## 2 Fluorine Occupation Patterns in Layered Oxylfluoride Perovskite  
### Regular or Random Anion Occupation Pattern in the Perovskite Blocks  
Early in the study on the layered oxyfluoride perovskite, high temperature solid-state reaction, one of the easiest synthetic methods, was commonly employed. However, the variety of transition metals in the reported oxyfluoride compounds is quite limited, mainly due to the high chemical stability of the simple starting fluoride materials. To the best of our knowledge, the first example of the RP-type layered perovskite compound is K\({}_{2}\)NbO\({}_{3}\)F, which was reported in 1962 by [PERSON] and [PERSON] [15]. As shown in Figure 2(a), the niobium oxyfluoride adopts the tetragonal structure in the space group of _I4/mmm_ with octahedral coordination around Nb atom and O/F site disorder at the apical sites. The preferential occupation of the fluoride anion at the apical sites elongated the Nb-O/F bonds (2.0642 A) along the \(c\) axis compared with those (1.9780 A) in the \(ab\) plane. Subsequently, the same authors reported an isostructural iron oxyfluoride, Sr\({}_{2}\)FeO\({}_{3}\)F [16] and determined the crystal structure to be _I4/mmm_. However, [PERSON] and his collaborators demonstrated that the exact crystal symmetry could be described as _P4/mmm_[17]. In contrast to K\({}_{2}\)NbO\({}_{3}\)F, the Fe counterpart possesses the O/F site order at the apical sites leading to a strong distortion of the FeO\({}_{5}\)F octahedron (see Figure 2(b)). In fact, the bond length between Fe and O or F is 1.904 or 2.730 A. Therefore, the iron metal center effectively takes a square pyramidal coordination against five O\({}^{2-}\) anions. [PERSON] _et al._ also extended the layered oxyfluoride system to Ba\({}_{2}\)BO\({}_{3}\)F (\(B\) = Sc and In) [18]. Both compounds exhibit preferential occupation by F\({}^{-}\) anions at the apical sites, but the anion-site order/disorder in \(B\) = In/Sc. In addition to the RP-type layered perovskite, Dion-Jacobson (DJ) and Aurivillius (AV) -type layered oxyfluoride phases are reported. The formulas of DJ and AV phases are expressed as _AA'\({}_{n-1}B_{n}\)_O\({}_{3n+1}\) and (Bi\({}_{2}\)O\({}_{2}\))(_A'\({}_{n-1}B_{n}\)_O\({}_{3n+1}\)_), respectively. _A_SrNb\({}_{2}\)O\({}_{6}\)F (_A_ = Li, Na, Rb) [19] (Figure 3) and Rb_Ln_TiNbO\({}_{6}\)F (_Ln_ = La, Pr, Nd) [20] were synthesized by conventional solid-state reaction. In contrast to the above RP phases, the F atoms prefer to occupy the equatorial and central apical anion sites in the double-layered perovskite block, not the terminal apical ones, because the covalency of the chemical bond between Nb and the terminal apical oxygen is incompatible with the ionicity of the Nb-F bond. On the other hand, [PERSON] _et al._ reported the reductive fluorination of DJ-RbLaNb\({}_{2}\)O\({}_{7}\) and RP-NaYTiO\({}_{4}\) into RbLaNb\({}_{2}\)O\({}_{7-x}\)F\({}_{x}\) and NaYTiO\({}_{4-x}\)F\({}_{x}\) using poly(vinylidene)fluoride (PVDF) [21]. PVDF or poly(tetrafluoroethylene) (PTFE) are effective fluorinating agents, utilized by [PERSON] for the first time [11]. This fluorination proceeds in a topotactic manner; the framework of the precursor is maintained through the reaction. While _A_SrNb\({}_{2}\)O\({}_{6}\)F and Rb_Ln_TiNbO\({}_{6}\)F with the non-magneticcations are insulating, RbLaNb\({}_{2}\)O\({}_{7-x}\)F\({}_{x}\) possesses mixed valence states between Nb\({}^{4+}\) and Nb\({}^{5+}\) cations, which makes it electrically conductive. For \(n=2\) RP-type layered perovskite, Ba\({}_{3}\)In\({}_{2}\)O\({}_{5}\)F\({}_{2}\)[22] and Sr\({}_{3}\)Fe\({}_{2}\)O\({}_{6}\)F\({}_{0.68}\)[17] are known. Common to both compounds, fluorine atoms occupy the terminal apical sites. In comparison with Ba\({}_{3}\)In\({}_{2}\)O\({}_{5}\)F\({}_{2}\), synthesized by conventional high-temperature reaction, Sr\({}_{3}\)Fe\({}_{2}\)O\({}_{6}\)F\({}_{0.68}\) is obtained by a low-temperature fluorination using F\({}_{2}\) gas.