Anionic Ordering in Pb$_2$Ti$_4$O$_9$F$_2$ Revisited by Nuclear Magnetic Resonance and Density Functional Theory

TL;DR

This study combines NMR and DFT calculations to analyze fluorine atom ordering in Pb$_2$Ti$_4$O$_9$F$_2$, revealing preferential site occupation and the influence of Pb lone pairs on this ordering.

Contribution

It provides a detailed understanding of F atom site preferences in Pb$_2$Ti$_4$O$_9$F$_2$ using combined experimental and computational methods, highlighting the role of Pb lone pairs.

Findings

F atoms occupy two sites in a 73:27 ratio.

DFT explains site preference and reproduces occupation ratio.

Pb lone pair influences F site occupancy.

Abstract

A combination of $^{19}$F magic angle spinning (MAS) nuclear magnetic resonance (NMR) and density functional theory (DFT) were used to study the ordering of F atoms in Pb$_2$Ti$_4$O$_9$F$_2$. This analysis revealed that F atoms predominantly occupy two of the six available inequivalent sites in a ratio of 73:27. DFT-based calculations explained the preference of F occupation on these sites and quantitatively reproduced the experimental occupation ratio, independent of the choice of functional. We concluded that the Pb atom's 6$s^2$ lone pair may play a role ($\sim$0.1 eV/f.u.) in determining the majority and minority F occupation sites with partial density of states and crystal orbital Hamiltonian population analyses applied to the DFT wave functions.