The variation of tetrahedral bond lengths in sodic plagioclase feldspars

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 Al_1+xSi_3?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 Al_br is a linkage factor to account for the Al content of adjacent tetrahedral sites, where the formal charge on the (Na_1?xCa_x) 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 2Θ₁₃₁-2Θ_1¯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).