BX6 Octahedra Research Articles

Advancements and challenges in molecular/hybrid perovskites for piezoelectric nanogenerator application: A comprehensive review

Molecular perovskites are a class of materials that have attracted considerable attention in recent years due to their unique physical characteristics, structural properties, and diverse applications. These materials are also known as Hybrid Organic-Inorganic Perovskite (HOIP) and are denoted by the general formula ABX3. HOIP materials feature an organic or inorganic molecular cation (A), a metal or molecular cation (B), and a molecular anionic bridging ligand (X). The perovskite structure comprises BX6 octahedra that share corners, forming a three-dimensional network. The remarkable properties of molecular perovskites arise from their intrinsic polarization, resulting from the presence of polar organic cations in hybrid perovskites that possess a constant electric dipole moment. The alignment of these dipoles plays a crucial role in the properties of molecular perovskites. Consequently, this polarization can be harnessed to capture ambient mechanical energy and convert it into electrical energy. This review paper provides a comprehensive overview of molecular perovskites, focusing on their physical characteristics, synthesis methods, and multifunctional applications, particularly in piezoelectric nanogenerators. Furthermore, it addresses the challenges and opportunities associated with boosting their piezoelectric performance and integrating them with nanogenerator technology and flexible devices. Recent advances and breakthroughs in molecular perovskite-based nanogenerators are highlighted, including lead-free, metal-free, double perovskite materials, etc. Finally, the paper proposes future directions and perspectives for further research and innovation in this dynamic field.

Strain-Driven Solid-Solid Crystal Conversion in Chiral Hybrid Pseudo-Perovskites with Paramagnetic-to-Ferromagnetic Transition.

Hybrid organic-inorganic perovskites (HOIPs) are promising stimuli-responsive materials (SPMs) owing to their molecular softness and tailorable structural dimensionality. The design of mechanically responsive HOIPs requires an in-depth understanding of how lattice strain induces intermolecular rearrangement that impacts physical properties. While chirality transfer from an organic cation to an inorganic lattice is known to influence chiral-optical properties, its effect on strain-induced phase conversion has not been explored. As opposed to achiral or racemic organic cations, chiral organic cations can potentially afford a new dimension in strain-responsive structural change. Herein, we demonstrate that mechanical strain induces a solid phase crystal conversion in chiral halide pseudo-perovskite single crystals (R/S)-(FE)2CuCl4 (FE = (4-Fluorophenyl)ethylamine) from a 0D isolated CuCl4 tetrahedral to 1D corner-sharing CuFCl5 octahedral framework via the incorporation of Cu···F interaction and N-H···F hydrogen bonding. This strain-induced crystal-to-crystal conversion involves the connection of neighboring 0D CuCl4 tetrahedra via Cu2+-Cl--Cu2+ linkages as well as the incorporation of a F-terminated organic cation as one of the X atoms in BX6 octahedra, leading to a reduced band gap and paramagnetic-to-ferromagnetic conversion. Control experiments using nonchiral or racemic perovskite analogs show the absence of such solid phase conversion. To demonstrate pressure-sensitive properties, the 0D phase is dispersed in water-soluble poly(vinyl alcohol) (PVA) polymer, which can be applied to a large-scale pressure-induced array display on fibrous Spandex substrates via a screen-printing method.

Two 3D Rubidium Halide Organic-Inorganic Hybrid Perovskite Ferroelectrics Templated by Quasi-Spherical Organic Amine 1,4-Diazabicyclo[3.2.2]nonane.

The emergence of (CH3 NH3 )PbI3 has brought the development of three-dimensional (3D) organic-inorganic hybrid perovskite (OIHP) structures with ABX3 type to a higher level; however, most 3D frameworks are constructed by corner-sharing of BX6 octahedra. Herein, we substituted the spherical molecule 1,4-diazabicyclo[2.2.2]octane (2.2.2-dabco) with 1,4-diazabicyclo[3.2.2]nonane (1,4-3.2.2-dabcn) as a template to react with RbX (X=Br, I) in the corresponding HX acids under the consideration of reducing the molecular symmetry. Two 3D OIHP compounds [1,4-3.2.2-H2 dabcn]RbI3 ⋅H2 O (1) and [1,4-3.2.2-H2 dabcn]RbBr3 (2) crystallized in non-centrosymmetric point group mm2 before the phase transition point were isolated. Among them, the 3D inorganic framework of 1 is constructed by sharing the corner of [RbI6 ] octahedra, while that of 2 is constructed by sharing the corner and face of [RbBr6 ] octahedra to acquire large cavities to accommodate the organic amine cation [1,4-3.2.2-H2 dabcn]2+ ; this 3D framework type is unprecedented in the OIHPs. As expected, compounds 1 and 2 exhibit reversible phase transition, dielectric and second harmonic generation (SHG) and ferroelectric properties, in which the phase transition temperature of 2 at 374 K is much higher than compound 1 at 280 K.

