Expanding frontiers in materials chemistry and physics with multiple anions. — TEI-tagged view

Hiroshi KageyamapersName, Katsuro HayashipersName, Kazuhiko MaedapersName, J. Paul AttfieldpersName, Zenji HiroipersName, James M. RondinellipersName, Kenneth R. PoeppelmeierpersName (2018date). “Expanding frontiers in materials chemistry and physics with multiple anions..” Nature Communicationstitle·j.

Object of study — mixed-anion compoundsterm·dom, mainly oxide-derived, as a materials platform

Research question — what multiple anions contribute to the synthesis, characterisation and properties of solid-state materialsterm·dom

Contribution — a reviewterm·mth of progress, status and prospects of mixed-anion compoundsterm·dom across synthesis, characterisation and properties

Full text — tagged

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Expanding frontiers in materials chemistry and physics with multiple anions.

Abstract During the last century, inorganic oxideterm·dom compounds laid foundations for materials synthesis, characterization, and technology translation by adding new functions into devices previously dominated by main-group element semiconductor compounds. Today, compounds with multiple anions beyond the single-oxide ion, such as oxyhalides and oxyhydridesterm·key, offer a new materials platform from which superior functionality may arise. Here we reviewterm·mth the recent progress, status, and future prospects and challenges facing the development and deployment of mixed-anion compoundsterm·dom, focusing mainly on oxide-derived materials. We devote attention to the crucial roles that multiple anions play during synthesis, characterization, and in the physical properties of these materials. We discuss the opportunities enabled by recent advances in synthetic approaches for design of both local and overall structure, state-of-the-art characterization techniques to distinguish unique structural and chemical states, and chemical/physical properties emerging from the synergy of multiple anions for catalysisterm·key, energy conversion, and electronic materials.

Introduction The continuing growth of many modern technologies is driven by the development of functional solid-state materialsterm·dom, such as metal oxidesterm·dom, fluorides, and nitrides that adopt a range of structural types and compositions. The accumulation of knowledge based on experimental data (or at times “chemical intuition”) and computational modeling and validations has led to extensive knowledge of these “single-anion” materials and affords further prediction of properties. Most of these results derive from variations in metal cation chemistry, as opposed to the anion, when examining structure-property relationships.

A multiple or mixed-anion compoundterm·dom is a solid-state materialterm·dom containing more than one anionic species in a single phase, such as oxyfluoridesterm·dom (oxide-fluorideterm·dom) and oxynitridesterm·key (oxide-nitride). Unlike oxidesterm·dom, which exhibit diverse chemistries and structures often known from mineralogy, the structures of most mixed-anion compoundsterm·dom, among other aspects, are less explored with much to learn. This is readily seen when looking at the local structure of these compounds where the metal cation is bonded to more than one anionic ligand to form a heterolepticterm·key polyhedron (Box 1 ). The different anionic characteristics, such as charge, ionic radii, electronegativity, and polarizability (Table 1 ) add new dimensions to control and tune the electronic and atomic structure of materials, which may support phenomena inaccessible to a single-anion analog. Table 1 Basic parameters of anions-forming elements and their ions Atomic properties Anionic properties Isotope with non-zero nuclear spin, I a Natural abundance (%) b Neutron coherent scattering length (fm) c Ionization energy (kJ/mol) d Electron affinity (kJ/mol) e Pauling’s electronegativity f Formal valence/electronic configuration Coordination number/ionic radius (pm) g Polarizability (Å 3 ) h H −3.7390 1312.0 72 2.20 –1 127–152 1 H 1/2 99.985 −3.7406 [He] 2 H 1 0.015 6.671 N 9.36 1402.3 –8 3.04 –3 IV 146 14 N 1 99.63 9.37 [Ne] O 5.803 1313.9 141 3.44 –2 II 135 1.68 (MgO) ( 16 O) 99.762 5.803 (–780) [Ne] III 136 3.17 (BaO) 17 O 1 0.04 5.78 IV 138 1.79 × 10 −1.766/V ( 18 O) 0.2 5.84 VI 140 VIII 142 F 19 F 1/2 100 5.654 1681.0 328 3.98 –1 II 128.5 0.89 (LiF) [Ne] III 130 1.36 (CsF) IV 131 0.82 × 10 −3.000/V VI 133 P 31 P 1/2 100 5.13 1011.8 72 2.19 −3 212 [Ar] S 2.847 999.6 200 2.58 −2 VI 184 4.60 (MgS) ( 32 S) 95.02 2.804 (–492) [Ar] 6.41 (BaS) 33 S 3/2 0.76 4.74 Cl 9.5770 1251.2 349 3.16 –1 VI 181 2.88 (LiCl) 35 Cl 3/2 75.77 11.65 [Ar] 3.47 (RbCl) 37 Cl 3/2 24.23 3.08 3.88 × 10 −1.800/V As 75 As 3/2 100 6.58 947.0 78 2.18 –3 222 [Kr] Se 7.970 941.0 195 2.55 –2 VI 198 77 Se 1/2 7.6 8.25 [Kr] Br 6.795 1139.9 325 2.96 –1 VI 196 3.99 (LiBr) 79 Br 3/2 50.69 6.80 [Kr] 4.67 (RbBr) 81 Br 3/2 49.31 6.79 Sb 5.57 834 103 2.05 –3 [Xe] Te 5.80 869.3 190 2.10 –2 VI 221 [Xe] I 127 I 5/2 100 5.28 1008.4 295 2.66 –1 VI 220 [Xe] Bi 8.532 703 2.02 –3 [Rn] a Ref. 105 ; isotopes with zero nuclear spin are indicated in parentheses b Ref. 105 c NIST center for neutron research, neutron scattering lengths and cross sections, https://www.ncnr.nist.gov/resources/n-lengths/ d Ref. 106 e Ref. 106 ; second electron affinity is indicated in parentheses f Ref. 106 g Ionic radii with 107 and without 106 specifying the coordination number. Ionic radii for H are derived from those discussed in ref. 108 h Values with chemical formula in parentheses are those experimentally estimated in compounds with rock salt structure 109 . The equations as a function of the anion molar volume, V , evaluated in ref. 110 Such anion-centered chemistry and physics is still in its infancy; there is much unexplored space, making it perhaps the most untapped field of materials sciences and giving new challenges and opportunities. In this reviewterm·mth, we aim to describe the current status and scope, as well as outline future prospects and challenges surrounding mixed-anionterm·key (mostly oxideterm·dom based) compounds, in particular, focusing on crucial roles of multiple anions in synthesis, characterization, and chemical and physical properties. Note that we had to be selective in materials and references because of the limited space. We provided mainly reviewsterm·mth or selected references, which could be an entry point to the literature search for readers who need additional information.

