Perovskite-related ReO₃-type structures

Abstract

Materials with the perovskite ABX₃ structure play a major role across materials chemistry and physics as a consequence of their ubiquity and wide range of useful properties. ReO₃-type structures can be described as ABX₃ perovskites in which the A-cation site is unoccupied, giving rise to the general composition BX₃, where B is typically a cation and X is a bridging anion. The chemical diversity of such structures is extensive, ranging from simple oxides and fluorides, such as WO₃ and AlF₃, to complex structures in which the bridging anion is polyatomic, such as in the Prussian blue-related cyanides Fe(CN)₃ and CoPt(CN)₆. The same ReO₃-type structure is found in metal–organic frameworks, for example, ln (im)₃(im = imidazolate) and the well-known MOF-5 structure, where the B-site cation is polyatomic. The extended 3D connectivity and openness of this structure type leads to compounds with interesting and often unusual properties. Notable among these properties are negative thermal expansion (for example, ScF₃), photocatalysis (for example, CoSn(OH)₆), thermoelectricity (for example, CoAs₃) and superconductivity in a phase that is controversially described as SH₃ with a doubly interpenetrating ReO₃ structure. We present an account of this exciting family of materials and discuss future opportunities in the area.

Recent developments in photovoltaic devices with active layers containing hybrid perovskite halides, such as (MA)PbI₃(MA = methylammonium)¹, have drawn our attention once more to the importance and versatility of perovskite-based materials. These iconic materials, of general formula ABX₃ (FIG. 1a), have a long and distinguished history, with milestones including the discoveries of ferroelectric BaTiO₃ (REF.²), ferromagnetic SrRuO₃ (REF.³), superconducting YBa₂Cu₃O₇ (REF.⁴), magnetoresistive (La_xSr_1−x)MnO₃ (REF.⁵) and multi-ferroic BiMnO₃ (REF.⁶). Striking breakthroughs in the hybrid perovskite area include the discoveries of ferro-electric and multiferroic behaviour in formates, such as (DMA)Mn(HCOO)₃(DMA = dimethylammonium), where the X anion is an organic linker rather than a simple halide or oxide anion⁷, and ferroelectric, metal-free perovskites ((N-methyl-N′-diazabicyclo[2.2.2] octonium)-ammonium triiodides)⁸.

Fig. 1 |. General structures of perovskites and ReO₃.

a | The ABX₃ perovskite structure, exemplified by cubic SrTiO_3. b | The ReO₃ structure, illustrated by ReO₃ itself, contains no cation on the A-site. It is therefore an array of corner-sharing BX₆ octahedra. Panels a and b are drawn to scale to remind the reader that the ReO₃ unit cell is smaller because of the smaller size of the Re⁶⁺ cation. c | The ReO₃ structure, drawn to show its extended 3D connectivity. The VESTA software suite was used to create all visualizations of crystal structures in this manuscript²⁵².

It is often overlooked that the ABX₃ perovskite structure is based on an even simpler structure type in which there are no cations in the A-site cavities. Such BX₃-type structures (where B is typically a metal) are most notably illustrated by the eponymous ReO₃ structure (FIG. 1 b,c). This comprises a network of ReO₆ octahedra that share common corners in three dimensions, in this case with an Re–O–Re angle of 180° (although such linear linkages are unusual for most ReO₃-type materials). Recalling that the perovskite family now comprises an extensive range of compounds with both simple and complex X-anion linkers⁹, we have begun to explore the extent to which this is also true for ReO₃-type materials. Our article addresses this question, drawing together examples of ReO₃-type phases, ranging from simple oxides and halides, such as WO₃ and ScF₃, to systems containing more complex linkers and nodes, such as the formates M^III(HCOO)₃(M = metal), hypophosphites M^III(H₂POO)₃, imidazolates M^III(C₃N₂H₃)₃ and borohydrides Ln(BH₄)₃ (Ln = lanthanide). We show that this family is far more extensive than has hitherto been recognized, and that the members display a remarkable range of functionality that almost matches that of perovskites. FIGURE 2 illustrates this point, showing the timelines of discoveries and properties of these ReO₃-type materials, as well as their considerable chemical scope. Furthermore, our survey of the literature suggests that there are several chemical families that have yet to be explored.

Fig. 2 |. Timeline of ReO₃-type materials.

It is interesting to note the long time period between discoveries and reported properties, as well as the diverse chemical compositions and functionalities of ReO₃-type materials. IRMOF, isoreticular MOF; MOF, metal–organic framework.

One characteristic of ReO₃-type structures is their openness, which is immediately apparent when comparing the structure of ReO₃ with the perovskite structure (FIG. 1). This feature is even more striking in expanded ReO₃ structures, such as those in which the X-site has a multiatom linker. Several aspects of the openness influence the structures and properties of ReO₃ materials. In terms of the structures, the openness often results in tilting of the BX₆ octahedra, leading to more stable structures with bent B–X–B linkages¹⁰. Tilting of octahedra in perovskites has been extensively studied^11–13, including the analysis of group–subgroup relationships, and the concepts in this area have been extended to multiatom X-site linkers^14,15. These ideas can be applied to ReO₃-type structures, but will not be discussed further here. However, we note that tilting, or the absence of it, can significantly affect electronic and magnetic properties, for example, in ReO₃ itself and some structures with cyanide X-site linkers. Turning to other manifestations of the openness of ReO₃-type structures, cation insertion into the vacant A-site cavity is often facile, both in terms of the availability of space and the ease of ion transport; this has enabled applications in the area of rechargeable batteries. The openness also amplifies the vibrational properties associated with the X-site linkers, which has led to outstanding examples of negative thermal expansion (NTE). Finally, systems with multiatom X-site linkers, where the openness is particularly high, can accommodate guest molecules in the A-site cavities, in some cases leading to interesting adsorption–desorption behaviour.

This Review begins with a focus on simple inorganic compounds, especially the oxides, fluorides and oxyfluorides, and then explores more complex phases with multiatom linkers on the X-site. We note that one requirement for the adoption of the ReO₃-type structure is that the chemistry must be able to support octahedral connectivity at the B-sites. Bearing this in mind, we shall also consider some metal–organic frameworks (MOFs) in which the B-site node is polyatomic, the most striking of which is MOF-5 (REF.¹⁶).

Inorganic systems

The inorganic ReO₃-type materials are the oldest and most established compounds discussed in this Review. The first documented example is the pigment Prussian blue in the early 1720s, which we know today to belong to this structure type. Of the inorganic ReO₃-type compounds, those with single-atom X⁻ linkers predominate, with the fluorides being the most numerous. The fluorides are followed in prevalence by the hydroxides, oxyfluorides and intermetallics, and then the oxides and nitrides. Although the cyanides predate all other inorganic ReO₃-type compounds, we prefer to organize this section on inorganic systems based on the date of crystallographic structure determination. We therefore lead with the eponymous ReO₃, and progress accordingly.

Oxides.

ReO₃, which is deep red in colour, was first reported in the early 1930s, when its synthesis was described and its structure determined by powder X-ray diffraction¹⁷. However, it was not until 1965, when Goodenough and co-workers reported that it was a metallic conductor, that it attracted the attention of the scientific community¹⁸. Oxide conductors were rarities at that time, and the behaviour of ReO₃ was particularly eye-catching because its conductivity was almost as high as that of copper. That finding led to subsequent studies of the electronic structure of ReO₃, which involves band formation from overlap between the rhenium 5d(t_2g) and oxygen 2p(p_x or p_y) orbitals¹⁹. More than 50 years after the work of Goodenough and co-workers, ReO₃ remains the most striking example of a metallic transition-metal oxide.