Phase transitions and (p-T-X) behaviour of centrosymmetric perovskites: modelling with transformed crystallographic data.

A reversible transformation of the unit-cell parameters and atomic coordinates of centrosymmetric perovskites ABX3 into a Cartesian space is defined. Analytical expressions for the three vectors for the pseudocubic cell and three vectors for a BX6 octahedron are derived for space groups Pbmn, Cmcm, Ibmm, P4/mbm, P4/nmc, I4/mcm and R3c. The following structural parameters may be derived from these vectors: up to six pseudocubic parameters defining octahedral geometry; length- and angle-based octahedral distortion parameters λ and σ; inclination angles of tilted octahedra, θ1, θ2 and θ3; angles of tilt of octahedra; AX12:BX6 polyhedral volume ratio, VA/VB; parameters ηA and ηB defining the relative contraction of inner AX8 polyhedra and expansion of BX6 octahedra due to octahedral tilting. The application of these parameters is demonstrated by reference to published crystal structures. The variation of ηA and ηB with temperature in the compositional series SrxBa1-xSnO3 and SrxBa1-xHfO3, as well as the temperature series of BaPbO3 and CaTiO3, is related to the sequence of phases Pbmn → Ibmm→ Pm3m. Stabilization of the Cmcm phase is likewise interpreted in terms of these two parameters for NaTaO3 and NaNbO3. The pressure evolution of the structures of MgSiO3, YAlO3, (La1-xNdx)GaO3 (0 ≤ x ≤ 1) and YAl0.25Cr0.75O3 is modelled with the appropriate structural parameters, thereby also addressing the characteristics of the Pbmn → R3c transition. Simulation of MgSiO3 up to 125 GPa and of YAlO3 up to 52 GPa in space group Pbnm is carried out by using the Birch-Murnaghan equation of state. In both cases, full sets of oxygen coordinates assuming regular octahedra are generated. Octahedral distortion is also modelled in the latter system and predicted to have a key influence on structural evolution and the sequence of phase transitions. The core modelling procedures are made available as a Microsoft Excel file.

Effect of static local distortions vs. dynamic motions on the stability and band gaps of cubic oxide and halide perovskites

Ternary ABX3 perovskites made of corner-sharing BX6 octahedra have long featured prominently in solid-state chemistry and condensed matter physics. Still, the joint understanding of their two main subgroups—halides and oxides—has not been fully developed. Indeed, unlike the case in simpler compounds having a single, robust repeated motif (“monomorphous”), certain cubic perovskites can manifest a non-thermal (= intrinsic) distribution of local motifs (“polymorphous networks”). Such static deformations can include positional degrees of freedom (e.g., atomic displacements and octahedral tilting) or magnetic moment degrees of freedom in paramagnets. Unlike thermal motion, such static distortions do not time-average to zero, being an expression of the intrinsic symmetry breaking preference of the chemical bonding. The present study compares electronic structure features of oxide and halide perovskites starting from the static polymorphous distribution of motifs described by Density Functional Theory (DFT) minimization of the internal energy, continuing to finite temperature thermal disorder modeled via finite temperature DFT molecular dynamics. We find that (i) different oxide vs. halide ABX3 compounds adopt different energy-lowering symmetry-breaking modes. The calculated pair distribution function (PDF) of SrTiO3 from the first-principles agrees with recently measured PDF. (ii) In both oxides and halides, such static distortions lead to band gap blueshifts with respect to undistorted cubic Pm-3m structure. (iii) For oxide perovskites, high-temperature molecular dynamics simulations initiated from the statically distorted polymorphous structures reveal that the thermally-induced distortions can lead to a band gap redshift. (iv) In contrast, for cubic halide perovskite CsPbI3, both the intrinsic distortions and the thermal distortions contribute in tandem to band gap blueshift, the former, intrinsic effect being dominant. (v) In the oxide SrTiO3 and CaTiO3 (but not in halide) perovskites, octahedral tilting leads to the emergence of a distinct Γ–Γ direct band gap component as a secondary valley minimum to the well-known indirect R–Γ gap. Understanding such intrinsic vs. thermal effects on oxide vs. halide perovskites holds the potential for designing target electronic properties.

