation were either The extent to which various parameters correlate with imprecise or not corrected for thermal motion. In support apparent SiO bond lengths, R(SiO), observed for silicates of his claim, he completed weighted and unweighted lin- has been the subject of debate since Cruickshank (1961) ear regression analyses on the same data set (omitting the first proposed, from his (d-p)7r-bonding model, that R(SiO) imprecise data), with the tridymite data corrected for should correlate inversely with LSiOSi. At that time, few thermal motion using the riding model and data for four precise bond-length and angle data were available, and disilicates that have a constant Po value of 2.0. As the so the correlation could not be tested. Following refine- resulting r2 value was about zero, he concluded that the ments of diffraction data recorded at room temperature R(SiO) vs. LSiOSi correlation does not exist for crystal and pressure for a number of silica polymorphs and feld- structures like the silica polymorphs for which Po = 2.0. spars, Brown et al. (1969) undertook a study of the ap- This result led him to question the validity of Cruick- parent tetrahedral TO bond lengths, R(TO), T = AI,Si, shank's (1961) (d-p)7r-bonding model as a general bond- observed for these framework structures and concluded ing theory for the silicates. On the other hand, Taylor that R(TO) correlates inversely with L TOT. Baur (1971) (1972) completed an unweighted regression analysis of observed a similar correlation between R(SiO) and LSiOSi the bond-length data for the silica polymorphs (without for the disilicates, but he ascribed it to a more funda- the keatite data), each measured at room temperature and mental correlation between R(SiO) and Po, the sum of for quartz, measured at high temperatures, all corrected the Pauling strengths of the bonds reaching each oxide for thermal motion again using the riding model. He found ion bonded to Si. In the silica polymorphs, Po has a con- that the R(SiO) vs. LSiOSi correlation is significant at the stant value of 2.0, whereas it varies in both the feldspars 95% level with an r2 value of 0.20. and the disilicates. If the variation in R(SiO) is not de- In a theoretical study of SiO bond length vs. LSiOSi pendent upon LSiOSi in silicates for which Po = 2.0, as variations in silicates, Gibbs et al. (1972) undertook asserted by Baur (1971), then the correlation observed semiempirical molecular orbital calculations of the Mul- for the silica polymorphs would be a contradiction. How- liken overlap populations, n(SiO), of the SiO bridging ever, Baur (1971) claimed that this is not a contradiction bonds in an Si20?6 disilicate ion. They found that n(SiO) 0003-004X/90/0708-0748$02.00 748 BOISEN ET AL.: SiO BOND LENGTH AND STRUCTURAL PARAMETERS 749 correlates inversely with -secLSiOSi, despite the as- dependence on sumption in the calculations that all of the SiO bond lengths are constant. Since larger n(SiO) values are usu- 1 /,(0) = ally associated with shorter bonds, wider angles are pre- 1 - secLSiOSi dicted to involve shorter bonds. In a test of this predic- tion, Gibbs et al. (1977) collected a relatively precise set than on -secLSiOSi. The parameter /,(0) was derived of diffraction data for the high-pressure silica polymorph from hybridization theory (Coulson, 1952) and defines, coesite, which contains eight nonequivalent SiO bond for the SiO bonds of an SiOSi disiloxy group, the fraction lengths and five nonequivalent SiOSi angles. The coesite of s character of the orbitals on the bridging 0 involved structure is an ideal system for testing the significance of in bond formation. According to the theory, the greater a correlation between bond length and angle because its the s character, the shorter the bond length. SiOSi angles exhibit a relatively wide range of values from In a more recent study of the correlation between R(SiO) 137 to 180°. A regression analysis of the resulting SiO and LSiOSi for the silica polymorphs, Baur and Ohta bond-length and -secLSiOSi data shows that the corre- (1982) undertook a linear regression analysis of the bond- lation is highly significant, with an rZvalue of 0.96. Gibbs length and angle data recorded for low quartz for pres- et al. (1977) also found that n(SiO) values calculated for sures up to about 60 kbar (Levien et aI., 1980) and for the silicate tetrahedra in coesite serve to rank R(SiO) with low cristobalite (Dollase, 1965), synthetic low tridymite shorter bonds involving larger overlap populations. In a (Baur, 1977), C2/c coesite (Gibbs et aI., 1977) and P2/a study of a more recent refinement of the low tridymite coesite (Kirfel et aI., 1979), all recorded at 1 atm. Al- structure, which yielded a relatively large number of bond- though the correlation between R(SiO) and -sec(LSiOSi) length and angle data, Baur (1977) undertook a regression was found to be highly significant, the calculations indi- analysis of the SiO bond length as a function of cated that only 9% of the variation in the apparent bond -secLSiOSi for a data set that included data for several lengths could be explained by such a model. The failure silica polymorphs (including the more recent data set for of the model to explain a larger percentage of the varia- low tridymite but omitting that for coesite) and for eight tion in R(SiO) may be ascribed to the fact that one or other silicates, all of which have a constant Po value of more essential parameters (such as pressure) were not in- 2.0. As only 4% of the variation of R(SiO) could be ex- cluded as independent variables in their analysis. The plained in terms of a linear dependence on -secLSiOSi, Konnert and Appleman (1978) data set for low tridymite he again concluded that the relationship between R(SiO) was not included in the linear regression analysis because and -secLSiOSi could not be viewed as a general prop- the Si-Si separations in its structure were constrained not erty ofSiO bonds involving charged-balanced oxide ions. to exceed 3.08 A during its refinement. He also asserted that the correlation found by Gibbs et In a molecular orbital modeling of the coesite structure al. (1977) for coesite would "disappear when larger, less- as a function of pressure, Ross and Meagher (1984) ob- biased samples are studied." Structural analyses com- served that the R(SiO) vs. -secLSiOSi relationship holds pleted for quartz (Levien et aI., 1980), with data recorded for data collected at a fixed pressure. The inclusion by at a number of pressures up to about 60 kbar, seemed to Baur and Ohta (1982) of the low quartz data recorded at support his assertion, with R(SiO) observed to increase a variety of pressures in their linear regression analysis with increasing -secLSiOSi (Baur and Ohta, 1982). without the presence of pressure as an independent vari- However, as will be shown later, when pressure is includ- able may make it impossible to draw valid conclusions ed as a variable in a multiple regression analysis with about the correlation. Smyth et al. (1987) have under- R(SiO) as the dependent variable, pressure becomes a taken a refinement of coesite diffraction data recorded at highly significant independent variable along with 15 and 298 K and have observed that R(SiO) of the min- -secLSiOSi. With the publication by Konnert and Ap- eral and those recorded for cristobalite and quartz at a pleman (1978) of a careful restrained-parameter refine- variety of temperatures are highly correlated with ment of the structure of a low tridymite crystal that pro- -secLSiOSi with an r2 of 0.89.
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