Accessible Requires Authentication Published by De Gruyter December 7, 2020

The incompressibility of atoms at high pressures

Gerald V. Gibbs, David F. Cox and Nancy L. Ross ORCID logo
From the journal American Mineralogist

Abstract

The structures of the silica polymorphs α-quartz and stishovite have been geometry optimized at highly simulated isotropic pressure within the framework of Density Functional Theory. The atoms of the high-pressure polymorph stishovite are virtually incompressible with the bonded radii for Si and O atoms decreasing by only 0.04 and 0.08 Å, respectively, at 100 GPa. In compensating for the increase in the effective interatomic potential associated with the compression of the Si-O bonded interactions, the electron density at the bond critical point between the bonded pair increases from 0.69 to 0.89 e/ Å3. The bonded radii of the Si and O atoms for α-quartz decrease by 0.006 and 0.008 Å, respectively, between 1 bar and 26.4 GPa. The impact of simulated, isotropic pressure on the bonded radii of the atoms for three perovskites YAlO3, LaAlO3, and CaSnO3 was also examined at high pressure. For the YAlO3 perovskite, the bonded radii for Y and Al decrease by 0.06 and 0.05 Å, respectively, at 80 GPa, while the electron density between the bonded atoms increases by 0.12 and 0.15 e/Å3, on average. The calculations also show that the coordination number of the Y atom increases from 9 to 10 while the coordination number of the O1 atom increases concomitantly in the structure from 5 to 6 at 20 GPa. Hence pressure not only promotes an increase in the coordination number of the metal atoms but also a necessary concomitant increase in the coordination number of the O atoms. The bonded radii, determined at a lower pressure between 0.0 and 15 GPa for LaAlO3 and CaSnO3, decrease a smaller amount with the radii for the La and Ca atoms decreasing by 0.03 and 0.04 Å, respectively, while the radii for the smaller Al and Sn atoms decrease by 0.01 and 0.02 Å, respectively. In general, O atoms are more compressible than the metal atoms, but overall the calculations demonstrate that the bonded radii for the atoms in crystals are virtually incompressible when subjected to high pressure. The reason that the bonded radii change little when subjected to high pressure is ascribed to the changes in the effective interatomic potentials that result in increased repulsion when the atoms are squeezed together.

Funding source: National Science Foundation

Award Identifier / Grant number: EAR-1118691

Funding statement: N.L.R. acknowledges support from the National Science Foundation (Grant No. EAR-1118691).

References cited

Angel, R.J., Allan, D.R., Milletich, R., and Finger, L.W. (1997) The use of quartz as an internal pressure standard in high-pressure crystallography. Journal of Applied Crystallography, 30, 461–466. Search in Google Scholar

Bader, R.F.W. (1985) Atoms in molecules. Accounts of Chemical Research, 18(1), 9–15. Search in Google Scholar

Bader, R.F.W. (1990) Atoms in Molecules: A quantum theory. Oxford University Press, New York. Search in Google Scholar

Bader, R.F.W. (2009) Bond paths are not chemical bonds. Journal of Physical Chemistry A, 113(38), 10391–10396. Search in Google Scholar

Bader, R.F.W., and Matta, C.F. (2004) Atomic charges are measurable quantum expectation values: A rebuttal of criticisms of QTAIM charges. Journal of Physical Chemistry A, 108(40), 8385–8394. Search in Google Scholar

Gibbs, G.V., Rosso, K.M., Teter, D.M., Boisen, M.B. Jr., and Bukowinski, M.S.T. (1999) Model structures and properties of the electron density distribution for low quartz at pressure: A study of the Si O bond. Journal of Molecular Structure, 485-486, 13–25. Search in Google Scholar

Gibbs, G.V., Whitten, A.E., Spackman, M.A., Stimpfl, M., Downs, R.T., and Carducci, M.D. (2003) An exploration of theoretical and experimental electron density distributions and Si O bonded interactions for the silica polymorph coesite. Journal of Physical Chemistry B, 107(47), 12996–13006. Search in Google Scholar

Gibbs, G.V., Wang, D., Hin, C., Ross, N.L., Cox, D.F., Crawford, T.D., Spackman, M.A., and Angel, R.J. (2012) Properties of atoms under pressure: Bonded interactions of the atoms in three perovskites. The Journal of Chemical Physics, 137(16), 164313. Search in Google Scholar

