The role of the bonding interatomic distances in multicomponent copper oxides are a lot discussed now for the understanding of physics and chemistry of these interesting compounds.
Zachariasen [1] and Brown [2] bond valence model is used to express the charge changes distribution resulting from the changes in the occupation number of oxygen atoms around copper, as the copper oxidation state.
The bond valence $s_{ij}$ of an ion at the distance $R_{ij}$ is defined by
\begin{displaymath}
s_{ij} = exp(R_{o} - R_{ij} / B)
\end{displaymath}
where B = 0.37 \AA
and $R_{o}$= the reference distance depending on the type of ions forming bond.
The sum of bond valences around ion is close to its oxidation state $V_{ij}$
\begin{displaymath}
V_{j} = \sum_{j} s_{ij} = \sum_{j} exp(R_{o} - R_{ij}/0.37)
\end{displaymath}
The changes of bond length with the oxygen stoichiometry both in CuO and high-T$_{c}$ superconductor (BiPb)$_{2}$Sr$_{2}$Ca$_{2}$Cu$_{3}$O$_{y}$ were investigated by the X-ray diffraction. Experiments were carried out on powder diffractometers XRD7 and HZG4 with filtered CuK$_{\alpha}$ radiation.
The positions of atoms submitted by the Rietveld method were displayed by the program MDRAW that allows to investigate the local oxygen arrangement around the Cu atoms. In CuO samples the bond trans-plane distance Cu -O changes on the dependence on oxygen stoichiometry. This change is more evident (obvious) on the angle variation. Oxygen deficiency in superconducting high-T$_{c}$ phase is manifested in the lower transition temperature T$_{c}$ and in small changes of oxygen and non-oxygen atom positions.
1. W.H.Zachariasen: J.Less-Comm.Metals 62(1978) 1
2. I.D.Brown, D.Altermatt: Acta Cryst.B41(1985) 244