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

TL;DR

This study uses first-principles DFT calculations to analyze $^{17}$O NMR chemical shielding in complex perovskites, revealing a linear relationship with bond lengths and providing insights into local structures.

Contribution

It demonstrates the effectiveness of combining DFT and GIPAW methods to predict NMR shifts and challenges previous assumptions about Ti clustering in PZT.

Findings

$^{17}$O NMR shifts vary linearly with transition-metal/oxygen bond length.

Results support using NMR and first-principles calculations to probe local structures.

Findings suggest no Ti clustering in PZT based on NMR data.

Abstract

First-principles density functional theory (DFT) oxygen chemical shift tensors were calculated for A(B,B$^{\prime}$)O$_3$ perovskite alloys Pb(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 periodic boundary conditions were used. Results from both methods are in good agreement for PZT and prototypical perovskites. PMN results were obtained using only GIPAW. Both isotropic $\delta_\mathrm{iso}$ and axial $\delta_\mathrm{ax}$ chemical shifts were found to vary approximately linearly as a function of the nearest-distance transition-metal/oxygen bond length,$r_\mathrm{s}$. Using these results, we argue against Ti clustering in PZT, as conjectured from recent $^{17}$O NMR magic-angle-spinning measurements. Our findings indicate that $^{17}$O NMR measurements, coupled with first-principles calculations, can be an important probe of local structure in complex perovskite solid solutions.