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We present a comprehensive review of the structural chemistry of hybrid lead halides of stoichiometry APbX4, A2PbX4 or AAPbX4, where A and A are organic ammonium cations and X = Cl, Br or I. These compounds may be considered as layered perovskites, containing isolated, infinite layers of corner-sharing PbX4 octahedra separated by the organic species. We first extract over 250 crystal structures from the CCDC and classify them in terms of unit cell metrics and crystal symmetry. Symmetry mode analysis is then used to identify the nature of key structural distortions of the [PbX4] layers. Two generic types of distortion are prevalent in this family: tilting of the octahedral units and shifts of the inorganic layers relative to each other. Although the octahedral tilting modes are well-known in the crystallography of purely inorganic perovskites, the additional layer shift modes are shown to enrich enormously the structural options available in layered hybrid perovskites. Some examples and trends are discussed in more detail in order to show how the nature of the interlayer organic species can influence the overall structural architecture, although the main aim of the paper is to encourage workers in the field to make use of the systematic crystallographic methods used here to further understand and rationalise their own compounds, and perhaps to be able to design-in particular structural features in future work., Comment: 62 pages, 20 figures, 5 tables

We report the crystal structures and magnetic properties of two psuedo-polymorphs of the $S=1/2$ Ti$^{3+}$ coordination framework, KTi(C$_2$O$_4$)$_2\cdot$xH$_2$O. Single-crystal X-ray and powder neutron diffraction measurements on $\alpha$-KTi(C$_2$O$_4$)$_2\cdot$xH$_2$O confirm its structure in the tetragonal $I4/mcm$ space group with a square planar arrangement of Ti$^{3+}$ ions. Magnetometry and specific heat measurements reveal weak antiferromagnetic interactions, with $J_1\approx7$ K and $J_2/J_1=0.11$ indicating a slight frustration of nearest- and next-nearest-neighbor interactions. Below $1.8$ K, $\alpha$ undergoes a transition to G-type antiferromagnetic order with magnetic moments aligned along the $c$ axis of the tetragonal structure. The estimated ordered moment of Ti$^{3+}$ in $\alpha$ is suppressed from its spin-only value to $0.62(3)~\mu_B$, thus verifying the two-dimensional nature of the magnetic interactions within the system. $\beta$-KTi(C$_2$O$_4$)$_2\cdot$2H$_2$O, on the other hand, realises a three-dimensional diamond-like magnetic network of Ti$^{3+}$ moments within a hexagonal $P6_222$ structure. An antiferromagnetic exchange coupling of $J\approx54$ K -- an order of magnitude larger than in $\alpha$ -- is extracted from magnetometry and specific heat data. $\beta$ undergoes N\'eel ordering at $T_N=28$ K, with the magnetic moments aligned within the $ab$ plane and a slightly reduced ordered moment of $0.79~\mu_B$ per Ti$^{3+}$. Through density-functional theory calculations, we address the origin of the large difference in the exchange parameters between the $\alpha$ and $\beta$ psuedo-polymorphs. Given their observed magnetic behaviors, we propose $\alpha$-KTi(C$_2$O$_4$)$_2\cdot$xH$_2$O and $\beta$-KTi(C$_2$O$_4$)$_2\cdot$2H$_2$O as close to ideal model $S=1/2$ Heisenberg square and diamond lattice antiferromagnets, respectively., Comment: 12 pages, 7 figures

High-temperature phase behavior in the system LixNa1-xNbO3 has been studied by using high-resolution powder neutron diffraction. Each of the three compositions studied in the Na-rich part of the phase diagram (x = 0.03, 0.08 and 0.12) shows evidence for distinct and complex structural modulations based on different tilting schemes of NbO6 octahedral units. Whilst octahedral tilting is prevalent in the structural chemistry of perovskites the nature of complexity of the phases observed here is unprecedented. Neither of the long-range tilt phases observed in NaNbO3 itself occurs here; instead a novel phase with a well-defined 4-fold superlattice is observed for the composition Li0.12Na0.88NbO3, and yet more complex phases with modulations based on 20-fold and 30-fold repeats are observed for Li0.03Na0.97NbO3 and Li0.08Na0.92NbO3, respectively. This peculiar structural behavior makes the system LixNa1-xNbO3 the most structurally complex 'simple' perovskite known.

