## 2 Fluorine Occupation Patterns in Layered Oxylfluoride Perovskite
### Regular or Random Anion Occupation Pattern in the Perovskite Blocks
As shown in Figure 4, the precursor Sr\({}_{3}\)Fe\({}_{2}\)O\({}_{6}\) has an oxygen vacancy at the central apical site, but its oxidative fluorination causes local migration of the terminal apical site to the original oxygen vacant site. Because the intercalated F atoms occupy the terminal apical sites with O, the deviation of the O-Fe-O bond angle in the plane from the ideal 180\({}^{\circ}\) is only 7.6\({}^{\circ}\), much smaller  
Figure 2: Crystal structure of **(a)** K\({}_{2}\)NbO\({}_{3}\)F, **(b)** Sr\({}_{2}\)FeO\({}_{3}\)F, and **(c)** Sr\({}_{2}\)CoO\({}_{3}\)F. Solid line represents the unit cell. than the corresponding value of 15.28\({}^{\circ}\) in Ba\({}_{3}\)In\({}_{2}\)O\({}_{5}\)F\({}_{2}\) with full fluorine occupation of the terminal apical sites. Three kinds of AV-type layered oxyfluoride perovskites, Bi\({}_{2}\)BO\({}_{5}\)F (\(B\) = Nb, Ta) and Bi\({}_{2}\)TiO\({}_{4}\)F\({}_{2}\) (Figure 5), were synthesized by [PERSON] [23]. Later work presented the ferroelectric phase transitions at \(T_{\text{C}}\) = 303, 283, and 284 K, respectively, but the relationship between the crystal structure and the ferroelectricity is still controversial. Hydrothermal synthesis yields better sample quality than conventional solid-state reaction [24]. Bi\({}_{2}\)TiO\({}_{4}\)F\({}_{2}\) adopts the simple body-centered tetragonal structure in the space group _I_/_mmm_[24] while Bi\({}_{2}\)NbO\({}_{5}\)F is proposed to adopt _Pbca_ symmetry [25]. These  
Figure 4: Crystal structure of **(a)** Sr\({}_{3}\)Fe\({}_{2}\)O\({}_{6}\) and **(b)** Sr\({}_{3}\)Fe\({}_{2}\)O\({}_{6}\)F\({}_{0.86}\). **(c)** Fluorination process of Sr\({}_{3}\)Fe\({}_{2}\)O\({}_{6}\) to Sr\({}_{3}\)Fe\({}_{2}\)O\({}_{6}\)F\({}_{0.86}\), showing rearrangement of oxide and fluoride anions. centrosymmetric crystal structures contradict the requirement for the ferroelectricity. In fact, the reexamination of electrical properties in Bi\({}_{2}\)NbO\({}_{5}\)F demonstrated neither second-harmonic generation nor a permittivity anomaly associated with ferroelectric phase transition reported previously. It is believed from bond-valence-sum calculations that F atoms tend to occupy the equatorial sites for Bi\({}_{2}\)TiO\({}_{4}\)F\({}_{2}\) or the apical sites for Bi\({}_{2}\)NbO\({}_{5}\)F.  
We would like to show a new class of anion ordered perovskite materials, KNaNbOF\({}_{5}\) and KNaMO\({}_{2}\)F\({}_{4}\) (\(M=\) Mo\({}^{6+}\), W\({}^{6+}\)) expressed as the general formula _ABB'_(O,F)\({}_{6}\)[12]. [PERSON] _et al._ successfully synthesized these three compounds by hydrothermal reaction. Layers of K\({}^{+}\) cations and cation vacancies are alternately located in the \(A\) site along the \(c\) axis, and Na\({}^{+}\) and \(B\) (Nb\({}^{5+}\), Mo\({}^{6+}\), W\({}^{6+}\)) cations are ordered in a rock salt configuration. More interestingly, fluoride anions are located in K\({}^{+}\) cation layers while apical oxide anions are located in the adjacent _A_-site layer containing the _A_-site vacancies. Similar to DJ-_A_SrNb\({}_{2}\)O\({}_{6}\)F, the Nb\({}^{5+}\) cation form short Nb=O bonds and one long Nb-F bond opposite the O\({}^{2-}\) anion, leading to strong distortion of the Nb\({}^{5+}\)-centered octahedron. This type of O/F anion order has never been seen in any other oxyfluorides. It is apparent that the cation order in both \(A\) and \(B\) sites influences the O/F anion order.