Correlations between frequency of infra-red active vibrational modes and copper-oxygen distance in copper oxides. Application to superconductors

The infra-red spectra of a large number of ternary Cu(II) oxides with at least a quasi square-planar coordination of oxygen around the copper ions have been studied. The frequency of the bands with the highest frequency,v_max, is found to correlate extremely well with the shortest Cu–O distance.v_max increases at an impressive rate of 20 cm^–1 per 0.01 Å when the Cu–O distance becomes less than 1.97 Å, which is the Cu²⁺–O^2– distance in square-planar CuO₄ complexes as obtained from empirical ionic radii considerations. The marked sensitivity may be used as a titration procedure not only to assign bands but also to obtain diagnostic information about local coordination in compounds derived, for example, from the YBa₂Cu₃O_7–d structure such as LaCaBaCu₃O_7–d. The only example where this correlation fails is in the two-layer non-superconducting oxides derived from La₂(Ca, Sr)Cu₂O₆. The significance of this result is discussed. The marked dependence of frequency on the bond-distance is qualitatively examined in terms of an increased electron-phonon coupling to account for the observed tendency of the superconducting transition temperature to go through a maximum as the average basal plane Cu–O distance is decreased.