Chiral Templating in a Hybrid Chromium Chloride Hydrate.

The synthesis and characterization of three new hybrid metal halide hydrates in which mer-[CrIIICl3(H2O)3]0 cocrystallizes alongside α-methylbenzylammonium chloride are described. The enantiomorphic crystals, ((R)-(+)-α-methylbenzylammonium)2(mer-[CrCl3(H2O)3])Cl2 ((R)-1) and ((S)-(-)-α-methylbenzylammonium)2(mer-[CrCl3(H2O)3])Cl2 ((S)-1), have C2221 space group symmetry and show mirrored circular dichroism signals. The racemate, (rac-α-methylbenzylammonium)2(mer-[CrCl3(H2O)3])Cl2 ((rac)-1), adopts a polar structure with Cm space group symmetry in which enantiomers are related by mirror planes within organic bilayers. Alongside detailed crystallography and magnetism of each compound, the optical properties of the mer-[CrIIICl3(H2O)3]0 unit are revisited. Understanding the intermolecular forces that stabilize each of these crystal structures lends insights into crystal engineering methodologies for stabilizing noncentrosymmetric hybrid metal halides.

The Magnetism of Nonstoichiometric Sr2Cr1+xRe1-xO6 (0 < x < 0.5) Double Perovskites.

The effect of nonstoichiometry on the cation distribution, crystal structure, and magnetic properties of a series of Cr-rich Sr2Cr1+xRe1-xO6 samples has been investigated. The double perovskite structure is maintained over a wide solid solution range that extends from x = 0 to approximately x = 0.5. For most of the solid solution range, the Cr-rich octahedral site maintains a nearly constant occupancy, 87% Cr and 13% Re, that is comparable to prior studies of Sr2CrReO6, while Cr steadily replaces Re on the other octahedral site. As x approaches 0.5, long-range Cr/Re ordering drops precipitously. Analysis of X-ray powder diffraction peak shapes reveals antiphase boundaries, associated with Cr/Re ordering, the concentration of which increases steadily with increasing x. Neutron powder diffraction studies confirm antiferromagnetic coupling between antisite Cr3+ ions and Cr3+ ions that occupy the normal sites, leading to site-dependent ferrimagnetic ordering. Density functional theory calculations indicate that chromium maintains a +3 oxidation state across the series, while the oxidation state of rhenium increases with increasing x. Calculations are also used to explore the energies of competing magnetic ground states. Except for the most chromium-rich compositions (x ≈ 0.5), site-dependent ferrimagnetism is retained with only a modest reduction in TC. The saturation magnetization steadily decreases as the chromium content increases due to a combination of Cr/Re antisite disorder and antiphase boundaries.

Coupled Compositional and Displacive Modulations in KLaMnWO6 Revealed by Atomic Resolution Imaging.

Complex compositional and displacive modulations of the crystal structure of KLaMnWO6 are imaged with atomic resolution by means of scanning transmission electron microscopy (STEM). This oxide is stabilized by cation vacancies leading to a La1+x/3K1-xMnWO6 stoichiometry. Compositional modulation on both the K and La layers are revealed in the high-angle annular dark-field STEM (HAADF-STEM) images. The compositional modulation within the La layer is coupled with the modulation of the octahedral tilting, which is exposed by imaging of the anion sublattice in annular bright-field STEM (ABF-STEM) images. These complex modulations are accommodated in a 5√2ap × 5√2ap × 2ap perovskite-type structure.

Interfacial Rashba-Effect-Induced Anisotropy in Nonmagnetic-Material-Ferrimagnetic-Insulator Bilayers.

Interfacial magnetic anisotropy in magnetic insulators has been largely unexplored. Recently, interface-induced skyrmions and electrical control of magnetization have been discovered in insulator-based heterostructures, which demand a thorough understanding of interfacial interactions in these materials. We observe a substantial, tunable interfacial magnetic anisotropy between Tm_{3}Fe_{5}O_{12} epitaxial thin films and fifteen nonmagnetic materials spanning a significant portion of the periodic table, which we attribute to Rashba spin-orbit coupling. Our results show a clear distinction between nonmagnetic capping layers from the d block and the p block. This work offers a new path for controlling magnetic phases in magnetic insulators for low-loss spintronic applications.

