Monovalent inorganic gallium compounds are very rare, whereas this is not the case for indium compounds. As the chemistry of Ga(I) can be assumed to be dominated by its lone pair that favors unsymmetrical environments, the influence of the lone pair of In(I) is usually not very pronounced. Thus, there are very few isostructural Ga and In compounds. Starting from the elements, we have now obtained the new telluridogallates(I) REGaTe₂ and related compounds REInTe₂ (RE = La – Nd). Although their orthorhombic unit-cell dimensions are similar, the structures combine modular entities in different ways that enable more or less space for lone pairs. In the case of In-containing compounds, data were collected using microfocused synchrotron radiation from microcrystals that were selected and pre-characterized by electron microscopy

The compounds REGaTe₂ crystallize in the non-centrosymmetric space group Pmc2₁, their lattice parameters reflect the lanthanide contraction. In contrast to telluridogallates(III) such as CuGaTe₂ [1] and AgGaTe₂ [2] that contain [GaTe₄] tetrahedral, its characteristical structural feature is a chain of GaTe₃ pyramids sharing two Te atoms with neighboring pyramids. This would be typical for a telluridogallate(I), however, chemical bonding and charge distribution are not trivial. Bond valence sums confirm the electron-precise description according to RE^IIIGa^ITe^-II₂, and the coordination of gallium(I) is pyramidal as expected for a lone-pair atom. Bader charges for LaGaTe₂ (La +1.5, Ga +0.5, Te ‑0.8 – ‑0.9) suggest only partial electron transfer. Thus, REGaTe₂ are rare examples of compounds with exclusively monovalent Ga atoms, probably the first one without organic residues. In NdGaTe₂, a short Nd-Ga distance of 3.13 Å is a possible indication of an interaction of the lone pair of Ga(I) with the Nd atoms. This is stronger than, for example, in NdGaSb₂ (Nd-Ga distance 3.35 Å),[3] which has a different structure and bonding situation. Similar Nd-Ga distances are observed in intermetallic phases such as NdGa [4] or NdGaRh [5], so that a description as an oxidized intermetallic phase may also be considered. A formal consideration in the framework of the Zintl concept would assume a mixed chain-like [Ga^(‑2)Te⁽⁰⁾Te^(-1)]^3- polyanion; note that in these formal “charges” are note expected correspond to oxidation states. It is consistent with all descriptions that the distances of 2.67 Å to the terminal Te atom are shorter than those to Te atoms bridging along the chain (2.95 Å). Interactions between the polyanionic chains appear negligible. The Nd atoms are located in single-capped trigonal prisms of Te atoms, with Ga atoms forming two additional caps.

In contrast, compounds REInTe₂ are centrosymmetric, they adopt a structure with the space group Amm2. Although this can, in principle, be related to the structure of REGaTe₂ by group-subgroup relationships, the cationic modules are not shifted against each other in the indium compounds. The indium atoms are located in capped trigonal prisms that show little lone-pair influence, their environment is more symmetrical. Although these polyhedra are interconnected in a fashion that is similar to the one in REGaTe₂, the distances between the chains are not much larger than the ones within the chains so that the compound is a rare-earth indium (I) telluride rather than a telluridoindate(I) with a discrete polyanion. Still, bond valence sums correspond to RE^IIIIn^ITe^-II₂. The anionic In- or Ga-containing substructures thus show a pronounced influence on the arrangement of the cationic substructures – they interconnect similar modules is different ways. The CrB structure type may be regarded as an aristotype of both arrangements.

[1] T. Plirdpring, K. Kurosaki, A. Kosuga, T. Day, S. Firdosy, V. Ravi, G. J. Snyder, A. Harnwunggmoung, T. Sugahara, Y. Ohishi (2012) Adv. Mater. 24, 3622.
[2] S. Chatraphorn, T. Panmatarite, S. Pramatus, A. Prichavudhi, R. Kritayakirana, J.‐O. Berananda, V. Sayakanit, J. C. Woolley (1985) J. Appl. Phys. 57, 1791.
[3] A. M. Mills, A. Mar, (2001) J. Am. Chem. Soc. 123, 1151.
[4] S. P. Yatsenko, A. A. Semyannikov, B. G. Semenov, K. A. Chuntonov (1979) J. Less-Common Met. 64, 185.
[5] F. Hulliger, (1996) J. Alloys Compd. 239, 131.

