The variation of tetrahedral bond lengths in sodic plagioclase feldspars |
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| Authors: | Michael W Phillips Paul H Ribbe |
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| Institution: | 1. Department of Geological Sciences, Virginia Polytechnic Institute and State University, 24061, Blacksburg, Virginia, USA
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| Abstract: | Multiple linear regression analysis has been applied to the geometric and chemical variables in sodic plagioclases in order to determine their relative effects on individual T-O bond lengths in the Al1+xSi3?xO8 tetrahedral framework. Using data from crystal structure analyses of low and high albite, An16 and An28, and assuming that low albite is completely ordered, 1 $$\begin{gathered} {\text{T}} - {\text{O = 1}}{\text{.568}} + {\text{(0}}{\text{.122) x (Al content of the T site)]}} \hfill \\ {\text{ }} - {\text{(0}}{\text{.037) x (}}\Delta {\text{{\rm A}l}}_{{\text{br}}} )] + 0.063){\text{ x }}(\Sigma {\text{}}q{\text{/(Na,Ca}} - {\text{O)}}^{\text{2}} ])] \hfill \\ {\text{ }} + {\text{(0}}{\text{.029) x (}} - {\text{1/cosT}} - {\text{O}} - {\text{T)]}} \hfill \\ \end{gathered}$$ where the Al content of a particular tetrahedral (T) site can be estimated from empirically-derived determinative curves, where Δ Albr is a linkage factor to account for the Al content of adjacent tetrahedral sites, where the formal charge on the (Na1?xCax) atom is q=1+x, and where T-O-T is the inter-tetrahedral angle involving the T-O bond. For sodic plagioclases it is essential to know only the anorthite content and the 2Θ131-2Θ1¯31 spacing (CuK α radiation) in order to determine the independent variables in this equation and thus to evaluate the individual T-O distances. The 64 individual T-O distances predicted for the four sodic plagioclases by this equation agree well with the observed T-O bond lengths (σ=0.004 Å; r=0.994), and the method has been used by way of example to rationalize the T-O bond lengths in analcime (cf. Ferraris, Jones and Yerkess, 1972). |
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