Four Lead-free Layered Double Perovskites with the n = 1 Ruddlesden-Popper Structure.

Herein we report the synthesis, structure, and band gaps of four layered halide double perovskites, i.e., BA2Cu0.5In0.5Cl4, BA2Ag0.5In0.5Cl4, BA2Ag0.5Sb0.5Cl4, and BA2Ag0.5Sb0.5Br4 [BA = butylammonium = CH3(CH2)3NH3+], each of which has the n = 1 Ruddlesden-Popper structure. In addition, the crystal structure of BA2Ag0.5Bi0.5Br4 is revisited and that of BA2PbCl4 is reported for the first time. Only BA2Ag0.5Sb0.5Cl4 has the tetragonal I4/mmm symmetry of the undistorted Ruddlesden-Popper structure. The other five compounds have orthorhombic structures due to tilts of the octahedra and orientational ordering of the butylammonium groups. As the lateral dimensions of the inorganic layer decrease, the c/a ratio increases due to decreased interdigitation of the alkyl ends of the butylammonium cations. This structural feature may help to explain the increased stability of the bromide phases with respect to the chloride phases. There are features in the diffraction patterns of BA2Ag0.5Bi0.5Br4 and BA2Cu0.5In0.5Cl4 that suggest ordering of octahedral cations within the layers, but in those compounds there appears to be a high concentration of stacking faults between layers that limits long-range, three-dimensional ordering of cations. In the other cases the scattering powers of the cations (Ag/Sb and Ag/In) are too similar to say anything definitive about cation ordering. The band gaps of these compounds range from 2.65 to 4.27 eV, with the bromide compositions possessing smaller band gaps than the chlorides. The band gaps of layered BA2M0.5M'0.5X4 compositions studied here are roughly 0.5-0.8 eV larger than analogous Cs2MM'X6 cubic double perovskites due to a combination of dimensional reduction (3D → 2D), distortions of the octahedral environment around the M/M' ions, and octahedral tilting distortions.

Rb3InCl6: A Monoclinic Double Perovskite Derivative with Bright Sb3+-Activated Photoluminescence.

Here, we present the synthesis and crystal structure of Rb3InCl6 prepared from air stable reagents via a two-step process that proceeds through the intermediate Rb2InCl5·H2O. Rb3InCl6 crystallizes with the Rb3YCl6 structure type (C2/c), which can be derived from the double perovskite structure by noncooperative tilting of isolated [InCl6]3- octahedra. Despite this lowering of symmetry, the optical properties are similar to the cubic double perovskite Cs2NaInCl6. Partial substitution of In3+ with Sb3+ in Rb3InCl6 results in intense cyan-green photoluminescence originating from localized 5s2 to 5s15p1 electronic transitions of [SbCl6]3- polyatomic anions. In comparison with the cubic double perovskite phosphor Cs2NaInCl6:Sb3+, the octahedral tilting distortion increases the electronic isolation of the In/Sb-centered octahedra thus facilitating electron and hole localization on Sb3+ sites, leading to bright photoluminescence. The distorted crystal structure also leads to a larger Stokes shift (1.29 eV) and a corresponding red shift of the emission peak (λmax = 522 nm) compared to the more symmetric Cs2NaInCl6:Sb3+ (Stokes shift ≈ 0.94 eV, λmax = 445 nm).

Broadband White Emission in Cs2AgIn1-xBixCl6 Phosphors.

The photoluminescent properties of the lead-free double perovskite solid solution Cs2AgIn1-xBixCl6 have been investigated. The In3+ end member, Cs2AgInCl6, is a direct gap semiconductor that absorbs UV light (λ < 350 nm) and shows little to no photoluminescence. Incorporation of Bi3+ leads to a strong sub-band gap absorption that peaks in the near UV (∼360 nm) and extends into the visible. This absorption, which is thought to originate from localized 6s2 → 6s1p1 transitions on Bi3+ ions, is split by a Jahn-Teller distortion of the excited state. In-rich samples show strong photoluminescence that is attributed to radiative decay of self-trapped excitons, with a broad emission peak of significant intensity from 450 to 750 nm. The color of the emitted light is best described as yellow-white (λmax ≈ 625 nm), due to the extreme breadth of the emission peak (fwhm ≈ 217(2) nm). The excitation spectrum extends out to 450 nm for samples near x = 0.25, while the photoluminescent quantum yield (PLQY) reaches a maximum of 39 ± 3% in the x = 0.167 sample. The emission characteristics, which include a correlated color temperature (CCT) of 3119 K and a color rendering index (CRI) of 85, coupled with an excitation spectrum that can be driven by visible photons emitted from a Ga1-xInxN LED, make Cs2AgIn1-xBixCl6 phosphors promising for use in solid state white lighting applications.

