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Empirical electronic polarizabilities for use in refractive index measurements at 589.3 nm: Hydroxyl polarizabilities

  • Robert D. Shannon , Reinhard X. Fischer and Christian Van Alsenoy
Published/Copyright: July 27, 2023
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American Mineralogist
From the journal American Mineralogist Volume 108 Issue 8

Abstract

Refractive indices of minerals and inorganic compounds can be calculated from their chemical compositions using the additivity rule for electronic polarizabilities and converting the sum of polarizabilities α using the Anderson-Eggleton relationship:

α A E = n D 2 − 1 V m 4 π + 4 π 3 − 2.26 n D 2 − 1

with the molar volume Vm solved for the mean refractive index nD at 589.3 nm. Whereas the polarizability of cations is a single parameter, the polarizability of anions is described by a two-parameter term α − = α − 0 ⋅ 10 − N o / V a n 1.20 with α– = anion polarizability, Van = anion molar volume, and the two least-squares parameters α − 0 (corresponding to free-ion polarizability) and No. For hydroxyls, Shannon and Fischer (2016) introduced different parameter sets for non-H-bonded hydroxyls α − o = 1.79 Å3, No = 1.792 Å3.6) and moderately strong H-bonded hydroxyls α − 0 = 1.73 Å3, No = 2.042 Å3.6). In an effort to understand the lower polarizability of the H-bonded hydroxyl ions, we have evaluated observed and calculated polarizabilities, O-H, H∙∙∙O, O∙∙∙O distances, and O-H∙∙∙O angles in 10 minerals with non-hydrogen-bonded hydroxyls (mean <O∙∙∙O> distance 3.143 Å, mean <H∙∙∙O> distance 2.352 Å), in seven minerals with H-bonded-hydroxyls (<O∙∙∙O> = 2.739 Å, <H∙∙∙O> = 1.856 Å), and in 10 minerals with very strongly H-bonded hydroxyls (<O∙∙∙O> = 2.531 Å, <H∙∙∙O> = 1.525 Å). On the basis of quantum chemical cluster calculations using atomic parameters of well determined crystal structures of hydroxyl containing compounds, we found that calculated intrinsic polarizabilities of OH are correlated with the hydrogen bond lengths H∙∙∙O and O∙∙∙O between donor and acceptor of the H-bond. This is demonstrated for LiOH, brucite [Mg(OH)2], portlandite [Ca(OH)2], clinometaborite (β-HBO2), sassolite (H3BO3), archerite (KH2PO4), kalicinite (KHCO3), metaborite (γ-HBO2), and NaPO2(OH)2.

Thus, we find that these summed intrinsic polarizabilities for OH-bonds which are involved in H-bonding are significantly lower than the corresponding summed intrinsic polarizabilities for OH-bonds not involved in H-bonding. We attribute the reduction in polarizability of hydroxyl ions in clinometaborite, sassolite, archerite, kalicinite and metaborite, and the compound NaPO2(OH)2 to the presence of H-bonds and a reduction of Hirshfeld atomic charge on the O atom.

Keywords: Hydroxyl polarizabilities; refractive indices; electronic polarizabilities; intrinsic polarizabilities; hydrogen bonding

Acknowledgments

We thank Ruth Shannon for the tabulation of data, and Frank Hawthorne and an anonymous reviewer for improving the manuscript.

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Received: 2022-07-18
Accepted: 2022-09-17
Published Online: 2023-07-27
Published in Print: 2023-08-28

© 2023 by Mineralogical Society of America

Articles in the same Issue

  1. Experimental study of apatite-fluid interaction and partitioning of rare earth elements at 150 and 250 °C
  2. Assimilation of xenocrystic apatite in peraluminous granitic magmas
  3. Cathodoluminescence of iron oxides and oxyhydroxides
  4. The effect of elemental diffusion on the application of olivine-composition-based magmatic thermometry, oxybarometry, and hygrometry: A case study of olivine phenocrysts from the Jiagedaqi basalts, northeast China
  5. Characterization of nano-minerals and nanoparticles in supergene rare earth element mineralization related to chemical weathering of granites
  6. Atomic-scale interlayer friction of gibbsite is lower than brucite due to interactions of hydroxyls
  7. The spatial and temporal evolution of mineral discoveries and their impact on mineral rarity
  8. The role of parent lithology in nanoscale clay-mineral transformations in a subtropical monsoonal climate
  9. Discovery of terrestrial andreyivanovite, FeCrP, and the effect of Cr and V substitution on the low-pressure barringerite-allabogdanite transition
  10. Microstructural changes and Pb mobility during the zircon to reidite transformation: Implications for planetary impact chronology
  11. Thermal equation of state of ice-VII revisited by single-crystal X-ray diffraction
  12. Empirical electronic polarizabilities for use in refractive index measurements at 589.3 nm: Hydroxyl polarizabilities
  13. High-pressure behavior of 3.65 Å phase: Insights from Raman spectroscopy
  14. High-pressure phase transition and equation of state of hydrous Al-bearing silica
  15. Memorial of Maryellen Cameron (1943−2022)
  16. New Mineral Names
https://doi.org/10.2138/am-2022-8717
Keywords for this article
Hydroxyl polarizabilities; refractive indices; electronic polarizabilities; intrinsic polarizabilities; hydrogen bonding

Articles in the same Issue

  1. Experimental study of apatite-fluid interaction and partitioning of rare earth elements at 150 and 250 °C
  2. Assimilation of xenocrystic apatite in peraluminous granitic magmas
  3. Cathodoluminescence of iron oxides and oxyhydroxides
  4. The effect of elemental diffusion on the application of olivine-composition-based magmatic thermometry, oxybarometry, and hygrometry: A case study of olivine phenocrysts from the Jiagedaqi basalts, northeast China
  5. Characterization of nano-minerals and nanoparticles in supergene rare earth element mineralization related to chemical weathering of granites
  6. Atomic-scale interlayer friction of gibbsite is lower than brucite due to interactions of hydroxyls
  7. The spatial and temporal evolution of mineral discoveries and their impact on mineral rarity
  8. The role of parent lithology in nanoscale clay-mineral transformations in a subtropical monsoonal climate
  9. Discovery of terrestrial andreyivanovite, FeCrP, and the effect of Cr and V substitution on the low-pressure barringerite-allabogdanite transition
  10. Microstructural changes and Pb mobility during the zircon to reidite transformation: Implications for planetary impact chronology
  11. Thermal equation of state of ice-VII revisited by single-crystal X-ray diffraction
  12. Empirical electronic polarizabilities for use in refractive index measurements at 589.3 nm: Hydroxyl polarizabilities
  13. High-pressure behavior of 3.65 Å phase: Insights from Raman spectroscopy
  14. High-pressure phase transition and equation of state of hydrous Al-bearing silica
  15. Memorial of Maryellen Cameron (1943−2022)
  16. New Mineral Names
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