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Exploration of structure and bonding in stishovite with fourier and pseudoatom refinement methods using single crystal and powder X-ray diffraction data

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Abstract

The structure and bonding in stishovite, SiO2, is explored with Fourier summation and pseudoatom refinement of merged x-ray single crystal and powder diffraction data. Replacement of the 25 lowest-angle, highly extinction-affected, single crystal reflections with structure factors obtained from low-extinction powder diffraction data has resulted in a significant improvement in the analysis compared with earlier studies. The deformation electron density, total electrostatic potential and total and valence electron densities are mapped. Accumulations of electron density are observed in both SiO bonds, together with non-bonding features displayed about the oxygen on both sides of a plane formed by three bonds with Si. Deficits of electron density between O atoms across the shared-edges are rationalized in terms of the Pauli exclusion principle. There is no evidence for strong repulsion of Si atoms across the same ring. The total electrostatic potential has a continuous low value for the vacant channels in the structure along c with localized minima between O atoms on opposite sides of the channel. The sizes of Si and O are related to the electron density and to the electrostatic potential.

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References

  • Bader RFW, Beddall PM, Cade PE (1971) Partitioning and characterization of molecular charge distributions. J Am Chem Soc 93:3095–3107

    Google Scholar 

  • Baur WH (1976) Rutile-type compounds V. Refinement of MnO2 and MgF2. Acta Crystallogr B 32:2200–2204

    Article  Google Scholar 

  • Baur WH, Khan AA (1971) Rutile-type compounds. IV. SiO2, GeO2 and a comparison with other rutile-type structures. Acta Crystallogr B 27:2133–2139

    Article  Google Scholar 

  • Becker P (1977) The theoretical models of extinction. Their domain of applicability. Acta Crystallogr A 33:243–249

    Google Scholar 

  • Becker PJ, Coppens P (1974a) Extinction within the limit of validity of the Darwin transfer equations. I. General formalisms for primary and secondary extinction and their application to spherical crystals. Acta Crystallogr A 30:129–147

    Google Scholar 

  • Becker PJ, Coppens P (1974b) Extinction within the limit of validity of the Darwin transfer equations. II. Refinement of extinction in spherical crystals of SrF2 and LiF. Acta Crystallogr A 30:148–153

    Google Scholar 

  • Bragg WL (1937) Atomic structure of minerals. Cornell University Press, Ithaca, New York

    Google Scholar 

  • Burdett JK, McLarnan TJ (1984) An orbital interpretation of Pauling's rules. Am Mineral 69:601–621

    Google Scholar 

  • Clementi E (1965) Tables of atomic functions. IBM Journal of Research and Development 9:supplement

  • Clementi E, Roetti C (1974) Roothaan-Hartree-Fock atomic wave-functions. At Data Nucl Data Tables 14:177–478

    Google Scholar 

  • Cohen ML (1981) Pseudopotentials and crystal structure. In: O'Keeffe M and Navrotsky A (eds) Structure and bonding in crystals I. Academic Press, London, 25–48

    Google Scholar 

  • Cromer DT, Liberman D (1970) Relativistic calculations of anomalous scattering factors for X-rays. J Chem Phys 53:1891–1898

    Article  Google Scholar 

  • Downs JW, Hill RJ, Newton MD, Tossell JA, Gibbs GV (1982) Theoretical and experimental charge distributions in euclase and stishovite. In: Coppens P, Hall MB (eds) Electron distributions and the chemical bond. Plenum Press, New York, pp 173–189

    Google Scholar 

  • Finger LW, Gibbs GV (1985) A derivation of bonded radii from theoretical molecular charge distributions. EOS, Transactions, American Geophysical Union, 66:356–357

    Google Scholar 

  • Fink MJ, Haller KJ, West R, Michl J (1984) Tetramesitylcyclodisiloxane: A cyclic siloxane with an unusual structure. J Am Chem Soc 106:822–823

    Article  Google Scholar 

  • Gibbs GV (1982) Molecules as models for bonding in silicates. Am Mineral 67:421–450

    Google Scholar 

  • Gonschorek W (1982) X-ray charge density study of rutile (TiO2). Z Kristallogr 160:187–203

    Google Scholar 

  • Gupta A, Tossell JA (1983) Quantum mechanical studies of distortions and polymerization of borate polyhedra. Am Miner 68:989–995

    Google Scholar 

  • Hehre WJ, Ditchfield R, Stewart RF, Pople JA (1970) Self-consistent molecular orbital methods. IV. Use of Gaussian expansions of Slater-type orbitals. Extension to second-row molecules. J Chem Phys 52:2769–2773

    Article  Google Scholar 

  • Hill RJ, Newton MD, Gibbs GV (1983) A crystal chemical study of stishovite. J Solid State Chem 47:185–200

    Article  Google Scholar 

  • McLean AD, Yoshimine M (1967) Tables of linear molecule wave functions. IBM Journal of Research and Development, supplement of November 1967

  • O'Keeffe M, Hyde BG (1978a) On Si-O-Si configurations in silicates. Acta Crystallogr B 34:27–32

    Google Scholar 

  • O'Keeffe M, Hyde BG (1978b) Non-bonded interactions and the crystal chemistry of tetrahedral structures related to the wurtzite type (B4). Acta Crystallogr B 34:3519–3528

    Google Scholar 

  • O'Keeffe M, Hyde BG (1981) The role of nonbonded forces in crystals. In: O'Keeffe M, Navrotsky A (eds) Structure and bonding in crystals I. Academic Press, London, pp 227–254