Precise Molecular Design Toward Organic-Inorganic Zinc Chloride ABX3 Ferroelectrics.

Organic-inorganic ABX3 (A, B = cations, X = anion) hybrids with perovskite structure have recently attracted tremendous interest due to their structural tunability and rich functional properties, such as ferroelectricity. However, ABX3 hybrid ferroelectrics with other structures have rarely been reported. Here, we successfully designed an ABX3 hybrid ferroelectric [(CH3)3NCH2F]ZnCl3 with a spontaneous polarization of 4.8 μC/cm2 by the molecular modification of [(CH3)4N]ZnCl3 through hydrogen/halogen substitution. It is the first zinc halide ABX3 ferroelectric, which contains one-dimensional [ZnCl3]-n chains of corner-sharing ZnCl4 tetrahedra, distinct from the anionic framework of corner-sharing or face-sharing BX6 octahedra in the ABX3 perovskites. From zero dimension to one dimension, the high symmetry of ZnCl4 tetrahedra is broken, and all of them align along one direction to form a polar [ZnCl3]-n chain, beneficial to the generation of ferroelectricity. This finding provides an efficient polar anionic framework for enriching the family of hybrid ferroelectrics by assembling with various cations and should inspire further exploration of new classes of organic-inorganic ABX3 ferroelectrics.

Effect of chemical nature of atoms on the electronic, dielectric, and dynamical properties of ABX3 halide perovskite

AbstractFirst‐principles calculations within density functional theory were performed on a series of halide perovskite compounds ABX3(A: Cs or Rb; B:Pb or Sn). Their electronic structure, lattice dynamics, and dielectric properties were studied in relationship with the change in atom species at each one of the three inequivalent crystallographic sites, to explain the origin of these properties. Thus, the variation of the bandgap with the overlap between the B cation lone pair and the electronic states of halide atoms, as well as with the distortion of the BX6 octahedra network is discussed. It is shown that the vibrational modes, phonon frequencies, atomic displacements, and the possible ferroelectric instability in these compounds are dependent on masses of atoms, volume of AX12 polyhedron, as well as on streoactivity of Pb lone pair. Also, the Born effective charges, dielectric constant, spontaneous polarization, and infrared spectra are calculated. The relation between these dielectric properties and the ions dynamics is discussed.

The Low-Dimensional Three-Dimensional Tin Halide Perovskite: Film Characterization and Device Performance

Halide perovskite solar cells (PSCs) are considered as one of the most promising candidates for the next generation solar cells as their power conversion efficiency (PCE) has rapidly increased up to 25.2%. However, the most efficient halide perovskite materials all contain toxic lead. Replacing the lead cation with environmentally friendly tin (Sn) is proposed as an important alternative. Today, the inferior performance of Sn-based PSCs mainly due to two challenging issues, namely the facile oxidation of Sn2+ to Sn4+ and the low formation energies of Sn vacancies. Two-dimensional (2D) halide perovskite, in which the large sized organic cations confine the corner sharing BX6 octahedra, exhibits higher formation energy than that of three-dimensional (3D) structure halide perovskite. The approach of mixing a small amount of 2D into 3D Sn-based perovskites was demonstrated as an efficient method to produce high performance perovskite films. In this review, we first provide an overview of key points for making high performance PSCs. Then we give an introduction to the physical parameters of 3D ASnX3 (MA+, FA+, and Cs+) perovskite and a photovoltaic device based on them, followed by an overview of 2D/3D halide perovskites based on ASnX3 (MA+ and FA+) and their optoelectronic applications. The current challenges and a future outlook of Sn-based PSCs are discussed in the end. This review will give readers a better understanding of the 2D/3D Sn-based PSCs.

Anion Distribution, Structural Distortion, and Symmetry-Driven Optical Band Gap Bowing in Mixed Halide Cs2SnX6 Vacancy Ordered Double Perovskites.

