Geometric distribution of CuO chains in YBa2Cu3O6+x

Statistics of CuO chains in basal planes of YBa2Cu3O6+x high-Tc superconductor has been studied in terms of two dimensional asymmetric next-to-nearest-neighbor Ising (ASYNNNI) model, with accentuation on distribution of CuO chains per different chain lengths. It has been shown that the fraction p(l) of CuO chains containing l oxygen ions (i.e., having the length equal to l), satisfies so-called “law of geometric distribution” p(l) = ω(1 − ω)l−1, where the quantity ω is equal to the inverse of average chain length lav in the system, for given values of oxygen content x and temperature T. In the case of ortho-II (OII) structural phase, the geometric chain probability distribution is shown to hold separately for each of two different sublattices of oxygen sites, commonly known as α1 and α2, with respectively defined lavα1(x,T) and lavα2(x,T). The theoretically derived result of the chain probability distribution p(l) is shown to be in a remarkable agreement with the results obtained out of extensive Monte Carlo calculations that were made within region of stability of orthorhombic structural phases in (x, T) space. The relevance of chain length distribution for accurate count of the number of transferred electronic holes to superconducting CuO2 layers has been pointed out and expression for hole concentration has been derived. The concept of critical chain length for charge transfer mechanism was briefly discussed.