## 2 Fluorine Occupation Patterns in Layered Oxylfluoride Perovskite
### Fluorine Insertion into Only Interstitial Sites between the Perovskite Blocks  
There are a few examples that involve fluorine insertion into only interstitial sites between the perovskite block layers. The RP-type layered manganese oxides, LaSrMnO\({}_{4}\) (_n_ = 1) and _Ln_1.2 Sr\({}_{1.8}\)Mn\({}_{2}\)O\({}_{7}\) (_Ln_ = Pr, Nd, Sm, Eu, and Gd) (_n_ = 2), accommodate fluorine in the (La/Sr)O rock-salt layers between the Mn-O perovskite blocks, followed by large expansion of the _c_-axis of 1 \(\sim\) 3 A (see Figure 6). Utilization of F\({}_{2}\) gas, NH\({}_{4}\)F, CuF\({}_{2}\) or PVDF as a fluorination agent at low temperatures yields LaSrMnO\({}_{4}\)F\({}_{2}\)[26, 27] and _Ln_1.2 Sr\({}_{1.8}\)Mn\({}_{2}\)O\({}_{7}\)F\({}_{2}\)[26, 28] where fluorine is inserted in each perovskite block. In addition, heating these fluorinated compounds with the corresponding precursors in appropriate ratios results in a staged intercalation structure, namely LaSrMnO\({}_{4}\)F [27, 29] and La\({}_{1.2}\)Sr\({}_{1.8}\)Mn\({}_{2}\)O\({}_{7}\)F [27] where F is inserted between alternate rock-salt layers. It should be noted that the F sites in the rock-salt layers are different between LaSrMnO\({}_{4}\)F and LaSrMnO\({}_{4}\)F\({}_{2}\), and La\({}_{1.2}\)Sr\({}_{1.8}\)Mn\({}_{2}\)O\({}_{7}\)F\({}_{2}\); the F atoms in LaSrMnO\({}_{4}\)F and La\({}_{1.2}\)Sr\({}_{1.8}\)Mn\({}_{2}\)O\({}_{7}\)F are located in the interlayer space so as to bridge between La/Sr and the apical oxygen, while the F atoms in LaSrMnO\({}_{4}\)F\({}_{2}\) and _Ln_1.2 Sr\({}_{1.8}\)Mn\({}_{2}\)O\({}_{7}\)F\({}_{2}\) occupy tetrahedral sites of (La/Sr)\({}_{4}\) in the rock-salt layers. In spite of the valences of Mn cations close to 4+, no long-range magnetic order is observed down to 5 K.  
The \(n\) = 2 RP phase Sr\({}_{3}\)Ru\({}_{2}\)O\({}_{7}\) is also fluorinated using CuF\({}_{2}\) to give the oxyfluoride Sr\({}_{3}\)Ru\({}_{2}\)O\({}_{7}\)F\({}_{2}\)[30]. In the fluorinated phase, fluorine is inserted in the tetrahedral sites of Sr\({}_{4}\) in rock-salt layers between perovskite blocks (see Figure 7). The precursor crystallizes in the tetragonal structure with \(I\)4/_mmm_, but the fluorine insertion lowers the crystal symmetry to orthorhombic symmetry (_Pbam_), which is associated with rotation and tilting of the RuO\({}_{6}\) octahedra. The magnetic properties also change after the fluorination reaction, from the ferromagnetic state with _T_\({}_{\rm C}\) = 105 K to weak ferromagnetic state with _T_\({}_{\rm N}\) = 185 K.  
F\({}_{2}\)O\({}_{3}\)F\({}_{2}\).  
Fluorination of the RP-Ba\({}_{2-x}\)Sr\({}_{x}\)PdO\({}_{3}\) (\(0\leq x\leq 1.5\)) by PVDF involves unusual oxygen displacement through anion exchange [31, 32], which is different from the case of the fluorination of Sr\({}_{3}\)Fe\({}_{2}\)O\({}_{6}\) described above [17]. As shown in Figure 8, the structure of Ba\({}_{2-x}\)Sr\({}_{x}\)PdO\({}_{3}\) comprises corner-linked chains of PdO\({}_{4}\) squares along the \(a\)-axis, similar to the one-dimensional structure in Sr\({}_{2}\)CuO\({}_{3}\). Fluorination to Ba\({}_{2-x}\)Sr\({}_{x}\)PdO\({}_{2}\)F\({}_{2}\) involves structural conversion to \(T\)-structure (isostructural with Nd\({}_{2}\)CuO\({}_{4}\)), namely rearrangement of the PdO\({}_{4}\) network from a 1-D chain to a 2-D plane. The remaining O\({}^{2-}\) anions in the apical site move to the original vacant site and the two inserted F\({}^{-}\) anions build fluorite block layer with Ba/Sr cations. Because the Pd\({}^{2+}\) cation exhibits a strong preference for square lattice geometry, no additional fluorine insertion at the apical sites is allowed.