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Empirical electronic polarizabilities of ions for the prediction and interpretation of refractive indices: Oxides and oxysalts

  • Robert D. Shannon and Reinhard X. Fischer EMAIL logo
Published/Copyright: September 30, 2016
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American Mineralogist
From the journal American Mineralogist Volume 101 Issue 10

Abstract

An extensive set of refractive indices determined at λ = 589.3 nm (nD) from ~2600 measurements on 1200 minerals, 675 synthetic compounds, ~200 F-containing compounds, 65 Cl-containing compounds, 500 non-hydrogen-bonded hydroxyl-containing compounds, and ~175 moderately strong hydrogen-bonded hydroxyl-containing compounds and 35 minerals with very strong H-bonded hydroxides was used to obtain mean total polarizabilities. These data, using the Anderson-Eggleton relationship

αT=(nD2−1)Vm4π+(4π3−c)(nD2−1)

where αT = the total polarizability of a mineral or compound, nD = the refractive index at λ = 589.3 nm, Vm = molar volume in Å3, and c = 2.26, in conjunction with the polarizability additivity rule and a least-squares procedure, were used to obtain 270 electronic polarizabilities for 76 cations in various coordinations, H2O, 5 HxOy species [(H3O)+,(H5O2)+,(H3O2)−,(H4O4)4−,(H7O4)−],NH4+, and 4 anions (F–, Cl–, OH–, O2–).

Anion polarizabilities are a function of anion volume, Van, according to α−=α−O⋅10−No/Van1.20 where α– = anion polarizability, α−O = free-ion polarizability, and Van = anion molar volume. Cation polarizabilities depend on cation coordination according to a light-scattering (LS) model with the polarizability given by α(CN)=(a1+a2CNe−a3CN)−1 where CN = number of nearest neighbor ions (cation-anion interactions), and a1, a2, and a3 are refinable parameters. This expression allowed fitting polarizability values for Li+, Na+, K+, Rb+, Cs+, Mg2+, Ca2+, Sr2+, Ba2+, Mn2+, Fe2+, Y3+, (Lu3+-La3+), Zr4+, and Th4+. Compounds with: (1) structures containing lone-pair and uranyl ions; (2) sterically strained (SS) structures [e.g., Na4.4Ca3.8Si6O18 (combeite), Δ = 6% and Ca3Mg2Si2O8 (merwinite), Δ = 4%]; (3) corner-shared octahedral (CSO) network and chain structures such as perovskites, tungsten bronzes, and titanite-related structures [e.g., MTiO3 (M = Ca, Sr, Ba), Δ = 9–12% and KNbO3, Δ = 10%]; (4) edge-shared Fe3+ and Mn3+ structures (ESO) such as goethite (FeOOH, Δ = 6%); and (5) compounds exhibiting fast-ion conductivity, showed systematic deviations between observed and calculated polarizabilities and thus were excluded from the regression analysis. The refinement for ~2600 polarizability values using 76 cation polarizabilities with values for Li+ → Cs+, Ag+, Be2+ → Ba2+, Mn2+/3+, Fe2+/3+, Co2+, Cu+/2+, Zn2+, B3+ → In3+, Fe3+, Cr3+, Sc3+, Y3+, Lu3+ → La3+, C4+ → Sn4+, Ti3+/4+, Zr4+, Hf 4+, Th4+, V5+, Mo6+, and W6+ in varying CN’s, yields a standard deviation of the least-squares fit of 0.27 (corresponding to an R2 value of 0.9997) and no discrepancies between observed and calculated polarizabilities, Δ > 3%.

Using

nD=4πα(2.26−4π3)α+Vm+1

the mean refractive index can be calculated from the chemical composition and the polarizabilities of ions determined here. The calculated mean values of <nD> for 54 common minerals and 650 minerals and synthetic compounds differ by <2% from the observed values.

