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Title: Insights into the crystal chemistry of Earth materials rendered by electron density distributions: Pauling's rules revisited

Pauling's first two rules are examined in terms of the accumulation of the electron density between bonded pairs of atoms for a relatively large number of oxide and silicate crystals and siloxane molecules. The distribution of the electron density shows that the radius of the oxygen atom is not fixed, but that it actually decreases systematically from ~1.40 Å to ~ 0.65 Å as the polarizing power and the electronegativity of the bonded metal atoms increase and the distribution of the O atom is progressively polarized and contracted along the bond vectors by the impact of the bonded interactions. The contractions result in an aspherical oxygen atom that displays as many different bonded “radii” as it has bonded interactions. The bonded radii for the metal atoms match the Shannon and Prewitt ionic radii for the more electropositive atoms like potassium and sodium, but they are systematically larger for the more electronegative atoms like aluminum, silicon and phosphorous. Pauling's first rule is based on the assumption that the radius of the oxide anion is fixed and that the radii of the cations are such that radius sum of the spherical oxide anion and a cation necessarily equals the separation between themore » cation-anion bonded pair with the coordination number of the cation being determined by the ratio of the radii of the cation and anion. In the case of the bonded radii, the sum of the bonded radii for the metal atoms and the oxide anion necessarily equals the bond lengths by virtue of the way that the bonded radii were determined in the partitioning of the electron density along the bond path into metal and O atom parts. But, the radius ratio for the O and M atoms is an unsatisfactory rule for determining the coordination number of the metal atom inasmuch as a bonded O atom is not, in general, spherical, and its size varies substantially along its bonded directions. But by counting the number of bond paths that radiate from a bonded atom, the coordination number of the atom is determined uniquely independent of the asphericity and sizes of the atom. A power law connection established between the bond lengths and bond strengths for crystals and molecules is mirrored by a comparable power law connection between bond length and the accumulation of the electron density between bonded pairs of atoms, a connection that is consistent with Pauling's electroneutrality postulate that the charges of the atoms in an oxide are negligibly small. The connection indicates that a one-to-one correspondence exists between the accumulation between a pair of bonded atoms and the Pauling bond strength for M-O bonded interaction for all atoms of the periodic table. The connection provides a common basis for understanding the success of the manifold applications that have been made with the bond valence theory model together with the modeling of crystal structures, chemical zoning, leaching and cation transport in batteries and the like. We believe that the wide spread applications of the model in mineralogy and material science owes much of its success to the direct connection between bond strength and the quantum mechanical observable, the electron density distribution. Comparable power law expressions established for the bonded interactions for both crystals and molecules support Pauling's assertion that his second rule has significance for molecules as well as for crystals. A simple expression is found that provides a one to one connection between the accumulation of the electron density between bonded M and O atoms and the Pauling bond strength for all M atoms of the periodic table with ~ 95 % of the variation of the bond strength being explained in terms of a linear dependence on the accumulated electron density. Compelling evidence is presented that supports the argument that the Si-O bonded interactions for tiny siloxane molecules and silicate crystals are chemically equivalent.« less
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Journal ID: ISSN 0003--004X; 39937; KC0302060
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Resource Type:
Journal Article
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Journal Name: American Mineralogist, 99(5-6):1071-1084; Journal Volume: 99; Journal Issue: 5-6
Research Org:
Pacific Northwest National Laboratory (PNNL), Richland, WA (US), Environmental Molecular Sciences Laboratory (EMSL)
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Country of Publication:
United States
Environmental Molecular Sciences Laboratory