The Canadian Mineralogist
Volume 34, pages 595-603 (1996)
OPTICAL PROPERTIES OF C2/c PYROXENES: A POINT-DIPOLE EXPLANATION
RICHARD N. ABBOTT, JR.*
Department of Geology, University of the West Indies, Mona, Kingston 7, Jamaica
* Correspondence to: Department of Geology, Appalachian State University, Boone, North Carolina 28608, U.S.A.
Abstract
Using point-dipole theory (Abbott 1993, 1994a, b), electronic polarizabilities ( p) were determined for various M1, M2 and T cations,
bridging (Ob) and non-bridging (Onb) oxygen atoms in thirteen C2/c pyroxenes. Because the number of variable polarizabilities (5) exceeds
the number of constraints (4) on the optical properties ( , , , Z c, for a given wavelength of incident light), there are an infinite number of
solutions (combinations of calculated values for p) for each of which the discrepancy (expressed as a least square residual, R) between calculated
and observed optical properties is a minimum. In order to find the correct solution for each clinopyroxene, solutions were determined for several
fixed values of p(T). For each fixed value of p(T), the solution is unique, within the limits of precision of the least-squares procedure.
Unrealistic solutions were then rejected. For a particular clinopyroxene, solutions proved to be similar and reasonable wherever the final (minimum)
value for R is very small. For each clinopyroxene, the best solution (set of p values) was taken to be the one giving the smallest possible R-value.
The calculations show the following: (1) For an element present in more than one structure, p can vary considerably from one structure to
another in ways that are not clearly related to chemical composition or structure; thus calculated values for p(T) range from 0.105 to 0.40 Å3, those
for p(Ca), from 0.25 to 1.03 Å3, those for p(Ob), from 1.16 to 1.55 Å3, and those for p(Onb), from 1.29 to 1.60 Å3. (2) For each structure, the sum
of the calculated p values for one unit cell is consistently less by the same amount (approximately 5%) than the sum of p values calculated from the
Lorentz-Lorenz formula using the observed indices of refraction. (3) The optic-axial half-angle, V , decreases with increasing p(T), from V = 64 ,
p(T) = 0.105 Å3 in kosmochlor to V = 27 , p(T) = 0.40 Å3 in subsilicic titanoan aluminian diopside. The relationship is well defined but
distinctly nonlinear. (4) The relationship between extinction angle Z c and the ratio p(Ob)/ p(Onb) is approximately linear, Z c = -350 p(Ob)/ p(Onb)
+ 420, (Z c in ; + in obtuse a c), such that Z c increases with decreasing p(Ob)/ p(Onb).