Structures at the Atomic Level of Cobalt, Zinc and Lead Niobates (with an Appendix: Atomic structure of cobalt niobate crystal)

Abstract

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 108 0 , as in a pentagon. The experimental finding 1-3 of the E8 symmetry in the magnetic properties of cobalt niobate, CoNb 2 O 6 provoked the author's interest to look into the atomic structures of niobates. It was found 4-7 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 forms 8 , which are the cations and anions of the atom (A), i.e., d(AA) = d(AA)/φ + d(AA)/φ 2 , where φ (= 5 1/2 + 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)/φ 2 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 radii 4-7 .

Simple and Exact Additivity of Atomic and Ionic Radii in Various Types of Bonds in Small as Well as Large Molecules

“…This surprising result shows that the Golden ratio which manifests in the geometry of many creations in the Universe [4] is right in core of the atom! Thus, the ratio of the electrostatic radii of the electron and proton in the hydrogen atom is the Golden ratio, and an atom is a unique construction of Nature [37][38][39][40][41][42][43][44][45][46][47][48][49]. On finding that the covalent bond length d(HH) between the two hydrogen atoms in the molecule H 2 is the diagonal of a square with the Bohr radius as a side, and since the latter is divided into two Golden sections, a e =a B /φ and a p =a B /φ 2 , pertaining to the electron and proton, d(HH) is actually the sum, d(HH)=2 On subtracting the cationic radius, d(H + ) from the bond length of partially ionic alkali metal hydrides and hydrogen halides, it was found that the alkali metal cations are Golden sections of the respective interatomic distances in the metal lattice and the halogens have their covalent radii (which are half the covalent bond length).…”