Postsynthetic Metal Exchange in a Metal-Organic Framework Assembled from Co(III) Diphosphine Pincer Complexes.

A Zr metal-organic framework (MOF) 1-CoCl3 has been synthesized by solvothermal reaction of ZrCl4 with a carboxylic acid-functionalized CoIII-PNNNP pincer complex H4(L-CoCl3) ([L-CoCl3]4- = [(2,6-(NHPAr2)2C6H3)CoCl3]4-, Ar = p-C6H4CO2-). The structure of 1-CoCl3 has been determined by X-ray powder diffraction and exhibits a csq topology that differs from previously reported ftw-net Zr MOFs assembled from related PdII- and PtII-PNNNP pincer complexes. The Co-PNNNP pincer species readily demetallate upon reduction of CoIII to CoII, allowing for transmetalation with late second and third row transition metals in both the homogeneous complex and 1-CoCl3. Reaction of 1-CoCl3 with [Rh(nbd)Cl]2 (nbd = 2,5-nobornadiene) results in complete Rh/Co metal exchange at the supported diphosphine pincer complexes to generate 1-RhCl, which has been inaccessible by direct solvothermal synthesis. Treating 1-CoCl3 with PtCl2(SMe2)2 in the presence of the mild reductant NEt3 resulted in nearly complete Co substitution by Pt. In addition, a mixed metal pincer MOF, 1-PtRh, was generated by sequential substitution of Co with Pt followed by Rh.

The Crystal Structure and Magnetic Behavior of Quinary Osmate and Ruthenate Double Perovskites La ABB'O6 ( A = Ca, Sr; B = Co, Ni; B' = Ru, Os).

Six La ABB'O6 ( A = Ca, Sr; B = Co, Ni; B' = Ru, Os) double perovskites were synthesized, several for the first time, and their crystal structures and magnetic behavior were characterized with neutron powder diffraction and direct-current and alternating-current magnetometry. All six compounds crystallize with P21 /n space group symmetry, resulting from a- a- c+ octahedral tilting and complete rock salt ordering of transition-metal ions. Despite the electronic configurations of the transition-metal ions, either d8-d3 or d7-d3, not one of the six compounds shows ferromagnetism as predicted by the Goodenough-Kanamori rules. LaSrNiOsO6, LaSrNiRuO6, and LaCaNiRuO6 display long-range antiferromagnetic order, while LaCaNiOsO6, LaCaCoOsO6, and LaSrCoOsO6 exhibit spin-glass behavior. These compounds are compared to the previously studied LaCaCoRuO6 and LaSrCoRuO6, both of which order antiferromagnetically. The observed variations in magnetic properties can be attributed largely to the response of competing superexchange pathways due to changes in B-O- B' bond angles, differences in the radial extent of the 4d ( B' = Ru) and 5d ( B' = Os) orbitals, and filling of the t2g orbitals of the 3d ion.

Evaluating NaREMgWO6 (RE = La, Gd, Y) Doubly Ordered Double Perovskites as Eu3+ Phosphor Hosts.