Mixed-anionterm·key directed strategies Understanding of mixed-anion compoundsterm·dom is still growing, but recent studies have unveiled several key features that are otherwise inaccessible in traditional single-anion compounds, as summarized in Fig. 1 . Replacing oxideterm·dom ligands in coordination octahedra or tetrahedra with other anions can differentiate the binding energy (Fig. 1e ), which may benefit chemical reaction and anionic diffusion (Fig. 1f ). It might also cause a (local) symmetry breaking (Fig. 1d ) or create a cis / trans degree of freedom (Fig. 1c ). The latter is a familiar ingredient in coordination chemistry, but less so in solid-state chemistry. Additionally, the crystal field splitting (CFS) can be tuned to the extent that is only allowed in coordination complexes, while retaining the original polyhedral shape and connectivity (Fig. 1a ). An extensive modification of band (electronic) structures is also noteworthy, leading to a reduced dimensionality (Fig. 1g ) and an upward shift of valence band maximum (VBM) (Fig. 1b ). Fig. 1 What mixed-anion compoundsterm·dom can do (Concepts 1a–1h). a Extensive tuning of CFS. Replacement of one oxygen with a different anion allows extensive tuning of CFS even when the octahedron stays rigid. b Non-oxide anion with lower electronegativity (vs. oxideterm·dom) in semiconductors raises the VBM and narrows the band gap, affording visible light applications like water splittingterm·key catalysisterm·key 51 , 52 and pigmentation 49 . c Local degree of freedom. An MO 4 X 2 octahedron has cis and trans geometries, major parameters widely exploited in coordination chemistry, but less so in solid-state chemistry. When MO 4 X 2 octahedra with cis or trans preference are connected to form an extended lattice, various non-trivial structures can appear, some of which have ‘correlated disorder’ 34 , 38 . d Local coordination asymmetry. The O h symmetry of the rigid octahedron is lost by replacing one and three ligands, leading to C 4 and C 3 symmetry. e , f Covalency and ionicity can be tuned to acquire desired functions. A weakly bonded ligand to a metal centre can generate functions related to anion diffusion (anionic conductivity) and anion reaction at the surface (catalysisterm·key), whereas the structural stability is secured by strongly bonded counter ligands 13 , 69 , 70 . g Dimensional reduction. Alternate stacking of layers of different anions, which can be rationalized utilizing, e.g., HSAB concept and Hume-Rothery rules 78 , have potential to enhance two-dimensionality, leading to novel properties, including high -T c superconductivity 81 , 82 , 103 . h Inclusion of molecular anions further widens possibilities. Available parameters, include anisotropic shape, magnetic moment (e.g., S = 1/2 moment in O 2 − ) and additional (anisotropic) bonding (e.g., bonding to hydrogen in BH 4 – ) 99 – 101 Oxyhydridesterm·key (oxideterm·dom hydridesterm·key), containing oxideterm·dom and negatively charged hydrideterm·key (H – ) anions, are rare but can be remarkable materials. Several features specific to hydrideterm·key are given in Fig. 2 . Hydrogen is the simplest (and lightest) element with one electron and one proton, giving the hydrideterm·key anion distinct characteristics that differentiate it from other anions. For example, its bipolar nature and moderate electronegativity allow covalent, metallic, and ionic bonding, depending on the electronegativity of the element with which hydrogen bonds. This is schematically represented by the unconventional periodic table of elements (Fig. 2b ) 1 , where values of electronegativity, ionization potential, and electron affinity are shown in the upper left, lower left, and lower right corner of each box. Related to this, the extraordinary flexibility in size of hydrideterm·key (Fig. 2a ) and possible reactions involving the zwitterionic nature (Fig. 2d ) may bring about unprecedented functions. The flexible nature of hydrideterm·key is also evident in its polarizability, as the refractive index of LiH (1.985) is significantly larger than that of LiF (1.392) despite the fewer number of electrons. Finally, H – is the only anion which does not possess p orbitals in the valence shell. The lack of p orbitals in the outermost shell (Fig. 2c ) significantly distinguishes its chemical bonding nature and its magnetic interaction with other anions. Fig. 2 Specific features of hydrideterm·key anion H – (Concepts 2a–2d). a As opposed to other anions, H – is highly flexible in size (right, exaggerated for clarity), with ionic radii of ∼130-153 pm found in metal hydridesterm·key. This means that H – (or more precisely H δ– ) can adapt itself to a given local environment. This appears to