Gibbs, G.V., Ross, N.L., Cox, D.F., Rosso, K.M., Iversen, B.B., and Spackman, M.A. (2013) Bonded radii and the contraction of the electron density of the oxygen atom by bonded interactions. The Journal of Physical Chemistry A, 117(7), 1632–1640. Search in Google Scholar

Glazer, A. (1972) The classification of tilted octahedra in perovskites. Acta Crystallographica, B28(11), 3384–3392. Search in Google Scholar

Grochala, W., Hoffmann, R., Feng, J., and Ashcroft, N.W. (2007) The chemical imagination at work in very tight places. Angewandte Chemie-International Edition, 46(20), 3620–3642. Search in Google Scholar

Hazen, R.M., Finger, L.W., Hemley, R.J., and Mao, H.K. (1989) High-pressure crystal chemistry and amorphization of alpha-quartz. Solid State Communications, 72(5), 507–511. Search in Google Scholar

Hill, F.C., Gibbs, G.V., and Boisen, M.B. (1994) Bond stretching force-constants and compressibilities of nitride, oxide, and sulfide coordination polyhedra in molecules and crystals. Structural Chemistry, 5(6), 349–355. Search in Google Scholar

Nicoll, J.S., Gibbs, G.V., Boisen, M.B., Downs, R.T., and Bartelmehs, K.L. (1994) Bond length and radii variations in fluoride and oxide molecules and crystals. Physics and Chemistry of Minerals, 20(8), 617–624. Search in Google Scholar

Prencipe, M., and Nestola, F. (2006) Minerals at high pressure. Mechanics of compression from quantum mechanical calculations in a case study: the beryl (Al4Be6Si12O36 Physics and Chemistry of Minerals, 34, 37–52. Search in Google Scholar

Prewitt, C.T., and Downs, R.T. (1998) High-pressure crystal chemistry. In R.J. Hemley, Ed., Ultrahigh-pressure mineralogy: Physics and chemistry of the Earth’s deep interior, 37, p. 283–317. Reviews in Mineralogy and Geochemistry, Mineralogical Society of America, Chantilly, Virginia. Search in Google Scholar

Ross, N.L., Shu, J.F., Hazen, R.M., and Gasparik, T. (1990) High-pressure crystal-chemistry of stishovite. American Mineralogist, 75(7-8), 739–747. Search in Google Scholar

Ross, N.L., Zhao, J., and Angel, R.J. (2004) High-pressure single-crystal X-ray diffraction study of YAlO3 perovskite. Journal of Solid State Chemistry, 177(4-5), 1276–1284. Search in Google Scholar

Runtz, G.R., Bader, R.F.W., and Messer, R.R. (1977) Definition of bond paths and bond directions in terms of molecular charge-distribution. Canadian Journal of Chemistry-Revue Canadienne De Chimie, 55(16), 3040–3045. Search in Google Scholar

Sasaki, S., Fujino, K., Takeuchi, Y., and Sadanaga, R. (1980) On the estimation of atomic charges by the X-ray method for some oxides and silicates. Acta Crystallographica, A36(6), 904–915. Search in Google Scholar

Shannon, R.D., and Prewitt, C.T. (1969) Effective ionic radii in oxides and fluorides. Acta Crystallographica, B25, 925–946. Search in Google Scholar

Wang, D. (2012) Some aspects of the crystal chemistry of perovskites under high pressures. Geosciences, Ph,D. thesis, Virginia Polytechnic Institute and State University, Blacksburg, Virginia. Search in Google Scholar

Woodward, P. (1997) Octahedral tilting in perovskites. I. Geometrical considerations. Acta Crystallographica, B53(1), 32–43. Search in Google Scholar

Zhao, J., Ross, N.L., and Angel, R.J. (2004) Tilting and distortion of CaSnO3 perovskite to 7 GPa determined from single-crystal X-ray diffraction. Physics and Chemistry of Minerals, 31(5), 299–305. Search in Google Scholar

Received: 2019-05-21
Accepted: 2020-05-31
Published Online: 2020-12-07
Published in Print: 2020-12-16

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