Symmetry analysis of anion order, cation-vacancy order, and octahedral tilting in oxyfluoride double perovskites

In simple homoanionic double perovskites, the possible phase space based on octahedral tilting and cation ordering has been established and is useful in resolving known structures as well as performing computational studies to determine viable phase transitions [1] [2]. However, a similar study incorporating octahedral tilting and ordering in heteroanionic materials has yet to be carried out. Initial work in oxynitrides has determined that by coupling octahedral tilting and anion ordering, it is possible to further lower the phase symmetries of materials [3]. This coupling can also be used to break inversion symmetry, leading to improvement in dielectric responses and ferroelectricity. Here we use the P4/nmm phase of [ ]KNaNbOF₅ as a prototype structure to explore how independently and in combination anion ordering, A-site vacancy ordering, and octahedral tilting lead to variations in symmetries [4]. We apply materials physics principles to understand commonalities among the structure space and perform electronic structure calculation to ascertain the microscopic origins.
[1] Acta.Cryst.(2003).B59,463-471
[2] Jou.Sol.St.Chem.(2006)179,4,1076-1085
[3] Cryst.GrowthDes.(2013)13,10,4623-4629
[4] Crys. (2011),1,1,3-14