ReO₃ and WO₃ are the only binary oxides that crystallize with the ReO₃-type structure, but although structurally similar, their properties are quite different. For example, at room temperature, ReO₃ is pcu (primitive cubic) and conductive, whereas WO₃ is monoclinic and insulating. The difference lies in their contrasting M–O–M bond angles: ReO₃ has angles of 180°, and WO₃ has angles between 165° and 179°(REF.²⁰). This distortion is a consequence of the propensity for tungsten atoms to be displaced from the ideal cubic location in the WO₆ octahedral environments, which density functional theory calculations suggest is caused by non-populated antibonding orbitals in the conduction band. In ReO₃, this is the reverse, as the antibonding orbitals are populated and the tendency to displace is discouraged²¹. This theory has been supported by experiments, because solid solutions of ReO₃ and WO₃(Re_x W_1−xO₃) become cubic at an x value of 0.25; this change is also marked by an increase in conductivity²²

Not only is the cubic ReO₃ structure stable up to its 673 K melting point²³ (in contrast to WO₃, which undergoes multiple first-order phase transitions with temperature), it also displays NTE^23,24 — the phenomenon where a material contracts instead of expanding when heated. This property is useful in composites, where the strain from the positive thermal expansion of one phase can be offset by the NTE of another²⁵. Rodriguez et al. described how for ReO₃ samples with high static disorder of oxygen, NTE was diminished²⁶. The weakened NTE is a consequence of the oxygen disorder, which alters the state of the antibonding band, reducing the Fermi pressure responsible for the rigidity of the structure. In a more holistic sense, NTE is commonly seen in materials with corner-connected M–X polyhedra that undergo concerted tilting or rocking motions when transverse vibrations (the movement of X species perpendicular to the M–X–M bond) are excited²⁷. Famous NTE compounds, such as ZrW₂O₈, Prussian blues and zeolites, all display some form of excited transverse vibrational modes related to their NTE behaviour²⁷. We shall see other striking examples of NTE in ReO₃-type systems in some of the following sections.

In addition to exhibiting NTE, ReO₃ displays pressure-induced first-order phase transitions. These pressure-dependent phase transitions (which involve octahedral rotations) occur as a stress relief²⁸, as the ReO₆ octahedra do not distort easily because of the strong Re–O bonds²⁹. These phase transitions have been examined via diffraction experiments^30–32; however, a pressure phase diagram was only resolved in 2015 with the implementation of high-pressure Raman studies³³. In addition to physical pressure, chemical pressure in the form of lithiation can induce phase transitions in ReO₃, as was first examined in the 1980s by Cava et al.^34,35, and more recently by Melot and co-workers³⁶, where considerable correlated rotations of the corner-sharing ReO₆ octahedra are observed upon lithiation.

Lastly, although ReO₃ has generated a large amount of interest, it should not be overlooked that WO₃ is an attractive wide band-gap semiconductor that can be tuned through intercalation, temperature, doping and nanostructuring. In particular, nanostructuring is an attractive strategy to stabilize one of the three other WO₃ phases at room temperature³⁷ or to increase the surface area for enhanced chemical functionality. For example, earlier work on WO₃ for its use as a photochromic^38,39, electrochromic⁴⁰, photocatalytic⁴¹, super-conductive⁴², ferroelectric⁴³ and gas-sensing^44–47 material is still relevant and continues to inform active areas of research¹⁷. This includes photoelectrochemical^48–52, photochromic⁵³, conductive⁵⁴, anodic⁵⁵, photocatalytic^56–59, thermoelectric^60,61 and gas-sensing^62,63 applications.

One recent work used WO₃ as an electron conductor in a core–shell nanowire BiVO₄ photoanode for photoelectrochemical water oxidation⁶⁴. This study was significant because the core–shell nanowire design leveraged the high light absorption of BiVO₄, whilst mitigating its low transport properties with WO₃. Another example demonstrated the use of an apoferritin-encapsulated, nanoparticle-coated WO₃ material for sensitive detection of certain molecules in exhaled breath, and thus its great promise for reliable, non-invasive, diagnosis of diseases⁶². Lastly, WO₃ is able to tune the surface charge transfer of diamond, resulting in improved p-type sheet conductivity and thermal stability⁶⁵. In fact, the transfer doping efficiency with WO₃ was the highest (for the given surface area) reported to date, marking a substantial advance in 2D diamond-based electronic devices. This study and earlier work on WO₃ attest to this material’s suitability for a wide variety of applications.

Nitrides.

The anti-ReO₃ crystal structure of Cu₃N was determined in 1938 by Juza and Hahn⁶⁶, not long after the discovery of ReO₃, and has been confirmed in subsequent work⁶⁷. Its crystal structure in space group $Pm\overline{3}m$ is the same as that of ReO₃ because the N–Cu–N bond angles are also 180°. Under high pressure, Cu₃N transforms to a simple tetragonal structure, which is not surprising given the open nature of the structure⁶⁸. There has not been a detailed study of NTE in Cu₃N; however, it has been indicated that there is little, if any, expansion in the temperature range of 4–100K (REF.⁶⁹). Since its discovery, more than 50 years lapsed before the growth of thin films was reported⁷⁰ and attention was drawn to the semiconducting properties of Cu₃N. Shortly thereafter, in 1990, it was shown that such films, which are typically green, could be used as an optical data-recording medium using infrared light⁷¹. The films were made by irradiating copper with nitrogen ions during film deposition onto a substrate because copper does not react with nitrogen gas (although bulk samples can be made from the reaction between CuF₂ and NH₃)⁷². Since 1990, there has been extensive work on the preparation of high-quality thin films using various methods, especially magnetron sputtering and radio-frequency plasma jets.

In addition to its potential for use in optical data storage, Cu₃N has been proposed as a defect-tolerant semi-conductor for photovoltaic applications⁷³. Moreover, in condensed matter physics, it has been suggested as a model for a new type of topological semimetal exhibiting Dirac line nodes near the Fermi energy on doping with non-magnetic transition metal atoms, such as zinc and palladium⁷⁴ (FIG. 3). For energy storage, Cu₃N has been studied as a cathode material of lithium-ion batteries, although the chemistry is complex and may preclude its adoption by industry⁷⁵. It has also been studied as a cathode for oxygen reduction in alkaline fuel cells⁷⁶.

Fig. 3 |. Electronic structures of inverse perovskite nitrides.

a | Electronic structure of Cu₃NZn. b | Electronic structure of Cu₃NPd. The orange circles indicate the Dirac points in the band structures of these inversion-symmetric Dirac materials. The inset in panel a is a sketch of the Brillouin zone. Adapted with permission from REF.⁷⁴, American Physical Society.

Dark-blue sodium nitride, Na₃N, which is iso-structural to Cu₃N, has been prepared by the reaction of metallic sodium or liquid NaK alloy with plasma-activated nitrogen at low pressures⁷⁷.Na₃N decomposes above 377 K into its constituent elements, with a standard enthalpy of formation of approximately +64 kJ mol⁻¹(REF⁷⁸), making it a rare example of a metastable ReO₃-type structure. The band gap of Na₃N is in the range 0.5–1.0eV, which is similar to that of Cu₃N. Na₃N shows no phase change down to 20 K, but does exhibit strongly anisotropic effects⁷⁹. There is no tilting of the NNa₆ octahedra, and nor is there any NTE, which is surprising. However, similar to Cu₃N,Na₃N may exhibit topological semimetal behaviour⁸⁰. It is also worth noting that neither Li₃N nor K₃N adopt the anti-ReO₃-type structure^81,82.

Fluorides and oxyfluorides.

ReO₃-type fluoride materials, of general formula MF₃, are more common than their oxide counterparts owing to the greater prevalence of 3+ oxidation-state metals. The M-site metals for MF₃ compounds include scandium⁸³, cobalt⁸⁴, aluminium⁸⁵, chromium⁸⁶, vanadium⁸⁷, titanium⁸⁸ and iron⁸⁶. It is worth noting that rare-earth cations — even the smallest example of lutetium (ionic radius of 0.861 Å)^89,90 — are too large to adopt the octahedral coordination required for the ReO₃-type structure. The majority of the single-metal ReO₃-type fluoride compounds adopt a rhombohedral distorted variant structure at room temperature, with the exceptions being ScF₃ — a notable NTE material — and MnF₃, which is Jahn–Teller distorted⁸³. As will become apparent throughout this Review, the majority of inorganic ReO₃-type materials have been studied for properties that are exhibited by ReO₃ itself: curious thermal expansion, as a host for guest cations and unusual pressure-dependent structural behaviour. This does not mean, however, that they do not, or cannot, display other attractive properties.

ScF₃ is perhaps the best-known MF₃ compound because it displays a remarkable temperature range of NTE as a consequence of the transverse vibrations of the fluorine anions⁹¹ (FIG. 4a,b depicts ReO₃ behaviour for comparison). From 10 K to approximately 1100 K, the material does not undergo first-order phase transitions, in contrast to ReO₃ (REF.⁹²) (although a possible quantum phase transition has been reported)⁹³, and displays a coefficient of NTE near −8 ppm K⁻¹ at room temperature. This coefficient of NTE is comparable to −9 ppm K⁻¹ for the well-known NTE compound ZrW₂O₈ (REF.⁸³). Furthermore, it was shown that the degree of NTE in ScF₃ is particle size dependent⁹⁴, and can be tuned between NTE, zero thermal expansion and positive thermal expansion by nanostructuring the product⁹⁵. The tunability has been ascribed to local symmetry breaking as the particle size is decreased; that is, the local structure is rhombohedrally distorted (as evidenced by pair distribution studies) but appears cubic on average. The source of this local symmetry breaking is thought to be the increased surface pressure from the decreased particle size. This tuning can also be achieved by zirconium doping⁹⁶. In addition, it has been found that NTE in ScF₃ can be turned off by doping with a small amount of iron and intercalating an equal amount of lithium into the vacant A-sites⁹⁷. The inclusion of lithium ions limits the transverse vibrations of the fluoride ions, in much the same way as guest molecules can dampen NTE in other porous NTE materials^98–102.