Growing interest in the design of functional materials with increasingly complex crystal structures calls for a more detailed understanding of structure-property relationships in inorganic solids. Whereby functional material properties are often linked to irregular bond distances, deciphering the causal mechanisms underlying bond-length variation, and the extent to which bond lengths vary in solids, has important implications in the design of new materials and the optimization of their functional properties.

Investigation of the relation between bond-length variation and the expression of functional material properties begins with systematization of chemical-bonding behavior via large-scale bond-length dispersion analysis. Completion of the largest bond-length dispersion analysis to date for inorganic solids (177,446 reliable bond lengths hand-picked from 9210 crystal-structure refinements for oxides [1]; 6,770 bond lengths from 720 crystal-structure refinements for nitrides [2]; 33,626 bond lengths from 1832 crystal-structure refinements for chalcogenides [3]) recently enabled straightforward identification of anomalous (i.e. irregular) bonding behavior for all ions of the periodic table observed bonding to O^2-, N^3-, and S^2-/Se^2-/Te^2-. In addition to comprehensive description of bond-length variations in inorganic solids, the large amount of data on anomalous coordination environments provided by this undertaking allows (1) conclusive resolution of the causal mechanisms underlying bond-length variation in inorganic solids, and (2) quantification of the extent to which these causal mechanisms result in bond-length variation.

In a sample of 266 highly irregular coordination polyhedra covering 85 transition-metal ion configurations bonded to O^2-, the most common cause of bond-length variation is observed to be non-local bond-topological asymmetry — a widely overlooked phenomenon whose associated bond-length variation results from asymmetric patterns of a priori bond valences — followed closely by the pseudo Jahn-Teller effect (PJTE). Two new indices, and , calculated on the basis of crystallographic site, are proposed to quantify bond-length variation arising from bond-topological and crystallographic mechanisms in extended solids; is defined as the mean weighted deviation between the bond valences of a given polyhedron and that of its regular variant with equal bond lengths, while similarly quantifies the difference between a priori and observed bond valences. Bond-topological mechanisms of bond-length variation are (1) non-local bond-topological asymmetry and (2) multiple-bond formation, while crystallographic mechanisms are (3) electronic effects (e.g. vibronic mixing, lone-pair stereoactivity), and (4) crystal-structure effects (e.g. structural incommensuration).

Comprehensive bond-length dispersion analyses for inorganic nitrides [2] and chalcogenides [3] reveal several “phenomenological gaps” compared to their oxide counterparts, thus providing synthetic opportunities via the transposing of anomalously bonded coordination units bearing functional properties into new compositional and/or structural spaces. Resolving the contribution of (static) bond-topological vs (tunable) crystallographic mechanisms of bond-length variation via the and indices, combined with their spatial resolution within the coordination polyhedron and unit cell, is proposed to quantify the effective tunable extent of a functional property for a given crystal structure, e.g. via alteration of the responsible coordination unit(s). The known extent for which bond-topological and crystallographic mechanisms materialize into bond-length variations, provided by large-scale bond-length dispersion analyses, guides optimization of these properties within the constraints of physically realistic crystal structures. Such information is essential to the design of new materials with (1) increasingly complex crystal structures, and (2) superior functional properties.

[1] Gagné, O. C. & Hawthorne, F. C. (2016). Acta Cryst. B72, 602–625; Gagné, O. C. (2018). Acta Cryst. B74, 49–62; Gagné, O. C. & Hawthorne, F. C. (2018a). Acta Cryst. B74, 63–78; Gagné, O. C. & Hawthorne, F. C. (2018b). Acta Cryst. B74, 79–96; Gagné, O. C. & Hawthorne, F. C. ChemRxiv 11605698.