hold for oxyhydridesterm·key 12 and is important for the hydrideterm·key detection and characterization by 1 H-NMR (Fig. 4b ) 44 . A high-pressure study revealed that H – is extremely compressible 9 . b A periodic table of elements, taken from ref. 1 . Justifications of hydrogen positioning above carbon arise from a half filled outer shell and a similarity in electronegativity to group IV elements (C, Si…). c The lack of π symmetry in H – 1 s orbital allows this ligand to act as a “π-blocker” (or orbital scissors) with respect to t 2g orbitals of a transition metal, leading to the dimensional reduction in Fig. 1g 9 , 89 . A fairly strong σ bonding is suggested between e g and H – 1 s orbitals 8 . d Hydrideterm·key anion is regarded as a highly labile ligand, which, combined with the electron donating nature of hydrideterm·key, allow versatile opportunities for oxyhydridesterm·key, including hydrideterm·key anion conductivity 70 , topochemical reactions 13 , 14 , and catalysisterm·key 95 . Shown in this panel is a theoretically proposed non-trivial hydrideterm·key diffusion process in SrTiO 3 104 , involving electron transfer from/to the titanium cation, being analogous to the so-called proton coupled electron transfer (PCET)—“electron coupled hydrideterm·key transfer” (ECHT). Fixation of such transient “two-electron released state” is realized in H – ion-doped 12CaO·7Al 2 O 3 by UV-light excitation 47 Synthesis beyond heat and beat Conventional inorganic materials are mostly oxidesterm·dom, due to the fact that the Earth’s atmosphere contains mainly reactive oxygen (and inert nitrogen). Thus, metal oxidesterm·dom are conventionally synthesized by high-temperature solid-state reactions, sometime called ‘heat and beat’ (or ‘shake and bake’) processing. A major difficulty in preparing mixed-anion compoundsterm·dom in the same way lies in the differing volatilities of precursors (oxidesterm·dom, chlorides, hydridesterm·key, and so on), so simple heating of mixed starting reagents often ends up with single-anion compounds, though some can be prepared in air (e.g., LaCl 3 + 0.5O 2 → LaOCl + Cl 2 ). For this reason, the preparation of mixed anionterm·key compounds often requires controlled atmospheres, such as in vacuum or under various flowing gases (Cl 2 , F 2 , NH 3 , CS 2 , and so on) (Fig. 3a ) or exploits alternative synthesis methods, including soft-chemistry (Fig. 3b ), solvothermal synthesis, or thin-film growth techniques (Fig. 3c ) and high-pressure synthesis (Fig. 3d ). Fig. 3 Synthetic approaches for mixed anionterm·key compounds. a Traditional high-temperature solid-state reactions. Controlled atmospheres, such as flowing gases (NH 3 , Cl 2 , CS 2 , and so on) and in a vacuum are often necessary. Gas-phase or surface reactions may be important. For example, owing to the dissociation of NH 3 to H 2 and inert N 2 at elevated temperatures, processing conditions, such as an ammonia flow rate need to be carefully chosen. b Topochemical reactions to allow a rational design of structures (Fig. 1f ). Low-temperature treatment of oxidesterm·dom with some reagents cause different anions to insert or exchange while maintaining the structural features. Multistep reactions have been also accessible 13 , 14 . c Epitaxial thin film growths and solvothermal reactions as a bottom-up process. Chemical bonding from ions of a substrate lattice yield metastable phases 19 . Local geometry can be manipulated by applying tensile or compressive strain from the substrate 20 , 21 . Solvothermal reactions offer an opportunity to prepare compounds with well-defined local structures. High throughput screening is possible with the Teflon pouch approach. d High-pressure reactions. High pressure can prevent some reagents from dissociation or evaporation (upper) 22 – 26 , 41 , and also stabilize dense structures (lower) 27 . e Computational tools. In particular, the rapid advancement of computational methods provides unprecedented opportunities for predicting and understanding mixed-anion compoundsterm·dom. DFT = density functional theory, MC = Monte Carlo, ML = machine learning, AI = artificial intelligence For example, a high-temperature ammonolysis reaction (under NH 3 flow) is employed 2 , instead of inert N 2 , to obtain many oxynitrideterm·key semiconductors, including AMO 2 N (A = Ba, Sr, Ca; M = Ta, Nb) with a high dielectric constant due to the larger polarizability of nitrogen (Fig. 1e ) 3 . However, the ammonolysis reaction involves the dissociation of NH 3 –N 2 and H 2 (Fig. 3a ) and thus provides a highly reducing atmosphere, which gives a certain constraint on available metals. To increase the reactivity of ammonia, a microwave oven is used to generate an ammonia plasma 2 .

