Matches in SemOpenAlex for { <https://semopenalex.org/work/W4206910790> ?p ?o ?g. }
- W4206910790 endingPage "1248" @default.
- W4206910790 startingPage "1219" @default.
- W4206910790 abstract "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." @default.
- W4206910790 created "2022-01-26" @default.
- W4206910790 creator A5002171426 @default.
- W4206910790 creator A5055546274 @default.
- W4206910790 creator A5071136942 @default.
- W4206910790 date "2022-07-01" @default.
- W4206910790 modified "2023-10-10" @default.
- W4206910790 title "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" @default.
- W4206910790 cites W1519304025 @default.
- W4206910790 cites W1876742417 @default.
- W4206910790 cites W1895958371 @default.
- W4206910790 cites W1913712610 @default.
- W4206910790 cites W1964940327 @default.
- W4206910790 cites W1965944029 @default.
- W4206910790 cites W1966289980 @default.
- W4206910790 cites W1973302955 @default.
- W4206910790 cites W1975652443 @default.
- W4206910790 cites W1977808065 @default.
- W4206910790 cites W1980821083 @default.
- W4206910790 cites W1981338907 @default.
- W4206910790 cites W1982927349 @default.
- W4206910790 cites W1983374168 @default.
- W4206910790 cites W1984522603 @default.
- W4206910790 cites W1985935098 @default.
- W4206910790 cites W1986487840 @default.
- W4206910790 cites W1986527664 @default.
- W4206910790 cites W1989977424 @default.
- W4206910790 cites W1990413373 @default.
- W4206910790 cites W1990655794 @default.
- W4206910790 cites W1990822402 @default.
- W4206910790 cites W1993904324 @default.
- W4206910790 cites W1994135464 @default.
- W4206910790 cites W1995661188 @default.
- W4206910790 cites W1996124099 @default.
- W4206910790 cites W1996355671 @default.
- W4206910790 cites W2000083814 @default.
- W4206910790 cites W2002403064 @default.
- W4206910790 cites W2004798478 @default.
- W4206910790 cites W2004807536 @default.
- W4206910790 cites W2008766708 @default.
- W4206910790 cites W2008838573 @default.
- W4206910790 cites W2010785223 @default.
- W4206910790 cites W2012171620 @default.
- W4206910790 cites W2012315868 @default.
- W4206910790 cites W2013628555 @default.
- W4206910790 cites W2014054424 @default.
- W4206910790 cites W2014416110 @default.
- W4206910790 cites W2017652251 @default.
- W4206910790 cites W2020049665 @default.
- W4206910790 cites W2024495825 @default.
- W4206910790 cites W2025377862 @default.
- W4206910790 cites W2027939791 @default.
- W4206910790 cites W2030946335 @default.
- W4206910790 cites W2030976617 @default.
- W4206910790 cites W2032519807 @default.
- W4206910790 cites W2033597564 @default.
- W4206910790 cites W2034003688 @default.
- W4206910790 cites W2035054233 @default.
- W4206910790 cites W2036580473 @default.
- W4206910790 cites W2037001985 @default.
- W4206910790 cites W2037588390 @default.
- W4206910790 cites W2037941449 @default.
- W4206910790 cites W2040892840 @default.
- W4206910790 cites W2041726686 @default.
- W4206910790 cites W2043618721 @default.
- W4206910790 cites W2043706313 @default.
- W4206910790 cites W2044099476 @default.
- W4206910790 cites W2044238202 @default.
- W4206910790 cites W2044741566 @default.
- W4206910790 cites W2045465826 @default.
- W4206910790 cites W2047580474 @default.
- W4206910790 cites W2048457266 @default.
- W4206910790 cites W2053441820 @default.
- W4206910790 cites W2056457021 @default.
- W4206910790 cites W2057454703 @default.
- W4206910790 cites W2058098574 @default.
- W4206910790 cites W2059006499 @default.
- W4206910790 cites W2059539080 @default.
- W4206910790 cites W2059943090 @default.
- W4206910790 cites W2060326597 @default.
- W4206910790 cites W2061613392 @default.
- W4206910790 cites W2064002302 @default.
- W4206910790 cites W2064389914 @default.
- W4206910790 cites W2064940710 @default.
- W4206910790 cites W2067290481 @default.
- W4206910790 cites W2067326287 @default.
- W4206910790 cites W2068944345 @default.
- W4206910790 cites W2071883351 @default.
- W4206910790 cites W2072399917 @default.
- W4206910790 cites W2072938953 @default.
- W4206910790 cites W2074019256 @default.
- W4206910790 cites W2074836128 @default.
- W4206910790 cites W2076692729 @default.
- W4206910790 cites W2076843280 @default.
- W4206910790 cites W2079071528 @default.
- W4206910790 cites W2080369083 @default.
- W4206910790 cites W2080390417 @default.
- W4206910790 cites W2081083878 @default.