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Pauling’s rules for oxide-based minerals: A re-examination based on quantum mechanical constraints and modern applications of bond-valence theory to Earth materials

  • Gerald V. Gibbs , Frank C. Hawthorne and Gordon E. Brown
Published/Copyright: July 2, 2022
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American Mineralogist
From the journal American Mineralogist Volume 107 Issue 7

Abstract

Since their introduction in 1929, Pauling’s five rules have been used by scientists from many disciplines to rationalize and predict stable arrangements of atoms and coordination polyhedra in crystalline solids; amorphous materials such as silicate glasses and melts; nanomaterials, poorly crystalline solids; aqueous cation and anion complexes; and sorption complexes at mineral-aqueous solution interfaces. The predictive power of these simple yet powerful rules was challenged recently by George et al. (2020), who performed a statistical analysis of the performance of Pauling’s five rules for about 5000 oxide crystal structures. They concluded that only 13% of the oxides satisfy the last four rules simultaneously and that the second rule has the most exceptions. They also found that Pauling’s first rule is satisfied for only 66% of the coordination environments tested and concluded that no simple rule linking ionic radius to coordination environment will be predictive due to the variable quality of univalent radii.

We address these concerns and discuss quantum mechanical calculations that complement Pauling’s rules, particularly his first (radius sum and radius ratio rule) and second (electrostatic valence rule) rules. We also present a more realistic view of the bonded radii of atoms, derived by determining the local minimum in the electron density distribution measured along trajectories between bonded atoms known as bond paths, i.e., the bond critical point (rc). Electron density at the bond critical point is a quantum mechanical observable that correlates well with Pauling bond strength. Moreover, a metal atom in a polyhedron has as many bonded radii as it has bonded interactions, resulting in metal and O atoms that may not be spherical. O atoms, for example, are not spherical in many oxide-based crystal structures. Instead, the electron density of a bonded oxygen is often highly distorted or polarized, with its bonded radius decreasing systematically from ~1.38 Å when bonded to highly electropositive atoms like sodium to 0.64 Å when bonded to highly electronegative atoms like nitrogen. Bonded radii determined for metal atoms match the Shannon (1976) radii for more electropositive atoms, but the match decreases systematically as the electronegativities of the M atoms increase. As a result, significant departures from the radius ratio rule in the analysis by George et al. (2020) is not surprising. We offer a modified, more fundamental version of Pauling’s first rule and demonstrate that the second rule has a one-to-one connection between the electron density accumulated between the bonded atoms at the bond critical point and the Pauling bond strength of the bonded interaction.

Pauling’s second rule implicitly assumes that bond strength is invariant with bond length for a given pair of bonded atoms. Many studies have since shown that this is not the case, and Brown and Shannon (1973) developed an equation and a set of parameters to describe the relation between bond length and bond strength, now redefined as bond valence to avoid confusion with Pauling bond-strength. Brown (1980) used the valence-sum rule, together with the path rule and the valence-matching principle, as the three axioms of bond-valence theory (BVT), a powerful method for understanding many otherwise elusive aspects of crystals and also their participation in dynamic processes. We show how a priori bond-valence calculations can predict unstrained bond-lengths and how bond-valence mapping can locate low-Z atoms in a crystal structure (e.g., Li) or examine possible diffusion pathways for atoms through crystal structures.

In addition, we briefly discuss Pauling’s third, fourth, and fifth rules, the first two of which concern the sharing of polyhedron elements (edges and faces) and the common instability associated with structures in which a polyhedron shares an edge or face with another polyhedron and contains high-valence cations. The olivine [α-(MgxFe1–x)2SiO4] crystal structure is used to illustrate the distortions from hexagonal close-packing of O atoms caused by metal-metal repulsion across shared polyhedron edges.

We conclude by discussing several applications of BVT to Earth materials, including the use of BVT to: (1) locate H+ ions in crystal structures, including the location of protons in the crystal structures of nominally anhydrous minerals in Earth’s mantle; (2) determine how strongly bonded (usually anionic) structural units interact with weakly bonded (usually cationic) interstitial complexes in complex uranyl-oxide and uranyl-oxysalt minerals using the valence-matching principle; (3) calculate Lewis acid strengths of cations and Lewis base strengths of anions; (4) determine how (H2O) groups can function as bond-valence transformers by dividing one bond into two bonds of half the bond valence; (5) help characterize products of sorption reactions of aqueous cations (e.g., Co2+ and Pb2+) and oxyanions [e.g., selenate (Se6+O4)2− and selenite (Se4+O3)2−] at mineral-aqueous solution interfaces and the important role of protons in these reactions; and (6) help characterize the local coordination environments of highly charged cations (e.g., Zr4+, Ti4+, U4+, U5+, and U6+) in silicate glasses and melts.

Keywords: Pauling’s rules; bonded radii; bonded interactions; bond paths; bond valence theory; bond valence analysis of crystal structures; bond valence analysis of water in nominally anhydrous mantle minerals; bond valence analysis of proton, cation, and oxyanion sorption complexes; application of bond-valence theory to uranyl-oxide and uranyl-oxysalt minerals; bond-valence analysis of proton, cation, and oxyanion adsorption at mineral-aqueous solution interfaces; bond-valence and XAFS analysis of the local coordination environments of highly charged cations in silicate glasses

Acknowledgments

The preparation of this review was stimulated by the recent paper of George et al. (2020), which evaluated the success of Pauling’s five rules, both singly and in combination, in predicting stable atom and polyhedron arrangements in over 5000 oxide-based crystal structures in the Inorganic Crystal Structure Data Base.

The Three Amigos, who have known each other professionally for the past 50+ years, decided to write this review with the hope that it might help students in a broad range of scientific disciplines, as well as their mentors, understand the major contribution made by Linus Pauling when he introduced his rules in 1929, and by David Brown, who introduced BVT in 1980. We were all fortunate to get to know both Linus Pauling and David Brown—the two stars of this review. G.B. thanks his co-author and Ph.D. mentor (G.V.G.) for introducing him to the principles of crystal chemistry, X‑ray crystallography, and structural chemistry, as well as for his unfailing guidance and friendship over the past 55 years. G.B. also acknowledges Linus Pauling for writing The Nature of the Chemical Bond and the Structure of Molecules and Crystals: An Introduction to Modern Structural Chemistry, first published in 1939. The third edition of this book, published in 1960, has had a major influence on our understanding of chemical bonding in Earth materials. In addition, G.B. thanks his many excellent graduate students, postdocs, and faculty colleagues at Stanford over the past 47 years, particularly John Bargar (SLAC National Accelerator Laboratory), the late Steven Towle, Peggy O’Day (U.C. Merced), and the late George Parks (Stanford University) for the stimulating and fruitful collaborations we had involving adsorption reactions of aqueous cations and oxyanions at mineral-aqueous solution interfaces. G.B. also thanks former postdoc Professor Francois Farges (Muséum National d’Histoire Naturelle, Paris), who was responsible for much of the work on our joint studies of the local structural environments of high-valence cations in aluminosilicate and titanosilicate glasses and melts. Finally, G.B. thanks the U.S. National Science Foundation (Chemistry and Geosciences Directorates) and the U.S. Department of Energy, Basic Energy Sciences and Biological and Environmental Research for their generous support of his research program over the past 45 years and their support of the two main synchrotron light sources (the Stanford Synchrotron Radiation Lightsource at SLAC National Accelerator Laboratory and the Advanced Photon Source at Argonne National Laboratory) where most of G.B.’s synchrotron-based studies of sorption complexes at mineral-water interfaces and his studies of structure-property relations in silicate glasses and melts were done. G.V.G. owes a debt to the late Richard Bader for tutoring him about the Feynman force exerted on the nuclei and the Ehrenfest force exerted on the electrons of the bonded atoms. Another of us (F.C.H.) was a graduate student from 1968 to 1973 at McMaster University, working in the Materials Research Institute where he was exposed on a daily basis to David Brown, Bob Shannon, and other scientific luminaries at coffee breaks and lunch. The result was a friendship between a geologist, a physicist, and a chemist that has lasted until the present time, with innumerable emails concerning the physics and chemistry of chemical bonding and its influence on the properties and behavior of solids. F.C.H. takes pleasure in acknowledging the enormous influence that David and Bob have had on his knowledge and understanding of crystals.