Mixed anion compounds in the Fm3̅m vacancy ordered perovskite structure were synthesized and characterized experimentally and computationally with a focus on compounds where A = Cs+. Pure anion Cs2SnX6 compounds were formed with X = Cl, Br, and I using a room temperature solution phase method. Mixed anion compounds were formed as solid solutions of Cs2SnCl6 and Cs2SnBr6 and a second series from Cs2SnBr6 and Cs2SnI6. Single phase structures formed across the entirety of both composition series with no evidence of long-range anion ordering observed by diffraction. A distortion of the cubic A2BX6 structure was identified in which the spacing of the BX6 octahedra changes to accommodate the A site cation without reduction of overall symmetry. Optical band gap values varied with anion composition between 4.89 eV in Cs2SnCl6 to 1.35 eV in Cs2SnI6 but proved highly nonlinear with changes in composition. In mixed halide compounds, it was found that lower energy optical transitions appeared that were not present in the pure halide compounds, and this was attributed to lowering of the local symmetry within the tin halide octahedra. The electronic structure was characterized by photoemission spectroscopy, and Raman spectroscopy revealed vibrational modes in the mixed halide compounds that could be assigned to particular mixed halide octahedra. This analysis was used to determine the distribution of octahedra types in mixed anion compounds, which was found to be consistent with a near-random distribution of halide anions throughout the structure, although some deviations from random halide distribution were noted in mixed iodide–bromide compounds, where the larger iodide anions preferentially adopted trans configurations.

Unique Freezing Dynamics of Flexible Guest Cations in the First Molecular Postperovskite Ferroelectric: (C 5 H 13 NBr)[Mn(N(CN) 2 ) 3

Ferroelectricity is usually found in cubic and hexagonal perovskites consisting of corner- and faced-shared BX6 octahedra, respectively. In contrast, another important branch of perovskites, postpe...

Synthesis of new perovskite-type oxyfluorides, BaInO2F and comparison of the structure among perovskite-type oxyfluorides

Most perovskite-type oxyfluorides have a cubic structure even though the tolerance factors of these compounds are not unity. In this study, new perovskite-type oxyfluorides, BaInO2F, with a tolerance factor less than unity was synthesized and its crystal structure was compared with other perovskite-type oxyfluorides. In addition, its local structure was investigated using the atomic pair distribution function (PDF) technique. BaInO2F was synthesized by a low-temperature fluorination method, and its structure was cubic with an abnormally large displacement factor of anions. By comparing the structures of various perovskite-type oxyfluorides, we found that the ion species showing abnormally large displacement factor varied with the tolerance factors. In the case of BaFeO2F, the abnormally large displacement factor of the B-site ion, Fe3+, originated from the displacement of the Fe3+ ion from the center of a BX6 octahedron along <110> direction. According to the PDF analysis, the local structure of BaInO2F was not cubic but a triclinic system with tilted and distorted BX6 octahedra. On the basis of these results, we considred that the structure of oxyfluorides with a tolerance factor less than unity was relaxed by the tilt of the octahedra, similar to perovskite-type oxides. The long-range order of the anion displacements, however, was suppressed by the structural disorder arising from the random distribution of oxide and fluoride ions, therefore the average structure observed by diffraction methods was predicted to be a cubic structure.

Stability Trend of Tilted Perovskites

Halide perovskites, with prototype cubic phase ABX3, undergo various phase transitions accompanied by rigid rotations of corner-sharing BX6 octahedra. Using first-principles density functional theory calculations, we have performed a comprehensive investigation of all of the possible octahedral tilting in 18 halide perovskites ABX3 (A = Cs, Rb, and K; B = Pb and Sn; and X = I, Br, and Cl) and found that the stabilization energies, i.e., energy differences between cubic and the most stable tilted phases, are linearly correlated with the tolerance factor t. Moreover, the tilt energies, i.e., energy differences between cubic and various tilted phases, are linearly correlated with the change of atomic packing fractions (Δη), indicating the importance of the atomic packing fraction on the stabilities of distorted perovskites. This work may provide guidance for searching proper perovskite ABX3 to extend distorted perovskite for wide applications, such as thermochromics.

Photovoltaic Rudorffites: Lead-Free Silver Bismuth Halides Alternative to Hybrid Lead Halide Perovskites.

