Evidence for $M_B$ and $M_C$ phases in the morphotropic phase boundary region of $\left(1\mathrm{}-x\right)\left[\mathrm{Pb}\right({\mathrm{Mg}}_{1/3}{\mathrm{Nb}}_{2/3}\left){\mathrm{O}}_3\right]-x{\mathrm{PbTiO}}_3:$ A Rietveld study

We present here the results of the room-temperature dielectric measurements and Rietveld analysis of the powder x-ray diffraction data on $\left(1\mathrm{}-x\right)\left[\mathrm{Pb}\right({\mathrm{Mg}}_{1/3}{\mathrm{Nb}}_{2/3}\left){\mathrm{O}}_3\right]-x{\mathrm{PbTiO}}_3(\mathrm{PMN}-x\mathrm{PT})$ in the composition range $0.20<~x<~0.45$ to show that the morphotropic phase boundary region contains two monoclinic phases with space groups Cm (or $M_B$ type) and Pm (or $M_C$ type) stable in the composition ranges $0.27<~x<~0.30$ and $0.31<~x<~0.34,$ respectively. The structure of $\mathrm{PMN}-x\mathrm{PT}$ in the composition ranges $0<~x<~0.26$ and $0.35<~x<~1$ is found to be rhombohedral (R3m) and tetragonal (P4mm), respectively. These results are compared with the predictions of Vanderbilt & Cohen’s theory.