Finally, we thank several anonymous reviewers as well as American Mineralogist Editor Don Baker for careful reviews of our manuscript.

  1. Manuscript handled by Jie Xu,

References cited

Aboud, S., Wilcox, J., and Brown, G.E. Jr. (2011) Density functional theory investigation of the interaction of water with α-Al2O3 and α-Fe2O3 (1102) surfaces: Implications for surface reactivity. Physical Review B, 83, 125407.10.1103/PhysRevB.83.125407Search in Google Scholar

Al-Abadleh, H.A., and Grassian, V.H. (2003a) Oxide surfaces as environmental interfaces. Surface Science Reports, 52, 63–161.10.1016/j.surfrep.2003.09.001Search in Google Scholar

Al-Abadleh, H.A., and Grassian, V.H. (2003b) FT-IR study of water adsorption on aluminum oxide surfaces. Langmuir, 19, 341–347.10.1021/la026208aSearch in Google Scholar

Arai, Y., and Sparks, D.L. (2001) ATR-FTIR spectroscopic investigation on phosphate adsorption mechanisms at the ferrihydrite-water interface. Journal of Colloid and Interface Science, 241, 317–326.10.1006/jcis.2001.7773Search in Google Scholar

Bader, R. F.W. (1990) Atoms in Molecules: A Quantum Theory. Oxford University Press.Search in Google Scholar

Bader, R. F.W. (2009) Bond paths are not chemical bonds. The Journal of Physical Chemistry. A, 113, 10391–10396.10.1021/jp906341rSearch in Google Scholar

Bandura, A.V., Sykes, D.G., Shapovalov, V., Troung, T.N., Kubicki, J.D., and Evarestov, R.A. (2004) Adsorption of water on the TiO2 (rutile) (110) surface: A comparison of periodic and embedded cluster calculations. The Journal of Physical Chemistry B, 108, 7844–7853.10.1021/jp037141iSearch in Google Scholar

Bargar, J.R., Towle, S.N., Brown, G.E. Jr., and Parks, G.A. (1996) Outer-sphere lead(II) adsorbed at specific surface sites on single crystal α-alumina. Geochimica et Cosmochimica Acta, 60, 3541–3547.10.1016/0016-7037(96)00222-0Search in Google Scholar

Bargar, J.R., Brown, G.E. Jr., and Parks, G.A. (1997a) Surface complexation of Pb(II) at oxide-water interfaces: I. XAFS and bond-valence determination of mononuclear and polynuclear Pb(II) sorption products on aluminum oxides. Geochimica et Cosmochimica Acta, 61, 2617–2637.10.1016/S0016-7037(97)00124-5Search in Google Scholar

Bargar, J.R., Brown, G.E. Jr., and Parks, G.A. (1997b) Surface complexation of Pb(II) at oxide-water interfaces: II. XAFS and bond-valence determination of mononuclear Pb(II) sorption products and surface functional groups on iron oxides. Geochimica et Cosmochimica Acta, 61, 2639–2652.10.1016/S0016-7037(97)00125-7Search in Google Scholar

Bargar, J.R., Towle, S.N., Brown, G.E. Jr., and Parks, G.A. (1997c) Structure, composition, and reactivity of Pb(II) and Co(II) sorption products and surface functional groups on single-crystal α-Al2O3. Journal of Colloid and Interface Science, 185, 473–493.10.1006/jcis.1996.4574Search in Google Scholar PubMed

Barlow, W. (1883) Probable nature of the internal symmetry of crystals. Nature, 29, 186–188.10.1038/029186a0Search in Google Scholar

Barlow, W. (1894) Ueber die geometrischen Eigenschaften homogener starrer Structuren und ihre Anwendung auf Krystalle. Zeitschrift für Kristallographie—Crystalline Materials, 23, 1–63.10.1524/zkri.1894.23.1.1Search in Google Scholar

Baur, W.H. (1981) Interatomic distance predictions for computer simulation of crystal structures. In M. O’Keeffe and A. Navrotsky, Structure and Bonding in Crystals, Vol. II, 31–52. Academic Press, Elsevier.10.1016/B978-0-12-525102-0.50008-6Search in Google Scholar

Bedzyk, M.J., Bilderback, D., White, J., Abruna, H.D., and Bommarito, G.M. (1986) Probing electrochemical interfaces with X-ray standing waves. The Journal of Physical Chemistry, 90, 4926–4928.10.1021/j100412a011Search in Google Scholar

Bedzyk, M.J., Bommarito, G.M., Caffrey, M., and Penner, T.L. (1990) Diffuse double layer at a membrane-aqueous interface measured with X-ray standing waves. Science, 248, 52–56.10.1126/science.2321026Search in Google Scholar PubMed

Bell, D.R., and Rossman, G.R. (1992) Water in the Earth’s mantle: The role of nominally anhydrous minerals. Science, 255, 1391–1397.10.1126/science.255.5050.1391Search in Google Scholar PubMed

Bickmore, B.R., Tadanier, C.J., Rosso, K.M., Monn, W.D., and Eggett, D.L. (2004) Bond-valence methods for pKa prediction: Critical reanalysis and a new approach. Geochimica et Cosmochimica Acta, 68, 2025–2042.10.1016/j.gca.2003.11.008Search in Google Scholar

Bickmore, B.R., Rosso, K.M., Tadanier, C.J., Bylaska, E.J., and Doud, D. (2006) Bond-valence methods for pKa prediction: II. Bond-valence, electrostatic, molecular geometry, and solvation effects. Geochimica et Cosmochimica Acta, 70, 4057–4071.10.1016/j.gca.2006.06.006Search in Google Scholar

Birle, J.D., Gibbs, G.V., Moore, P.B., and Smith, J.V. (1968) Crystal structures of natural olivines. American Mineralogist, 53, 807–824.Search in Google Scholar

Bloch, A.N., and Schatteman, G.C. (1980) Quantum-defect orbital radii and the structural chemistry of simple solids. In M. O’Keeffe and A. Navrotsky, Eds., Structure and Bonding in Crystals, vol. I, p. 49–72. Academic Press.10.1016/B978-0-12-525101-3.50010-3Search in Google Scholar

Bragg, W.H. (1912) X-rays and crystals. Nature, 90, 360–361.10.1038/090360d0Search in Google Scholar

Bragg, W.H. (1913) The reflection of X-rays by crystals. Proceedings of the Royal Society of London, 89A, 248–277.10.4159/harvard.9780674366701.c30Search in Google Scholar

Bragg, W.L. (1913a) The diffraction of short electromagnetic waves by a crystal. Proceedings of the Cambridge Philosophical Society, 17, 43–57.Search in Google Scholar

Bragg, W.L. (1913b) The structure of some crystals as indicated by their diffraction of X-rays. Proceedings of the Royal Society of London, A89, 248.10.1098/rspa.1913.0083Search in Google Scholar

Bragg, W.L. (1920) The arrangement of atoms in crystals. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 40, 169–189.10.1038/106725a0Search in Google Scholar

Bragg, W.L. (1937) Atomic Structure of Minerals. Cornell University Press.Search in Google Scholar

Bragg, W.H., and Bragg, W.L. (1913) The reflection of X-rays by crystals. Proceedings of the Royal Society of London, 88A, 428–438.10.4159/harvard.9780674366701.c30Search in Google Scholar

