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Structures at the Atomic Level of , and 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 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 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 are close to 1080, as in a pentagon.

The experimental finding1-3 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

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 (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 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

. 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- Clusters Nb3On (n = 3-8): Photoelectron

Spectroscopy and 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 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 surfaces with alcohols,

amines and . 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 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

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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. NbOs.b. PbOs.b.

PbNb2O6 0.203 0.210 0.242 Data (Ref) 0.203 (11) 0.210 (15) 0.240 (16)

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FIG. 1:

0.25

0.23

0.21

0.19 Bond lengths from literature /nm

0.17 0.17 0.19 0.21 0.23 0.25 Bond lengths as radii sum /nm

NbO(db) NbO(-)sb NbO(sb) CoO(-)sb ZnO(-)sb PbO(sb) 1:1 line

FIG 1. Comparison of the bond lengths from the literature11-16 with the sums of the Nature Precedings : hdl:10101/npre.2011.6059.1 Posted 24 Jun 2011 radii of adjacent atoms and or ions (see Table II) in cobalt, zinc and lead niobates.

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FIG. 2 (a) - (f):

- (a) CoNb2O6; Radii (nm): Nb (0.143), Od.b. (0.06), O s.b. (0.083), Co2+ (0.096). Area per molecule: 0.48 nm x 1.18 nm = 0.57 nm2.

- (b) CoNb2O6; Radii (nm): Nb (0.143), Od.b. (0.06), O s.b. (0.083), Co2+ (0.096). Area per molecule: 0.59 nm x 1.17 nm = 0.69 nm2.

Nature Precedings : hdl:10101/npre.2011.6059.1 Posted 24 Jun 2011

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- (c) ZnNb2O6; Radii (nm): Nb (0.143), Od.b. (0.06), O s.b. (0.083), Zn2+ (0.102). Area per molecule: 0.48 nm x 1.18 nm = 0.57 nm2.

- (d) ZnNb2O6; Radii (nm): Nb (0.143), Od.b. (0.06), O s.b. (0.083), Zn2+ (0.102). Area per molecule: 0.58 nm x 1.17 nm = 0.68 nm2.

Nature Precedings : hdl:10101/npre.2011.6059.1 Posted 24 Jun 2011

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(e) PbNb2O6; Radii (nm): Nb (0.143), Od.b. (0.060), Os.b. (0.067), Pb (0.175). Area per molecule: 0.46 nm x 1.24 nm = 0.57 nm2.

(f) PbNb2O6; Radii (nm): Nb (0.143), Od.b. (0.060), Os.b. (0.067), Pb (0.175). Area per molecule: 0.50 nm x 1.24 nm = 0.62 nm2.

Nature Precedings : hdl:10101/npre.2011.6059.1 Posted 24 Jun 2011

FIG 2 (a) - (f). Atomic structures of niobates based in additivity of radii of adjacent

2+ - 2+ - atoms or ions: (a) & (b) Co (O s.b.NbO2)2, (c) & (d) Zn (O s.b.NbO2)2 and (e) & (f)

2+ - 2+ Pb(Os.b.NbO2)2. All atoms have covalent radii and Co , O s.b. and Zn ions have

Golden ratio (φ) based radii. (Subscripts: d.b. = double bond, s.b. = single bond,

2+ - 2+ - dotted lines in the bonds, (Co O s.b.) and (Zn O s.b.) are ionic bonds; dotted and full

- lines in (O s.b.Nb) are partial ionic bonds.