G${\mathrm{dBa}}_2$${\mathrm{Cu}}_{3\mathrm{-}\mathit{x}}$${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$ and ${\mathrm{YBa}}_2$${\mathrm{Cu}}_{3\mathrm{-}\mathit{x}}$${\mathrm{M}}_{\mathit{x}}$${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$ (M=Fe, Co, and Ni) high-${\mathit{T}}_{\mathit{c}}$ superconductors were prepared by conventional ceramic-processing techniques and characterized by measuring the critical temperature as a function of later quenching from various temperatures. For the Fe-substituted compositions, the ${\mathit{T}}_{\mathit{c}}$ for the Y-based samples increase while the ${\mathit{T}}_{\mathit{c}}$ for the Gd-based samples decrease with increasing quench temperatures. Assuming that quenching from elevated temperatures retains the atomic configurations stable at high temperatures, a possible interpretation of these data can be made in terms of a redistribution of Fe from the equilibrium preferred Cu(1) chain sites to the Cu(2) plane sites. A comparison of the data for the Y- and Gd-based superconductors suggests local magnetic interactions between Gd and Fe(2) ions. The data are consistent with superconductivity localized in the Cu-O planes. Gd-based, Co-substituted compositions exhibit behavior similar to Fe-substituted compositions upon quenching treatment. Analysis of Gd-based, Ni-substituted data suggests that two independent processes—thermal disorder and loss of oxygen from the unit cell—operate at high temperatures and determine the final transition-metal distribution. With two independent processes operating at high temperatures, an intrinsic difficulty in determining the transition-metal site-preference energies in the high-${\mathit{T}}_{\mathit{c}}$ superconductors is indicated.

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