Fig. 4 |. Lattice constant as a function of temperature.

a | The change in lattice constant, a, for ScF₃ obtained from a combination of data from synchrotron X-ray diffraction and neutron diffraction. b | The change in lattice constant for ReO₃ based on data from neutron diffraction experiments. The cubic ReO₃ structure is shown as an overlay (95% thermal ellipsoids). Note the magnitude of the negative thermal expansion is much greater for ScF₃ than for ReO_3• Panel a is adapted with permission from REF.⁸³, American Chemical Society. Panel b is adapted from REF.²⁶ (Rodriguez, E. E. et al. The role of static disorder in negative thermal expansion in ReO_3•J. Appl. Phys. 105, 114901, 2009), with the permission of AIP Publishing.

Redox-active MF₃ materials that have been examined as intercalation materials for batteries include those where M = Ti, V, Mn, Co or Fe (REFS^103,104). The predominant focus has been on FeF₃ because it displays the most promising charge–discharge profile, a viable voltage range (2–4 V) and increased thermal stability upon lithiation¹⁰⁵. However, because of the low electrical conductivity of FeF₃ (and fluorides in general), ball-milling with a conductive carbon to increase electron transport is always needed. In the case of FeF₃, a reversible capacity of 80mAhg⁻¹ is achievable after this process¹⁰³. Aside from conductive carbon additives, nanostructuring FeF₃ to increase the surface area for lithiation^106–110 and doping with cobalt have been studied as ways to increase conductivity. However, theory suggests that FeF₃ becomes less stable with cobalt doping¹¹¹ and tends to form a tungsten bronze-related structure, which is a possible battery material in its own right¹¹². The tungsten bronze structure is also observed with iron fluoride hydrate, FeF₃•0.33 H₂O, and is found to perform in a manner similar to the cobalt-doped compound in battery applications¹¹³. Lastly, there are reports that the perovskite NaFeF₃ can be completely (100%) desodiated and sodiated reversibly, and is of interest for sodium battery cathodes¹¹⁴.

Double-fluoride ReO₃-type compounds, with the general formula MM′F₆, come in many varieties. Examples include Sn²⁺Sn⁴⁺F₆(REF.¹¹⁵), M²⁺(Zr)F₆ compounds (where M = Fe (REFS^116,117), Pd (REF.¹¹⁸), Co (REF.¹¹⁹), Zn (REF.¹¹⁹), Mg (REF.¹²⁰), Cu (REF.¹²¹), V (REFS^122,123), Ti (REF.¹²²), Ca (REFS^117,124), Cr (REF.¹¹⁷)), M²⁺(Hf)F₆ compounds (where M = V, Ti (REF.¹²²)), MMoF₆ compounds (where M = Na (REF.¹²⁵), Cu (REF.¹²⁶)), MNbF₆ compounds (where M = Cr (REF.¹²⁶), V (REFS^123,127)) and NaSbF₆ (REF.¹²⁸). Some of these compounds display NTE^124,129,130, gas adsorption under pressure¹²⁴ as well as Jahn–Teller distortions governed by the M²⁺ character^117,121,123. There are also recent reports of YbZrFF₇ (REF.¹³¹), which displays NTE below room temperature and zero thermal expansion at 300 K, and Mg_{1 − x}Zr_{1 + x}F_{6 + 2x} compounds in which the degree of thermal expansion can be tuned by varying x (REF.¹³²).

ReO₃-type oxyfluorides with the general formula MO_xF_y(M = Ti (REF.¹³³), V (REF.¹³⁴), Ta (REF.¹³⁵), Nb (REFS^133,135), Zr (REF.¹³⁶), Mo (REF.¹³⁷)) are also known, with the first example reported in the 1950s¹³⁵. They are predominantly tertiary compounds, but there are examples of quaternary compounds, like the non-stoichiometric Nb_0.55Zr_0.45O_1.1F_0.8 (REF.¹³⁶), CrNb₂O₄F₅ and Fe₂Nb₃O₆F₉ (REF.¹³⁸), and MgNb₂O₃F₆ and MgTi₂OF₈ (REF.¹³⁹). ReO₃-type oxyfluorides have been primarily studied as intercalation materials for use in batteries^133,134, with the greater class of oxyfluorides viewed as a favourable middle ground between oxides and fluorides, leveraging the high voltage levels of the fluorides and increased stability of the oxides (owing to the more covalent M–O bonds). As with all battery materials, understanding the underlying crystal chemistry of each compound is important, because the anion and cation orders have a substantial impact on material performance. For example, samples of NbO₂F and TaO₂F prepared via solution routes (rather than conventional solid-state routes) were found to have vacancies and hydroxide (OH⁻) ions, which were introduced during preparation¹⁴⁰. In the same study, it was shown that precise solid-state preparation of the materials produced samples with less vacancies or hydroxide contamination. The X-ray data of the phases prepared by the solid state route could be treated with a supercell model to describe the anion ordering motif.

Another example of a ReO₃-type oxyfluoride is VO₂F, which was applied as a cathode material¹³⁴. For context, it is best to define the terminology, as well as provide reference points for battery comparison. Commercialized lithium ion batteries have specific capacities of between 100 and 200mAh g⁻¹ at a voltage of about 3.7 V, and will last between 600 and 3000 cycles¹⁴¹. The C-rate describes the charge and discharge rates of a battery, and the optimal C-rate depends on the application. A C-rate of 1 corresponds to a battery discharging completely in 1 h (a C-rate of 2 corresponds to a battery discharging twice as fast.) Typically, higher C-rates reduce achievable capacities for batteries because more stress is put onto the device. When VO₂F (theoretical capacity of 462mAh g⁻¹) was applied as a cathode, it demonstrated a reversible capacity of 250mAh g⁻¹ at 2.2 V (one equivalent of Li, C/50 with graphene additive). However, if the material is cycled past 2.2 V (more than one equivalent of Li, C/50), it undergoes a conversion reaction, which reduces its cycling performance. This work was followed by a report where VO₂F prepared via ball-milling (as opposed to the high-temperature solid-state synthesis of the original report¹⁴²) had a reversible cyclability of 208 mAh g⁻¹ at 2.2 V, but at an improved cycle rate of C/20. If cycled to lower voltages, this VO₂F material undergoes an irreversible phase change, to what has been shown to be a disordered rock-salt phase^142–144. This material was reported¹⁴⁴ to deliver 276 mAh g⁻¹ (1.04 molLi) and 206 mAh g⁻¹ (0.8 molLi) at C/20 in its first and second cycles, respectively, with 97.5% capacity maintenance after 100 cycles. If taken to the irreversible rock-salt phase, 406 mAh g⁻¹ (1.54 molLi, C/60)capacity was achieved, but with only 60% capacity retention after 50 cycles.

Hydroxides.

The ReO₃-type hydroxides, commonly (and confusingly) referred to in the literature as hydroxide perovskites, M(OH)₃ or MM′(OH)₆, are a naturally occurring class of ReO₃-type materials well known to mineralogists¹⁴⁵, with some synthetic examples joining the ranks. Although there is still much to be understood about their fundamental crystal chemistry, members of this material class show promise as oxygen evolution reaction (OER) catalysts.

