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Structures of Cobalt, Zinc and Lead Niobates Based On 1 Structures at the Atomic Level of Cobalt, Zinc and Lead Niobates Raji Heyrovska Institute of Biophysics, Academy of Sciences of the Czech Republic, 135 Kralovopolska, 612 65 Brno, Czech Republic. Email: [email protected] The author has found in recent years that bond lengths are exact sums of the radii of adjacent atoms and or ions, where the ions have Golden ratio based radii. This work was prompted by the exciting observation last year of the Golden ratio in the magnetic properties of cobalt niobate. It is shown here that in cobalt and zinc niobates, cobalt, zinc and oxygen ions have Golden ratio based ionic radii, whereas in lead niobate, all atoms have covalent radii. Also, the angles at the single bond oxygen anion and atom are close to 1080, as in a pentagon. 1-3 The experimental finding of the E8 symmetry in the magnetic properties of cobalt niobate, CoNb2O6 provoked the author's interest to look into the atomic Nature Precedings : hdl:10101/npre.2011.6059.1 Posted 24 Jun 2011 structures of niobates. It was found4-7 in recent years that the Golden sections of the covalent bond lengths d(AA) between two atoms of the same kind are sums of the radii of Pauling's ionic resonance forms8, which are the cations and anions of the atom (A), i.e., d(AA) = d(AA)/φ + d(AA)/φ2, where φ (= 51/2 + 1)/2 is the Golden ratio. In particular, the inter-ionic distances in all alkali halides (M+X-) were shown to be exact sums of the Golden ratio based ionic radii, d(M+) = d(MM)/φ2 and d(X-) = d(XX)/φ. On this basis, the bond lengths d(AB) in molecules between any two atoms and or ions were found to be sums of the atomic and or ionic radii4-7. 2 9a Presented here are the structures of CoNb2O6 and zinc niobate , ZnNb2O6, in 2+ 2+ - which Co and Zn ions are bound to two oxygen anions, O s.b., and that of lead 9b niobate , PbNb2O6, where all bonds are covalent. 10 The covalent bond lengths d(AA) taken from are (in nm): d(NbNb)bcc = 0.2858, d(CoCo)hcp = 0.2507, d(ZnZn) = 0.2665, d(PbPb) = 0.350, d(OO)d.b. = 0.1207 and 8 d(OO)s.b. = 0.134, (subscripts, bcc: body centered cubic; hcp: hexagonal close packed; d.b.: double bond, s.b.: single bond). In the hcp cobalt lattice, the axial ratio 2+ c/a = 0.407/0.251 = 1.62 (close to φ). The φ-based ionic radii (Rφ) in nm are: Co = 2 2+ 2 - 0.2507/φ = 0.096, Zn = 0.2665/φ = 0.102, O s.b. = 0.134/φ = 0.083. These radii are assembled in Table I. The bond lengths, d(NbNb) = 0.2858 ~ b/2 and d(CoCo) = 0.2507 ~ c/2, where b (= 0.5702 nm) and c (= 0.5038 nm) are the lattice parameters in the cobalt niobate crystal (see supplementary material in1). With these radii, the various bond lengths calculated as the sums of the radii of the adjacent atoms or ions are presented in Table II. Also given in the same Table are the bond lengths from the literature10-15 closest to the radii sum obtained here. Figure 1 shows the 1:1 correlation of the bond length data from the literature with the radii sum obtained here. Nature Precedings : hdl:10101/npre.2011.6059.1 Posted 24 Jun 2011 Figures 2 (a) - (f) show the atomic structures of cobalt, zinc and lead niobates drawn to scale with bond lengths as the sum of the radii of the adjacent atoms and or ions. In figure 2 (a) for cobalt niobate, the two oxygen anions are on the same side of the cobalt ion and in figure 2 (b), the oxygen anions are on diametrically opposite sides of the cobalt ion. Figures 2 (c) and (d) for zinc niobate are similar to figures 2 (a) and (b) for cobalt niobate. Figures 2 (e) and (f) are for lead niobate with the two oxygen atoms of single bond covalent radii bound to the central lead atom with covalent radius. Note that all the structures are zigzag as in the zigzag ferromagnetic 3 Ising chains1. It is interesting to see that the diagonal of the rectangle in figure 2 (a) is equal to 0.482 + 1.182 = 1.272 = (51/2b)2, where b = 0.57 nm is the lattice parameter1 of cobalt niobate and 51/2 = 2φ -1. The diagonal in the rectangle in figure 2 (b) is equal to 0.592 + 1.172 = 1.312 ~ [51/2(0.59)]2 = 1.322. The bond angles at oxygen in, NbO-Co2+, NbO-Zn2+ and NbOPb are probably close to 1080, as in7 HOH ~ 1040, FOF ~ 1030 and ClOCl ~ 1110. These are comparable with the angle 1080 in the pentagon, in the geometry of which the Golden ratio occurs extensively. Thus, the