We report ferrielectricity in a single-phase crystal, TSCC -- tris-sarcosine calcium chloride [(CH3NHCH2COOH)3CaCl2]. Ferrielectricity is well known in smectic liquid crystals but almost unknown in true crystalline solids. Pulvari reported it in 1960 in mixtures of ferroelectrics and antiferroelectrics, but only at high fields. TSCC exhibits a second-order displacive phase transition near Tc = 130 K that can be lowered to a Quantum Critical Point at zero Kelvin via Br- or I-substitution, and phases predicted to be antiferroelectric at high pressure and low temperatures. Unusually, the size of the primitive unit cell does not increase. We measure hysteresis loops and polarization below T = 64 K and clear Raman evidence for this transition, as well of another transition near 47-50 K. X-ray and neutron studies below Tc = 130K show there is an antiferroelectric displacement out of plane of two sarcosine groups; but these are antiparallel displacements are of different magnitude, leading to a bias voltage that grows with decreasing T. A monoclinic subgroup C2 may be possible at the lowest temperatures (T<64K or T<48K), but no direct evidence exists for a crystal class lower than orthorhombic., Comment: 21 pages; 8 figures; 25 references

A new organically-templated vanadium (III) fluoride, (NH4)2(C2H8N)[V3F12], has been prepared using an ionothermal approach. This compound has a unique layered structure featuring distorted S = 1 kagome planes separated by the cationic species. The compound exhibits magnetic frustration, with a canted antiferromagnetic ground state. On further cooling within the ground state a pronounced change in magnetisation kinetics is observed., Comment: 14 pages, 13 figures

Rb2SnCu3F12 has been studied using synchrotron powder X-ray diffraction, powder neutron diffraction and single crystal X-ray diffraction at a range of temperatures (100 to 500 K). A broad but clear phase transition, possibly of re-entrant character, is found to occur in the powder form, whereas the corresponding transition is not seen in the single crystal., Comment: 3 pages, 4 figures

We report a detailed high-resolution powder neutron diffraction investigation of the structural behaviour of the multiferroic hexagonal polymorph of YMnO3 between room temperature and 1403 K. The study was aimed at resolving previous uncertainties regarding the nature of the paraelectric- ferroelectric transition and the possibilities of any secondary structural transitions. We observe a clear transition at 1258 +/- 14 K corresponding to a unit cell tripling and a change in space group from centrosymmetric P6_3/mmc to polar P6_3cm. Despite the fact that this symmetry permits ferroelectricity, our experimental data for this transition analysed in terms of symmetry-adapted displacement modes clearly supports previous theoretical analysis that the transition is driven primarily by the antiferrodistortive K3 mode. We therefore verify previous suggestions that YMnO3 is an improper ferrielectric. Furthermore, our data confirm that the previously suggested intermediate phase with space group P6_3/mcm does not occur. However, we do find evidence for an isosymmetric phase transition (i.e. P6_3cm to P6_3cm) at ~920 K which involves a sharp decrease in polarization. This secondary transition correlates well with several previous reports of anomalies in physical properties in this temperature region and may be related to Y-O hybridization., Comment: Submitted to PRB

High temperature powder neutron diffraction experiments have been conducted around the reported beta-gamma, insulator-metal phase transition (~ 930 C) in BiFeO3. The results demonstrate that while a small volume contraction is observed at the transition temperature, consistent with an insulator-metal transition, both the beta and gamma phase of BiFeO3 exhibit orthorhombic symmetry i.e. no further increase of symmetry occurs under the present experimental conditions, contrary to previous suggestions. Furthermore we observe the gamma orthorhombic phase to persist up to a temperature of approximately 950 C before complete decomposition into Bi2Fe4O9 (and liquid Bi2O3), which subsequently begins to decompose at approximately 960 C.

A detailed investigation using variable temperature powder neutron diffraction demonstrates that BiFeO3 undergoes a phase transition from the ferroelectric alpha phase (rhombohedral, R3c) to a paraelectric beta phase (orthorhombic, Pbnm) between 820 oC and 830 oC. Co-existence of both phases over a finite temperature interval, together with abrupt changes in key structural parameters, confirm that the transition is firstorder. The beta phase corresponds to the GdFeO3-type perovskite. The metastability of BiFeO3 relative to Bi2Fe4O9 above 810 oC precludes observation of a reported cubic gamma phase above 925 oC under the present experimental conditions.