Understanding structural distortions in hybrid layered perovskites with the n = 1 Ruddlesden–Popper structure

Abstract

A symmetry mode analysis yields 47 symmetrically distinct patterns of octahedral tilting in hybrid organic–inorganic layered perovskites that adopt the n = 1 Ruddlesden–Popper (RP) structure. The crystal structures of compounds belonging to this family are compared with the predictions of the symmetry analysis. Approximately 88% of the 140 unique structures have symmetries that agree with those expected based on octahedral tilting alone, while the remaining compounds have additional structural features that further lower the symmetry, such as asymmetric packing of bulky organic cations, distortions of metal-centered octahedra or a shift of the inorganic layers that deviates from the a/2 + b/2 shift associated with the RP structure. The structures of real compounds are heterogeneously distributed amongst the various tilt systems, with only 9 of the 47 tilt systems represented. No examples of in-phase ψ-tilts about the a and/or b axes of the undistorted parent structure were found, while at the other extreme ∼66% of the known structures possess a combination of out-of-phase ϕ-tilts about the a and/or b axes and θ-tilts (rotations) about the c axis. The latter combination leads to favorable hydrogen bonding interactions that accommodate the chemically inequivalent halide ions within the inorganic layers. In some compounds, primarily those that contain either Pb2+ or Sn2+, favorable hydrogen bonding interactions can also be achieved by distortions of the octahedra in combination with θ-tilts.

Structure Directing Forces in Hybrid Layered Double Perovskites Containing Aromatic Organic Cations

“…The ϕ-tilts push the bridging halides out of the plane containing the inorganic cations and simultaneously move the terminal halides closer to one of the four neighboring −NH 3 + groups. This distortion facilitates the formation of shorter, stronger hydrogen bonds to the terminal halide ions, as discussed in ref . Hydrogen bond lengths and angles for the four cation-ordered RP phases reported here can be found in the Supporting Information (Table S7).…”

“…The intralayer edge-toface packing seen in both double perovskites is also found in (BzA) 2 PbX 4 (X = Cl, Br, I) 10,54,55 and (BzA) 2 CdCl 4 . 56 Much like a traditional hydrogen bond, the strength of the CH−π edge-to-face interaction is dictated by (1) the distance between the hydrogen atom on one phenyl ring and the plane of an adjacent phenyl ring, and (2) the angle between the carbon and hydrogen on one phenyl ring and the centroid of an adjacent phenyl ring. Shorter distances and angles closer to 180°are indicative of stronger interactions.…”

“…30 The octahedra that make up the inorganic layers can undergo cooperative distortions by rotating about one or more of the local 4-fold axes of the octahedra, lowering the symmetry of the structure in the process. The symmetry consequences of octahedral tilting were originally studied by Hatch et al 30 Recently, the analysis was revisited and expanded upon by Liu et al 1 Aleksandrov categorized the tilts/rotations of the octahedra into three different categories: θ-, ϕ-, and ψ-tilts, as shown in Figure 1. 31 The θ-tilts correspond to a rotation of each octahedron about the 4-fold axes that run parallel to the c-axis of the parent unit cell (i.e., normal to the layers).…”

“…A bar over the tilt, θ̅ or ϕ̅, signifies that the direction of the tilt is opposite from one layer to the next. A more thorough description of octahedral tilting in layered perovskites can be found in ref .…”

“…First, various octahedral tilting patterns were applied to the K 2 NiF 4 structure, following the procedure outlined by Liu at al. 1 These subgroups were then selected as the parent structure, and occupational distortions corresponding to chessboard ordering were applied. In this manner, the symmetry consequences of octahedral tilting and cation ordering in n = 1 RP phases were mapped out and are summarized in Table 1.…”