Three doubly ordered double perovskites NaREMgWO6 (RE = La, Gd, Y) have been synthesized via traditional solid-state methods, doped with Eu3+, and characterized to evaluate their promise as Eu3+ phosphor hosts. NaYMgWO6, a new member of the family, was found to crystallize in the P21 space group and is isostructural with NaGdMgWO6. Emissions characteristic of Eu3+ ions (5D0 → 7F4,3,2,1,0) were observed, with the most intense transition being the 5D0 → 7F2 transition near 615 nm. Substitution of Eu3+ onto a more compressed RE site in the NaY1-xEuxMgWO6 and NaGd1-xEuxMgWO6 hosts results in a blue shift of the charge-transfer excitation band and an increase in the intensity of the 5D0 → 7F2 transition compared to NaLa1-xEuxMgWO6. All of the hosts can incorporate high concentrations of Eu3+ before concentration quenching is observed. When the rare-earth ion is either Gd3+ or Y3+, good energetic overlap between the Eu3+ charge-transfer band and the absorption of the host lattice results in sensitization and energy transfer from the perovskite host lattice to the Eu3+ activator sites. These hosts display comparable if not better luminescence than Y2O3:Eu3+, a commonly used commercial standard, demonstrating their promise as red phosphors.

Structural, Magnetic, and Optical Properties of A3V4(PO4)6 (A = Mg, Mn, Fe, Co, Ni).

Combined synchrotron and neutron powder diffraction indicates that A3V4(PO4)6 (A = Mg, Mn, Fe, Co, Ni) compounds crystallize with triclinic P1̅ symmetry. Lattice parameters expand as expected with successive increases in the ionic radius of the A(2+) ion. Cation disorder on the octahedral sites increases as the ionic radii of A(2+) ion decreases. Direct-current magnetic susceptibility measurements indicate that all compounds with magnetic A(2+) ions order anti-ferromagnetically with transition temperatures ranging from 12 to 15 K. Effective magnetic moments for A3V4(PO4)6 (A = Mg, Mn, Fe, Co, Ni) are 5.16, 11.04, 10.08, 9.76, and 7.96 µB per formula unit, respectively, in line with calculated values for high-spin transition metal ions. With the exception of Co3V4(PO4)6 the ultraviolet-visible spectra are dominated by d-d transitions of the V(3+) ions. The striking emerald green color of Co3V4(PO4)6 arises from the combined effects of d-d transitions involving both V(3+) and Co(2+).

Probing the links between structure and magnetism in Sr(2-x)Ca(x)FeOsO6 double perovskites.

The synthesis, structure, and properties of the ordered double perovskites Sr2FeOsO6, Ca2FeOsO6, and SrCaFeOsO6 are reported. The latter two compounds have monoclinic P21/n symmetry and a(-)a(-)b(+) tilting of the octahedra, while Sr2FeOsO6 is tetragonal with I4/m symmetry and a(0)a(0)c(-) tilting. Magnetic measurements indicate and neutron powder diffraction studies confirm that Ca2FeOsO6 is a ferrimagnet with a Curie temperature of 350 K. The ferrimagnetism is retained if half of the Ca(2+) ions are replaced with larger Sr(2+) ions to form SrCaFeOsO6 (T(C) = 210 K). This substitution reduces the degree of octahedral tilting, but unlike most perovskites, the magnetic ordering temperature decreases as the Fe-O-Os bond angles approach a linear geometry. In contrast, Sr2FeOsO6 orders antiferromagnetically, as previously reported. X-ray absorption spectroscopy confirms the assignment of Fe(III) and Os(V) oxidation states for all three compounds. In these insulating double perovskites, the magnetic ground state is governed by a competition between the four-bond Fe-O-Os-O-Fe antiferromagnetic superexchange coupling of Fe(III) ions and the two-bond Fe-O-Os antiferromagnetic superexchange coupling between neighboring Fe(III) and Os(V) ions. When the Fe-O-Os bonds are linear, as they are in the c direction in Sr2FeOsO6, the four-bond coupling between Fe(III) ions prevails. The competition shifts in favor of antiferromagnetic coupling of Fe(III) and Os(V) as the Fe-O-Os bond angles bend in response to chemical pressure.

Order-disorder transition involving the A-site cations in Ln3+Mn3V4O12 perovskites.

