Titanium-Oxygen Bond Length -Bond Valence Relationship

A bond length–bond valence correlation is a simple method of checking and evaluating molecular structures and is of great interest in chemistry, biology, geology, and material science. Recently, we used quantum-mechanical arguments to derive Pauling’s bond length-valence relationship and to define the adjustable fitting parameter b in terms of atomic-orbital exponents. Improved orbital exponents were generated for elements 1-103 using published atomic radii and single-bond covalent radii as well as a continuous function for effective principal quantum number. In this study, we use orbital exponents for titanium (Ti) and oxygen (O) to generate a bond length-valence relationship for Ti-O bonds. Recent crystallographic Ti-O bond lengths from 32 environments were collected and converted to Ti-O bond valences to check the reliability of the bond length-valence relationship where Ro was found (bond length of unit valence). This relationship is expected to apply to any Ti-O bond regardless of environment, physical state, or oxidation number

Fintar o destino: between the colonial bond and a postcolonial double-bind

The article addresses Fernando Vendrell’s Fintar o destino [Dribbling Fate] (1998) by considering the appropriation of sports by the Portuguese Estado Novo’s colonialist ideology and policies (inspired by Gilberto Freyre’s lusotropicalist theories). In parallel, it highlights the role that football in particular plays in underwriting and simultaneously undermining affective, cultural, and economic bonds and binds between Cape Verde and Portugal, pre- and post-independence. The connections between former colony and metropolis, as viewed through the lens of the increasingly globalized and commercialized world of football, go beyond (post)colonial nostalgia, as sport may be seen — the emergence of neo-colonial patterns notwithstanding — to provide a platform for a reimagining of individual and collective hopes and challenges

Bond Length - Bond Valence Relationships for Carbon - Carbon and Carbon - Oxygen Bonds

In the present study, relationships are developed for determining bond orders (also referred to as bond valences or bond numbers) from published bond lengths for carbon-carbon (C-C) and carbon-oxygen (C-O) bonds. The relationships are based on Pauling’s empirical formula s = exp((Ro-R)/b)), where s is the bond order, R is the corresponding bond length, Ro is the unit valence bond length, and b is a fitting parameter. We use a recently derived relationship for the b parameter in terms of the bonding atoms’ published atomic orbital exponents. The resulting equations were checked against published x-ray diffraction (XRD) data for 176 carbon systems with 540 published C-C bond lengths, and 50 oxygen systems having 72 published C-O bond lengths. The C-C and C-O bond length-valence relationships are shown to have sufficient applicability and accuracy for use in any bonding environment, regardless of physical state or oxidation number

Neutron diffraction and Raman studies of the incorporation of sulfate in silicate glasses

The oxidation state, coordination and local environment of sulphur in alkali silicate (R2O-SiO2; R= Na, Li) and alkali-alkaline earth silicate (Na2O-MO-SiO2; M= Ca, Ba) glasses have been investigated using neutron diffraction and Raman spectroscopy. With analyses of both the individual total neutron correlation functions, and of suitable doped-undoped differences, the S-O bonds and (O-O)S correlations were clearly isolated from the other overlapping correlations due to Si-O and (O-O)Si distances in the SiO4 tetrahedra, and the modifier-oxygen (R-O and M-O) distances. Clear evidence was obtained that the sulphur is present as SO4 2- groups, confirmed by the observation in the Raman spectra of the symmetric S-O stretch mode of SO4 2- groups. The modifier-oxygen bond length distributions were deconvoluted from the neutron correlation functions by fitting. The Na-O and Li-O bond length distributions were clearly asymmetric, whereas no evidence was obtained for asymmetry of the Ca-O and Ba-O distributions. A consideration of the bonding shows that the oxygen atoms in the SO4 2- groups do not participate in the silicate network, and as such constitute a third type of oxygen, ‘non-network oxygen’, in addition to the bridging and non-bridging oxygens that are bonded to silicon atoms. Thus each individual sulphate group is surrounded by a shell of modifier, and is not connected directly to the silicate network. The addition of SO3 to the glass leads to a conversion of oxygen atoms within the silicate network from non-bridging to bridging, so that there is a repolymerisation of the silicate network. There is evidence that SO3 doping leads to changes in the form of the distribution of Na-O bond lengths, with a reduction in the fitted short bond coordination number, and an increase in the fitted long bond coordination number, and this is consistent with a repolymerisation of the silicate network. In contrast, there is no evidence that SO3 doping leads to a change in the distribution of Li-O bond lengths, with a total Li-O coordination number consistently in excess of four

Monte Carlo Algorithm for Simulating Reversible Aggregation of Multisite Particles

We present an efficient and exact Monte Carlo algorithm to simulate reversible aggregation of particles with dedicated binding sites. This method introduces a novel data structure of dynamic bond tree to record clusters and sequences of bond formations. The algorithm achieves a constant time cost for processing cluster association and a cost between $\mathcal{O}(\log M)$ and $\mathcal{O}(M)$ for processing bond dissociation in clusters with $M$ bonds. The algorithm is statistically exact and can reproduce results obtained by the standard method. We applied the method to simulate a trivalent ligand and a bivalent receptor clustering system and obtained an average scaling of $\mathcal{O}(M^{0.45})$ for processing bond dissociation in acyclic aggregation, compared to a linear scaling with the cluster size in standard methods. The algorithm also demands substantially less memory than the conventional method.Comment: 8 pages, 3 figure

Anisotropic superexchange of a 90 degree Cu-O-Cu bond

The magnetic anisotropy af a rectangular Cu-O-Cu bond is investigated in second order of the spin-orbit interaction. Such a bond is characteristic for cuprates having edge sharing CuO_2 chains, and exists also in the Cu_3O_4 plane or in ladder compounds. For a ferromagnetic coupling between the copper spins an easy axis is found perpendicular to the copper oxygen plaquettes in agreement with the experimental spin structure of Li_2CuO_2. In addition, a pseudo-dipolar interaction is derived. Its estimation in the case of the Cu_3O_4 plane (which is present for instance in Ba_2Cu_3O_4Cl_2 or Sr_2Cu_3O_4Cl_2) gives a value which is however two orders of magnitude smaller than the usual dipole-dipole interaction.Comment: 6 pages, 2 figures, improved referenc