The single ReO₃-type hydroxides, M(OH)₃, include varieties where M^III = Al (REF.¹⁴⁶),Ga REF.¹⁴⁷), Fe (REFS^148,149), Sc (REF.¹⁵⁰), In (REFS^150,151), Lu (REF.¹⁵²) or Yb (REF.¹⁵³). The gallium, indium and iron phases occur naturally, although all except for iron can be prepared synthetically. The most common preparations are metathesis reactions, usually between a MCl₃ species and NaOH (to form a gel), which is then washed and heated with more base to crystallize the compound. Early reports of the scandium¹⁵⁰, indium^150,151 and lutetium¹⁵² compounds described their structures, including a neutron diffraction study to establish the locations of the hydrogen atoms¹⁵². In the case of In(OH₃) (FIG. 5a), we draw attention to how the hydrogen bonding follows a four-ring (square) pattern; however, there are also ‘zigzag’ and ‘crankshaft’ hydrogen bonding patterns, which guide the structures of the hydroxide materials¹⁴⁵. Pure Yb(OH)₃ has eluded synthetic efforts, although it is known to form solid solutions (up to 25% ytterbium) with both Lu(OH)₃ and In(OH)₃ (REF.¹⁵³). As stated, Fe(OH)₃•nH₂O (bernalite) is a curious case¹⁵⁴. There are no definitive reports of a laboratory-prepared ReO₃-type Fe(OH)₃, but there are reports of a ‘Fe(OH)₃ powder’, which is distinct from the Fe(OH)₃ gels that form in high-pH Fe³⁺ cation-containing solutions. This powder, we suspect, is the amorphous version of the ReO₃-type compound, with considerable disorder owing to water molecules inside the cavities. This Fe(OH)₃ powder has been studied with Mössbauer and magnetic susceptibility techniques to differentiate it from the gels, albeit without definitive structural characterization^148,149. For the most part, these single-metal materials have fewer applications than the double hydroxides, although In(OH)₃ can be synthesized with nanomorphology and has been converted to the more industrially relevant In₂O₃ whilst maintaining its nanostructure¹⁵⁵.

Fig. 5 |. Structural similarities between In(OH)₃ and CoAs₃.

a | Structure of In(OH)_3• b | Structure of CoAs_3• Panels a and b are drawn to scale. The bonding between As atoms follows the same motif as the ‘ice-rules’ hydrogen bonding in In(OH)_3• c | CoAs₃, emphasizing the 12-coordinate cavity, or cage, that can be filled with a cation. This cation ‘rattles’ inside the cavity, increasing thermoelectric performance via phonon scattering. Atom legend: indium, grey; oxygen, orange; hydrogen, white; cobalt, blue; arsenic, red; and 12-coordinate cavity, yellow.

There are numerous mineral examples of double ReO₃-type hydroxides, MM^′(OH)₆, with a heavy predominance of stannates (the formal precursor is stannic acid, Sn(OH)₄). Some examples are CaSn(OH)₆ (burtite), FeSn(OH)₆ (natanite), ZnSn(OH)₆ (vismirnovite) and MnSn(OH)₆ (wickmanite)¹⁴⁵. These stannate minerals crystallize in cubic space groups (except for MnSn(OH)₆, which is reported to be tetragonal) and exhibit cation ordering. There are also other minerals, such as Fe³⁺Sn⁴⁺(OH)₅O (jeanbandyite), NaSb⁵⁺(OH)₆ (mopungite) and Fe²⁺Ge⁴⁺(OH)₆ (stottite), that are not stannates. Synthetic varieties of double ReO₃ hydroxide compounds, such as CuSn(OH)₆ (REF.¹⁵⁶), CoSn(OH)₆ (REF.¹⁵⁷) and SrSn(OH)₆(REF¹⁵⁸), are also known, with the latter example by Woodward and co-workers illustrating that the ionic sizes and electronegativities of the M-site cations are important characteristics for ReO₃-type structure formation. This concept was made evident by demonstrating that LiSb⁵⁺(OH)₆ and BaSn(OH)₆ both crystallize in other structural motifs¹⁵⁸.

Magnetic studies of double ReO₃-type hydroxide materials have revealed that materials with strong charge ordering (for example, MnSn(OH)₆ and CoSn(OH)₆) are paramagnetic down to 2 K, but with CoSn(OH)₆ displaying uncompensated spin interactions near 28 K owing to the single-anion anisotropy of the octahedral Co^II atom¹⁵⁷. FeSn(OH)₆ and FeSn(OH)₅O (where the former forms the latter when left in air for a few hours) have also been examined¹⁵⁹, with FeSn(OH)₆ exhibiting paramagnetism down to 1.4 K and FeSn(OH)₅O ordering antiferromagnetically at 4 K. Additionally, bulk Jahn–Teller-distorted CuSn(OH)₆ (REF.¹⁵⁶) displays weak antiferromagnetic behaviour and a spin-Peierls transition in strong magnetic fields at about 78 K (REF.¹⁶⁰).

Double ReO₃-type hydroxide materials have found recent relevance as both photocatalysts and OER catalysts. Their photocatalytic performance is linked to how, when exposed to ultraviolet light, they generate OH^•− radicals, which can degrade organic molecules¹⁶¹. The compounds ZnSn(OH)₆ (REF.¹⁶²) and CoSn(OH)₆) (REF.¹⁶³) have been of particular focus. The power of defect engineering to improve OER performance was demonstrated by the out-performance of an argon plasma-treated sample of Co_0.90Fe_0.10Sn(OH)₆ compared with a non-plasma-treated sample¹⁶⁴. Owing to the weak Sn–OH bonds, argon plasma treatment selectively removes tin to expose more active iron and cobalt sites, while increasing the micropore size of the material. The treated sample required a much lower overpotential for catalysis (270 mV at 10 mA cm⁻², with a Tafel slope of 42.3 mV dec⁻¹) than the non-plasma-treated material (420 mV at 10 mA cm⁻², with a Tafel slope of 77.0 mV dec⁻¹). For context, the lower the Tafel slope¹⁶⁵, the more rapid the kinetics for OER (whilst holding reaction conditions constant). In another example, an electrochemical activation process was used to remove the Sn⁴⁺ cations from the SnFeNi hydroxide system¹⁶⁶. The resulting SnFeNi hydroxide material performed comparably with the well-known OER material IrO₂. With the added benefit of being made from Earth-abundant metals, these tin-containing hydroxides are a promising direction for material research.

As indicated in the examples above, control over the vacancies and morphology of a double ReO₃-type hydroxide are essential to their use as functional materials. Such chemical control was exemplified by Nielson et al.¹⁵⁷, who demonstrated that if the hydrolysis of the Sn⁴⁺ ion can be kinetically controlled during the formation of CoSn(OH)₆ and MnSn(OH)₆ (by using a competing F⁻ anion), then defined charge ordering of the metals can be achieved. This control is significant because if charge ordering can be maximized, then materials like OER catalysts should have the maximum number of surface-active sites available after argon plasma treatment.

Lastly, the ordering of the metals affects the hydrogen-bonding tendencies in certain systems, which, as stated above, is a strong guide for the structure of the ReO₃-type hydroxides. In future work, it will be important to explore how greater synthetic control might encourage certain hydrogen-bonding arrangements (that is, different polymorphs). Mineralogists have highlighted some of the significant, more fundamental questions in this class of materials¹⁴⁵, with the overarching problem being that the crystallographic understanding (for example, space groups) of most ReO₃-type hydroxides is not definitive. This is an area where better synthetic control could elucidate why certain polymorphs are favoured in certain systems. Specifically, studies with variable temperature and pressure¹⁶⁷ may unravel the poorly understood phase transitions of these materials. Finally, with an average cavity diameter of 4.5 Å, small molecules could be intercalated into hydroxide materials; however, understanding how the hydroxide groups may play a role in guest-molecule intercalation is an open question.

Alloys.

Skutterudite is a mineral that was named after the city of Skotterud, Norway, where it was first discovered in 1845. The naturally occurring version is a cobalt arsenide, CoAs₃, which also contains some nickel and iron on the cobalt site (FIG. 5b). The structure of the mineral form was first examined by X-ray diffraction in 1928 by Oftedal¹⁶⁸, who showed that it was cubic with space group $Im\overline{3}$. A more precise determination was carried out by Mandel and Donohue in 1971 (REF.¹⁶⁹). The structure is formed from a network of corner-sharing CoAs₆ octahedra, as in ReO₃; however, these octahedra are sufficiently tilted that the arsenic atoms form approximately planar As₄ units (FIC. 5b). For the As₄ unit to be square, the x and y values of the As coordinates must obey the so-called Oftedal relationship, 2(y + z) = 1. However, in the determination by Mandel and Donohue, the values of x and y are such that the As₄ unit is rectangular with edges of 2.57 and 2.46 Å, respectively. There is a significant amount of As–As bonding in CoAs₃; hence, the system can be regarded as a Zintl phase¹⁷⁰. The structure is analogous to that of In(OH)₃, where the hydrogen bonding creates a square pattern (FIG. 5a), and indeed the two systems adopt the same $Im\overline{3}$ space group. Several closely related families of naturally occurring and synthetic alloys adopt the skutterudite structure. This MX₃ family is known for M = Fe, Co, Ni, Ru, Rh, Ir or Os and X = As, Sb or P. However, we are not aware of any examples with M-site ordering, which is common for more ionic systems, as discussed previously.

