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All sourcesNASA NTRSDOE OSTI
DOE OSTI2016

New insights into the application of the valence rules in Zintl phases—Crystal and electronic structures of Ba{sub 7}Ga{sub 4}P{sub 9}, Ba{sub 7}Ga{sub 4}As{sub 9}, Ba{sub 7}Al{sub 4}Sb{sub 9}, Ba{sub 6}CaAl{sub 4}Sb{sub 9}, and Ba{sub 6}CaGa{sub 4}Sb{sub 9}

Crystals of three new ternary pnictides—Ba{sub 7}Al{sub 4}Sb{sub 9}, Ba{sub 7}Ga{sub 4}P{sub 9}, and Ba{sub 7}Ga{sub 4}As{sub 9} have been prepared by reactions of the respective elements in molten Al or Pb fluxes. Single-crystal X-ray diffraction studies reveal that the three phases are isotypic, crystallizing in the orthorhombic Ba{sub 7}Ga{sub 4}Sb{sub 9}-type structure (space group Pmmn, Pearson symbol oP40, Z=2), for which only the prototype is known. The structure is based on TrPn{sub 4} tetrahedra (Tr=Al, Ga; Pn=P, As, Sb), connected in an intricate scheme into 1D-ribbons. Long interchain Pn–Pn bonds (d{sub P–P}>3.0 Å; d{sub As–As}>3.1 Å; d{sub Sb–Sb}>3.3 Å) account for the realization of 2D-layers, separated by Ba{sup 2+} cations. Applying the classic valance rules to rationalize the bonding apparently fails, and Ba{sub 7}Ga{sub 4}Sb{sub 9} has long been known as a metallic Zintl phase. Earlier theoretical calculations, both empirical and ab-initio, suggest that the possible metallic properties originate from filled anti-bonding Pn–Pn states, and the special roles of the “cations” in this crystal structure. To experimentally probe this hypothesis, we sought to synthesize the ordered quaternary phases Ba{sub 6}CaTr{sub 4}Sb{sub 9} (Tr=Al, Ga). Single-crystal X-ray diffraction work confirms Ba{sub 6.145(3)}Ca{sub 0.855}Al{sub 4}Sb{sub 9} and Ba{sub 6.235(3)}Ca{sub 0.765}Ga{sub 4}Sb{sub 9}, with Ca atoms preferably substituting Ba on one of the three available sites. The nuances of the five crystal structures are discussed, and the chemical bonding in Ba{sub 7}Ga{sub 4}As{sub 9} is interrogated by tight-binding linear muffin-tin orbital calculations. - Graphical abstract: The new Zintl phases—Ba{sub 7}Al{sub 4}Sb{sub 9}, Ba{sub 7}Ga{sub 4}P{sub 9}, and Ba{sub 7}Ga{sub 4}As{sub 9}, and their quaternary variants Ba{sub 6}CaTr{sub 4}Sb{sub 9} (Tr=Al, Ga)—crystallize in the Ba{sub 7}Ga{sub 4}Sb{sub 9} structure type. The structures are based on TrPn{sub 4} tetrahedra (a perspective of the crystal structure is shown, as viewed along the c axis). - Highlights: • Ba{sub 7}Al{sub 4}Sb{sub 9}, Ba{sub 7}Ga{sub 4}P{sub 9}, and Ba{sub 7}Ga{sub 4}As{sub 9} are new compounds in the respective phase diagrams. • The quaternary phases Ba{sub 6}CaTr{sub 4}Sb{sub 9} (Tr=Al, Ga) show nearly ordered Ba/Ca distribution. • Very weak Pn–Pn bonds and pairing distortion are observed for Ba{sub 7}Ga{sub 4}Pn{sub 9} (Pn=P, As).

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2015

A Near-Threshold Shape Resonance in the Valence-Shell Photoabsorption of Linear Alkynes

The room-temperature photoabsorption spectra of a number of linear alkynes with internal triple bonds (e.g., 2-butyne, 2-pentyne, and 2- and 3-hexyne) show similar resonances just above the lowest ionization threshold of the neutral molecules. These features result in a substantial enhancement of the photoabsorption cross sections relative to the cross sections of alkynes with terminal triple bonds (e.g., propyne, 1-butyne, 1-pentyne,...). Based on earlier work on 2-butyne [Xu et al., J. Chem. Phys. 2012, 136, 154303], these features are assigned to excitation from the neutral highest occupied molecular orbital (HOMO) to a shape resonance with g (l = 4) character and approximate pi symmetry. This generic behavior results from the similarity of the HOMOs in all internal alkynes, as well as the similarity of the corresponding g pi virtual orbital in the continuum. Theoretical calculations of the absorption spectrum above the ionization threshold for the 2- and 3-alkynes show the presence of a shape resonance when the coupling between the two degenerate or nearly degenerate pi channels is included, with a dominant contribution from l = 4. These calculations thus confirm the qualitative arguments for the importance of the l = 4 continuum near threshold for internal alkynes, which should also apply to other linear internal alkynes and alkynyl radicals. The 1-alkynes do not have such high partial waves present in the shape resonance. The lower l partial waves in these systems are consistent with the broader features observed in the corresponding spectra.

photoabsorption↗
DOE OSTI2022

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

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.

Geochemistry & Geophysics↗