Hybrid CPbX3 (C: Cs, CH3 NH3 ; X: Br, I) perovskites possess excellent photovoltaic properties but are highly toxic, which hinders their practical application. Unfortunately, all Pb-free alternatives based on Sn and Ge are extremely unstable. Although stable and non-toxic C2 ABX6 double perovskites based on alternating corner-shared AX6 and BX6 octahedra (A=Ag, Cu; B=Bi, Sb) are possible, they have indirect and wide band gaps of over 2 eV. However, is it necessary to keep the corner-shared perovskite structure to retain good photovoltaic properties? Here, we demonstrate another family of photovoltaic halides based on edge-shared AX6 and BX6 octahedra with the general formula Aa Bb Xx (x=a+3 b) such as Ag3 BiI6 , Ag2 BiI5 , AgBiI4 , AgBi2 I7 . As perovskites were named after their prototype oxide CaTiO3 discovered by Lev Perovski, we propose to name these new ABX halides as rudorffites after Walter Rüdorff, who discovered their prototype oxide NaVO2 . We studied structural and optoelectronic properties of several highly stable and promising Ag-Bi-I photovoltaic rudorffites that feature direct band gaps in the range of 1.79-1.83 eV and demonstrated a proof-of-concept FTO/c-m-TiO2 /Ag3 BiI6 /PTAA/Au (FTO: fluorine-doped tin oxide, PTAA: poly[bis(4-phenyl)(2,4,6-trimethylphenyl)amine], c: compact, m: mesoporous) solar cell with photoconversion efficiency of 4.3 %.

Local tetragonal distortions of the (CrF6)3− and (FeF6)3− octahedral clusters in Cr3+- and Fe3+-doped tetragonal Rb2KGaF6 crystals

ABSTRACTThe local tetragonal distortions (α − α0) (where α is the angle defined as tgα = R⊥/R//, R⊥ and R// are the metal–ligand distances parallel with and normal to the C4 axis, α0 = 45° is the same angle in cubic symmetry) of (CrF6)3− and (FeF6)3− octahedral clusters in the tetragonal Rb2KGaF6 crystals are estimated by analyzing their electron paramagnetic resonance (EPR) zero-field splittings D. The results indicate that the two impurity octahedra and hence the host (GaF6)3− octahedra are tetragonally elongated. The distortion (α − α0) in magnitude differs from impurity to impurity because of the different sizes and natures of these impurities. These results are analogous to those in ABX3 and doped ABX3 perovskite crystals where the cubic-to-tetragonal phase transition is due to the rotation of BX6 octahedra associated with the release or elongation of B–X bond along the C4 rotational axis.

High-pressure synthesis, structure, phase relation of polar LiNbO3-type ZnTiO3

Ferroelectricity, piezoelectricity, pyroelectricity, and second-order nonlinear optical behavior are technologically important. Because these properties are attributable to the noncentrosymmetric (NCS) structure[1], the search for materials exhibiting such characteristics must begin with a search of NCS materials. Among them, LiNbO3-type (LN-type) compounds with a chemical formula of ABX3 exhibit NSC structures with hexagonal polar space group R3c whose BX6 octahedra three-dimensionally share their corners the same as perovskite-type compounds[2]. In LN-type compounds, the A cation - B cation repulsion directs the spontaneous polarization along c-axis(Fig. 1). Therefore, we might find attractive functional properties by the selection of constituent ions based on their having a naturally occurring polar LN-type structure attributable to the cation-cation repulsion. With the ideas mentioned above, we have investigated the high-pressure synthesis and characterization of novel LN-type oxides such as ZnSnO3, PbNiO3, CdPbO3 as well as known MnMO3 (M = Ti, Sn). Recently, we have successfully synthesized a polar LN-type titanate ZnTiO3 (LN-ZTO) under high pressure and high temperature [3]. The first principles calculation indicates that LN-ZTO is a meta-stable phase obtained by the transformation in the decompression process from the perovskite-type phase, which is stable at high pressure and high temperature. The Rietveld structural refinement reveals that LN-ZTO exhibits greater intra-distortion of the TiO6 in LN-ZTO than that of the SnO6 in LN-type ZnSnO3 (LN-ZSO). The estimated spontaneous polarization are greater than those of LN-ZSO, which is attributed to the great displacement of Ti along c-axis and the greater Born effective charge of Ti (+6.1) than that of Sn (+4.1). Furthermore, the spontaneous polarization of LN-ZTO is greater than that of LiNbO3, indicating that LN-ZTO, like LiNbO3, is a candidate ferroelectric material with high performance. The second harmonic generation (SHG) response of LN-ZTO is 24 times greater than that of LN-ZSO. The findings indicate that the intra-octahedral distortion, spontaneous polarization, and SHG response are caused by the stabilization of the polar LN-type structure and reinforced by the second-order Jahn-Teller effect attributable to the orbital interaction between oxygen ions and d0 ions such as Ti4+. We also discuss the relationship between the intra-distortion of BO6 and polarity in several LN-type oxides.

