Copper-oxygen bond length and self-doping inR2CuO4(R=Pr, Nd, Sm, Eu, Gd)

Bond-length mismatch between alternate layers of the T’ ${\mathit{R}}_2$ ${\mathrm{CuO}}_4$ intergrowth structure introduces a stretching of the Cu-O bond length in the ${\mathrm{CuO}}_2$ planes. The bond-length mismatch is relieved by self-doping. The character of the self-doping is probed by measurements of thermopower and lattice parameters for quenched and air-annealed samples. For R=Sm, Eu, or Gd, oxygen vacancies in the R/${\mathrm{O}}_2$/R layers reduce the intralayer compressive stress and introduce antibonding ${\mathrm{\sigma }}^{\mathrm{*}}$(${\mathit{x}}^{2\mathrm{-}}$ ${\mathit{y}}^2$) electrons into the ${\mathrm{CuO}}_2$ planes to relieve their intraplanar tensile stress. In ${\mathrm{Nd}}_2$ ${\mathrm{CuO}}_4$, a displacement of some oxygen to c-axis sites in the NdO layer permits essentially complete relief of the bond-length mismatch, and the annealed compound is slightly oxidized. The self-doping in ${\mathrm{Pr}}_2$ ${\mathrm{CuO}}_4$ involves an internal redox reaction, and the possibilities of Pr(4+/3+) versus peroxide formation are evaluated. The data also indicate a decrease in Madelung energy with increasing Cu-O bond length at the threshold for a transition in n-type transport from small-polaron to intermediate-size-polaron character.