A crossover from the A-site-ordered double-perovskite structure with Im3̅ cubic symmetry to the simple-perovskite structure with Pnma orthorhombic symmetry is found in LnMn3V4O12 (Ln = La, Nd, Gd, Y, Lu) synthesized under high-pressure conditions. Relatively large Ln(3+) ions (La(3+), Nd(3+), and Gd(3+)) induce the a(+)a(+)a(+) in-phase cooperative tilting of the VO6 octahedra, resulting in the A-site-ordered double-perovskite structure with chemical composition Ln(3+)Mn(2+)3V(3.75+)4O12. Compounds with small Ln(3+) ions like Y(3+) and Lu(3+), on the other hand, crystallize with the Pnma simple-perovskite structure with chemical composition (Ln(3+)1/4Mn(2+)3/4)V(3.75+)O3, where the Ln(3+) and Mn(2+) ions are disordered at the A site. The random distribution of the small A-site cation induces the a(-)b(+)a(-) tilting distortion of the VO6 octahedra. The observed phase crossover is well explained by the structural stability calculation based on the bond-valence-sum model, and the most stable crystal structure gives the smallest unit-cell volume. This A-site-cation size-dependent phase transition between the A-site-ordered double-perovskite and A-site-disordered simple-perovskite structures in LnMn3V4O12 is thus a result of the structural stability due to the cooperative tilting of the VO6 octahedra. The Mn(2+) ions at the A'(A) site contribute local magnetic moments, whereas the V(3.75+) ions at the B site play a role in metallic conduction. The observed magnetic behaviors are consistent with the order-disorder distribution of the Mn(2+) ions at the A site, antiferromagnetism in the A-site-ordered double perovskites, and magnetic spin glass in the A-site-disordered simple perovskites.

Metal-to-metal charge transfer in AWO4 (A = Mg, Mn, Co, Ni, Cu, or Zn) compounds with the wolframite structure.

Using a combination of UV-visible spectroscopy and electronic structure calculations, we have characterized the electronic structures and optical properties of AWO4 (A = Mn, Co, Ni, Cu, Zn, or Mg) tungstates with the wolframite structure. In MgWO4 and ZnWO4, the lowest energy optical excitation is a ligand to metal charge transfer (LMCT) excitation from oxygen 2p nonbonding orbitals to antibonding W 5d orbitals. The energy of the LMCT transition in these two compounds is 3.95 eV for ZnWO4 and 4.06 eV for MgWO4. The charge transfer energies observed for the other compounds are significantly smaller, falling in the visible region of the spectrum and ranging from 2.3 to 3.0 eV. In these compounds, the partially occupied 3d orbitals of the A(2+) ion act as the HOMO, rather than the O 2p orbitals. The lowest energy charge transfer excitation now becomes a metal-to-metal charge transfer (MMCT) excitation, where an electron is transferred from the occupied 3d orbitals of the A(2+) ion to unoccupied antibonding W 5d states. The MMCT value for CuWO4 of 2.31 eV is the lowest in this series due to distortions of the crystal structure driven by the d(9) configuration of the Cu(2+) ion that lower the crystal symmetry to triclinic. The results of this study have important implications for the application of these and related materials as photocatalysts, photoanodes, pigments, and phosphors.

Hydrothermal crystal growth and structure determination of double hydroxides LiSb(OH)6, BaSn(OH)6, and SrSn(OH)6.

Colorless single crystals of LiSb(OH)6, SrSn(OH)6, and BaSn(OH)6, which are useful as precursors for the synthesis of LiSbO3, SrSnO3, and BaSnO3, were synthesized by a low-temperature hydrothermal method using a Teflon-lined autoclave at 380 K. The crystal structures were determined by single-crystal X-ray diffraction measurements. LiSb(OH)6 crystallizes in the trigonal space group P3̅1m with a = 5.3812(3)A, c = 9.8195(7)A, V = 246.25(3)A(3), Z = 2. In this layered structure, [Li2Sb(OH)6](+) and [Sb(OH)6](-) layers are alternately stacked along the c-direction. The [Li2Sb(OH)6](+) layer can be regarded as a cation-ordered CdCl2 layer. The [Sb(OH)6)](-) layer is built up from isolated [Sb(OH)6](-) octahedra, which are linked to each other via hydrogen bonding within the layer. BaSn(OH)6 and SrSn(OH)6 crystallize with monoclinic P21/n space group symmetry. The monoclinic structure possesses a CsCl-type packing of Ba(2+)/Sr(2+) cations and [Sn(OH)6](2-) anions. The [Sn(OH)6](2-) polyhedra are connected to each other through hydrogen bonding to form a three-dimensional framework. The factors that favor these hitherto unknown crystal structures are discussed using a structure map that compares various M(OH)3 and M'M″(OH)6 compounds.

