A structural phase transformation in the ${\mathrm{CuO}}_2$ planes of ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_x$ has been observed at the onset of the overdoped regime, $x=6.95\mathrm{}$. We have measured as a function of $x$ the dimpling in the ${\mathrm{CuO}}_2$ planes by EXAFS, and the O(2,3) in-phase $\left(A_{1g}\right)$ mode by Raman scattering. The data show for $x\ge 6.95$ anomalously large static displacements of the Cu(2) atoms off the O(2,3) layer and a gap in the distribution of the O(2,3) in-phase Raman shifts. We conclude the structure of overdoped ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_x$ to be a martensitic form of the optimum doped crystal.

Systematic Raman measurements have been carried out on the $\mathrm{Y}{\mathrm{Ba}}_2{\mathrm{Cu}}_3{\mathrm{O}}_x$ superconductors with very well-defined oxygen concentration $6.4<x<\mathrm{}7.0\mathrm{}$. In contrast to the literature, the frequencies of some of the phonons do not vary linearly with the oxygen content. The variation of the phonon characteristics of the apex oxygen mode with doping is consistent with the development of superstructures. A softening of the phonon due to the in-phase vibrations ($A_g$ mode) of the plane oxygen atoms takes place in the overdoped region.

A systematic Raman study in the visible and the near IR has been carried out on $\mathrm{Y}{\mathrm{Ba}}_2{\mathrm{Cu}}_3{\mathrm{O}}_x$ samples, with isotopic substitution of ${}_{}{}^{18}{}_{}{}^{}\mathrm{O}$ for ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$, and for oxygen concentrations in the range $x=6.44-6.98\mathrm{}$. A small but clear deviation from harmonic behavior has been detected for the frequency shift of the in-phase mode and, to a less extent, of the apex mode, relative to the out-of-phase phonon. The deviation increases towards low concentrations of oxygen. A disagreement of the present work for the apical mode, with a previous investigation using IR excitation, is attributed to the contribution of several phases to the apex mode in the underdoped region and the possible IR resonance of the "ortho-II" phase.