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First-principles density functional theory (DFT) oxygen chemical shifttensors were calculated for A(B,B$^{\prime}$)O$_3$ perovskite alloysPb(Zr$_{1/2}$Ti$_{1/2}$)O$_3$ (PZT) and Pb(Mg$_{1/3}$Nb$_{2/3}$)O$_3$ (PMN).Quantum chemistry methods for embedded clusters and the GIPAW method [C.\ J.\Pickard and F.\ Mauri, {\it Phys. Rev. B} {\bf 63} 245101 (2001)] for periodicboundary conditions were used. Results from both methods are in good agreementfor PZT and prototypical perovskites. PMN results were obtained using onlyGIPAW. Both isotropic $\delta_\mathrm{iso}$ and axial $\delta_\mathrm{ax}$chemical shifts were found to vary approximately linearly as a function of thenearest-distance transition-metal/oxygen bond length,$r_\mathrm{s}$. Usingthese results, we argue against Ti clustering in PZT, as conjectured fromrecent $^{17}$O NMR magic-angle-spinning measurements. Our findings indicatethat $^{17}$O NMR measurements, coupled with first-principles calculations, canbe an important probe of local structure in complex perovskite solid solutions.

journal of chemical physics online/the journal of chemical physics/journal of chemical physics

First-principles calculations of $^{17}$O NMR chemical shielding in  Pb(Zr$_{1/2}$Ti$_{1/2}$)O$_3$ and Pb(Mg$_{1/3}$Nb$_{2/3}$)O$_3$: linear  dependence on transition-metal/oxygen bond lengths