Phase separation and softening of the $O2, 3$ in-phase mode in the $\mathrm{Y}{\mathrm{Ba}}_2{\mathrm{Cu}}_3{\mathrm{O}}_x$ superconductors

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.