The variation of tetrahedral bond lengths in sodic plagioclase feldspars

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, $$\begin{gathered} {\text{T}} - {\text{O = 1}}{\text{.568}} + {\text{[(0}}{\text{.122) x (Al content of the T site)]}} \hfill \\ {\text{ }} - {\text{[(0}}{\text{.037) x (}}\Delta {\text{{\rm A}l}}_{{\text{br}}} )] + [0.063){\text{ x }}(\Sigma {\text{[}}q{\text{/(Na,Ca}} - {\text{O)}}^{\text{2}} ])] \hfill \\ {\text{ }} + {\text{[(0}}{\text{.029) x (}} - {\text{1/cosT}} - {\text{O}} - {\text{T)]}} \hfill \\ \end{gathered}$$ (1) 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 (CuKα radiation) in order to determine the independent variables in this equation and thus to evaluate the individual T-O distances.