Composition dependence of the diffuse scattering in the relaxor ferroelectric compound(1−x)Pb(Mg1∕3Nb2∕3)O3−xPbTiO3(0≤x≤0.40)

Abstract

We have used neutron diffraction to characterize the diffuse scattering in five single crystals of the relaxor ferroelectric $(1\ensuremath{-}x)\mathrm{Pb}({\mathrm{Mg}}_{1∕3}{\mathrm{Nb}}_{2∕3}){\mathrm{O}}_{3}\ensuremath{-}x{\mathrm{PbTiO}}_{3}$ $(\mathrm{PMN}\text{\ensuremath{-}}x\mathrm{PT})$ with $x=0$, 10, 20, 30, and 40%. The addition of ferroelectric ${\mathrm{PbTiO}}_{3}$ modifies the well-known ``butterfly'' and ``ellipsoidal'' diffuse scattering patterns observed in pure PMN $(x=0)$, which are believed to be associated with the presence of randomly oriented polar nanoregions. In particular, the anisotropy of the diffuse scattering diminishes as the PT content increases. The spatial correlation length $\ensuremath{\xi}$ along the $[1\overline{1}0]$ direction derived from the width of the diffuse scattering at room temperature increases from $12.6\phantom{\rule{0.3em}{0ex}}\mathrm{\AA{}}$ for PMN to $350\phantom{\rule{0.3em}{0ex}}\mathrm{\AA{}}$ for PMN-20%PT. In addition, the diffuse scattering intensity at $q=0$ grows and reaches a maximum value around the morphotropic phase boundary (MPB), which suggests that it is proportional to the dielectric susceptibility. Beyond $x=30%$, a concentration very close to the MPB, no diffuse scattering is observed below ${T}_{C}$, and well-defined critical behavior appears near ${T}_{C}$. By contrast, the diffuse scattering for $x\ensuremath{\le}20$% persists down to low temperatures, where the system retains an average cubic structure $({T}_{C}=0)$. Finally, the anisotropic soft transverse optic (TO) modes observed in PMN are found to be isotropic for PMN-30%PT, which strongly suggests a connection between the anisotropic diffuse scattering and the TO modes.