Local structure in perovskite relaxor ferroelectrics by ${}^{207}\mathrm{Pb}$ NMR

The ${}^{207}\mathrm{Pb}$ static, magic-angle spinning (MAS), and two-dimensional phase-adjusted spinning sidebands (2D-PASS) NMR experiments have been performed on $\left(1\mathrm{}-x\right)\mathrm{PMN}/x\mathrm{PSN}$ [where PMN stands for $\mathrm{Pb}\left({\mathrm{Mg}}_{1/3}{\mathrm{Nb}}_{2/3}\right){\mathrm{O}}_3$ and PSN stands for $\mathrm{Pb}\left({\mathrm{Sc}}_{1/2}{\mathrm{Nb}}_{1/2}\right){\mathrm{O}}_3]$ relaxor ferroelectrics. These materials have inherent chemical and positional disorder that results in very low-resolution static and MAS spectra. Only in 2D-PASS spectra can isotropic and anisotropic chemical shifts be separated. The isotropic chemical shift ${\delta }_{\mathrm{iso}}$ ranges from $-1800$ to $-900\mathrm{ppm}$ and the anisotropic chemical shift ${\delta }_{\mathrm{aniso}}$ ranges from $-700$ to $-230\mathrm{ppm}$ with asymmetry parameter $\eta$ ranging from 0.5 to 1. Strong linear correlations between isotropic and anisotropic chemical shifts show that Pb-O bonds vary from more ionic to more covalent environments. The isotropic chemical shift measures the shortest Pb-O bond length and its distribution is quantitatively described. Such distribution is used to examine two competing models of Pb displacements; the direction of displacement is random in the spherical model but specific in the unique direction model. The spherical model is unable to yield the observed distribution of the shortest Pb-O bond length. The unique direction model may fit the observed distribution, but it is unable to discern the direction of the Pb displacement. This model fits experiments equally well with any given direction. However, the distribution parameters strongly depend on the direction; for PMN at $27°\mathrm{C},$ $r_0\left(\sigma \right)=0.455\mathrm{}\left(0.039\right),$ 0.302(0.023), and 0.381(0.030) Å for [001], [011], and [111], respectively, where $r_0$ and $\sigma$ are, respectively, the mean and standard deviation of the Gaussian distribution of the Pb displacement from the ideal position.