Abstract
The Gladstone−Dale relation(1) gives the index of refraction of light through a material as a sum of the optical properties of its oxide components. However, the calculated optical properties of ionic solids are only approximated from the composition, as the refraction also depends on the crystal structure. The Gladstone−Dale relation is now modified so that the specific refractivity of an ion depends on the distance (d) and angle to the surrounding ions (i.e., the structure) and falls off as 1/d2 (in a Coulomb-like manner). Using single values for the refractivity of ions, the calculated and measured indices of refraction agree within n ± 0.0005 (4σ) for the garnet group minerals. Alternatively, with the structural formula from a measured composition, the density can be calculated from the index of refraction or the unit cell volume.
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