The Circular Model of the Atom

PART IV

SUPERCONDUCTIVITY

Copper Valence

One of the controversies within high T_c superconductor theory is copper valence. Copper oxides are both in the chains and planes in YBCO cell structure, as well as the lanthanide structure. Copper (I), and copper (II) are in both structures, and copper (III), has been suggested as present to account for the mixed valence state with oxygen deficient compounds. For example, the mixed valence state ratio of copper to oxygen is 2.33. To account for this, valence (III) copper was introduced, but little definitive evidence of its existence in superconductivity cells has emerged.

Chen, Callaway, and Misen have written, "A problem which has received much attention in regard to the electronic structure of YBa₂Cu₃O₇ is the question of the valence of the copper atoms. If an elementary ionic model is adopted, a non-integral value of 2.3 is obtained, suggesting that two of the Cu atoms should be in the Cu²⁺ state, and one in the Cu³⁺....The possible existence of Cu³⁺ is controversial. A closely related question concerns the question of magnetic moments on the copper atoms. In a localized picture, a Cu²⁺ ion would be expected to have a S = 1/2 and a moment" [1].

An explanation of the magnetic moment problem can be made with the Circular Model of the Atom and copper's position when attempting to measure the magnetic moment. (copper II would fall into the full integer octet and would not be affected).

With the use of the new Circular Model of the Atom a different approach is suggested. Spin + 1/2 electrons have dissimilar energy than - 1/2 spin electrons. In the new model using the "aufbrau" principle of electron buildup for each element, the spin states have a general separation into hemispheres. By adjusting for spin states at shell closures, we find strongly positive and strongly negative states within the atom. Nonstoichiometric chemistry of superconductors has to adjust or compensate for this clumping of negative spins. This is part of the reason for oxygen deficiency in cation/anion ratios in superconducting perovskites.

Another cause of nonstoichiometric chemistry's difficulties is with the present periodic table. It does not exhibit polarity positions relative to each element. For example copper is abutting the positive pole in its elemental state. The first ionization of copper results in the electron next to the pole being removed from elemental copper in the 4S¹ position.

No problem, but what happens to the second ionization state of copper? We now have a pole that acts as a barrier. We also have a law of alternative multiplicities which pertains to individual atoms and ions. Hence, the second ionization of copper movement is contrary to normal ionization behavior resulting in the 3D10 position. This polarity barrier could be a related antecedent influence by the Madelung-rule which results in irregular energy levels. "For example, 4s-levels (K 19, Ca 20) are filled before 3d (Sc 21, Zn 30), or 5s (Rb 37, Sr 38), before 4d (Y 39, Cd 48), etc.. This rule is called Madelung-rule (or Goudschmidt rule).... There is to be no complete derivation of the Madelung rule from electronic correlation theory" [2].

Second ionization copper moves energetically farther from the pole in the positive field. Compensation then requires more oxygen or negative spin element in a nonstoichiometric compound to achieve superconducting status. This is where Ca, Sr, and Ba render importance in high T_c compounds. They all have sliding electrons from S shell to D shell configurations. They have the effect of keeping the cation/anion balance neutral for superconductivity.

[1] Chen, H., Callaway, J., & Misra, P. K., 1988. Phys. Rev. B. 38, p. 195.

[2] Barut, A. O., 1972. Group Structure of the Periodic System. The Structure of Matter, Rutherford Centennial Symposium. Canturbury: University of Canterbury, pp. 126-127.