O/F anion order in Pb$_2$Ti$_4$O$_9$F$_2$ stabilized by the 6$s^2$ lone pair electrons of Pb$^{2+}$

Abstract

Understanding the mechanisms of anionic ordering in mixed anion compounds is a crucial factor for designing their structural and functional properties. Some oxyfluorides are known to exhibit the F − ordering. The ordering is accompanied by a tetragonal distortion, which is believed to be originated by the 6s 2 lone pairs of Bi and Pb. To elucidate the role played by the lone pair, we studied isostructural Bi 2 Ti 4 O 11 and Pb 2 Ti 4 O 9 F 2 with a combination of synchrotron X-ray diffraction techniques and ab initio calculations. Bi 2 Ti 4 O 11 undergoes antiferroelectric-paraelectric transitions from C2/c to C2/m. Meanwhile, Pb 2 Ti 4 O 9 F 2 does not, because F − selectively occupies the closest anion site to Bi/Pb and reduces the distortion. The question on why a particular site is selectively occupied by F − in Pb 2 Ti 4 O 9 F 2 becomes important to understand the role of 6s 2 lone pair electrons for stabilizing the anion order. Our DFT ab initio calculations reproduced the same anionic arrangement in terms of the total energy. However, this energy gain cannot be fully explained by the electrostatic (Madelung) potential alone, being an exception of the Pauling's second rule. We explain the reason focusing on the steric effects of 6s lone pairs. This manuscript has been authored by UT-Battelle, LLC, under Contract No. DE-AC05-00OR22725 with the US Department of Energy (DOE). The US Government retains and the publisher, by accepting the article for publication, acknowledges that the United States Government retains a nonexclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this manuscript, or allow others to do so, for US Government purposes. Ichibha provided a large part of the calculation results. Ichibha and Fernando wrote the paper coworking with the other authors. DOE will provide public access to these results of federally sponsored research in accordance with the DOE Public Access Plan (http://energy.gov/downloads/doe-public-access-plan).