The high reactivity of the anionic species, often gaseous in elemental form, can conversely be an advantage in tailoring anions in extended solids at low temperature. Topochemical insertion and exchange reactions (Fig. 3b ), which provide metastable mixed-anionterm·key phases from precursors (typically oxidesterm·dom) in a rational, chemically designed manner, have been developed over the last two decades 4 . A proper choice of reagents and host structures is essential in directing reactions in a desired way. Consider for example oxyfluoridesterm·dom: a F 2 treatment can give an oxidative fluorination involving F-intercalation (e.g., LaSrMn 3+ O 4 → LaSrMn 5+ O 4 F 2 ), while poly(tetrafluoroethylene), known as Telfon, acts as a reductant and may lead to reductive fluorination involving O/F-exchange (e.g., RbLaNb 5+ 2 O 7 → RbLaNb 4.5+ 2 O 6 F) 5 , 6 .

The hydrideterm·key anion is strongly reductive in nature, with a large standard redox potential of −2.2 V (H − /H 2 vs. SHE), so a transition metal oxyhydrideterm·key appears impossible to stabilize. However, topochemical reaction using metal hydridesterm·key, such as CaH 2 has opened a new avenue, yielding as the first example LaSrCoO 3 H 0.7 (Co 1.7+ , d 7.3 ) in 2002 7 . Density functional theory (DFT) calculations revealed the presence of fairly strong σ bonding between Co e g and H 1 s orbitals 8 . On the other hand, the formation of BaTiO 2.4 H 0.6 (Ti 3.4+ ; d 0.6 ), SrVO 2 H (V 3+ ; d 2 ), and SrCrO 2 H (Cr 3+ ; d 3 ) is not readily rationalized since Ti/V/Cr t 2g and H 1 s orbitals are orthogonal (Fig. 2c) 9 – 11 . Since all the known transition-metal oxyhydridesterm·key exist with alkali and alkaline earth elements 12 , inclusion of any highly electropositive cation appears to be needed to make hydrogen with its moderate electronegativity (Fig. 2b) become negatively charged. This may explain why TiO 2 does not incorporate hydrideterm·key.

The observation of H/D exchange in BaTiO 2.4 H 0.6 when heated in deuterium gas at ~400 °C indicates the labile nature of H – (Fig. 1f ) 10 . The lability of hydrideterm·key in BaTiO 2.4 H 0.6 (and other oxyhydridesterm·key) enables further topochemical anion exchange reactions (Fig. 3b ) 11 , 13 , 14 . When BaTiO 2.4 H 0.6 is used as a precursor, the ammonolysis reaction temperature (>1000 °C) is remarkably lowered to 350 °C, yielding BaTiO 2.4 N 0.4 13 . Even N 2 flow at 400 °C gave the same product, demonstrating the ability of H – to activate the nitrogen molecule. This hydrideterm·key exchange chemistry is general, yielding other mixed-anion compoundsterm·dom, such as oxide-hydride-hydroxide BaTiO 2.5 H 0.25 (OH) 0.25 14 .

Solvothermal synthesis is a synthetic method in which reactions occur in solution (i.e., water in the case of hydrothermal synthesis) inside a sealed vessel at temperatures near the boiling point of the solvent and pressures greater than atmospheric pressure 15 . Liquid-phase transport of the reactants allows for rapid nucleation and subsequent growth of a crystalline product with controlled morphology. This method produces crystals at lower temperatures and on shorter timescales than typical solid-state reactions. It also increases the likelihood of formation of mixed-anion compoundsterm·dom (e.g., halide hydroxides, oxyhalides), which are often unfavored at higher temperatures. Solvothermal syntheses have been very successful in producing materials with acentric coordination environments that lead to noncentrosymmetric (NCS) structures having desirable properties, such as piezoelectricity, pyroelectricity, and nonlinear optical activity 16 .

Direct fluorination of oxidesterm·dom with F 2 (g) or HF(g) is quite effective with minimal risk of side products. The handling of caustic, reactive gases, however, requires particularly specialized gas-phase reactors. In contrast, hydrothermal synthesis in hydrofluoric acid, or solutions of alkali fluorides, may be the easiest and safest route. The Teflon pouch approach is an efficient process to allow for fast development of discovery–based syntheses of new materials because various reactions can be performed in separate, small Teflon reaction pouches under identical, autogeneous conditions in an autoclave (Fig. 3c ). Up to six reactions can be run in a 125 mL vessel.

Crystallographic long range ordering of oxideterm·dom and fluoride anions has historically been a challenge, but materials based on anionic coordination polyhedra [MO m F 6– m ] n – (where ( m , n ) = (1, 2) for M = V 5+ , Nb 5+ , Ta 5+ , (2, 2) for M = Mo 6+ , W 6+ , and (3, 3) for M = Mo 6+ ) have been solvothermally prepared without apparent anion-site disorder (Fig. 3c ) 16 . In the ordered perovskite KNaNbOF 5 and CsNaNbOF 5 (with the general formula AM'MX 6 (M' = alkali metal, M = 2 nd order Jahn-Teller d 0 metal)), the interactions of the [NbOF 5 ] 2– anion with the combination of Na/K or Na/Cs differ significantly. The NCS structure (KNaNbOF 5 ) maintains a larger primary electronic distortion of the [NbOF 5 ] 2– anion along with a low coordination number of the K + ion, consistent with the largest bond strain index. In contrast, the Cs + ions of the centrosymmetric structure (CsNaNbOF 5 ) can exhibit higher coordination numbers and the [NbOF 5 ] 2– anion exhibits a greatly reduced primary distortion. Theoretically, the group-theoretical method was applied to investigate anion ordering in the cubic perovskite, establishing 261 ordered low-symmetry structures, each with a unique space-group symmetry 17 . These idealized structures are considered as aristotypes with different derivatives formed by tilting of MO 6 octahedra, providing a guide for designing NCS properties.