Brown, G.E. Jr. (1980) Crystal chemistry of the olivines and silicate spinels. Reviews in Mineralogy, 5, 275–381.Search in Google Scholar

Brown, G.E. Jr. (1990) Spectroscopic studies of chemisorption reaction mechanisms at oxide/ water interfaces. Reviews in Mineralogy, 23, 309–363.10.1515/9781501509131-012Search in Google Scholar

Brown, G.E. Jr. (2001) How minerals react with water. Science, 294, 67–69.10.1126/science.1063544Search in Google Scholar PubMed

Brown, G.E. Jr., and Calas, G. (2012) Mineral-aqueous solution interfaces and their impact on the environment. Geochemical Perspectives, 1, 483–742.10.7185/geochempersp.1.4Search in Google Scholar

Brown, G.E. Jr., and Parks, G.A. (2001) Sorption of trace elements from aqueous media: Modern perspectives from spectroscopic studies and comments on adsorption in the marine environment. International Geology Review, 43, 963–1073.10.1080/00206810109465060Search in Google Scholar

Brown, G.E. Jr., and Sturchio, N.C. (2002) An overview of synchrotron radiation applications to low temperature geochemistry and environmental science. Reviews in Mineralogy and Geochemistry, 49, 1–115.10.2138/gsrmg.49.1.1Search in Google Scholar

Brown, G.E. Jr., Farges, F., and Calas, G. (1995) X-ray scattering and X-ray spectroscopy studies of silicate melts. Reviews in Mineralogy, 32, 317–410.10.1515/9781501509384-011Search in Google Scholar

Brown, G.E. Jr., Henrich, V.E., Casey, W.H., Clark, D.L., Eggleston, C., Felmy, A., Goodman, D.W., Grätzel, M., Maciel, G., McCarthy, M.I., and others (1999) Metal oxide surfaces and their interactions with aqueous solutions and microbial organisms. Chemical Reviews, 99, 77–174.10.1021/cr980011zSearch in Google Scholar PubMed

Brown, I.D (1981) The bond-valence method: An empirical approach to chemical structure and bonding. In M. O’Keeffe and A. Navrotsky, Structure and Bonding in Crystals, vol. II, p. 1–30. Academic Press.10.1016/B978-0-12-525102-0.50007-4Search in Google Scholar

Brown, I.D (1987) Recent developments in the bond valence model of inorganic bonding. Physics and Chemistry of Minerals, 15, 30–34.10.1007/BF00307605Search in Google Scholar

Brown, I.D (1988) What factors determine cation coordination number. Acta Crystallographica, B44, 545–553.10.1107/S0108768188007712Search in Google Scholar

Brown, I.D (2002a) The Chemical Bond in Inorganic Chemistry. The Bond Valence Model. Oxford University Press.Search in Google Scholar

Brown, I.D (2002b) Topology and chemistry. Structural Chemistry, 13, 339–355.10.1023/A:1015872125545Search in Google Scholar

Brown, I.D (2009) Recent developments in the methods and applications of the bond valence model. Chemical Reviews, 109, 6858–6919.10.1021/cr900053kSearch in Google Scholar PubMed PubMed Central

Brown, I.D (2016) The Chemical Bond in Inorganic Chemistry. The Bond Valence Model, 2nd ed. Oxford University Press.10.1093/acprof:oso/9780198742951.001.0001Search in Google Scholar

Brown, I.D., and Altermatt, D. (1985) Bond-valence parameters obtained from a systematic analysis of the Inorganic Crystal Structure Database. Acta Crystallographica, B41, 244–247.10.1107/S0108768185002063Search in Google Scholar

Brown, I.D., and Shannon, R.D. (1973) Empirical bond-strength–bond-length curves from oxides. Acta Crystallographica, A29, 266–282.10.1107/S0567739473000689Search in Google Scholar

Burdett, J.K., and Hawthorne, F.C. (1993) An orbital approach to the theory of bond valence. American Mineralogist, 78, 884–892.Search in Google Scholar

Burdett, J.K., Price, G.D., and Price, S.L. (1981) Factors influencing solid-state structure—An analysis using pseudopotential radii structural maps. Physical Review B, 24, 2903–2912.10.1103/PhysRevB.24.2903Search in Google Scholar

Cameron, M., Sueno, S., Prewitt, C.T., and Papike, J.J. (1973) High-temperature crystal chemistry of acmite, diopside, hedenbergite, jadeite, spodumene and ureyite. American Mineralogist, 58, 594–618.Search in Google Scholar

Carabante, I., Grahn, M., Holmgren, A., and Hedlund, J. (2010) In situ ATR-FTIR studies on the competitive adsorption of arsenate and phosphate on ferrihydrite. Journal of Colloid & Interface Science, 351, 525–531.10.1016/j.jcis.2010.07.064Search in Google Scholar

Catti, M., Pavese, A., and Price, G.D. (1993) Quantum mechanical Hartree-Fock study of calcite (CaCO3) at variable pressure, and comparison with magnesite (MgCO3). Physics and Chemistry of Minerals, 20, 104–110.10.1007/BF00207203Search in Google Scholar

Chelikowsky, J.R., and Phillips, J.C. (1977) Orbital model of thermochemical parameters. Physical Review Letters, 39, 1687–1691.10.1103/PhysRevLett.39.1687Search in Google Scholar

Clark, J.R., Appleman, D.E., and Papike, J.J. (1969) Crystal-chemical characterization of clinopyroxenes based on eight new structure refinements. Mineralogical Society of America Special Paper, 2, 31–50.Search in Google Scholar

Cohen, M.L. (1980) Pseudopotentials and crystal structure. In M. O’Keeffe and A. Navrotsky, Eds., Structure and Bonding in Crystals, vol. I, p. 25–48. Academic Press, Elsevier.10.1016/B978-0-12-525101-3.50009-7Search in Google Scholar

Dalton, J. (1808) A New System of Chemical Philosophy, pp. 587. R. Bickerstaff, Strand, London.10.5479/sil.324338.39088000885681Search in Google Scholar

de Picciotto, L.A., Adendorff, K.T., Liles, D.C., and Thackeray, M.M. (1993) Structural characterization of Li1+xV3O8 insertion electrodes by single-crystal X-ray diffraction. Solid State Ionics, 62, 297–307.10.1016/0167-2738(93)90386-HSearch in Google Scholar

Demartin, F., Diella, V., Gramaccioli, C.M., and Pezzotta, F. (2001) Schiavinatoite, (Nb,Ta)BO4, the Nb analogue of behierite. European Journal of Mineralogy, 13, 159–165.10.1127/0935-1221/01/0013-0159Search in Google Scholar

Eng, P.J., Trainor, T.P., Brown, G.E. Jr., Waychunas, G.A., Newville, M., Sutton, S.R., and Rivers, M.L. (2000) Structure of the hydrated α-Al2O3 (0001) surface. Science, 288, 1029–1033.10.1126/science.288.5468.1029Search in Google Scholar

Farges, F., and Brown, G.E. Jr. (1996) An empirical model for the anharmonic analysis of high-temperature XAFS spectra of oxide compounds with applications to the coordination environment of Ni in NiO, γ-Ni2SiO4, and Ni-bearing Na-disilicate glass and melt. Chemical Geology, 128, 93–106.10.1016/0009-2541(95)00165-4Search in Google Scholar

Farges, F., Ponader, C.W., and Brown, G.E. Jr. (1991) Structural environments of incompatible elements in silicate glass/melt systems: I. Zr at trace levels. Geochimica et Cosmochimica Acta, 55, 1563–1574.10.1016/0016-7037(91)90128-RSearch in Google Scholar

Farges, F., Ponader, C.W., Calas, G., and Brown, G.E. Jr. (1992) Structural environments of incompatible elements in silicate glass/melt systems: II. U(IV), U(V), and U(VI). Geochimica et Cosmochimica Acta, 56, 4205–4220.10.1016/0016-7037(92)90261-GSearch in Google Scholar