Normal mode determination of perovskite crystal structures with octahedral rotations: theory and applications

Nuclear site analysis methods are used to enumerate the normal modes of ABX3 perovskite polymorphs with octahedral rotations. We provide the modes of the 14 subgroups of the cubic aristotype describing the Glazer octahedral tilt patterns, which are obtained from rotations of the BX6 octahedra with different sense and amplitude about high-symmetry axes. We tabulate all normal modes of each tilt system and specify the contribution of each atomic species to the mode displacement pattern, elucidating the physical meaning of the symmetry unique modes. We have systematically generated 705 schematic atomic displacement patterns for the normal modes of all 15 (14 rotated + 1 unrotated) Glazer tilt systems. We show through some illustrative examples how to use these tables to identify the octahedral rotations, symmetric breathing, and first-order Jahn–Teller anti-symmetric breathing distortions of the BX6 octahedra, and the associated Raman selection rules. We anticipate that these tables and schematics will be useful in understanding the lattice dynamics of bulk perovskites and could serve as a reference point in elucidating the atomic origins of a wide range of physical properties of synthetic perovskite thin films and superlattices.

Electron Diffraction of Li-conducting Perovskites with Both Tilting of BX6 Octahedra and Layered Ordering of A-cations

not Available.

Electron diffraction of ABX 3 perovskites with both layered ordering of A cations and tilting of BX 6 octahedra

It is shown that 21 ABX(3) perovskites with tilted BX(6) octahedra and layered ordering of A cations can be generated on the basis of group-subgroup relations. These structures (with 16 different space groups) are classified into ten diffraction types in terms of the conditions for superstructure reflections caused by the ordering of A cations, tilting of BX(6) octahedra and structural absences. SAED (selected-area electron diffraction) allows the distinction of seven of the 21 different perovskites, while additional symmetry analysis by CBED (convergent-beam electron diffraction) is needed for the remaining 14 structures. The space groups of lithium lanthanum titanate pseudomorphs (with discrete chemical compositions) are successfully deduced by electron diffraction experiments.

Effect of A-site cation radius on ordering of BX6 octahedra in (K,Na)MgF3 perovskite

We present a structural model for (K,Na)MgF3 perovskite using results from high-resolution synchrotron X-ray powder diffraction and nuclear magnetic resonance (NMR) spectroscopy. (K,Na)MgF3 perovskite is found to transition from orthorhombic (Pbnm) to tetragonal (P4/mbm) to cubic (Pm3̅m) as potassium concentration is increased. These phase transitions are not accompanied by a discontinuity in pseudo-cubic unit-cell volume and occur close to compositions (K0.37Na0.63)MgF3 and (K0.47Na0.53)MgF3, respectively. 19F NMR spectra indicate that the Na+ and K+ cations do not occupy the A cation site at random and end-member local environments are favored for all compositions. Based on results from both X-ray diffraction and NMR, we propose that diffuse diffraction is the result of strain between coexisting regions of different octahedra (MgF6) tilts brought about by the ionic radius mismatch of Na+ and K+ cations. We suggest A-site cations group with like cations as neighbors to reduce excess volume and total strain.

Symmetry classification of the layered perovskite-derived AnBnX3n+2 structures.

The effects of combinations of octahedral tilts on the symmetries of layered A(n)B(n)X(3n+2) structures were considered. Two complementary approaches were used to deduce the symmetries. The space groups associated with different tilt systems were determined for structures with different layer thicknesses (n values) and for structures with different layer stacking arrangements. For the most symmetrical tilts about the orthorhombic axes of the A(n)B(n)X(3n+2) structure, maximal group/subgroup relations were established. Comparison of these results with experimental data available in the literature suggests that the symmetries of most observed A(n)B(n)X(3n+2) compounds are fully determined by the tilt systems adopted by rigid BX(6) octahedra. The most common tilt system observed at room temperature is a combination of an in-phase tilt about an orthorhombic axis parallel to the pseudo-fourfold axis of the octahedron with a tilt about an orthorhombic axis perpendicular to the layers.