First-principles calculations of finite temperature Sc and O NMR parameters in Pb(Sc$_{2/3}$W$_{1/3}$)O$_3$

Understanding the dynamics of complex relaxor ferroelectrics is important to characterizing their large electromechanical coupling. Preliminary NMR measurements of Sc electric-field-gradients (EFG) in Pb(Sc$_{2/3}$W$_{1/3}$)O$_3$ (PSW) show a strong temperature dependence in the range $T = 250 - 330$ K. To understand this behavior, we use the first-principles GIPAW\footnote{C.~\ J.~\ Pickard and F.~\ Mauri, Phys. Rev. B {\bf 63}, 245101 (2001);} method within the Quantum Espresso (QE) package\footnote{P. Giannozzi et al., Journal of Physics: Condensed Matter {\bf 21}, 395502 (2009)} to calculate $^{45}$Sc and $^{17}$O chemical-shifts and EFG tensors. To study finite temperature effects, we incorporate the thermal expansion of the lattice and sample thermal disorder, using the phonon degrees of freedom. As in our previous studies of perovksites,\footnote{D.~\ L.~\ Pechkis, E.~\ J.~\ Walter, and H.~\ Krakauer. J.~\ Chem. Phys. {\bf 135}, 114507 (2011); {\em ibid.} {\bf 131}, 184511 (2009)} we show that the $^{17}$O chemical shifts in PSW also exhibit a linear correlation with the nearest-neighbor B-O bond length.