Farges, F., Brown, G.E. Jr., Navrotsky, A., Gan, H., and Rehr, J.J. (1996a) Coordination chemistry of titanium(IV) in silicate glasses and melts. Part II. Glasses at ambient and pressure. Geochimica et Cosmochimica Acta, 60, 3039–3053.10.1016/0016-7037(96)00145-7Search in Google Scholar

Farges, F., Brown, G.E. Jr., Navrotsky, A., Gan, H., and Rehr, J.J. (1996b) Coordination chemistry of titanium(IV) in silicate glasses and melts. Part III. Glasses and melts from ambient to high temperatures. Geochimica et Cosmochimica Acta, 60, 3055–3065.10.1016/0016-7037(96)00146-9Search in Google Scholar

Fenter, P.A. (2002) X-ray reflectivity as a probe of mineral-fluid interfaces: A user guide. Reviews in Mineralogy and Geochemistry, 49, 149–220.10.1515/9781501508882-009Search in Google Scholar

Fenter, P.A., and Sturchio, N.C. (2004) Mineral-water interfacial structures revealed by synchrotron X-ray scattering. Progress in Surface Science, 77, 171–258.10.1016/j.progsurf.2004.12.001Search in Google Scholar

Feynman, R.P. (1939) Forces in molecules. Physical Review, 56, 340–343.10.1103/PhysRev.56.340Search in Google Scholar

Friedrich, W., Knipping, P., and von Laue, M. (1912) Interferenz-Erscheinungen bei Röntgenstrahlen. Sitzungsberichte Der Mathematisch-Physikalischen Classe. K. B. Akademie der Wissenschaften zu Munchen, 42, 303–322.Search in Google Scholar

Gagné, O.C., and Hawthorne, F.C. (2015) Comprehensive derivation of bond-valence parameters for ion pairs involving oxygen. Acta Crystallographica, B71, 562–578.10.1107/S2052520615016297Search in Google Scholar PubMed PubMed Central

Gagné, O.C., and Hawthorne, F.C. (2017) Empirical Lewis-acid strengths for 135 cations bonded to oxygen. Acta Crystallographica, B73, 956–961.10.1107/S2052520617010988Search in Google Scholar PubMed

Gagné, O.C., and Hawthorne, F.C. (2018) Bond-length distributions for ions bonded to oxygen: Results for the non-metals and discussion of lone-pair stereoactivity and the polymerization of PO4. Acta Crystallographica, B74, 79–96.10.1107/S2052520617017541Search in Google Scholar

Gagné, O.C., and Hawthorne, F.C. (2020) Bond-length distributions for ions bonded to oxygen: Results for the transition metals and quantification of the factors underlying bond-length variation in inorganic solids. IUCrJ, 7, 581–629.10.1107/S2052252520005928Search in Google Scholar PubMed PubMed Central

Gagné, O.C., Mercier, P.H.J., and Hawthorne, F.C. (2018) A priori bond-valence and bond-length calculations in rock-forming minerals. Acta Crystallographica, B74, 470–482.10.1107/S2052520618010442Search in Google Scholar

Gatti, C. (2005) Chemical bonding in crystals: new directions. Zeitschrift für Kristallographie—Crystalline Materials, 220, 399–457.10.1524/zkri.220.5.399.65073Search in Google Scholar

George, J., Waroquiers, D., Stefano, D., Petretto, G., Rignanese, G.-M., and Hautier, G. (2020) The limited predictive power of the Pauling Rules. Angewandte Chemie, 132, 7639–7645.10.1002/ange.202000829Search in Google Scholar

Ghose, S.K., Waychunas, G.A., Trainor, T., and Eng, P.J. (2010) Hydrated goethite (alpha-FeOOH) (100) interface structure: Ordered water and surface functional groups. Geochimica et Cosmochimica Acta, 74, 1943–1953.10.1016/j.gca.2009.12.015Search in Google Scholar

Gibbs, G.V. (1982) Molecules as models for bonding in silicates. American Mineralogist, 67, 421–450.Search in Google Scholar

Gibbs, G.V., and Smith, J.V. (1965) Refinement of the crystal structure of synthetic pyrope. American Mineralogist, 50, 2023–2039.Search in Google Scholar

Gibbs, G.V., Finger, L.W., and Boisen, M.B. Jr. (1987) Molecular mimicry of the bond length-bond strength variations in oxide crystals. Physics and Chemistry of Minerals, 14, 327–331.10.1007/BF00309805Search in Google Scholar

Gibbs, G.V., Spackman, M.A., and Boisen, M.B. Jr. (1992) Bonded and promolecule radii for molecules and crystals. American Mineralogist, 7, 741–750.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, 13–25.10.1016/S0022-2860(99)00179-9Search in Google Scholar

Gibbs, G.V., Boisen, M.B. Jr., Beverly, L.L., and Rosso, K.M. (2001) A computational quantum chemical study of the bonded interactions in Earth materials and structurally and chemically related molecules. Reviews in Mineralogy and Geochemistry, 42, 345–381.10.1515/9781501508721-013Search in Google Scholar

Gibbs, G.V., Cox, D.F., Boisen, M.B. Jr., Downs, R.T., and Ross, N.L. (2003) The electron localization function: a tool for locating favorable proton docking sites in the silica polymorphs. Physics and Chemistry of Minerals, 30, 305–316.10.1007/s00269-003-0318-2Search in Google Scholar

Gibbs, G.V., Downs, R. T., Cox, D.F., Ross, N.L., Prewitt, C.T., Rosso, K.M., Lippmann, T., and Kirfel, A. (2008) Bonded interactions and the crystal chemistry of minerals: a review. Zeitschrift für Kristallographie, 223, 1–40.10.1524/zkri.2008.0002Search in Google Scholar

Gibbs, G.V., Wallace, A.F., Cox, D.F., Downs, R.T., Ross, N.L., and Rosso, K.M. (2009) Bonded interactions in silica polymorphs, silicates, and siloxane molecules. American Mineralogist, 94, 1085–1102.10.2138/am.2009.3215Search 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, 164313–164312.10.1063/1.4759075Search in Google Scholar PubMed

Gibbs, G.V., Ross, N.L., Cox, D.F., Rosso, K.M., Iversen, B.B., and Spackman, M.A. (2013a) Bonded radii and the contraction of the electron density of the oxygen atom by bonded interactions. The Journal of Physical Chemistry. A, 117, 1632–1640.10.1021/jp310462gSearch in Google Scholar PubMed

Gibbs, G.V., Ross, N.L., Cox, D.F., Rosso, K.M., Iversen, B.B., and Spackman, M.A. (2013b) Pauling bond strength, bond length and electron density distribution. Physics and Chemistry of Minerals, 41, 17–25.10.1007/s00269-013-0619-zSearch in Google Scholar

Gibbs, G.V., Ross, N.L., Cox, D.F., and Rosso, K.M. (2014) Insights into the crystal chemistry of Earth materials rendered by electron density distributions: Pauling’s rules revisited. American Mineralogist, 99, 1071–1108.10.2138/am.2014.4660Search in Google Scholar

Gibbs, G.V., Ross, N.L., and Cox, D.F. (2015) Bond length estimates for oxide crystals with a molecular power law expression. Physics and Chemistry of Minerals, 42, 587–593.10.1007/s00269-015-0746-9Search in Google Scholar

Gilbert, B., Erbs, J.J., Penn, R.L., Petkov, V., Spagnoli, D., and Waychunas, G.A. (2013) A disordered nanoparticle model for 6-line ferrihydrite. American Mineralogist, 98, 1465–1476.10.2138/am.2013.4421Search in Google Scholar

