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 X_Or (mole fraction of KAlSi₃O₈) and Y_x (one half of the optic axial angle 2V_x) by use of a simple determinative diagram based on the model

Σt₁ = (b₀ + b₁X_Or + b₂X_Orsin²V_x + b₃sin²V_x) / (a₀ + a₁X_Or + a₂X_Orsin²V_x + a₃sin²V_x).

Three sets of coefficients for this equation are required to account for three cases: (A) where X_Or ≤ 0.6; (B) where X_Or > 0.6 and O.A.P. (optical axial plane) ~ ⊥ (010); and (C) where X_Or > 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 X_Or and V_x) 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 n_a, n_b, and n_c 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 ≤ X_Or < 0.6 and 0.6 < X_Or ≤ 1.0.