The so-called ‘filled skutterudites’ are an exceptionally important extension of the skutterudite family. The first examples were reported by Jeitschko and Braun¹⁷¹, and can be thought of as A-site deficient perovskites, A_xMX₃, with x = 0.25 (that is, their general composition is AM₄X₁₂). We have chosen to include them in this Review because they are closer in composition to ReO₃ than perovskite and because of their interesting electronic properties. Typical cases include systems such as LnM₄X₁₂, where Ln = rare earth, M = Fe, Ru or Os and X = P, As or Sb. Superconductivity below 4.08 and 7.20 K was reported for LaFe₄P₁₂ and LaRu₄P₁₂, respectively, in 1981 by Meisner¹⁷², and magnetic ordering was found to occur at even lower temperatures when lanthanum was substituted by magnetic rare-earth elements, such as cerium, praseodymium and neodymium (superconductivity was not observed in the magnetic systems).

The initial discovery of superconductivity in LaFe₄P₁₂ and LaRu₄P₁₂ attracted the attention of the condensed-matter physics community and led to a large body of work on these materials. Beyond studies on superconductivity, the most exciting development was the establishment by Sales et al. in 1996 that some of the filled skutterudites were excellent thermoelectric materials with figures of merit (zT) in excess of 1.0 (REF.¹⁷³). It was already recognized that conventional skutterudites had the possibility to be good thermoelectrics¹⁷⁴, and filled skutterudites offer the opportunity for enhancement of their thermoelectric performance. In particular, the rattling of the cations in the large A-site voids (FIG. 5c), along with the ease with which disorder can be introduced into these systems, contribute to their excellent performance. These factors reduce the lattice thermal conductivity by scattering phonons as discussed by Snyder and Toberer¹⁷⁵. Subsequent developments in this area, including the use of filler cations with different charges, enabled the tuning of the carrier density, leading to systems with thermoelectric performance approaching that of state-of-the-art materials¹⁷⁶. For example, CoSb₃ filled with various combinations of barium, lanthanum and ytterbium has zT values of up to 1.7 at 850 K (for example, Ba_0.08La_0.05Yb_0.04Co₄Sb₁₂)¹⁷⁷, which are close to the highest values reported to date for stable materials operating at these temperatures.

The bulk of the work on skutterudites for thermoelectric and other applications has focused on filled systems. However, an excellent figure of merit was reported for an unfilled system in which the thermal conductivity was minimized by controlling the nanostructure and microstructure of the material by means of careful annealing¹⁷⁸. In this way, zT of 1.6 was obtained for a synthetic alloy of composition Co_23.4Sb_69.1Si_1.5Te_6,0, despite the absence of rattling cations in the A-site cavity. When the nanostructure and microstructure were not controlled by annealing, the thermal conductivity was approximately 4–5 times higher, leading to a 60% decrease in zT.

Cyanides.

In view of the extensive literature on perovskite-related cyanides, such as Prussian blue, Fe₄[Fe(CN)₆]₃•xH₂O(REF.¹⁷⁹), it is not surprising that similar ReO₃-type cyanides are known. These materials are generally referred to as Prussian blue analogues, although the literature does not differentiate between those that have cations on the A-sites (that is, perovskites) and those that do not (that is, ReO₃ types). Several cyanide-based examples with the ReO₃-type structure are known, including numerous bimetallic systems, such as M^IIPt^IV(CN)₆ (REF.¹⁸⁰), Ga^IIIFe^III(CN)₆ (REF.¹⁸¹) and Fe₄[Ru(CN)₆]₃•18H₂O (REF.¹⁸²). The A-site cavities are larger than those of the simple oxides and fluorides, and, as a result, often contain solvent, typically water. Anhydrous materials, solvated systems and thiocyanates are the focus of this section.

The simplest cyanide-based compounds are those where M = Al (REF.¹⁸³), Ga (REFS^184,185) or In (REF.¹⁸⁶). These materials are cubic, display varying degrees of cyanide disorder and are porous. For example, in the case of In(CN)₃, the compound incorporates krypton reversibly and hexane irreversibly¹⁸⁶. In terms of single-metal cyanides, Fe[Fe(CN)₆], normally described as Fe(CN)₃, is a particularly interesting case. It crystallizes in a doubled ReO₃-type structure with alternate Fe^III ions coordinated by six carbon atoms and six nitrogen atoms from the cyanide ions¹⁸⁷ (FIG. 6a). Fe[Fe(CN)₆] is sometimes known as Berlin green because of its historical use as a pigment in paintings. The cation ordering, which gives rise to the doubling of the basic ReO₃ unit cell, is made possible by having the two iron sites in low-spin d⁵ (FeC₆) and high-spin d⁵ (FeN₆) states. The cavity in the as-synthesized material contains some water, which can be removed under vacuum; samples of the anhydrous material have been studied as a function of temperature by synchrotron X-ray diffraction¹⁸⁷. Fe[Fe(CN)₆] can be prepared in bulk or with microstructured morphology without the need for surfactants by using K₃[Fe(CN)₆] and Na₂S₂O₃ as precursors¹⁸⁸. Like many ReO₃-type structures, it exhibits pronounced NTE over a wide temperature range, in this instance from 100 to 450 K (REF.¹⁷⁹). In a similar manner to the ReO₃-type oxides and fluorides, NTE is associated with transverse vibrations of the carbon and nitrogen atoms of the cyanides; these are especially strong for the nitrogen atoms owing to the long Fe–N bonds. In a variation on this theme, a guest dependence of NTE was reported for M^IIPt^IV(CN)₆ (M = Zn, Cd) by Goodwin et al.⁹⁸. The study showed that the transverse vibrations are dampened and NTE is suppressed by the inclusion of intercalated water (FIG. 6b). As a point of interest, this dampening of NTE via intercalation is also observed for a related (non-ReO₃-type) porous rare-earth cyanide compound¹⁸⁹, illustrating the similar structure–property relationships between this and the M^IIPt^IV(CN)₆ system.

Fig. 6 |. Prussian blue analogue materials.

a | Structure of Fe(CN)₃ (left), with scanning electron microscope image of Berlin green microcubes (right). b | Structure of dehydrated Cd^IIPt^IV(CN)₆ (left), with graph showing the relative volume change as a function of temperature for M^IIPt^IV(CN)₆(M = Zn, Cd) (right). The samples (as indicated by the arrows) were first heated (whereupon they dehydrated) and then cooled for the experiment. Intercalated water within the two compounds changes their negative thermal expansion behaviour by dampening the transverse vibrations of the–CN ligands. Atom legend: iron, light and dark green; carbon, brown; nitrogen, light blue; cadmium, grey; platinum, navy blue. Panel a (right) is adapted with permission from REF.¹⁸⁸, American Chemical Society. Panel b is adapted with permission from REF.⁹⁸, American Chemical Society.

The magnetic properties of a hydrated form of Fe[Fe(CN)₆] have been studied by low-temperature neutron diffraction, Mössbauer spectroscopy and magnetic susceptibility methods, with the system having been found to undergo a paramagnetic–ferromagnetic phase transition on cooling to 17.4 K (REF.¹⁹⁰). This observation is consistent with the weak ferromagnetic exchange coupling that is expected between low-spin d⁵ Fe^III and high-spin d⁵ Fe^III via the cyanide linker. There is also a long history of bimetallic Prussian blue analogues that have been studied for their magnetic properties¹⁹¹, mainly in the context of molecular magnetism. This area is particularly fruitful because the alternation of two different octahedrally coordinated cations that are linked by cyanide groups can give rise to a wide range of antiferromagnetic, ferromagnetic and ferrimagnetic behaviour.

Although research in this area has focused on systems with cations on the A-sites (which are therefore beyond the scope of this work), there are examples of magnetic cyanide-based materials that adopt the ReO₃-type structure. The most striking case is probably a phase with the approximate composition VCr(CN)₆•xH₂O, which has a ferrimagnetic ordering temperature of 315 K owing to strong superexchange interactions between the V and Cr^III ions¹⁹². The system is more complex than it initially appears, however, because vanadium is present in both the V^II and V^III oxidation states, leading to various possible magnetic interactions. Other examples are the Co^II–Mn^II–Cr^III compounds Co_xMn_{1 – x}[Cr(C–N)₆]_2/3•zH₂O (REF.¹⁹³), which, depending on the compound of choice within the family, can be tuned between ferromagnetic and antiferromagnetic coupling according to the relative humidity. The humidity-induced variations in these compounds are related to the coordination geometries of the cobalt ions, which in certain variants are undercoordinated owing to [Cr(CN)₆] vacancies and can be coordinated by water. A counter example is the iron–ruthenium Prussian blue analogue (Fe₄[Ru(CN)₆]₃•18H₂O) (REF.¹⁸²), which was examined in part for its potential magnetic behaviour but was found to display no ordering above 1.8 K. This material is nonetheless interesting because it demonstrates the effect of electron localization when compared with its Prussian blue parent and potassium-intercalated sibling (K_1.2Ru_3.6[Ru(CN)₆]₃), as the iron–ruthenium compound has decreased electrical conductivity and blue-shifted optical intervalence charge-transfer transitions.