Goldschmidt, V.M. (1926) Die gesetze der krystallochemie. Die Naturwissenschaften, 14, 477–485.10.1007/BF01507527Search in Google Scholar

Hawthorne, F.C. (1983) Graphical enumeration of polyhedral clusters. Acta Crystallographica, A39, 724–736.10.1107/S0108767383001452Search in Google Scholar

Hawthorne, F.C. (1992) The role of OH and H2O in oxide and oxysalt minerals. Zeitschrift für Kristallographie, 201, 183–206.10.1524/zkri.1992.201.3-4.183Search in Google Scholar

Hawthorne, F.C. (2012) A bond-topological approach to theoretical mineralogy: crystal structure, chemical composition and chemical reactions. Physics and Chemistry of Minerals, 39, 841–874.10.1007/s00269-012-0538-4Search in Google Scholar

Hawthorne, F.C. (2015) Toward theoretical mineralogy: a bond-topological approach. American Mineralogist, 100, 696–713.10.2138/am-2015-5114Search in Google Scholar

Hawthorne, F.C. (2018) A bond-topological approach to borate minerals: A brief review. Physics and Chemistry of Glasses: European Journal of Glass Science and Technology Part B, 59, 121–129.10.13036/17533562.59.3.023Search in Google Scholar

Hawthorne, F.C., and Herwig, S. (2021) A structure hierarchy for the aluminofluoride minerals. Canadian Mineralogist, 59, 211–241.10.3749/canmin.2000047Search in Google Scholar

Hawthorne, F.C., and Schindler, M. (2008) Understanding the weakly bonded constituents in oxysalt minerals. Zeitschrift für Kristallographie—Crystalline Materials, 223, 41–68.10.1524/zkri.2008.0003Search in Google Scholar

Hawthorne, F.C., and Schindler, M. (2014) Crystallization and dissolution in aqueous solution: A bond-valence approach. In I.D. Brown and K.R. Poeppelmeier, Eds., Bond Valences. Structure and Bonding, 158, p. 161–190. Springer.10.1007/430_2013_91Search in Google Scholar

Hawthorne, F.C., Oberti, R., Harlow, G.E., Maresch, W.V., Martin, R.F., Schumacher, J. C., and Welch, M.D. (2012) Nomenclature of the amphibole supergroup. American Mineralogist, 97, 2031–2048.10.2138/am.2012.4276Search in Google Scholar

Hayes, K.F., Roe, A.L., Brown, G.E. Jr., Hodgson, K.O., Leckie, J.O., and Parks, G.A. (1987) In-situ X-ray absorption study of surface complexes at oxide/water interfaces: selenium oxyanions on α-FeOOH. Science, 238, 783–786.10.1126/science.238.4828.783Search in Google Scholar PubMed

Hiemstra, T., Venema, P., and Riemsdijk, W.H.V. (1996) Intrinsic proton affinity of reactive surface groups of metal (hydr)oxides: The bond-valence principle. Journal of Colloid and Interface Science, 184, 680–692.10.1006/jcis.1996.0666Search in Google Scholar PubMed

Hirschmann, M.M., Aubaud, C., and Withers, A.C. (2005) Storage capacity of H2O in nominally anhydrous minerals in the upper mantle. Earth and Planetary Science Letters, 236, 167–181.10.1016/j.epsl.2005.04.022Search in Google Scholar

Hohenberg, P., and Kohn, W. (1964) Inhomogeneous electron gas. Physical Review, 136, B864–871.10.1103/PhysRev.136.B864Search in Google Scholar

Horiuchi, H., and Sawamoto, H. (1981) β-Mg2SiO4: Single crystal diffraction study. American Mineralogist, 66, 568–575.Search in Google Scholar

Huang, X.G., Xu, Y.S., and Karato, S.I. (2005) Water content in the transition zone from electrical conductivity of wadsleyite and ringwoodite. Nature, 434, 746–749.10.1038/nature03426Search in Google Scholar PubMed

Hüttig, G.F. (1920) Notiz zur Geometrie der Koordinationszahl. Zeitschrift für Anorganische und Allgemeine Chemie, 114, 24–26.10.1002/zaac.19201140103Search in Google Scholar

Ito, E., and Katsura, T. (1989) A temperature profile of the mantle transition zone. Geophysical Research Letters, 16, 425–428.10.1029/GL016i005p00425Search in Google Scholar

Johnson, S.B., Brown, G.E. Jr., Healy, T.W., and Scales, P.J. (2005) Adsorption of organic matter at mineral/water interfaces: 6. Effect of inner-sphere vs. outer-sphere adsorption on colloidal stability. Langmuir, 21, 6356–6365.10.1021/la047030qSearch in Google Scholar PubMed

Kirfel, A., Lippmann, T., Blaha, P., Schwarz, K., Cox, D.F., Rosso, K.M., and Gibbs, G.V. (2005) Electron density distribution and bond critical point properties for forsterite, Mg2SiO4, determined with synchrotron single crystal X-ray diffraction data. Physics and Chemistry of Minerals, 32, 301–313.10.1007/s00269-005-0468-5Search in Google Scholar

Kohlstedt, D.L., Keppler, H., and Rubie, D.C. (1996) Solubility of water in the α, β and γ phases of (Mg,Fe). Contributions to Mineralogy and Petrology, 123, 345–357.10.1007/s004100050161Search in Google Scholar

Kohn, W., and Sham, L.J. (1965) Self-consistent equations including exchange and correlation effects. Physical Review, 140, A1133–1138.10.1103/PhysRev.140.A1133Search in Google Scholar

Kumagai, N., Yu, A., and West, K. (1997) Li1−xNaxV3O8 as positive materials for secondary lithium batteries. Journal of Applied Electrochemistry, 27, 953–958.10.1023/A:1018457820021Search in Google Scholar

Kunitz, W. (1930) Die Isomorphieverhoiltnisse in der Hornblende-gruppe. Neues Jahrbuch für Mineralogie Abhandlungen, 60, 171–250.Search in Google Scholar

Landé, A. (1920) Uber die Grösse der Atome. Zeitschrift für Physik, 1, 191–197.10.1007/978-94-009-3981-3_16Search in Google Scholar

Li, Y.-P., and Burns, P.C. (2000) Investigations of crystal-chemical variability in lead uranyl oxide hydrates. I. Curite. Canadian Mineralogist, 38, 727–735.10.2113/gscanmin.38.3.727Search in Google Scholar

Liu, P., Kendelewicz, T., Brown, G.E. Jr., Nelson, E.J., and Chambers, S.A. (1998) Reaction of water with α-Al2O3 and α-Fe2O3 (0001) surfaces: synchrotron X-ray photoemission studies and thermodynamic calculations. Surface Science, 417, 53–65.10.1016/S0039-6028(98)00661-XSearch in Google Scholar

Mason, S.E., Iceman, C.R., Tanwar, K.S., Trainor, T.P., and Chaka, A.M. (2009) Pb(II) adsorption on isostructural hydrated alumina and hematite (0001) surfaces: A DFT study. The Journal of Physical Chemistry C, 113, 2159–2170.10.1021/jp807321eSearch in Google Scholar

Mason, S.E., Iceman, C.R., Trainor, T.P., and Chaka, A.M. (2010) Density functional theory study of clean, hydrated, and defective alumina (1102). Physical Review B, 81, 125423.10.1103/PhysRevB.81.125423Search in Google Scholar

Mason, S.E., Trainor, T.P., and Chaka, A.M. (2011) Hybridization-reactivity relationship in Pb(II) adsorption on α-Al2O3-water interfaces: A DFT study. The Journal of Physical Chemistry C, 115, 4008–4021.10.1021/jp108201fSearch in Google Scholar

Mozzi, R.L., and Warren, B.E. (1969) The structure of vitreous silica. Journal of Applied Crystallography, 2, 164–172.10.1107/S0021889869006868Search in Google Scholar