Structural degeneracy and formation of crystallographic domains in epitaxial LaFeO3 films revealed by machine-learning assisted 4D-STEM.

Structural domains and domain walls, inherent in single crystalline perovskite oxides, can significantly influence the properties of the material and therefore must be considered as a vital part of the design of the epitaxial oxide thin films. We employ 4D-STEM combined with machine learning (ML) to comprehensively characterize domain structures at both high spatial resolution and over a significant spatial extent. Using orthorhombic LaFeO3 as a model system, we explore the application of unsupervised and supervised ML in domain mapping, which demonstrates robustness against experiment uncertainties. The results reveal the consequential formation of multiple domains due to the structural degeneracy when LaFeO3 film is grown on cubic SrTiO3. In situ annealing of the film shows the mechanism of domain coarsening that potentially links to phase transition of LaFeO3 at high temperatures. Moreover, synthesis of LaFeO3 on DyScO3 illustrates that a less symmetric orthorhombic substrate inhibits the formation of domain walls, thereby contributing to the mitigation of structural degeneracy. High fidelity of our approach also highlights the potential for the domain mapping of other complicated materials and thin films.

Spin-orbital Jahn-Teller bipolarons.

Polarons and spin-orbit (SO) coupling are distinct quantum effects that play a critical role in charge transport and spin-orbitronics. Polarons originate from strong electron-phonon interaction and are ubiquitous in polarizable materials featuring electron localization, in particular 3d transition metal oxides (TMOs). On the other hand, the relativistic coupling between the spin and orbital angular momentum is notable in lattices with heavy atoms and develops in 5d TMOs, where electrons are spatially delocalized. Here we combine ab initio calculations and magnetic measurements to show that these two seemingly mutually exclusive interactions are entangled in the electron-doped SO-coupled Mott insulator Ba2Na1-xCaxOsO6 (0 < x < 1), unveiling the formation of spin-orbital bipolarons. Polaron charge trapping, favoured by the Jahn-Teller lattice activity, converts the Os 5d1 spin-orbital Jeff = 3/2 levels, characteristic of the parent compound Ba2NaOsO6 (BNOO), into a bipolaron 5d2 Jeff = 2 manifold, leading to the coexistence of different J-effective states in a single-phase material. The gradual increase of bipolarons with increasing doping creates robust in-gap states that prevents the transition to a metal phase even at ultrahigh doping, thus preserving the Mott gap across the entire doping range from d1 BNOO to d2 Ba2CaOsO6 (BCOO).

Independent ordering of two interpenetrating magnetic sublattices in the double perovskite Sr2CoOsO6.

The insulating, fully ordered, double perovskite Sr2CoOsO6 undergoes two magnetic phase transitions. The Os(VI) ions order antiferromagnetically with a propagation vector k = (1/2, 1/2, 0) below TN1 = 108 K, while the high-spin Co(II) ions order antiferromagnetically with a propagation vector k = (1/2, 0, 1/2) below TN2 = 70 K. Ordering of the Os(VI) spins is accompanied by a structural distortion from tetragonal I4/m symmetry to monoclinic I2/m symmetry, which reduces the frustration of the face centered cubic lattice of Os(VI) ions. Density functional theory calculations show that the long-range Os-O-Co-O-Os and Co-O-Os-O-Co superexchange interactions are considerably stronger than the shorter Os-O-Co interactions. The poor energetic overlap between the 3d orbitals of Co and the 5d orbitals of Os appears to be responsible for this unusual inversion in the strength of short and long-range superexchange interactions.

Gallium analogue of soluble Prussian blue KGa[Fe(CN)6]·nH2O: synthesis, characterization, and potential biomedical applications.

The gallium analogue of the soluble Prussian blue with the formula KGa[Fe(CN)6]·nH2O is synthesized and structurally characterized. A simple aqueous synthetic procedure for preparing nanoparticles of this novel coordination polymer is reported. The stability, in vitro ion exchange with ferrous ions, cytotoxicity, and cellular uptake of such nanoparticles coated with poly(vinylpyrrolidone) are investigated for potential applications of delivering Ga(3+) ions into cells or removing iron from cells.

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

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.