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 l(O), P (pressure), f (SD, B(O), and B(Si). The analysis of 94 bond-length data recorded for coesite at a variety ofpressures and temperatures indicates that all five of these variables make a signiflcant 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),I(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 A'with nearly 800/o of the observations clustered between 0.25 and 3.0 A, and the remaining values spread uniformly between 4.5 and 10.0 4,. A regression analysis carried out for these two populations separately indicates, for the data set with,B(O) values less than three, thatf(O) B(O), P, andf(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. INrnOnUCrrON 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) earregressionanalysesonthesamedataset(omittingthe first proposed, from his (d-p)zr-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 P value was about zero, he concluded that the ments of diffraction data recorded at room temperature R(SiO) vs. /SiOSi correlation does not exist for crystal and pressure for a number of silica polymorphs and feld- structures like the silica polymorphs for which p" : 2.0. spars, Brown et al. (1969) undertook a study of the ap- This result led him to question the validity of Cruickparent tetrahedral TO bond lengths, R(TO), T : Al,Si, shank's (1961) (d-phr-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 ITOT. Baur (1971) (1972) completed an unweighted regression analysis of observed a similar correlation between R(SiO) and ZSiOSi the bondJength 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 qluartz, 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 950/o level with an P value of 0.20.