The dependence of the SiO bond length on structural parameters in coesite, the silica polymorphs, and the clathrasils

Stepwise multiple regression analyses of the apparent R(SiO) bond lengths were completed 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 significant 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 linhas 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 refineresulting 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 feldstructures like the silica polymorphs for which Po = 2.0. spars, Brown et al. (1969) undertook a study of the apThis result led him to question the validity of Cruickparent tetrahedral TO bond lengths, R(TO), T = AI,Si, shank's (1961) (d-p)7r-bonding model as a general bondobserved 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 fundathe 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 conthat 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 deIn 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 Mulfor the silica polymorphs would be a contradiction. Howliken 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 correlates inversely with -secLSiOSi, despite the assumption in the calculations that all of the SiO bond lengths are constant. Since larger n(SiO) values are usually associated with shorter bonds, wider angles are predicted to involve shorter bonds. In a test of this prediction, Gibbs et al. (1977) collected a relatively precise set of diffraction data for the high-pressure silica polymorph coesite, which contains eight nonequivalent SiO bond lengths and five nonequivalent SiOSi angles. The coesite structure is an ideal system for testing the significance of a correlation between bond length and angle because its SiOSi angles exhibit a relatively wide range of values from 137 to 180°. A regression analysis of the resulting SiO bond-length and -secLSiOSi data shows that the correlation is highly significant, with an rZvalue of 0.96. Gibbs et al. (1977) also found that n(SiO) values calculated for the silicate tetrahedra in coesite serve to rank R(SiO) with shorter bonds involving larger overlap populations. In a study of a more recent refinement of the low tridymite structure, which yielded a relatively large number of bondlength and angle data, Baur (1977) undertook a regression analysis of the SiO bond length as a function of -secLSiOSi for a data set that included data for several silica polymorphs (including the more recent data set for low tridymite but omitting that for coesite) and for eight other silicates, all of which have a constant Po value of 2.0. As only 4% of the variation of R(SiO) could be explained in terms of a linear dependence on -secLSiOSi, he again concluded that the relationship between R(SiO) and -secLSiOSi could not be viewed as a general property ofSiO bonds involving charged-balanced oxide ions. He also asserted that the correlation found by Gibbs et al. (1977) for coesite would "disappear when larger, lessbiased samples are studied." Structural analyses completed for quartz (Levien et aI., 1980), with data recorded at a number of pressures up to about 60 kbar, seemed to support his assertion, with R(SiO) observed to increase with increasing -secLSiOSi (Baur and Ohta, 1982). However, as will be shown later, when pressure is included as a variable in a multiple regression analysis with R(SiO) as the dependent variable, pressure becomes a highly significant independent variable along with -secLSiOSi. With the publication by Konnert and Appleman (1978) of a careful restrained-parameter refinement of the structure of a low tridymite crystal that provided more than 300 individual R(SiO) data, Hill and Gibbs (1979) undertook a regression analysis of these data and of those published for low quartz, low cristobalite, and coesite, all of whose structures were determined at room pressure. Their analysis of this data set indicates that the correlation is highly significant with 74% of the variation in R(SiO) being explained in terms of a linear dependence on -secLSiOSi. In a nonempirical MO calculation of minimum-energy bond-length and angle data for the disilicic acid molecule H6Si207, Newton and Gibbs (1980) obtained theoretical data for the molecule that showed that slightly more of the variation in R(SiO) is explained in terms of a linear 749