Thin film growth of oxidesterm·dom using pulsed laser deposition (PLD) or molecular beam epitaxy (MBE) is another useful bottom-up approach to construct desired artificial lattices, which has significantly contributed to the progress of condensed matter physics in the last two decades 18 . More rarely, thin film growth has been shown to be a promising method to prepare mixed-anion compoundsterm·dom, avoiding potential problems in anion diffusion. Oxynitridesterm·key films are fabricated by nitrogen plasma-assisted PLD, while polyvinylidene fluoride (PDVF) is used to topochemically convert oxideterm·dom films to oxyfluorideterm·dom ones. TaON films grown on a (LaAlO 3 ) 0.3 (SrAl 0.5 Ta 0.5 O 3 ) 0.7 substrate adopt a metastable anatase structure with anion vacancies, leading to high-mobility electron transfer 19 . Tensile and compressive stresses from the substrate enables tailoring of the anion arrangement of a given structure. Compressively strained SrTaO 2 N films show a partial cis -to- trans conversion of TaO 4 N 2 octahedra (Fig. 3c ) 20 . An anion order/disorderterm·var transition can also be induced by strain engineering 21 . However, we note that there are still very few reports on mixed-anionterm·key films and most are thin film studies targeting optical (or surface) coating applications.

High pressure- and high-temperature conditions are typically used to stabilize dense materials through solid-state reactions or structural transformations. High-pressure reactions in sealed vessels prevent loss-of-volatile elements and so are particularly useful for anions, such as nitride to prevent loss-of-gaseous nitrogen (Fig. 3d ). Autoclaves can be used for reactions under nitrogen up to kbar pressures, but many syntheses of oxynitridesterm·key have used direct reactions between solid oxidesterm·dom and nitrides (or oxynitridesterm·key) in multi-anvil presses where pressures can be extended to 10’s of kbar (GPa) values. The spinel Ga 3 O 3 N 22 and AZrO 2 N perovskites (A = Pr, Nd, and Sm) 23 were synthesized by direct solid-state reaction between oxidesterm·dom and nitrides or oxynitridesterm·key under GPa pressures. The use of solid reagents (instead of NH 3 ) offers access to oxynitridesterm·key with middle-to-late transitions metals. A polar LiNbO 3 -type structure MnTaO 2 N with a helical spin order was recently synthesized at 6 GPa and 1400 °C 24 . A non-polar analog ZnTaO 2 N was also prepared 25 . New light atom materials have also been reported, such as the sphalerite-related boron oxynitrideterm·key B 6 N 4 O 3 synthesized from direct reaction between B 2 O 3 and hexagonal-BN at 15 GPa and temperatures above 1900 °C 26 . Pressurization of baddeleyite-structured TaON drives a transition to a cotunnite-type structure with a very high-bulk modulus of 370 GPa (Fig. 3d ) 27 .

Chemical and structural analyses Single crystal or powder diffraction methods are used to characterize many crystalline substances. A particular challenge for mixed-anionterm·key materials is to determine the distribution and degree of order-disorder of two or more anions. This complexity presents a challenge for both experiment and materials simulation (Fig. 3e ), where equilibrium structures consisting of ordered or disordered anion configurations may be used for electronic structure calculations, e.g., those based on DFT or many-body methods. Ultimately to assess the properties of a mixed-anionterm·key material, the structure must be known. To that end, a number of structure-search algorithms, including cluster expansions 28 , special quasirandom structures 29 , and genetic algorithms 30 , frequently applied to multicomponent alloys and single-anion compounds, could be used to assess phase stability and solve structures in multi-anion compounds. In combination with experimental methods (below), a more complete description of the local and crystal structure can be obtained. These methods are also important for obtaining interaction energies for effective model Hamiltonians to describe ordering and ferroic transitions 31 .

Experimentally, the anion distribution may be studied directly using the scattering contrast between the anionic elements or indirectly through the different sizes or coordination environments of the anions in the structure. Direct X-ray scattering contrast is poor between elements from the same row of the periodic table, such as N/O/F or As/Se/Br, and neutron scattering may be useful in some cases, for example, to differentiate N and O which have respective neutron scattering lengths of 9.36 and 5.83 fm (Table 1 ) in oxynitridesterm·key. Neutron scattering also enables the positions of these light atoms to be determined more precisely in the presence of heavy metal atoms than is usually possible from X-ray refinements.