Mrose, M.E., and Rose, H. J. (1962) Behierite, (Ta,Nb)BO4, a new mineral from Manjaka, Madagascar. Angewandte Chemie, 235.Search in Google Scholar

Nemsak, S., Shavorskiy, A., Karslioglu, O., Zegkinoglou, I., Rattanachata, A., Conlon, C.S., Keqi, A., Greene, P.K., Burks, E.C., Salmassi, F., and others (2014) Concentration and chemical-state profiles at heterogeneous interfaces with sub-nm accuracy from standing-wave ambient-pressure photoemission. Nature Communications, 5, 5441–5447.10.1038/ncomms6441Search in Google Scholar PubMed

Newberg, J.T., Starr, D.E., Yamamoto, S., Kaya, S., Kendelewicz, T., Mysak, E.R., Porsgaard, S., Salmeron, M.B., Brown, G.E., Nilsson, A., and Bluhm, H. (2011) Autocatalytic surface hydrolyxation of MgO(100) terrace sites observed under ambient conditions. The Journal of Physical Chemistry C, 115, 12864–12872.10.1021/jp200235vSearch in Google Scholar

Novak, G.A., and Gibbs, G.V. (1971) The crystal chemistry of the silicate garnets. American Mineralogist, 56, 791–825.Search in Google Scholar

Novak, P., Scheifele, W., Joho, F., and Haas, O. (1995) Electrochemical insertion of magnesium into hydrated vanadium bronzes. Journal of the Electrochemical Society, 142, 2544–2550.10.1149/1.2050051Search in Google Scholar

Ohtani, E. (2021) Hydration and dehydration in Earth’s interior. Annual Review of Earth and Planetary Sciences, 49, 253–278.10.1146/annurev-earth-080320-062509Search in Google Scholar

Ohtani, E., Litasov, K., Hosoya, T., Kubo, T., and Kondo, T. (2004) Water transport into the deep mantle and formation of a hydrous transition zone. Physics of the Earth and Planetary Interiors, 143-144, 255–269.10.1016/j.pepi.2003.09.015Search in Google Scholar

Panero, W.R., Smyth, J.R., Pigott, J.S., Liu, Z.X., and Frost, D.J. (2013) Hydrous ringwoodite to 5 K and 35 GPa: Multiple hydrogen bonding sites resolved with FTIR spectroscopy. American Mineralogist, 98, 637–642.10.2138/am.2013.3978Search in Google Scholar

Parks, G.A. (1965) The isoelectric points of solid oxides, solid hydroxides, and aqueous hydroxo complex systems. Chemical Reviews, 65, 177–198.10.1021/cr60234a002Search in Google Scholar

Parks, G.A. (1967) Aqueous surface chemistry of oxides and complex oxide minerals. Isoelectronic point and zero point of charge. In R.F. Gould, Ed., Equilibrium Concepts in Natural Water Systems: Advances in Chemistry Series, 67, 121–160. American Chemical Society.10.1021/ba-1967-0067.ch006Search in Google Scholar

Pauling, L. (1927) Sizes of ions and structure of ionic crystals. Journal of the American Chemical Society, 49, 765–792.10.1021/ja01402a019Search in Google Scholar

Pauling, L. (1929) The principles determining the structure of complex ionic crystals. Journal of the American Chemical Society, 51, 1010–1026.10.1021/ja01379a006Search in Google Scholar

Pauling, L. (1960) The Nature of the Chemical Bond and the Structure of Molecules and Crystals: An Introduction to Modern Structural Chemistry, 3rd ed. Cornell University Press, 644 p.Search in Google Scholar

Pauling, L., and Hendricks, S.B. (1925) The crystal structures of hematite and corundum. Journal of the American Chemical Society, 47, 781–790.10.1021/ja01680a027Search in Google Scholar

Pendás, A.M., and Hernández-Trujillo, J. (2012) The Ehrenfest force field: Topology and consequences for the definition of an atom in a molecule. The Journal of Chemical Physics, 137, 134101–134109.10.1063/1.4755326Search in Google Scholar PubMed

Pickering, I.J., Brown, G.E. Jr., and Tokunaga, T.K. (1995) X-ray absorption spectroscopy of selenium transformations in Kesterson Reservoir soils. Environmental Science & Technology, 29, 2456–2459.10.1021/es00009a043Search in Google Scholar PubMed

Preiser, C., Lösel, J., Brown, I.D., Kunz, M., and Skowron, A. (1999) Long range Coulomb forces and localized bonds. Acta Crystallographica, B55, 698–711.10.1107/S0108768199003961Search in Google Scholar PubMed

Prencipe, M. (2019) Quantum mechanics in Earth sciences: a one‑century‑old story. Rendiconti Lincei. Scienze Fisiche e Naturali, 30, 239–259.10.1007/s12210-018-0744-1Search in Google Scholar

Purevjav, N., Okuchi, T., Tomioka, N., Abe, J., and Harjo, S. (2014) Hydrogen site analysis of hydrous ringwoodite in mantle transition zone by pulsed neutron diffraction. Geophysical Research Letters, 41, 6718–6724.10.1002/2014GL061448Search in Google Scholar

Purevjav, N., Okuchi, T., Wang, X., Hoffman, C., and Tomioka, N. (2018) Determination of hydrogen site and occupancy in hydrous Mg2SiO4 spinel by single-crystal neutron diffraction. Acta Crystallographica, B74, 115–120.10.1107/S2052520618000616Search in Google Scholar

Runtz, G.R., Bader, R.F.T., and Messer, R.R. (1977) Definition of bond paths and bond directions in terms of the molecular charge distribution. Canadian Journal of Chemistry, 55, 3040–3045.10.1139/v77-422Search in Google Scholar

Sayers, D.E., Stern, E.A., and Lytle, F.W. (1971) New technique for investigating noncrystalline structures—Fourier analysis of extended X-ray absorption fine structure. Physical Review Letters, 27, 1204–1207.10.1103/PhysRevLett.27.1204Search in Google Scholar

Schindler, M., and Hawthorne, F.C. (2001a) A bond-valence approach to the structure, chemistry and paragenesis of hydroxy-hydrated oxysalt minerals: I. Theory. Canadian Mineralogist, 39, 1225–1242.10.2113/gscanmin.39.5.1225Search in Google Scholar

Schindler, M., and Hawthorne, F.C. (2001b) A bond-valence approach to the structure, chemistry and paragenesis of hydroxy-hydrated oxysalt minerals: II. Crystal structure and chemical composition of borate minerals. Canadian Mineralogist, 39, 1243–1256.10.2113/gscanmin.39.5.1225Search in Google Scholar

Schindler, M., and Hawthorne, F.C. (2001c) A bond-valence approach to the structure, chemistry and paragenesis of hydroxy-hydrated oxysalt minerals: III. Paragenesis of borate minerals. Canadian Mineralogist, 39, 1257–1274.10.2113/gscanmin.39.5.1225Search in Google Scholar

Schindler, M., and Hawthorne, F.C. (2004) A bond-valence approach to the uranyl-oxide hydroxy-hydrate minerals: Chemical composition and occurrence. Canadian Mineralogist, 42, 1601–1627.10.2113/gscanmin.42.6.1601Search in Google Scholar

Schindler, P.W., Furst, B., Dick, R., and Wolf, P.U. (1976a) Ligand properties of silanol groups. 1. Surface complex-formation with Fe3+, Cu2+, Cd2+ and Pb2+. Journal of Colloid and Interface Science, 55, 469–475.10.1016/0021-9797(76)90057-6Search in Google Scholar

Schindler, P.W., Wälti, E., and Furst, B. (1976b) The role of surface-hydroxyl groups in the surface chemistry of metal oxides. Chimia, 30, 107–109.Search in Google Scholar