In a comparison of polarizability analysis with 68 Gladstone-Dale compatibility index (CI) (Mandarino 1979, 1981) values rated as fair or poor, we find agreement in 32 instances. However, the remaining 36 examples show polarizability Δ values <3%. Thus, polarizability analysis may be a more reliable measure of the compatibility of a mineral’s refractive index, composition, and crystal structure.

Keywords: Electronic polarizabilities; refractive indices; Gladstone-Dale relationship; Anderson-Eggleton relationship; Lorenz-Lorentz relationship; Drude relationship; optical properties

Acknowledgments

We thank the Deutsche Forschungsgemeinschaft for financial support under Grant FI442/22-1. We gratefully acknowledge William Birch, George Harlow, Tony Kampf, Brian Kosnar, Stuart Mills, Ulf Hålenius, and Ekkehart Tillmanns for help with the search for rare minerals; Gabriele Ebert for providing hundreds of reprints of mineral literature; Bob Downs, Ed Grew, Joel Grice, Frank Hawthorne, David Hobart, Tony Kampf, Olaf Medenbach, George Rossman, and Elena Sokolova for providing innumerable data and advice on minerals and mineralogy; Ruth Shannon for tabulation and sorting of much of the data; and Manfred Burianek for providing single crystals for optical studies. The explanation for the many polarizability deviations of minerals was provided by Frank Hawthorne and Elena Sokolova. We are especially indebted to Frank Hawthorne, George Rossman, and Elena Sokolova for encouragement without which this work would never have been completed. We thank Mickey Gunter and an anonymous reviewer for their comments on the manuscript.

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Received: 2016-2-22
Accepted: 2016-5-25
Published Online: 2016-9-30
Published in Print: 2016-10-1

© 2016 by Walter de Gruyter Berlin/Boston

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  3. Chemistry and Mineralogy of Earth’s Mantle
  4. Graphite-diamond relations in mantle rocks: Evidence from an eclogitic xenolith from the Udachnaya kimberlite (Siberian Craton)
  5. Special Collection: From Magmas to Ore Deposits
  6. Association of cumulus apatite with compositionally unusual olivine and plagioclase in the Taihe Fe-Ti oxide ore-bearing layered mafic-ultramafic intrusion: Petrogenetic significance and implications for ore genesis
  7. Special collection: perspectives on origins and evolution of crustal magmas
  8. Repeated, multiscale, magmatic erosion and recycling in an upper-crustal pluton: implications for magma chamber dynamics and magma volume estimates
  9. Fluids in the Crust
  10. A new experimental approach to study fluid–rock equilibria at the slab-mantle interface based on the synthetic fluid inclusion technique
  11. Special collection: mechanisms, rates, and timescales of geochemical transport processes in the crust and mantle
  12. Fe-Mg interdiffusion in orthopyroxene
  13. Special Collection: Rates and Depths of Magma Ascent on Earth
  14. Error sources in single-clinopyroxene thermobarometry and a mantle geotherm for the Novinka kimberlite, Yakutia
  15. Water in nominally hydrous and anhydrous minerals
  16. Experimental hydration of natural volcanic clinopyroxene phenocrysts under hydrothermal pressures (0.5–3 kbar)
  17. Research Article
  18. Comparison of isoelectric points of single-crystal and polycrystalline α-Al2O3 and α-Fe2O3 surfaces
  19. Research Article
  20. Synthetic olivine capsules for use in experiments
  21. Research Article
  22. Visible and short-wave infrared reflectance spectroscopy of REE phosphate minerals
  23. Research Article
  24. Protolith carbon isotope ratios in cordierite from metamorphic and igneous rocks
  25. Research Article
  26. Empirical electronic polarizabilities of ions for the prediction and interpretation of refractive indices: Oxides and oxysalts
  27. Research Article
  28. A novel protocol for resolving feldspar crystals in synchrotron X-ray microtomographic images of crystallized natural magmas and synthetic analogs
  29. Research Article
  30. Silicic lunar volcanism: Testing the crustal melting model
  31. Research Article
  32. Transition metals in the transition zone: Crystal chemistry of minor element substitution in wadsleyite
  33. Research Article
  34. Experimental evidence of the formation of intermediate phases during transition of kaolinite into metakaolinite
  35. Letter
  36. Further observations related to a possible occurrence of terrestrial ahrensite
  37. Letter
  38. Chemical zoning and lattice distortion in uraninite from Olympic Dam, South Australia
  39. Research Article
  40. New Mineral Names
  41. Book Review
  42. Book review: Layered Intrusions
  43. Book Review
  44. Book Review: Mineral Resources, Economics and the Environment, 2nd edition
https://doi.org/10.2138/am-2016-5730
Keywords for this article
Electronic polarizabilities; refractive indices; Gladstone-Dale relationship; Anderson-Eggleton relationship; Lorenz-Lorentz relationship; Drude relationship; optical properties

