Quantifying Emptiness: On the Size of A-Site Vacancies in Tetragonal Tungsten Bronzes

Abstract

Tetragonal tungsten bronzes (TTBs) represent the second largest family of ferroelectric materials and are charac- terized by their range of lattice sites and ability to have filled or vacant sites. However, the impact of empty A-sites (cation vacancies) on the stability and properties of TTBs has not been investigated so far. This study aims to determine the relative size of cation vacancies and propose a model to extract cation and cation vacancy sizes from lattice parameters by deconvoluting average site sizes into the separate cation and cation vacancy contributions. Lattice parameters and crystallographic data of “empty” lead-free TTB niobates were collected and compared to first-principles calculations of Sr5−5xBa5xNb10O30 (SBNx) and Ba5−1.5xRExNb10O30 (BRENx, where RE = Bi3+, La3+, Sm3+, Y3+, or Dy3+). The neural network CHGNet was used for an initial screening of the complex configurational space of unfilled TTBs, followed by full geometry optimization of sets of configurations with the highest probabilities, using density functional theory (DFT). In empty TTBs, cation vacancies were found to take up more space than the cations that would normally be there. Vacancies at the A1-site require 13 % more space, while those at the A2-site need 6 % more space. The developed model showcases the same size trends extracted from the experimental data sets as for the DFT-optimized structures. This study is the first to report a detailed account of the effect of cation vacancies in TTBs and proposes a model to estimate the cation vacancy size, which is also useful when considering the stability of TTBs.