The Madelung Energy in Copper-Oxide-Based Ceramics

The Madelung energy in the (Y, Ca)(Ba, La) 2 Cu 3 O 6+δ system has been calculated in order to find the distribution of hole carriers among sites. We regard the compoundas a superconductor, when the lowest-energy distribution is such that holes enter sites in CuO 2 sheets, whereas we regard it as a semiconductor, when no holes enter sites in the CuO 2 sheets. Based on this criterion, we find a phase diagram, where the superconducting region is separated from the semi-conducting region by a boundary. A good agreement with the experimental finding by Tokura et al . is obtained, when account is taken of the ordering of exygen vacancies in the basal plane of Fig. 1 in the text. It is found that for some compounds with small δ(∼0.25), holes are spontaneously produced in CuO 2 sheets, so that the compounds may be a superconductor although their nominal hole content is zero.