Phase separation and internal strains in the mixed ${\mathrm{La}}_{0.5}{R}_{0.5}{\mathrm{Ba}}_2{\mathrm{Cu}}_3{\mathrm{O}}_y$ compounds $(R=\mathrm{r}\mathrm{a}\mathrm{r}\mathrm{e}-\mathrm{e}\mathrm{a}\mathrm{r}\mathrm{t}\mathrm{h}$ element)

The mixed phase ${\mathrm{La}}_{0.5}{R}_{0.5}{\mathrm{Ba}}_2{\mathrm{Cu}}_3{\mathrm{O}}_y$ (where R is yttrium or another rare earth) has been prepared using a variation of the solid-state reaction technique. X-ray diffraction and Raman measurements have been carried out to study the effect of the mixed rare-earth substitution at the site of the Y atom. The x-ray-diffraction measurements show characteristic changes in the interatomic distances, which are indicative of strains in the unit cell. A strain-relaxation mechanism is proposed, attributed to the separation of phases. In the micro-Raman spectra, an increase of the $A_g$ mode frequency of the apex oxygen with increasing average $\mathrm{La}-R$ ionic radius is observed, the mode frequencies corresponding to the Ba and the Cu(2) atoms remain practically unaffected, while in some compounds a new mode appears at ∼126 ${\mathrm{cm}}^{\mathrm{-}1}$. The in-phase vibrations of the plane oxygen atoms show a shift to a lower frequency compared with the $R{\mathrm{Ba}}_2{\mathrm{Cu}}_3{\mathrm{O}}_y$ samples, similar to the one observed in the overdoped ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_y(y>~6.92)$ system. Besides, the width of this phonon is considerably larger than in the ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_y$ compounds, attributable to the existence of phases with underdoped, optimally doped, and overdoped oxygen concentration. As concerns the changes induced in the $B_{1g}$ Raman active mode of the out-of-phase vibrations of the plane oxygen atoms, they are indicative of phases rich in either La, R, or an intermediate phase. Differences observed from the ${\mathrm{Pr}}_{1-x}{R}_x{\mathrm{Ba}}_2{\mathrm{Cu}}_3{\mathrm{O}}_y$ compounds prove that the phase formation mechanism is not a pure ion-size effect.