Articles in the same Issue

  1. Research Article
  2. Temporal histories of Cordilleran continental arcs: testing models for magmatic episodicity
  3. Chemistry and Mineralogy of Earth’s Mantle
  4. Graphite-diamond relations in mantle rocks: Evidence from an eclogitic xenolith from the Udachnaya kimberlite (Siberian Craton)
  5. Special Collection: From Magmas to Ore Deposits
  6. Association of cumulus apatite with compositionally unusual olivine and plagioclase in the Taihe Fe-Ti oxide ore-bearing layered mafic-ultramafic intrusion: Petrogenetic significance and implications for ore genesis
  7. Special collection: perspectives on origins and evolution of crustal magmas
  8. Repeated, multiscale, magmatic erosion and recycling in an upper-crustal pluton: implications for magma chamber dynamics and magma volume estimates
  9. Fluids in the Crust
  10. A new experimental approach to study fluid–rock equilibria at the slab-mantle interface based on the synthetic fluid inclusion technique
  11. Special collection: mechanisms, rates, and timescales of geochemical transport processes in the crust and mantle
  12. Fe-Mg interdiffusion in orthopyroxene
  13. Special Collection: Rates and Depths of Magma Ascent on Earth
  14. Error sources in single-clinopyroxene thermobarometry and a mantle geotherm for the Novinka kimberlite, Yakutia
  15. Water in nominally hydrous and anhydrous minerals
  16. Experimental hydration of natural volcanic clinopyroxene phenocrysts under hydrothermal pressures (0.5–3 kbar)
  17. Research Article
  18. Comparison of isoelectric points of single-crystal and polycrystalline α-Al2O3 and α-Fe2O3 surfaces
  19. Research Article
  20. Synthetic olivine capsules for use in experiments
  21. Research Article
  22. Visible and short-wave infrared reflectance spectroscopy of REE phosphate minerals
  23. Research Article
  24. Protolith carbon isotope ratios in cordierite from metamorphic and igneous rocks
  25. Research Article
  26. Empirical electronic polarizabilities of ions for the prediction and interpretation of refractive indices: Oxides and oxysalts
  27. Research Article
  28. A novel protocol for resolving feldspar crystals in synchrotron X-ray microtomographic images of crystallized natural magmas and synthetic analogs
  29. Research Article
  30. Silicic lunar volcanism: Testing the crustal melting model
  31. Research Article
  32. Transition metals in the transition zone: Crystal chemistry of minor element substitution in wadsleyite
  33. Research Article
  34. Experimental evidence of the formation of intermediate phases during transition of kaolinite into metakaolinite
  35. Letter
  36. Further observations related to a possible occurrence of terrestrial ahrensite
  37. Letter
  38. Chemical zoning and lattice distortion in uraninite from Olympic Dam, South Australia
  39. Research Article
  40. New Mineral Names
  41. Book Review
  42. Book review: Layered Intrusions
  43. Book Review
  44. Book Review: Mineral Resources, Economics and the Environment, 2nd edition
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