Alkali feldspars: ordering, composition and optical properties
For the entire alkali feldspar series, Σt₁ (total Al content in the T₁ sites, a quantitative measure of structural state or Al,Si long-range ordering) can be closely estimated from XOr (mole fraction of KAlSi₃O₈) and Yx (one half of the optic axial angle 2Vx) by use of a simple determinative diagram based on the model
Σt₁ = (b₀ + b₁XOr + b₂XOrsin²Vx + b₃sin²Vx) / (a₀ + a₁XOr + a₂XOrsin²Vx + a₃sin²Vx).
Three sets of coefficients for this equation are required to account for three cases: (A) where XOr ≤ 0.6; (B) where XOr > 0.6 and O.A.P. (optical axial plane) ~ ⊥ (010); and (C) where XOr > 0.6 and O.A.P. = (010). They are (multiplied by 1000):
Tested by the data from 109 alkali feldspars in the literature and the author's experiments, this model estimates Σt₁ (given XOr and Vx) with a standard error of 0.02, which is essentially the same as when Σt₁ is estimated from refined lattice parameters determined by X-ray diffraction methods.
The model was developed by assuming that the principal refractive indices for sodium light - symbolized as na, nb, and nc dependent upon whether the corresponding principal vibration axis was parallel or most nearly parallel to crystallographic axes a, b and c - varied linearly with Σt₁ for the high-sanidine to low-microcline series and for the low albite to high albite (or analbite) series. However, for the high albite to high sanidine solid solution series, as well as the low albite to low microcline series, neither density nor principal refractive indices vary linearly across the entire composition range, but they closely approached linearity between 0.0 ≤ XOr < 0.6 and 0.6 < XOr ≤ 1.0.