Schindler, M., Mutter, A., Hawthorne, F.C., and Putnis, A. (2004a) Prediction of crystal morphology of complex uranyl-sheet minerals. I. Theory. Canadian Mineralogist, 42, 1629–1649.10.2113/gscanmin.42.6.1629Search in Google Scholar

Schindler, M., Mutter, A., Hawthorne, F.C., and Putnis, A. (2004b) Prediction of crystal morphology of complex uranyl-sheet minerals. Canadian Mineralogist, 42, 1651–1666.10.2113/gscanmin.42.6.1629Search in Google Scholar

Schindler, M., Hawthorne, F.C., Alexander, M.A., Kutluoglu, R.A., Mandaliev, P., Halden, N.M., and Mitchell, R. M. (2006a) Na-Li-[V3O8] insertion electrodes: Structures and diffusion pathways. Journal of Solid State Chemistry, 179, 2616–2628.10.1016/j.jssc.2006.05.009Search in Google Scholar

Schindler, M., Huminicki, D.M.C., and Hawthorne, F.C. (2006b) Sulfate minerals: I. Bond topology and chemical composition. Canadian Mineralogist, 44, 1403–1429.10.2113/gscanmin.44.6.1403Search in Google Scholar

Schmandt, B., Jacobsen, S.D., Becker, T.W., Liu, Z., and Dueker, K.G. (2014) Dehydration melting at the top of the lower mantle. Nature, 344, 1265–1268.10.1126/science.1253358Search in Google Scholar PubMed

Shannon, R.D. (1976) Revised effective ionic radii and systematic studies of interatomic distances in halides and chalcogenides. Acta Crystallographica, A32, 751–767.10.1107/S0567739476001551Search in Google Scholar

Shannon, R.D., and Prewitt, C.T. (1969) Effective ionic radii in oxides and fluorides. Acta Crystallographica, B25, 925–946.10.1107/S0567740869003220Search in Google Scholar

Simons, G., and Bloch, A.N. (1973) Pauli-force model potential for solids. Physical Review B, 7, 2754–2761.10.1103/PhysRevB.7.2754Search in Google Scholar

Skinner, A.J., LaFemina, J.P., and Jensen, H.J.F. (1994) Structure and bonding of calcite: A theoretical study. American Mineralogist, 79, 205–214.Search in Google Scholar

Slater, J.C. (1964) Atomic radii in crystals. The Journal of Chemical Physics, 41, 3199–3204.10.1063/1.1725697Search in Google Scholar

Smyth, J.R. (1987) β-Mg2SiO4: A potential host for water in Earth’s mantle? American Mineralogist, 72, 1051–1055.Search in Google Scholar

Smyth, J.R. (1994) A model for hydrous wadsleyite (β-Mg2SiO4): An ocean in the Earth’s interior? American Mineralogist, 79, 1021–1024.Search in Google Scholar

Smyth, J.R., and Jacobsen, S.D. (2006) Nominally anhydrous minerals and Earth’s deep-water cycle. In S.D. Jacobsen and S. Van Der Lee, Eds., Earth’s Deep-Water Cycle, 320, p. 1–11. American Geophysical Union.10.1029/168GM02Search in Google Scholar

Smyth, J.R., Kawamoto, T., Jacobsen, S.D., Swope, R.J., Hervig, R.L., and Holloway, J. R. (1997) Crystal structure of monoclinic hydrous wadsleyite [β-(MgxFe1-x)2SiO4]. American Mineralogist, 82, 270–275.10.2138/am-1997-3-404Search in Google Scholar

Smyth, J.R., Holl, C.M., Frost, D.J., Jacobsen, S.D., Langenhorst, F., and McCammon, C.A. (2003) Structural systematics of hydrous ringwoodite and water in Earth’s interior. American Mineralogist, 88, 1402–1407.10.2138/am-2003-1001Search in Google Scholar

Smyth, J.R., Frost, D.J., Nestola, F., Holl, C.M., and Bromiley, G. (2006) Olivine hydration in the deep upper mantle: Effects of temperature and silica activity. Geophysical Research Letters, 33.10.1029/2006GL026194Search in Google Scholar

Stumm, W. (1992) Chemistry of the Solid-Water Interface: Processes at the Mineral-Water and Particle-Water Interfaces in Natural Systems. Wiley Interscience, 428 p.Search in Google Scholar

Stumm, W., Huang, C.P., and Jenkins, S.R. (1970) Specific chemical interaction affecting the stability of dispersed systems. Croatica Chemica Acta, 42, 223–245.Search in Google Scholar

Stumm, W., Wehrli, B., and Wieland, E. (1987) Surface complexation and its impact on geochemical kinetics. Croatica Chemica Acta, 60, 429–438.Search in Google Scholar

Sverjensky, D.A. (1994) Zero-point-of-charge prediction from crystal chemistry and solvation theory. Geochimica et Cosmochimica Acta, 58, 3123–3129.10.1016/0016-7037(94)90184-8Search in Google Scholar

Tait, K.T., Ercit, T.S., Abdu, Y.A., Černý, P., and Hawthorne, F.C. (2011) The crystal structure and crystal chemistry of Manitobaite, ideally (Na16◻)Mn2+ 25Al8(PO4)30, from Cross Lake, Manitoba. Canadian Mineralogist, 49, 1221–1242.10.3749/canmin.49.5.1221Search in Google Scholar

Taylor, M., and Brown, G.E. Jr. (1979) Structure of mineral glasses I: The feldspar glasses NaAlSi3O8, KAlSi3O8, CaAl2Si2O8. Geochimica et Cosmochimica Acta, 43, 61–75.10.1016/0016-7037(79)90047-4Search in Google Scholar

Thomas, S.-M., Jacobsen, S.D., Bina, C.R., Reichart, P., Moser, M., Hauri, E.H., Koch-Müller, M., Smyth, J.R., and Dollinger, G. (2015) Quantification of water in hydrous ringwoodite. Frontiers in Earth Science, 2, 38–10.10.3389/feart.2014.00038Search in Google Scholar

Thompson, A.B. (1992) Water in the Earth’s upper mantle. Nature, 358, 295–307.10.1038/358295a0Search in Google Scholar

Towle, S.N., Bargar, J.R., Brown, G.E. Jr., and Parks, G.A. (1999) Sorption of Co(II) on metal oxide surfaces: II. Identification of Co(II)(aq) adsorption sites on the (0001) and (102) surfaces of α-Al2O3 by grazing-incidence XAFS spectroscopy. Journal of Colloid and Interface Science, 217(2), 312–321.Search in Google Scholar

Trainor, T.P., Eng, P.J., Brown, G.E. Jr., Robinson, I.K., and De Santis, M. (2002) Crystal truncation rod diffraction study of the clean and hydrated α-Al2O3 (1102) surface. Surface Science, 496, 238–250.10.1016/S0039-6028(01)01617-XSearch in Google Scholar

Trainor, T.P., Chaka, A.M., Eng, P.J., Newville, M., Waychunas, G.A., Catalano, J.G., and Brown, G.E. Jr. (2004) Structure and reactivity of the hydrated hematite (0001) surface. Surface Science, 573, 204–224.10.1016/j.susc.2004.09.040Search in Google Scholar

Usher, C.R., Michel, A.E., and Grassian, V.H. (2003) Reactions on mineral dust. Chemical Reviews, 103, 4883–4939.10.1021/cr020657ySearch in Google Scholar PubMed

Waltersson, K. (1978) A method, based upon ‘bond strength’ calculations, for finding probable lithium sites in crystal structures. Acta Crystallographica, A34, 901–905.10.1107/S0567739478001862Search in Google Scholar

Wang, H., Lu, R., Downs, R.T., and Costin, G. (2006) Goethite, α-FeO(OH), from single crystal data. Acta Crystallographica, E62, i250–i252.Search in Google Scholar