Many materials based on Prussian blue analogues have been explored for use in sodium-ion batteries¹⁹⁴; however, work in this area has been hampered by low capacity and poor cyclability. In the case of Fe[Fe(CN)₆], the use of nanoparticles overcame these drawbacks, giving rise to a device with good kinetics, capacity and lifetime^195,196 (we note that this strategy also worked for FeF₃, as discussed earlier). There has also been work on lithium¹⁹⁷ and potassium¹⁹⁸ batteries with Fe[Fe(CN)₆].

Finally, we would like to mention a recent report on the first examples of thiocyanates with the ReO₃-type structure¹⁹⁹. The thiocyanate systems have the general composition M^III[Bi(SCN)₆] (with M = Fe, Cr, Sc), and there is strict alternation of Bi^III with the trivalent transition metal ions. This ordering is not surprising, given the expected local bonding preference between sulfur and Bi^III. These materials have band gaps in the visible or infrared regions, with the iron compound being as low as 1.20 eV, and are therefore strongly coloured and might be useful for applications that involve light harvesting. The A-site cavity is expected to be even larger than those in the cyanides described above; however, the porosity of thiocyanate systems is reduced owing to substantial monoclinic distortions of the hypothetical cubic structures. Nevertheless, the Cr^III compound exhibits reversible adsorption and desorption of water, forming a monohydrate. As in some of the other cyanides, the guest molecules influence thermal expansion; however, unlike cyanides, there is no NTE in these systems.

Borohydrides.

M^III borohydrides, M(BH₄)₃, sometimes crystallize in the ReO₃-type structure depending on the synthetic route and the size of the metal ion. A well-studied example is Y(BH₄)₃ (FIG. 7a), a promising hydrogen-storage material that is attractive because it degrades to H₂ gas and solid YB₄ under 1–5bar of partial hydrogen pressure (that is, a typical operating condition of a hydrogen-storage system)^200–202. Unlike other M^III borohydrides, which have common by-products like elemental boron or diborane, YB₄ is more easily converted back to Y(BH₄)₃, enabling a charge–discharge cycle²⁰³. Crystallographically, Y(BH)₄ is reminiscent of the oxide ReO₃-type phases, because it has two ReO₃-type polymorphs, α and β, which are both generated during ball-milling and coexist at room temperature. However, the denser and more distorted α-Y(BH₄)₃ phase can be converted to the less dense and cubic β-Y(BH₄)₃ phase upon heating to 433–453 K, ultimately decomposing at temperatures above 463 K. However, in contrast with the oxides, both phases show monotonic positive thermal expansion.

Fig. 7 |. ReO₃-type compounds with polyatomic linkers on the X-site.

a | Crystal structure of α–Y(BH₄)_3• Bonds are drawn between the Y and B atoms to emphasize the ReO₃-type structure, although these bonds are not present. In fact, the bonding between Y and H atoms guides the structure to be ReO₃-type²⁰⁰. Atom legend: yttrium, grey; boron, brown; hydrogen, white. b | Representative crystal structure with the ReO₃-type structure of α–M(H₂PO₂)₃, shown for M = Ga in the P2₁/n space group (90% ellipsoids, H atoms removed for clarity)²¹¹. Atom legend: gallium, turquoise; oxygen, orange; phosphorous, beige. c | Crystal structure of Fe(HCOO)₃ with interstitial CO₂ (water removed for clarity)²²⁰. Atom legend: iron, green; oxygen, orange; carbon, brown; hydrogen, white. d | Crystal structure of In(im)_3• The imidazolate (im) anions arrange in an alternating pattern in In(im)_3• to accommodate their size. Atom legend: indium, grey; nitrogen, blue; carbon, brown; hydrogen, white.

A systematic study of the M^III–BH₄ reaction system with M = lanthanide²⁰⁴ demonstrated the importance of the ionic radius of the M metal in determining whether the ReO₃-type structure is formed. Using ball-milling with a LiBH₄ precursor, the larger lanthanides (that is, lanthanum, cerium, praseodymium and neodymium) formed only the cubic LiM(BH₄)₃Cl structure, whereas those closer in size to yttrium (that is, antimony, gadolinium, terbium, dysprosium, erbium and ytterbium) all formed the α-Y(BH₄)₃ structure. The elements samarium, erbium and ytterbium are also stable in the β-Y(BH₄)₃ structure under certain conditions. Further experimentation yielded the distorted ReO₃-type M(BH₄)₃ (M = La, Ce) through the reaction of MCl₃ and LiBH₄ in toluene at room temperature, followed by extraction of M(BH₄)₃ using dimethyl sulfide [S(CH₃)₂] to form a solvated phase. Subsequent loss of S(CH₃)₂ from the adduct yields the M(BH₄)₃ phase²⁰⁵. The S(CH₃)₂ templating strategy combined with halide-free reagents (that is, a rare-earth hydride and S(CH₃)₂•BH₃) was then applied to generate new structures, including the cubic $Pa\overline{3}$ α-Pr(BH₄)₃ and α-Nd(BH₄)₃ structures²⁰⁶, and α-Ce(BH₄)₃,β₂-Pr(BH₄)₃,α-Lu(BH₄)₃ and β-Pr(BH₄)₃ (REF.²⁰⁰). The structures of the S(CH₃)₂-adduct intermediates as layered phases, reminiscent of layered perovskites, were also identified²⁰⁷. Although the ReO₃ phases are not direct precursors, the related Li(M(BH₄)₃) Cl phases may be used as fast lithium-ion conductors for solid-state battery electrolytes and gas storage²⁰⁸, with some lithium borohydride phases having been tested in devices²⁰⁹.

Hypophosphites.

Until recently, the compound V(H₂PO₂)₃ was the only example of a hypophosphite-containing ReO₃-type compound²¹⁰. From our recent work, V(H₂PO₂)₃ is now understood to be a member of a polymorphic family of ReO₃-type materials, M(H₂PO₂)₃, where M = Al, Ga or V (REF.²¹¹) (FIG. 7b). There are four polymorphs seen in this family (α, β, γ and δ), with each displaying different degrees of tilts and shifts of the M octahedra. Furthermore, the preference for each polymorph is determined by M, with each M(H₂PO₂)₃ forming at least two of the four polymorphs. The high-pressure (above 1 GPa) δ phase has been observed for Ga(H₂PO₂)₃, which prefers the less dense α phase at standard temperature and pressure. Synthetic control of each polymorph as a pure phase has yet to be achieved; however, to obtain at least one pure polymorph in each metal system, an acid-soluble oxide precursor should be used (such as γ-Al₂O₃ instead of corundum for the aluminium system). Interestingly, Al(H₂PO₂)₃ is an excellent bromine-free flame retardant in polymer blends²¹². As the structures of two polymorphs were only just reported for this system²¹¹, the possibility that one polymorph may perform better as a flame retardant than the other has yet to be explored.

Summary for inorganic structures.

Inorganic ReO₃-type materials are numerous and diverse. They range from single X-atom compounds, such as ReO₃ and ScF₃, to those with multiatom linkers, such as Ga(CN)₃ and Al(H₂PO₂)₃. In addition to compositional diversity, the properties are varied, although there are unifying themes between many compounds. These common themes include the sensitivity of magnetic and electronic properties to the M–X–M bond angles, and the ability to incorporate cations or neutral molecules in the A-site cavity. There are also many avenues for future research in this growing area. One example is to expand the families of double ReO₃-type materials; for example, currently only single-cation hypophosphites are known, but creating II-IV double ReO₃-type materials may introduce new properties into the family. In addition, the discovery of entirely new families of materials is possible. One example would be the azide (az) compounds M(az)₃, which may be explosive but could be promising as high-energy materials. Dicyanamides containing N(CN)₂⁻ are also of interest; these materials are known to form as perovskites²¹³ but have yet be realized as an ReO₃-type material.

