Abstract

For the entire homogeneous alkali feldspar series, the A1 content (∑t1) of the t1 tetrahedral sites is a measure of structural state: ∑t1 = 2t1 for monoclinic and ∑t1 = (t1o + t1m) for triclinic specimens. ∑t1 can be conveniently estimated from Vx (one-half of the optic axial angle 2 Vx) and XQr (mole fraction of KAlSi308) by using a simple determinative diagram or the equation  
t1b0+b1XOr+b2XOrsin2Vx+b3sin2Vxa0+a1XOr+a2XOrsin2Vx+a3sin2Vx
Three sets of coefficients (multiplied by 1000 in the following table) account for three regions of 2Vx-XOr space: case A, XOr ≤ 0.6; case B, XOr > 0.6 and O.A.P. (optic axial plane) perpendicular or approximately perpendicular to (010); and case C, XOr > 0.6 and O.A.P. parallel to (010).
Case a0 a1 a2 a3 b0 b1 b2 b3 
4.08 -2.35 0.95 -1.28 1.52 -0.18 -1.74 2.88 
1.69 1.63 -2.33 0.69 0.11 2.17 -2.70 3.46 
-1.69 -1.63 -0.70 2.38 -0.11 -2.17 -0.53 3.57 
Case a0 a1 a2 a3 b0 b1 b2 b3 
4.08 -2.35 0.95 -1.28 1.52 -0.18 -1.74 2.88 
1.69 1.63 -2.33 0.69 0.11 2.17 -2.70 3.46 
-1.69 -1.63 -0.70 2.38 -0.11 -2.17 -0.53 3.57 

Tested using data for 109 alkali feldspars whose ∑t1 values were independently estimated from lattice parameters and/or mean T-O bond lengths from crystal-structure analyses, this model estimates ∑t1 within ±0.02 for 83% and ±0.04 for 97% of them. This precision is the same as that from various models that rely on lattice parameters for estimation of St1, e.g., b-c, b-c*, 2θ(O6O)-2θ(2O4) methods, etc.

The model was developed by assuming that the principal refractive indices–symbolized as na, nb, and nc and defined as the principal refractive indices for light vibrating parallel or nearly parallel to crystallographic axes a, b, and c, respectively–vary linearly with ∑t1, for the high sanidine-low microcline series and for the low albite-high albite (or analbite) series. However, for the high albite-high sanidine solid-solution series, as well as the low albite-low microcline series, neither density nor principal refractive indices vary linearly across the entire composition range, but they closely approached linearity in segments between 0.0 ≤ XOr < 0.6 and 0.6 < XOr ≤ 1.0.

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