Occurrence of superconductivity in R2-z Ce z CuO4 and related compounds

The facts concerning the occurrence of superconductivity in R_2-z Ce _z CuO₄ and in R_2-z Th _z CuO₄ are studied using a combination of simple tools: a hard-sphere model, the self-consistent bond-valence-sum method and Madelung potential calculations. Doping by isolated substitutional Ce should produce Ce³⁺, and not Ce⁴⁺, causing us to conclude that the dopants are not isolated, but (Ce, O_interstitial) pairs, which make the material p type and not n type. The L = 0 magnetic rare-earth ions Gd and Cm are unsplit pair breakers, unlike the other magnetic rare-earth ions which lead to superconductivity. As the rare-earth ions become smaller, the c-axis length shortens; then the O ions rotate after they come into contact with one another. Eu_1.85Th_0.15CuO₄ does not superconduct because quadrivalent Th is too large to fit at the dopant site, but Eu_1.85Ce_0.15CuO₄ does superconduct because Ce fits.