Warren, B.E. (1930) The structure of tremolite H2Ca2Mg5(SiO3)8. Zeitschrift für Kristallographie—Crystalline Materials, 72, 42–57.10.1524/zkri.1930.72.1.42Search in Google Scholar

Wasastjerna, J.A. (1923) Radii of ions. Societas Scientiarum Fennica Communication Physics and Mathematics, 38, 1–25.Search in Google Scholar

Watson, E.B. (1979) Zircon saturation in felsic liquids: Experimental results and applications to trace element geochemistry. Contributions to Mineralogy and Petrology, 70, 407–419.10.1007/BF00371047Search in Google Scholar

Wilson, R.J. (1979) Introduction to Graph Theory. Longman, London.Search in Google Scholar

Winter, J.K., and Ghose, S. (1979) Thermal expansion and high-temperature crystal chemistry of the Al2SiO5 polymorphs. American Mineralogist, 64, 573–586.Search in Google Scholar

Yamamoto, S., Kendelewicz, T., Newberg, J.T., Ketteler, G., Starr, D.E., Mysak, E.R., Andersson, K., Ogasawara, H., Bluhm, H., Salmeron, M., Brown, G.E. Jr., and Nilsson, A. (2010) Water adsorption on α-Fe2O3(0001) at near ambient conditions. The Journal of Physical Chemistry C, 114, 2256–2266.10.1021/jp909876tSearch in Google Scholar

Yang, H., Lu, R., Downs, R.T., and Costin, G. (2006) Goethite, α-FeO(OH), from single crystal data. Acta Crystallographica, E62, i250–i252.10.1107/S1600536806047258Search in Google Scholar

Yoon, T.H., Johnson, S.B., Musgrave, C.B., and Brown, G.E. Jr. (2004) Adsorption of organic matter at mineral/water interfaces: I. ATR-FTIR spectroscopic and quantum chemical study of oxalate adsorbed at boehmite/water and corundum/water interfaces. Geochimica et Cosmochimica Acta, 68, 4505–4518.10.1016/j.gca.2004.04.025Search in Google Scholar

Zachariasen, W.H. (1954) Crystal chemical studies of the 5f-series of elements. XXIII. On the crystal chemistry of uranyl compounds and of related compounds of transuranic elements. Acta Crystallographica, 7, 795–799.10.1107/S0365110X54002472Search in Google Scholar

Zemann, J. (1986) The shortest known interpolyhedral O-O distance in a silicate. Zeitschrift für Kristallographie, 175, 299–303.Search in Google Scholar

Zunger, A. (1980) Systematization of the stable crystal structure of all AB-type binary compounds: A pseudopotential orbital radii approach. Physical Review B, 22, 5839 –5872.10.1103/PhysRevB.22.5839Search in Google Scholar

Zunger, A., and Cohen, M.L. (1978) Density-functional pseudopotential approach to crystal phase stability and electronic structure. Physical Review B, 18, 5449–5472.10.1103/PhysRevLett.41.53Search in Google Scholar
Received: 2020-12-22
Accepted: 2021-07-29
Published Online: 2022-07-02
Published in Print: 2022-07-26

© 2022 Mineralogical Society of America

Articles in the same Issue

  1. Highlights and Breakthroughs
  2. Mineral evolution heralds a new era for mineralogy
  3. MSA Review
  4. Pauling’s rules for oxide-based minerals: A re-examination based on quantum mechanical constraints and modern applications of bond-valence theory to Earth materials
  5. A cotunnite-type new high-pressure phase of Fe2S
  6. Density determination of liquid iron-nickel-sulfur at high pressure
  7. On the paragenetic modes of minerals: A mineral evolution perspective
  8. Lumping and splitting: Toward a classification of mineral natural kinds
  9. Thermal expansion of minerals in the amphibole supergroup
  10. A multi-faceted experimental study on the dynamic behavior of MgSiO3 glass in the Earth’s deep interior
  11. Origin of β-cristobalite in Libyan Desert Glass: The hottest naturally occurring silica polymorph?
  12. Time-resolved Raman and luminescence spectroscopy of synthetic REE-doped hydroxylapatites and natural apatites
  13. Reexamination of the structure of opal-A: A combined study of synchrotron X-ray diffraction and pair distribution function analysis
  14. A first-principles study of water in wadsleyite and ringwoodite: Implication for the 520 km discontinuity
  15. Inclusions in calcite phantom crystals suggest role of clay minerals in dolomite formation
  16. Crystal-chemical reinvestigation of probertite, CaNa[B5O7(OH)4]·3H2O, a mineral commodity of boron
  17. Crystal structure determination of orthorhombic variscite2O and its derivative AlPO4 structure at high temperature
  18. Transformation of Fe-bearing minerals from Dongsheng sandstone-type uranium deposit, Ordos Basin, north-central China: Implications for ore genesis
  19. Vaterite in a decrepitated diamond-bearing inclusion in zircon from a stromatic migmatite in the Chinese Sulu ultrahigh-pressure metamorphic belt
  20. Oxygen diffusion in garnet: Experimental calibration and implications for timescales of metamorphic processes and retention of primary O isotopic signatures
  21. Oxidation state of iron and Fe-Mg partitioning between olivine and basaltic martian melts
https://doi.org/10.2138/am-2021-7938
Keywords for this article
Pauling’s rules; bonded radii; bonded interactions; bond paths; bond valence theory; bond valence analysis of crystal structures; bond valence analysis of water in nominally anhydrous mantle minerals; bond valence analysis of proton, cation, and oxyanion sorption complexes; application of bond-valence theory to uranyl-oxide and uranyl-oxysalt minerals; bond-valence analysis of proton, cation, and oxyanion adsorption at mineral-aqueous solution interfaces; bond-valence and XAFS analysis of the local coordination environments of highly charged cations in silicate glasses

Articles in the same Issue

  1. Highlights and Breakthroughs
  2. Mineral evolution heralds a new era for mineralogy
  3. MSA Review
  4. Pauling’s rules for oxide-based minerals: A re-examination based on quantum mechanical constraints and modern applications of bond-valence theory to Earth materials
  5. A cotunnite-type new high-pressure phase of Fe2S
  6. Density determination of liquid iron-nickel-sulfur at high pressure
  7. On the paragenetic modes of minerals: A mineral evolution perspective
  8. Lumping and splitting: Toward a classification of mineral natural kinds
  9. Thermal expansion of minerals in the amphibole supergroup
  10. A multi-faceted experimental study on the dynamic behavior of MgSiO3 glass in the Earth’s deep interior
  11. Origin of β-cristobalite in Libyan Desert Glass: The hottest naturally occurring silica polymorph?
  12. Time-resolved Raman and luminescence spectroscopy of synthetic REE-doped hydroxylapatites and natural apatites
  13. Reexamination of the structure of opal-A: A combined study of synchrotron X-ray diffraction and pair distribution function analysis
  14. A first-principles study of water in wadsleyite and ringwoodite: Implication for the 520 km discontinuity
  15. Inclusions in calcite phantom crystals suggest role of clay minerals in dolomite formation
  16. Crystal-chemical reinvestigation of probertite, CaNa[B5O7(OH)4]·3H2O, a mineral commodity of boron
  17. Crystal structure determination of orthorhombic variscite2O and its derivative AlPO4 structure at high temperature
  18. Transformation of Fe-bearing minerals from Dongsheng sandstone-type uranium deposit, Ordos Basin, north-central China: Implications for ore genesis
  19. Vaterite in a decrepitated diamond-bearing inclusion in zircon from a stromatic migmatite in the Chinese Sulu ultrahigh-pressure metamorphic belt
  20. Oxygen diffusion in garnet: Experimental calibration and implications for timescales of metamorphic processes and retention of primary O isotopic signatures
  21. Oxidation state of iron and Fe-Mg partitioning between olivine and basaltic martian melts
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