Evidence for another low-temperature phase transition in tetragonal $\mathrm{Pb}\left({\mathrm{Zr}}_x{\mathrm{Ti}}_{1-x}\right){\mathrm{O}}_3$ $\mathrm{}(x=0.515,0.520\mathrm{})\mathrm{}$

Results of dielectric and resonance frequency ${(f}_r)$ measurements below room temperature are presented for $\mathrm{Pb}\left({\mathrm{Zr}}_x{\mathrm{Ti}}_{1-x}\right){\mathrm{O}}_3,$ $x=0.515\mathrm{}$ and 0.520. It is shown that the temperature coefficient of $f_r$ changes sign from negative to positive around 210 and 265 K for $x=0.520\mathrm{}$ and 200 and 260 K for $x=\mathrm{0.515.}\mathrm{}$ Anomalies in the real part of the dielectric constant $\left({\varepsilon }^{\prime }\right)$ are observed around the same temperatures at which the temperature coefficient of $f_r$ changes sign because of the electrostrictive coupling between the elastic and dielectric responses. Low-temperature powder x-ray-diffraction (XRD) data, however, reveal only one transition from the tetragonal to monoclinic phase similar to that reported by Noheda et al. [Phys. Rev. B, 61, 8687 (2000)]. Electron-diffraction data, on the other hand, reveal yet another structural transition at lower temperatures corresponding to the second anomaly in the ${\varepsilon }^{\prime }$ vs T and $f_r$ vs T curves. This second transition is shown to be a cell-doubling transition not observed by Noheda et al. in their XRD studies. The observation of superlattice reflections raises doubts about the correctness of the Cm space group proposed by Noheda et al. for the monoclinic phase of $\mathrm{Pb}\left({\mathrm{Zr}}_x{\mathrm{Ti}}_{1-x}\right){\mathrm{O}}_3$ below the second transition temperature.