Anions that have very similar X-ray and neutron scattering factors, such as oxideterm·dom and fluoride may be distinguished by their structural environments if well-ordered within a crystal structure. Differences in formal charge and size are captured by the popular bond valence sum (BVS) method 32 , but even a simple approach based on apportioning ideal bond valences from Pauling’s second crystal rule was found to account for anion orders in many oxyhalides and oxynitridesterm·key (Fig. 4a ) 33 . Increasing the formal anion charge tends to promote more covalent bonding to the metal cations and this can also enable anions to be distinguished; for example, vanadium forms very short ‘vanadyl’ bonds to oxideterm·dom but not fluoride in V 4+ and V 5+ oxyfluoridesterm·dom. Fig. 4 Chemical and structural characterizations for mixed-anion compoundsterm·dom. Hierarchical representations from long-range ordered structures to correlated disordered states, and to local structures. a Prediction of anion distributions in mixed-anionterm·key (O, N, F, Cl, and Br) crystals based on the Pauling’s second rule: a correlation between the charge of an anion site with the calculated bond strength sums for the relevant site from X-ray diffraction (XRD) and neutron diffraction (ND) refinements 33 . For example, the apical site of the Nb(O,F) 6 octahedron in K 2 NbO 3 F is favorably occupied by F – , while the equatorial site by N 3– in Sr 2 TaO 3 N. b Identification of H – using the correlation between the chemical shift (δ) of 1 H-NMR and the M–H distance ( d M–H ), where M is the neighboring cation (Fig. 2a ) 44 . An opposite dependence is seen for OH – . c Characterization of cis- and trans- coordination in AMO 2 N perovskites (Fig. 1c ). (Right) A tetragonal SrTaO 2 N structure ( P 4/ mmm ) with the equatorial site occupied equally by O/N and the apical site occupied completely by O, giving disordered cis- chains, where thick/thin lines correspond to M–N–M/M–O–M connections 34 . This model was deduced from the average site occupancies in b . The correlated anion disorder in AMON 2 perovskites is chemically symmetric through reversal of O and N. PDF analysis of neutron total scattering data for BaTaO 2 N reveals local O/N ordering originated from favorable cis -configuration of TaO 4 N 2 octahedra 39 . (Left) The trans -coordination in SrTaO 2 N film under lateral compressive strain is probed by polarized XANES and STEM-EELS 40 . Some data are reproduced with permission from each journal Between the limits of fully ordered and randomly disordered anions, there are many cases of intermediate anion orders with local clustering or extended correlations that may give rise to non-random site occupancies in the averaged crystal structure. A particularly widespread example of such correlated disorder is found in AMO 2 N and AMON 2 perovskite oxynitridesterm·key where layers of zig–zag MN chains (Fig. 4c ) result from strong-covalent interactions between high-valence transition metals M and nitride anions that promote local cis -MN 2 (or MO 4 N 2 ) configurations (Fig. 1c, e ). This order has been deduced from powder neutron refinements of O/N site occupancies in materials, such as SrMO 2 N (M = Nb, Ta) 34 , LaTaON 2 35 , and AVO 2 N (A = Pr, Nd) 36 , 37 perovskites. Local O/N correlations are also present in silicon oxynitridesterm·key where covalency tends to equalize the SiO 4– n N n compositions of all nitridosilicate tetrahedra, for example, in melilite-type Y 2 Si 3 O 3 N 4 38 .

Analysis of total X-ray or neutron scattering data, including diffuse features from short-range correlations, as well as the Bragg scattering, has been used to construct the pair distribution function (PDF) of interatomic distances in many materials. Fitting of the PDF can be a powerful tool for revealing short range structural correlations in crystalline materials, as well as in amorphous substances 39 . Scattering or size contrast between anions can be used to determine their local order, for example, neutron PDF analysis revealed the prevalence of local cis -TaN 2 configurations in the perovskite BaTaO 2 N (Fig. 4c ) 40 .

Complementary information for analyzing the neutron- or X-ray-PDFs can be acquired by other techniques, such as electron energy loss spectroscopy (EELS) combined with scanning transmission electron microscopy (STEM), X-ray absorption near edge structure (XANES) of X-ray absorption spectroscopy (Fig. 4c ), and magic angle-spinning (MAS) nuclear magnetic resonance (NMR) (Fig. 4b ), which provide not only anion composition but also the local structures. As opposed to the above diffraction methods that may have difficulty in distinguishing among O, F, and N, state-of-the-art STEM-EELS can determine atomic occupancy with a resolution of each atomic column in a crystal lattice. This is particularly advantageous for thin film samples, in which crystal orientation is well controlled but precise structural analysis by diffraction methods is not as applicable. XANES is also effective for identifying the above elements and determining their chemical states. Perovskite (Ca 1– x Sr x )TaO 2 N epitaxial films with controlled strains were analyzed using XANES with a polarized light source 41 . From the intensity of π-bonded states of O or N with Ta-5 d via excitation from O and N core levels, it was concluded that N preferably takes the trans configuration in the TaO 4 N 2 octahedron for compressive strain states, which was also supported by STEM-EELS and DFT calculations (Fig. 4c ).

NMR has also been effective for (local) structural determination of mixed-anion compoundsterm·dom 42 . Structural determination of industrially important Si–Al–O–N materials (SiAlON), which are solid solutions between Si 3 N 4 and Al 2 O 3 , by X-ray diffractometry is insufficient because X-ray scattering factors within the Si–Al and O–N pairs are similar; however, the high-resolution MAS-NMR method overcomes this challenge. Local coordination around the 29 Si and 27 Al nuclei was determined by MAS-NMR and their integration gives a full structural model for such oxynitrideterm·key materials 43 and, coupled with ab initio calculations, preferential Al–O clustering 44 .

High sensitivity is a hallmark of 1 H-NMR, enabling detection of H – with a concentration as low as 0.1% of the total anions. Coexistence of H + (or OH – ) and H – ions in a single material is not trivial because their thermodynamic stability is different and depends on oxygen partial pressure, p (O 2 ). However, these two species sometimes coexist due to non-equilibrium 14 or high-temperature equilibrium 45 . Recent 1 H-NMR has identified a ‘hidden’ hydrideterm·key anion and its local environment in hydroxyl-oxides like apatite Ca 10 (PO 4 ) 6 (OH) 2 45 . Here, the size flexibility of H – (Fig. 2a ) substantially changes the electron density (and relevant magnetic field shielding) at 1 H nuclei and hence the isotropic chemical shift of 1 H-NMR (Fig. 4b ).