observation1 of the Golden ratio in the magnetic properties of cobalt niobate is perhaps a reflection of the Golden ratio in the structure of the molecule. References 1. Coldea R. et al. Quantum Criticality in an Ising Chain: Experimental Evidence for Emergent E8 Symmetry. Science 327, 177-180 (2010). http://www.sciencemag.org/content/327/5962/177.full?ijkey=0MPWaFy0y5aMs&ke ytype=ref&siteid=sci; 2. Affleck, I. Nature 464, 362-363 (2010). Nature Precedings : hdl:10101/npre.2011.6059.1 Posted 24 Jun 2011 http://www.nature.com/nature/journal/v464/n7287/full/464362a.html 3. Shiga, D., 'Most beautiful' math structure appears in the lab for first time. New Scientist, January 2010. http://www.newscientist.com/article/dn18356-most- beautiful-math-structure-appears-in-lab-for-first-time.html 4. Heyrovska, R., The Golden ratio, ionic and atomic radii and bond lengths Mol. Phys. 103, 877-882 (2005). 4 5. Heyrovska, R., The Golden ratio in the creations of Nature arises in the architecture of atoms and ions. In: Sener, B. Innovations in Chemical Biology. Ch 12 (Springer com, 2009). 6. Heyrovska, R., Golden Sections of Interatomic Distances as Exact Ionic Radii and Additivity of Atomic and Ionic Radii in Chemical Bonds. http://arxiv.org/ftp/arxiv/papers/0902/0902.1184.pdf (2009). 7. Heyrovska, R. & Narayan, S. Atomic Structures of Molecules Based on Additivity of Atomic and/or Ionic Radii. http://precedings.nature.com/documents/3292/version/1 (2009). 8. Pauling, L. The Nature of the Chemical Bond. (Cornell Univ. Press, New York, 1960). 9. a) http://www.wolframalpha.com/input/?i=Zn%28NbO3%292&lk=1&a=ClashPrefs_* Chemical- b) http://www.wolframalpha.com/entities/chemicals/lead(II)niobate/ac/us/0u/ 10. http://www.webelements.com/ 11. Chen, W-J., Zhai, H-J., Zhang, Y-F. & Wang, L-S. On the Electronic and Nature Precedings : hdl:10101/npre.2011.6059.1 Posted 24 Jun 2011 - Structural Properties of Tri-Niobium Oxide Clusters Nb3On (n = 3-8): Photoelectron Spectroscopy and Density Functional Calculations. J. Phys. Chem. A 114, 5958-5966 (2010); http://www.chem.brown.edu/research/LSWang/publications/324.pdf 12. McQueen, T., Xu, Q., Andersen, E.N., Zandbergen, H.W. & Cava, R.J. Structures of the Reduced Niobium Oxides Nb12O29 and Nb22O54. http://arxiv.org/ftp/arxiv/papers/0708/0708.0673.pdf 13. Gubo, M., Ebensperger, C., Mayer, W., Hammer, L. & Heinz, K. Structural elements in the oxidation process of a single cobalt layer on Ir(100)-(1 x 1). Physical 5 Review B 83, 075435 (2011); http://www.fkp.uni-erlangen.de/literatur/pdf-kh/p289- SingleOxideLayer-PRB.pdf 14. Bach, R.D., Andres, J.L., Winter, J.E., Schlegel, H.B., Ball, J.C. & Holubka, J.W. A model for adhesion-producing interactions of zinc oxide surfaces with alcohols, amines and alkenes. J. Adhesion Sci. Technology, 8, 249-259 (1994); http://www.chem.wayne.edu/schlegel/Pub_folder/172.pdf 15. Turzhevsky, S.A., Novikov, D.L., Gubanov, V.A. & Freeman, A.J. Electronic structure and crystal chemistry of niobium oxide phases. Physical Review B, 50, Number 51 (1994). 16. Li, Y., Sergey V. Krivovichev, S.V. & Burns, P.C. Crystal Chemsitry of Lead Oxide Hydroxide Nitrates. I. The Crystal Structure of [Pb6O4](OH)(NO3)(CO3). J. Solid State Chemsitry, 153, 365-370 (2000); http://www.nd.edu/~pburns/pcb073.pdf Acknowledgment The author thanks the Institute of Biophysics of the Academy of Sciences of the Czech Republic for the financial support. Nature Precedings : hdl:10101/npre.2011.6059.1 Posted 24 Jun 2011 6 TABLE 1. Covalent radii (Rcov) and ionic radii (Rφ) in 2+ - 2+ - Co O 2(NbO2)2, Zn O 2(NbO2)2 and PbO2(NbO2)2, in nm. ============================================ - +2 Rcov (Nb) Rcov (Od.b) Rφ (O s.b.) Rφ (Co ) CoNb2O6 0.143 0.060 0.083 0.096 - +2 Rcov (Nb) Rcov (Od.b) Rφ (O s.b.) Rφ (Zn ) ZnNb2O6 0.143 0.060 0.083 0.102 Rcov (Nb) Rcov (Od.b) Rcov (Os.b) Rcov (Pb) PbNb2O6 0.143 0.060 0.067 0.175 2+ - 2+ - TABLE 2. Bond lengths in Co O 2(NbO2)2, Zn O 2(NbO2)2 and PbO2(NbO2)2 as sums of radii (upper values), in nm. ============================================== - 2+ - NbOd.b. NbO s.b. Co O s.b. CoNb2O6 0.203 0.226 0.179 Data (Ref) 0.203 (11) 0.226 (12) 0.182 (13) Nature Precedings : hdl:10101/npre.2011.6059.1 Posted 24 Jun 2011 - 2+ - NbOd.b. NbO s.b. Zn O s.b. ZnNb2O6 0.203 0.226 0.185 Data (Ref) 0.203 (11) 0.226 (12) 0.185 (14) NbOd.b.
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