[2] Gagné, O. C. (2020). ChemRxiv. 11626974

[3] Gagné, O. C. et al. (2020). In preparation

This study explored the pressure dependent polymorphism of BaRhO₃ within the 7 – 22 GPa pressure range. We report the synthesis of a previously undiscovered 6H perovskite polymorph of BaRhO₃, which was stabilised between 14 – 22 GPa, below which a previously known 4H polymorph is yielded.[1] From Rietveld analysis of synchrotron X-ray powder diffraction data, the polymorph was found to crystallise in the monoclinic C2/c 6H perovskite structure, similar to the analogous BaIrO₃ 6H polymorph which is also synthesised at high pressure.[2] This data analysis also confirms a 4+ oxidation state for Rh which we believe is stabilised by the extremely high oxygen pressures accessible via high pressure synthesis. Physical property measurements and electronic structure calculations were carried out on the 4H and 6H polymorphs. Both polymorphs were found to be Pauli paramagnetic metallic oxides. Resistivity measurements confirm a metallic state for the 4H polymorph, while bulk resistivity indicates semiconductivity for the 6H polymorph. We believe this semiconducting behaviour to arise due to grain boundary effects and not to be intrinsic. High Wilson ratios of approximately 2 for either compound indicate strong electron correlations which is rationalised by strong intermetallic interactions within the Rh₂O₉ dimers. Overall this study suggests that like the neighbouring Ru, Rh oxides display physical properties driven by competing localised and itinerant electron behaviour, and that the higher oxidation states of Rh are readily accessible under high pressure, high temperature conditions.

In recent years there has been tremendous interest in perovskite-like ABX₃ hybrid frameworks, built from inorganic and organic building blocks, for their semiconducting, ferroelectric and magnetic properties. Much of the attraction in these materials lies in the well-known chemical flexibility of perovskite structures, which allows them to accommodate a wide range of cations and anions, as is well known perovskite oxides. Much of this flexibility is enhanced in inorganic-organic perovskites both with respect to their chemistry e.g. their ability to incorporate a wide range of molecular A-site cations and ligands, distortion modes and mechanical flexibility. In one key aspect, however, hybrid perovskites currently have less flexibility compared to conventional perovskites, namely the range of formal charges of cations they can incorporate. This results from the ligands in these hybrid material almost always being monovalent, which essentially restricts the A and B sites to monovalent and divalent cations, respectively.

Recent work in our group has realised a combination of monovalent and divalent ligands in perovskite-like materials via replacing HCO₂^- linker with C₂O₄^2- ligands. Most interestingly this has yielded [(CH₂)₃N]Er(HCO₂)₂(C₂O₄) and [(CH₃)₂NH₂]Er(HCO₂)₂(C₂O₄), allowing monovalent organic A-site and trivalent B-site cations to be combined for the first time in a stoichiometric ABX₃ perovskite. Our presentation will discuss the synthesis, crystal structures and magnetic properties of these materials. These exhibit A-site cation ordering up to 500 K, which will likely make related phases of interest as ferroelectrics. The greater framework flexibility in [(CH₂)₃N]Er(HCO₂)₂(C₂O₄) leads to it exhibiting significant anisotropic negative thermal expansion while the more rigid [(CH₃)₂NH₂]Er(HCO₂)₂(C₂O₄) phase does not.

The second part of our presentation will focus on the related ALn(C₂O₄)_1.5(HCO₂) (Ln = Tb-Er) phases, where we find that replacing an additional formate ligand with oxalate leads to a structure with ordered ligand vacancies. This leads to larger channels in the materials, which is likely the cause of the disorded A-site cations in these materials; ultimately the presence and nature of these A-site cations, which could not be identified crystallographically, have been confirmed by neutron and infrared spectroscopy. These two new series of materials highlight the potential to expand the flexibility of hybrid perovskite and perovskite-like materials by incorporating divalent ligands, allowing their properties to be further tailored for applications.

Rubidium tetrachloro zincate (Rb₂ZnCl₄) belongs to A₂BX₄ crystal family with the β-K₂SO₄ structure type, which are known for their ferroelectric properties and successive phase transitions. Rb₂ZnCl₄ has an orthorhombic crystal structure with Pmcn as its space group in its normal phase and goes from a normal disordered structure to incommensurately modulated structure along its c-axis at 303 K, then goes to a commensurately modulated structure around 192 K (T_c). Here we report the temperature dependent crystal structure of Rb₂ZnCl₄ in an attempt to elucidate the relation between structure and physical properties of this compound.

In the incommensurate phase the modulation wave vector is given by q = (1/3 – δ) c*, where δ is the parameter which changes with temperature, it decreases with decrease in temperature and finally becomes zero at the lock-in phase transition temperature T_c . In Rb₂ZnCl₄ the modulation wave function changes from a sinusoidal harmonic function just below the incommensurate phase transition (303K) to a strongly anharmonic function near the lock-in phase transition at T_c. The modulation function in the incommensurate phase of Rb₂ZnCl₄ is not only given by displacive modulation but also modulations of atomic displacement parameters (ADPs) and anharmonic ADPs. The structural analysis together with the lattice dynamics studies help us to understand the relation between aperiodic order and physical properties.