Metal-organic frameworks

We have seen in the previous section that there are several inorganic systems with the ReO₃-type structure in which the anionic linkers are polyatomic. Such compounds are an interesting variation on the perovskite structure type because the vacant A-site may create a space that is large enough to accommodate adsorbed solvent or small gas molecules. This behaviour is seen in the cyanides and the thiocyanates, although the cavity in the hypophosphites is too small for even monatomic neon²¹¹. As the cavities defined by the larger molecular X-sites may even be large enough to deliver permanent porosity, there is a similarity between such systems and MOFs. Therefore, it is not surprising to find that there are several examples of ReO₃-type materials in which the linker is an organic anion. Such materials can be properly regarded as MOFs. Examples of such systems include materials based on a wide variety of organic linkers, such as formates, azolates, guanidinates and other, more complex ligands. We shall discuss these materials below, including some examples in which the B-site cation is replaced by a polyatomic cation which preserves the ReO₃-type structure by acting as an octahedral node that is linked in 3D by suitable organic anions.

The nomenclature for these materials in the MOF literature is varied, and includes the use of the terms pcu, α-polonium and reo networks. For simplicity, we shall largely refer to them as ReO₃-type structures.

Formates.

ABX₃ perovskite-type phases, where X = (HCOO)⁻ (formate) and B (or M) = Mg, Mn, Fe, Co, Ni, Cu, or Zn, have been extensively studied, as they are easily prepared using solution synthesis and show a wide range of interesting ferroelectric, magnetic and multiferroic properties^214–216. The classical Goldschmidt tolerance factor equation²¹⁷, which predicts the relative radii of cations and anions that are compatible with simple inorganic perovskite formation, has been extended to hybrid perovskites^218,219 and can be used to predict the sizes of the A cations that will stabilize the perovskite structure in systems such as AM^II(HCOO)₃• Because the cavity is quite substantial, large protonated amines, such as dimethylammonium, ${({\text{CH}}_3)}_2{\text{NH}}_2^{+}$, are required. Although the tolerance factor equation is not strictly applicable to ReO₃-type structures, it is not surprising to find that ReO₃-type systems of composition M^III(HCOO)₃ have been reported, albeit only in the presence of neutral guest molecules that occupy the A-site cavities.

In 1965, it was reported that V(HCOO)₃•HCOOH crystallizes in the ReO₃-type structure²²⁰, but a full structure determination for this compound has not been performed to date. However, the powder diffraction pattern²²⁰ was indexed on a body-centred cubic structure that is consistent with M^III formates reported more recently²²¹. In addition, some properties of V(HCOO)₃•HCOOH, such as density, are close to the values reported for the Fe(HCOO)₃•solvent phase (V³⁺ and Fe³⁺ having similar atomic weights and radii))²²¹. The neutral formic acid molecule, HCOOH, is expected to occupy the A-site.

Recent work²²¹ on the M^III(HCOO)₃ systems(M = Al, Fe, Ga, In) confirmed that these phases, which can be readily formed by solvothermal or reflux methods, adopt an ReO₃-type structure with neutral A-site occupants assigned as combinations of H₂O, CO₂ and HCOOH (FIG. 7c). All of these phases crystallize in the cubic $Im\overline{3}$ space group with a = 11.4–12.2 Å. Unlike other carboxylate MOFs, the molecules occupying the A-sites in the M^III(HCOO)₃ systems could not be liberated while keeping the framework intact, suggesting that these molecules may have a structural role through strong hydrogen bonding or that the M–O bonds are insufficiently strong to stabilize the framework in the absence of guests. An alternative form of the Fe(HCOO)₃•guest ReO₃-type phase was also reported²²², crystallizing in the trigonal $R\overline{3}c$ space group with a = 8.2 Å, c = 22.6 Å. It exhibits weak ferromagnetism below 50 K.

The formate ReO₃-type compounds could perhaps be regarded as the simplest MOF systems and can be made from inexpensive, Earth-abundant starting materials. Interestingly, they form preferentially in the presence of CO₂, and Al(HCOO)₃•xCO₂/yH₂O can be obtained by bubbling CO₂ through an aqueous solution containing Al(OH)₃ and formic acid²²¹. The fully stoichiometric phase, Al(HCOO)₃•CO₂, has yet to be achieved, but with a CO₂ loading of greater than 21 wt%, it is a possible material for CO₂ storage.

Nitrogen-containing organic linkers.

In light of what has been reported for the formates, where the ReO₃-type MOFs contain metal–oxygen bonds, it is reasonable to expect that MOFs with the ReO₃-type structure might also form with nitrogen-containing organic linkers that are capable of metal–nitrogen bonding. This bonding has so far been realized for guanidinates, 1,2,4-triazolates and imidazolates, although there are other systems that might be feasible.

Only one guanidinate with the ReO₃-type structure is known to exist, Yb(CN₃H₄)₃ (REF.²²³). This phase was synthesized in liquid ammonia and crystallizes in the cubic $Pn\overline{3}$ space group with a = 13.5 Å. Braced by the extensive hydrogen bonding between guanidinate anions, it has a relatively low density (1.9 g cm⁻³) and possible voids in its structure. Unlike many of the simple inorganic ReO₃-type systems, Yb(CN₃H₄)₃ shows positive thermal expansion rather than NTE. It is interesting to note that in perovskite and perovskite-related materials, guanidine can take the role of an anionic linker (guanidinate, as in Yb(CN₃H₄)₃) and an A-site cation (guanidinium, ${\text{C(NH}}_{\text{2}}{)}_3^{+}$, as in formate perovskites²²⁴ and vacancy-ordered double perovskites²²⁵). Control of pH is important in determining which of these two roles it assumes, as a strongly alkaline environment is needed to stabilize the gaunidinate anion.

Although azolates are a well-known building block for MOFs (particularly zeolitic imidazolate frameworks, in which imidazolates are the linkers), they are primarily used in tetrahedral coordination with M^II cations. Nevertheless, there are a small number of ReO₃-type structures based on azolates. For example, Yb(tz)₃(tz = 1,2,4-triazolate) was prepared from ytterbium metal and a melt of the azole, crystallizing in the cubic $Pm\overline{3}m$ space group with a = 6.8 Å (REF.²²⁶). Yb(tz)₃ is not strictly an ReO₃-type material, because some of the triazolate ligands coordinate in a bidentate manner; however, the overall architecture is ReO₃-like. This phase is well packed and shows no accessible porosity. Ga(tz)₃ was later reported²²⁷, forming at the interface between the immiscible liquid Ga metal and liquid triazole. This phase crystallizes in the cubic I23 space group with a = 12.3 Å. Gas sorption testing showed that Ga(tz)₃ is also a dense framework with no accessible porosity. We are not aware of any ReO₃-type structure based on 1,2,3-triazolate linkers.

More recently, imidazole was successfully used to form In(im)₃•xG (G = guest) ReO₃-type phases via different pathways, including ionothermal, solvothermal and solventless syntheses²²⁸. Three phases were obtained — phases I, II and III — with structural parameters of $Im\overline{3}$, a = 13.0 Å; $R\overline{3}$, a = 18.9 Å, c = 10.5 Å; and $R\overline{3}$, a = 9.1 Å,c = 22.3 Å (FIG. 7d). Although gas sorption showed no accessible porosity, varying amounts of unbound neutral molecules were trapped inside the framework cavities of phases I and II. Phase III was reported as a dense, guest-free structure. All structures were solved by powder X-ray diffraction, and the identities and quantities of neutral guest molecules in phases I and II were assigned by NMR spectroscopy to a range of molecules, including solvent and products of solvent decomposition²²⁸. The structures were distinguished by different octahedral tilting patterns. Phases I and II showed a reversible, discontinuous, hysteretic phase transition at ~363 K. The synthesis method affected the transition temperature, likely owing to the different guest molecules trapped within the framework. It seems unlikely that In^III is the only trivalent cation capable of forming ReO₃-type networks with imidazolate; thus, this is an interesting area for future exploration.

Systems with complex linkers.

There are several examples of positively-charged ReO₃-type MOFs with large organic linkers and charge-compensating anions in their A-site cavities²²⁹, but these are more like perovskites than ReO₃ systems (albeit with inverse polarity). These structures are sometimes referred to in the MOF literature as having an α-polonium-type structure (α-Po being the only simple cubic metal structure), irrespective of their charged framework and the presence of anions in the A-site cavities. An important example is provided by the large, neutral bis-imidazole ligands (FIG. 8), which form ReO₃-type frameworks with Cd²⁺ nodes²³⁰. It is particularly interesting that the frameworks are triply interpenetrating, presumably to reduce the unoccupied space in the channels. Such behaviour is also seen in some MOF-5-related materials discussed below. The positive charges of the frameworks in these structures are balanced by nitrate or tetrafluoroborate anions, which sit in the small cavities created by the interpenetrating ReO₃ nets. One would imagine that neutral frameworks of this type could be obtained using a trivalent cation in combination with anionic ligands.

