Abstract
A point-dipole calculation which incorporates an expression for the Lorentz-factor tensor has been used to model the effect of chemical substitution on refractive index and optic axial angle (2V). Isotropic electronic polarizabilities for the sodium D line are refined by least-squared methods from lattice dipole sums and observed refractive indices. Although the assumption of isotropic polarizability is unrealistic for many mineral structures, the model is useful in interpreting the relationship between structure, chemical composition, and optical properties.
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Abs-Wurmbach I, Langer K, Seifert F, Tillmans E (1981) The crystal chemistry of (Mn3+, Fe3+)-substituted andalusites (viridines and kanonaite), (Al1−x−y Mn3+Fe3+)2(O/SiO4): crystal structure refinements, Mössbauer, and polarized optical absorption spectra. Z Kristallogr 155:81–113
Armbruster Th, Bloss FD (1982) Orientation and effects of channel H2O and CO2 in cordierite. Am Mineral 67:284–291
Armbruster Th, Bürgi HB (1982) Orientation of CO2 in the cavity of cordierite, a single-crystal x-ray study at 100, 300 and 500 K. Fortschr Mineral 60, Beih 1:37–39
Armbruster Th, Irouschek A (1982) Cordierites from the Lepontine Alps: Na+Be⇋Al substitution, gas content, cell parameters and optics. Contrib Mineral Petrol 82:389–296
Armbruster Th (1986) Effect of H2O on the structure of low-cordierite, a single-crystal X-ray study. In: Crystal Chemistry of Minerals, Proceedings of the 13th general meeting of the International Mineralogical Association, Varna, September 19th–25th, 1982, Publishing House of the Bulgarian Acad of Sci, 485–503
Born M, Göppert-Mayer M (1933) Dynamische Gittertheorie der Kristalle. Handbuch der Physik XXIV, 2. Springer-Verlag, Berlin
Bragg WL (1924) The refractive indices of calcite and aragonite. Proc R Soc London Ser A 105:370–386
Burnham CW, Buerger MJ (1961) Refinement of the crystal structure of andalusite. Z Kristallogr 115:269–290
Carson DG, Rossman GR, Vaughn RW (1982) Orientation and motion of water molecules in cordierites: a proton nuclear magnetic resonance study. Phys Chem Minerals 8:14–19
Cohen HD (1966) Electric dipole polarizability of atoms by the Hartree-Fock method. III. The isoelectronic 10-electron series. J Chem Phys 45:10–12
Cole WF, Lancucki CI (1974) A refinement of the crystal structure of gypsum, CaSO4·2H2O. Acta Crystallogr B 30:921–929
Cummins PR, Dunmur DA, Munn RW, Newham RJ (1976) Applications of the Ewald method. I. Calculation of multiple lattice sums. Acta Crystallogr A 32:847–853
Gunter M, Bloss FD (1982) Andalusite-kanonaite series: lattice and optical parameters. Am Mineral 67:1218–1228
Hochella MF, Brown GE, Ross FK, Gibbs GV (1979) High-temperature crystal chemistry of hydrous Mg- and Fe-cordierites. Am Mineral 64:337–351
Ladell J (1965) Redetermination of the crystal structure of topaz: a preliminary account. Norelco Rep 12:34–39
Lager GA, Armbruster Th, Rotella FJ, Jorgensen JD, Hinks DG (1984) A crystallographic study of the low-temperature dehydration products of gypsum: hemihydrate CaSO4·0.50H2O and γ-CaSO4. Am Mineral 69:910–919
Lahiri J, Mukherji A (1967) Electrostatic polarizability and shielding factors for ions of neon configuration. Phys Rev 153:1386–1387
Langhoff PW (1965) Multipole polarizabilities and shielding factors from Hartee-Fock wave functions. Phys Rev 139:A1415-A1425
Lasaga AC, Cygan RT (1982) Electronic and ionic polarizabilities of silicate minerals. Am Mineral 67:328–334
Pauling L (1927) The theoretical prediction of the physical properties of many-electron atoms and ions. Mole refraction, diamagnetic susceptibility, and extension in space. Proc Roy Soc Lond Ser A 114:181–211
Pohl D (1978) Electronic polarizabilities of ions in doubly refracting crystals. Acta Crystallogr A 34:574–578
Pohl D, Eck JC, Klaska KH (1978) Determination of electronic polarizabilities of ions in orthosilicates. ActaCrystallogr A 34:1027–1028
Pohl D, Rath R (1979) Point-dipole theory and optical birefringence of calcite-type carbonates. Acta Crystallogr A 35:694–695
Ribbe PH, Gibbs GV (1971) The crystal structure of topaz and its relation to physical properties. Am Mineral 56:24–30
Ribbe PH, Rosenberg PE (1971) Optical and x-ray determination methods for fluorine in topaz. Am Mineral 56:1812–1821
Selkregg KR, Bloss FD (1980) Cordierites: compositional controls of Δ, cell parameters and optical properties. Am Mineral 65:522–533
Shelley D (1975) Manual of Optical Mineralogy. Elsevier Scientific Publishing Company, New York
Tröger WE (1982) Optische Bestimmung der gesteinsbildenden Minerale: Schweizerbart'sche Verlagsbuchhandlung Stuttgart
Zemann J, Zobetz E, Heger G, Völlenke H (1979) Strukturbestimmung eines OH-reichen Topases. Oesterr Akad Wiss Math-Naturwiss K1, Anzeiger 116:145–147
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Lager, G.A., Armbruster, T. & Pohl, D. Prediction of refractive indices in minerals from crystallographic data: Applications and limitations of the point-dipole model. Phys Chem Minerals 14, 177–180 (1987). https://doi.org/10.1007/BF00308222
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DOI: https://doi.org/10.1007/BF00308222