    Google Scholar 

  • O'Keeffe M, Hyde BG (1982) Anion coordination and cation packing in oxides. J Solid State Chem 44:24–31

    Article  Google Scholar 

  • O'Keeffe M, Gibbs GV (1985) Ab initio MO calculations on cyclodisiloxanes and other Si-X-Si-X rings and the problem of “Silica-w”. J Phys Chem 89:4574–4577

    Google Scholar 

  • O'Keeffe M, Stuart JA (1983) Bond energies in solid oxides. Inorg Chem 22:177–179

    Article  Google Scholar 

  • Pauling L (1929) The principles determining the structure of complex ionic crystals. J Am Chem Soc 51:1010–1026

    Google Scholar 

  • Presisinger A (1962) Structure of stishovite, high-pressure SiO2. Naturwissenschaften 49:345

    Google Scholar 

  • Price PF, Maslen EN, Mair SL (1978) Electron density studies III. A re-evaluation of the electron distribution in crystalline silicon. Acta Crystallogr A34:183–193

    Google Scholar 

  • Restori R, Schwarzenbach D (1984) Electron density distribution of rutile, TiO2. Abstract in Acta Crystallogr A40:C-158

  • Shannon RD, Prewitt CT (1969) Effective ionic radii in oxides and fluorides. Acta Crystallogr B 25:925–946

    Article  Google Scholar 

  • Shintani H, Sato S, Saito Y (1975) Electron-density distribution in rutile crystals. Acta Crystallogr B 31:1981–1982

    Article  Google Scholar 

  • Sinclair W, Ringwood AE (1978) Single crystal analysis of the structure of stishovite. Nature 272:714–715

    Article  Google Scholar 

  • Slater JC (1965) Quantum theory of molecules and solids, Vol. 2. McGraw-Hill, New York

    Google Scholar 

  • Spackman MA, Maslen EN (1986) Chemical properties from the promolecule. J Phys Chem 90:2020–2027

    Article  Google Scholar 

  • Spackman MA, Stewart RF (1981) Electrostatic potentials in crystals. In: Politzer P, Truhlar DG (eds) Chemical applications of atomic and molecular electrostatic potentials. Plenum Press, New York, pp 407–425

    Google Scholar 

  • Spackman MA, Stewart RF (1983) Crystalline electrostatic potentials in some simple mineral systems. Abstract L1, ACA Program and Abstracts, 11, No. 1, March 1983

  • Spackman MA, Stewart RF (1984) Electrostatic properties from accurate diffraction data. In: Hall SR, Ashida T (eds) Methods and applications in crystallographic computing. Oxford University Press, Oxford, pp 302–320

    Google Scholar 

  • Spackman MA, Stewart RF, LePage Y (1981) Maps of electrostatic properties from X-ray data for α-SiO2(s) and Al2O3(s). Abstract in Acta Crystallogr Suppl A 37:C-138

    Google Scholar 

  • Stewart RF (1973) Electron population analysis with generalized x-ray scattering factors: Higher multipoles. J Chem Phys 58:1668–1676

    Google Scholar 

  • Stewart RF (1976) Electron population analysis with rigid pseudoatoms. Acta Crystallogr A 32:565–574

    Google Scholar 

  • Stewart RF (1979) On the mapping of electrostatic properties from Bragg diffraction data. Chem Phys Lett 65:335–342

    Article  Google Scholar 

  • Stewart RF (1980) Partitioning of Hartree-Fock atomic form factors into core and valence shells. In: Becker P (ed) Electron and magnetization densities in molecules and crystals. Plenum Press, New York, pp 427–431

    Google Scholar 

  • Stewart RF, Spackman MA (1981) Charge density distributions. In: O'Keeffe M, Navrotsky A (eds) Structure and bonding in crystals I. Academic Press, London, pp 279–298

    Google Scholar 

  • Stishov SM, Belov NV (1962) The crystal structure of a new dense modification of silica SiO2. Dokl Akad Nauk SSSR 143:951–954

    Google Scholar 

  • Swaminathan S, Craven BM, Spackman MA, Stewart RF (1984) Theoretical and experimental studies of the charge density in urea. Acta Crystallogr B 40:398–404

    Google Scholar 

  • Tossell JA, Gibbs GV (1978) The use of molecular-orbital calculations on model systems for the prediction of bridging-bond-angle variations in siloxanes, silicates, silicon nitrides and silicon sulfides. Acta Crystallogr A 34:463–472

    Article  Google Scholar 

  • Vegard L (1916) Results of crystal analysis. Phil Mag 32:65–96

    Google Scholar 

  • Vidal JP, Vidal-Valat G, Galtier M, Kurki-Suonio K (1981) X-ray study of the charge distribution in MgF2. Acta Crystallogr A 37:826–837

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Crystallography, University of Pittsburgh, 15260, Pittsburgh, PA, USA

    M. A. Spackman

  2. CSIRO Division of Mineral Chemistry, P.O. Box 124, 3207, Port Melbourne, Victoria, Australia

    R. J. Hill

  3. Department of Geological Sciences, Virginia Polytechnic Institute and State University, 24061, Blacksburg, Virginia, USA

    G. V. Gibbs

Authors
  1. M. A. Spackman
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  2. R. J. Hill
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  3. G. V. Gibbs
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Spackman, M.A., Hill, R.J. & Gibbs, G.V. Exploration of structure and bonding in stishovite with fourier and pseudoatom refinement methods using single crystal and powder X-ray diffraction data. Phys Chem Minerals 14, 139–150 (1987). https://doi.org/10.1007/BF00308217

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  • DOI: https://doi.org/10.1007/BF00308217

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