Cage structures can incorporate various anionic species. Mayenite 12CaO·7Al 2 O 3 with a positively charged cage structure is shown to host many mono- or divalent guest anions (F – , Cl – , S 2– , O – , O 2 –, O 2 2– , C 2 2– , NH 2– , CN – , O 2– , OH – , and H – ) (Fig. 1h ) 46 . Raman and electron paramagnetic spin resonance (EPR) measurements show that active oxygen species of O – , O 2 – , and O 2 2– , less stable than O 2– in oxideterm·dom crystals and usually formed on surfaces transiently 47 , can stably exist in the cage. In a lightly hydride-doped mayenite, an irradiation of UV light induces a chemical reaction in the cage: H – + O 2– ⇔ 2e – + OH – (Fig. 2d ). Here, the e – is confined within the cage, like F + centers in alkali halides, and is responsible for a ‘permanent’ electrical conductivity as the reverse of the above reaction proceeds with a timescale of 10,000 years at room temperature 48 . Formation of transient atomic hydrogen during the photo-dissociation of H – is monitored by EPR, revealing that its lifetime of the atomic hydrogen is a few minutes at 40 K 49 .

Chemical properties Optical applications Many oxidesterm·dom have a wide band gap and so are transparent. Valence band engineering according to Fig. 1b is useful to make them responsive to visible light, the main component of solar spectrum. When the oxideterm·dom anion is substituted by other anions with less electronegativity like nitride (Table 1 ), the non-oxide p orbitals having high-potential energy extend the valence band and allow for visible-light absorption. Solid solutions of CaTaO 2 N and LaTaON 2 perovskites have tuneable colors that range from yellow to red via orange (500–600 nm in wavelengths), depending on the composition of the solid solutions 50 . These oxynitridesterm·key are potential non-toxic alternatives to chalcogenide-based inorganic pigments.

This strategy may be of particular importance for finding a photocatalyst which can split water to produce H 2 and O 2 under visible light. Otherwise, if oxidesterm·dom with a small band gap of < 3 eV (corresponding to λ > 400 nm) are used, the conduction band minimum (CBM, or flat-band potential) becomes more positive than the water reduction potential (0 V vs. NHE (normal hydrogen electrode) at pH 0), a limitation shown by Scaife 50 (Fig. 5a ). So far, various oxynitridesterm·key and oxysulfides that overcome this limitation have shown water splittingterm·key performance 52 – 54 . Some of them (e.g., ZrO 2 -grafted TaON) were found to be a useful component for Z-scheme type water splittingterm·key 55 and CO 2 reduction with the aid of a functional metal complex 56 . Fig. 5 Mixed-anionterm·key driven chemical functions. a Visible-light photocatalysis (Fig. 1b ). (Left) Flat-band potential as a function of the band gap, showing an empirical relation, E FB (NHE) ≈ 2.94— E g , for d 0 or d 10 oxideterm·dom semiconductors (‘Scaife plot’). 51 (Right) Powders of GaN, ZnO and their solid solution (Ga 0.58 Zn 0.42 )(N 0.58 O 0.42 ), and a time course data for overall water splittingterm·key under visible light using (Ga 0.87 Zn 0.13 )(N 0.83 O 0.16 ) with RuO 2 nanoparticle cocatalyst 59 . b Pleochroism (Fig. 1a ). Ca 3 ReO 5 Cl 2 crystals showing different optical densities for incident light polarized along the a , b , and c axes 68 . c Battery applications. (Top left) Energy of the redox couples of iron phosphate frameworks relative to the Fermi level of metallic lithium (Fig. 1a, b ) 72 . (Bottom left) Capacity versus cycle number for MoO 2.8 F 0.2 over the first 18 cycles (Fig. 1b, e ) 76 . (Right) A pure H – conductivity 71 . Discharge curve for a solid-state battery with the Ti/La 2 LiHO 3 /TiH 2 structure (Fig. 2a , b). d Thermoelectrics. (Left) Brillouin zone of PbTe 1– x Se x , where the anion tuning allows creation of low-degeneracy hole pockets (orange) and the high-degeneracy hole pockets (blue) 81 . (Right) Microstructures for nanoscale precipitates of a phase-segregated (2.5% K-doped) PbTe 0.7 S 0.3 80 . The lower panels show an enlarged image of cubic precipitates with the three-layered structure and its Fourier-transformed image. Some data shown here are reproduced with permission from each journal Unexpected changes in electronic structure are often found in mixed-anion compoundsterm·dom, which presents a challenge to predictive materials theory. Methods based on DFT require appropriate exchange-correlation functionals 57 , 58 to accurately describe the mixed bonding character presented in these materials. Alloying wide-gap semiconductors, GaN and ZnO, results in an unprecedented yellowish powder (Fig. 5a ), and this provides the first reproducible example of visible-light-driven overall water splittingterm·key 59 . Loaded with nanoparticulate Rh 2 O 3 –Cr 2 O 3 that works as an active site for H 2 evolution, (Ga 1– x Zn x )(N 1– x O x ) exhibited H 2 and O 2 evolution for >3 months 60 . One of the drawbacks of mixed anionterm·key photocatalysts in general is their instability against photo-induced holes. This is seen even in (Ga 1– x Zn x )(N 1– x O x ), where the photo-induced holes oxidize the N 3– anion, degrading its photocatalytic activity by self-decomposition 60 . Bi 4 NbO 8 Cl, a Sillen–Aurivillius layered perovskite, was recently shown to stably oxidize water without any surface modifications. The observed stability is attributed to highly dispersive O-2 p orbitals (dominating the VBM instead of Cl-3 p ) 61 . A recent study on a series of layered bismuth oxyhalides has revealed that Madelung site potentials of anions capture essential features of the valence band structures of these materials, enabling prediction and design of the valence band structures by manipulating the stacking sequence of layers (Fig. 1g ) 62 .