Fig. 8 |. Metal–organic framework with interpenetrating structure.

Triply interpenetrating metal–organic framework based on a bis-imidazole ligand. Adapted with permission from REF.²³⁰, Royal Society of Chemistry.

MOFs with polyatomic B-site cations.

In this final section on MOFs with the ReO₃-type structure, we shall focus on a more complex group of materials in which the cations on the B-site are polyatomic clusters linked by organic ligands. The most iconic example is MOF-5, where tetrahedral ${\text{Zn}}_4{\text{O}}_6^{+}$ clusters are connected by 1,4-benzenedi-carboxylate (1,4-bdc) anions to form a 3D network of composition [Zn₄O](1,4-bdc))₃ (REF.¹⁶) (FIG. 9a). This important discovery from Yaghi’s group led to the concept of reticular synthesi^231,232, whereby structures with even larger cavities could be obtained using longer linkers (FIG. 9b). By so doing, it is possible to tune the porosity of the MOF system for specific applications. This family of MOFs is, therefore, justifiably famous for being a model for the optimization of porous frameworks for applications in separation and catalytic processes²³³. As with many ReO₃-type structures, MOF-5 itself exhibits NTE²³⁴. We note that interpenetration is often found in structures containing longer linkers, which are used to synthesize some isoreticular MOFs, although steps can be taken to mitigate this outcome.

Fig. 9 |. MOFs with polyatomic B-site cations.

a | Structure of the metal–organic framework (MOF) MOF-5, with a Zn₄O unit on the octahedra B-site node and 1,4-bezenedicarboxylate anions on the X-site, of an ReO₃-type structure¹⁶. This structu light blue; oxygen, orange; carbon, brown; hydrogen, white. b | Isoreticular MOFs (IRMOFs), where IRMOF-1 = MOF-5. Atom legend: zinc, light blue; oxygen, red; carbon, black; yellow, void space. Panel b is adapted with permission from REF.²⁵³, Royal Society of Chemistry.

There can be endless variations on the MOF-5 theme if we allow for the possibility that the 1,4-benzenedi-carboxylate linker might bear substituents on the benzene rings. Yaghi and co-workers reported examples including −NH₂, −Br, −Cl and −NO₂, and referred to such systems as multivariate MOFs on account of the range of compositional variations that are possible, such as combining eight distinct functionalities into a single phase^235,236. The chemical variations are not solely of academic interest because it is possible to tune the adsorption behaviour of MOFs for particular applications. For example, by fine-tuning the composition of the MOF, the selectivity for CO₂ adsorption can be enhanced by up to 400% compared with CO adsorption²³⁵. Although we are not aware that this class of materials is being used commcrcully. the concept) described ire being used in other areas of MOF research.

There are symmetry constraints on the types of compunds.that can form an ReO₃-type network, because the building unit at the B-site node must be compatible with 6-fold connectivity²³⁷. This 6-fold connectivity is achieved in MOF-5 by using the two oxygen atoms from one. end of the 1,4-benzenedicarboxylate Carboxylate linkers to bond, to two different zinc ions in the cluster. In spite of this constraint, there are many other examples of systems that adopt the ReO₃-type structure (which is often referred to as the pcu topology in the MOF literature, although this appellation is sometimes interpreted more loosely than we have done in this Review). Eye-catching examples include a system in which the nodes use Cu₂(CO₂)₄ paddlewheel clusters as vertices²³⁸, and MFU-4 in which octahedral nodes based on (Zn₅Cl₄)⁶⁺ are linked by linear bis-triazolate ligands²³⁹. To give a sense of the scope of this area, we note that Snurr and co-workers have explored the methane storage and delivery capacity of 122,835 hypothetical pcu frameworks²⁴⁰ from the MOF database of Wilmer et al.²⁴¹. Although the majority of these frameworks have not been synthesized, a small number of them are predicted to have exceptional properties.

Many other MOFs that are described in the literature as of pcu type are not included here because they do not preserve the cubic or pseudo-cubic architecture of the ReO₃-type structures. Typically, they have different linkages along different axes, such as the pillared–layered phases^242,243 and other structures based on paddlewheel nodes²⁴⁴.

Summary for ReO₃-type MOFs.

The study of MOFs with the ReO₃-type structure is less well developed than the inorganic area, but is a rapidly developing field full of exciting opportunities. We note, in particular, that the ability to tune the size of the A-site cavity by changing the length of the organic linker can be achieved in MOFs but is not practical in inorganic systems. Consequently, the MOF materials are far more versatile for adsorption applications. Similarly, the option of tuning the chemical environment of the A-site cavity by changing the substituents on the linker ligands means that it is possible to, for example, make a cavity more polar or more acidic than it would be with a chemically unmodified linker. This versatility is usually not possible with inorganic frameworks. However, the inorganic materials are usually more thermally stable, and they typically offer better mechanical stability than is found in MOF systems²⁴⁵.

Concluding remarks

The chemical diversity of materials with the ReO₃-type structure is much greater than we had imagined when we began to think about this article in mid 2018. Furthermore, their properties and applications, both actual and potential, have also surpassed our expectations. The timeline shown in FIG. 2 highlights some of the important systems that have been developed over the last 80 years or more, from their initial discovery or structural characterization to the demonstration of their most striking properties. In addition to the remarkable range of their behaviour, we are struck by the long gaps between the initial discoveries of several of the materials and the establishment of their functionalities. In the case of ScF₃, for example, 70 years elapsed between the first structural characterization in 1939(REF.²⁴⁶) and the recognition of its outstanding NTE behaviour in 2010. Several new ReO₃-type families have been reported in the past decade, including the borohydrides, hypophosphites, guanidinates and imidazolates, although the properties of these families are yet to be explored.

An exciting discovery in 2015 revealed the superconducting nature of hydrogen sulfide, H₂S.H₂S transforms to H₃S under high pressure, and this new phase is superconducting with a critical temperature of 203 K (REF.²⁴⁷). This property was predicted in 2014 (REF.²⁴⁸) and subsequent work in 2016 indicated that the superconducting H₃S phase adopts a doubly interpenetrating ReO₃structure²⁴⁹. More recently, however, others have claimed that the superconducting phase is (SH⁻)(SH₃⁺) and adopts the perovskite structure with (SH⁻) on the A-site²⁵⁰, and density functional theory calculations broadly support the idea of a disproportionation of H₂S (REF.²⁵¹).

We noted at the beginning of the article that most of the ABX₃ perovskite families can form ReO₃ analogues, and vice versa, so it is appropriate at this point to revisit this issue and identify the structures where this has not yet been established. TABLE 1 presents several cases where the analogues are not known, or even where neither form is known but could exist. In some cases, such as the ReO₃ form of BiI₃, the compound prefers a layered structure, which is presumably stabilized by van der Waals interactions between the iodideions. For the hypothetical A^IB^II(OH)₃, it might be that the protons that protrude into the A-site cavity render it unsuitable for hosting a metallic cation. However, there are several nitrogen-containing linkers that might lend themselves to the formation of new ReO₃-type or perovskite families, although we note that some of these may be high-energy materials, such as the azides and the tetrazoles. Future work in these areas is needed and has the potential to produce new ReO₃-type phases with interesting and unusual properties.

Table 1 |.

Unknown ReO₃ analogues of known perovskite families or vice versa

Perovskite family	ReO3 analogue
(AmineH)PbX3	BiX3 (not reported)
AIBII(OH)3 (not reported)	MIII(OH)3
(AmineH)MII(N3)3	MIII(N3)3 (not reported)
(AmineH)MII(gua)3 (not reported)	MIII(gua)3
(AmineH)MII(im)3 (not reported)	MIII(im)3
(AmineH)MII(1,2,4-triazole)3 (not reported)	MIII(1,2,4-triazole)3
(AmineH)MII(1,2,3-triazole)3 (not reported)	MIII(1,2,3-triazole)3 (not reported)
(AmineH)MII(tetrazole)3 (not reported)	MIII(tetrazole)3 (not reported)
(AmineH)MII(dicyanamide)3	MIII(dicyanamide)3 (not reported)

The unknown phases are indicated as not reported. In some cases, such as with 1,2,3-triazole, both are unknown but might be expected to form. gua, guanidinate; im, imidazolate.