Anionic ordering in Pb₂Ti₄O₉F₂ revisited by nuclear magnetic resonance and density functional theory

Abstract

A combination of 19F magic angle spinning (MAS) nuclear magnetic resonance (NMR) and density functional theory (DFT) were used to study the ordering of F atoms in Pb₂Ti₄O₉F₂. 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 6s2 lone pair may play a role (∼0.1 eV per 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.