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THE OPTICAL ANALYSIS OF MINERALS

David K. Teertstra

Euclid Geometrics, 843 Queens Boulevard, Kitchener, Ontario N2M 1A6, Canada

E-mail address: en369{at}ncf.ca

Optical analysis combines the measurements of index of refraction (n) and density (D) to closely constrain the structural formula and hence to provide an independent check on composition. Physically, light of specific energy is refracted to a unique degree by each element, so that each photon follows the bonds through the structure of the mineral. The ionic refractivity generally increases with atomic number and is modified by the electrical environment of the bond at each crystallographic site. In general, n changes in proportion to D, such that n D and K = n/D for each mineral composition. From the change n/D of specific mechanisms of substitution, the per-ion contribution (i) to n and D are found with K = (k_id_i), where k_i is the ionic refractivity and d_i is the fractional density. The absolute contribution to density by an ion in the unit-cell volume is |d_i| = m_i/V_cell = w_iD, with D = m_i/V_cell. The fractional density d_i equals the weight fraction of the ion, d_i = w_i = a_iAW/FW, in which each ion (a_i) of atomic weight (AW) contributes to the formula weight (FW). The absolute contribution of the refractivity of Fe to n_almandine is |n_Fe| = k_Fe|d_Fe|. The number of atoms per formula unit in (Fe₂Mg)Al₂Si₃O₁₂ is indicated by K = [k(Fe²⁺)(2AW_Fe) + k(Mg²⁺)(AW_Mg) + k(Al³⁺)(2AW_Al) + k(Si⁴⁺)(3AW_Si) + k(O^2–)(12AW_O)]/FW. A solved set of k_i values yields the weight fractions of ions and the structural formula from the measured index of refraction and unit-cell edge or density.

Keywords: index of refraction, polarized light, optical mineralogy, photon, Gladstone–Dale relation, mineral composition, garnet.

This article has been cited by other articles:

				D. K. Teertstra INDEX-OF-REFRACTION AND UNIT-CELL CONSTRAINTS ON CATION VALENCE AND PATTERN OF ORDER IN GARNET-GROUP MINERALS Can Mineral, April 1, 2006; 44(2): 341 - 346. [Abstract] [Full Text] [PDF]