Oxynitridesterm·key doped with rare earth elements show photoluminescence. Here, substitution of O 2– for N 3– gives a greater CFS of the 5 d levels of rare earth elements, such as Eu 2+ (Fig. 1a ), extending the excitation and emission peaks to longer wavelengths. SiAlON, (Si 3– x Al x )(N 4– x O x ):Eu 2+ , and related phosphors undergo photoexcitation by absorbing blue light, and emitting yellow light, and hence are used in phosphor-converted white-light emitting LED lamps (WLEDs) 63 . Other important SiAlON-related phosphors used in WLEDs are the ASi 2 O 2 N 2 :Eu 2+ and A 2 Si 5 N 8 :Eu 2+ families (A = Ca, Sr, and Ba) 64 , the latter can be oxide-doped with Al 3+ providing charge compensation in A 2 Si 5− x Al x N 8− x O x :Eu 2+ ( x = 0–1) 65 . The high thermal and chemical stability arising from covalent M−N bonding (Fig. 1e ) leads to practical applications. Similar chemical tuning has been applied for oxyfluorideterm·dom type solid solutions, such as A II 3– x A III x MO 4 F family with A = Sr, Ca, Ba and M = Al, Ga (e.g., (Sr,Ba) 2.975 Ce 0.025 AlO 4 F) 66 , 67 .

Another interesting feature from the mixed-anionterm·key system is pleochroism, recently found in Ca 3 ReO 5 Cl 2 with the Re 6+ ion in a 5 d 1 configuration (Fig. 5b ) 68 . The heavily distorted octahedral coordination of Re 6+ by one Cl – and five O 2– anions along with the spatially extended 5 d orbitals gives rise to unique CFS energy levels (Fig. 1a ), much greater than for 3 d orbitals owing to stronger electrostatic interactions exerted from the ligands. The uni-directional alignment of these octahedra along the c -axis makes the d–d transitions highly anisotropic. As a result, this compound exhibits very different colors depending on the viewing direction, i.e., distinct pleochroism.

Anion conductors Certain anions are mobile in solids. The merit of a mixed-anionterm·key material is that it allows for anion diffusion by one (more ionic, less highly charged) anion and structural stability by the other (more covalent, more highly charged) anion (Fig. 1e, f ). This concept can be directly assessed using electronic structure methods, where calculations of intrinsic defect levels and diffusion barriers 69 can be correlated with changes in the anion lattice. A layered lanthanum oxychloride LaOCl is a Cl-ion conductor 70 . While La 2 O 3 and LaCl 3 are both sensitive to moisture, a critical disadvantage for practical applications, LaOCl is water-insoluble and exhibits Cl conductivity. An aliovalent Ca–for–La substitution generates vacancies at the chloride site and hence the Cl – conductivity is improved.

H – anion conductors are expected to provide high-energy storage and conversion devices because H – has an appropriate ionic size for fast diffusion (Fig. 2a ), a low electronegativity (Fig. 2b ) and a high-standard redox potential of H – /H 2 (−2.3 V), close to that of Mg/Mg 2+ (−2.4 V). A pure H – conduction in K 2 NiF 4 -type La 2 LiHO 3 has recently been demonstrated, using an all-solid-state TiH 2 /La 2 LiHO 3 /Ti cell (Fig. 5c ) 71 . The two-dimensional (2D) H – diffusion is further facilitated by introducing H – vacancies, leading to the activation energy of 68.4 kJ mol −1 for La 0.6 Sr 1.4 LiH 1.6 O 2 .

Battery electrodes Mixed-anionterm·key chemistry of oxyfluoridesterm·dom offers a new handle to tune the redox potential of battery electrodes. Here, instead of ‘direct’ valence (anion) band control described in Fig. 1b , anion substitution enables an ‘indirect’ manipulation of the cation band. The redox potential of the LiFeSO 4 F phase (tavorite) is higher than the LiFePO 4 phase (olivine) by 750 mV 72 . This primarily results from the weaker (more ionic) Fe–F bond as compared with the Fe–O bond (Fig. 1e ), which stabilizes the anti-bonding band of Fe e g orbitals (Fig. 5c ). Furthermore, Ag 2 V 2 O 6 F 2 (SVOF) is a battery material potentially used in cardiac defibrillators owing to a fast discharge rate and high-current density 73 . The silver density in SVOF is greater than that of the currently used industry standard cathode material Ag 2 V 4 O 11 (SVO) 74 and thus the current density above 3 V for SVOF (148 mAh/g) is greater than that for SVO (100 mAh/g). The current density above 3 V is sufficient and the potential at which it is delivered (3.52 V) is 300 mV greater than SVO owing to the fluoride incorporation (Fig. 1b ).

Multivalent batteries exhibit a number of potentially valuable advantages compared to current lithium technology. The first functional multivalent battery was constructed in 2000; this prototype used a magnesium metal anode against a low-voltage Chevrel phase cathode 75 . A significant barrier to the adoption of magnesium batteries is the lack of an available high-voltage cathode that can reversibly intercalate magnesium. Cathodes composed of layered molybdenum fluoro-bronze are found to reversibly intercalate magnesium 76 . MoO 2.8 F 0.2 , combined with a Mg-based electrolyte, gave a reversible capacity of nearly 80 mAh/g, an order of magnitude higher than isostructural α-MoO 3 with a similar particle size (Fig. 5c ). First-principles calculations revealed that the incorporation of fluoride within the crystal lattice reduces nearby molybdenum ions, enhancing in-plane electronic conductivity 77 . The associated increase in electronic screening reduces the activation barrier for Mg ion diffusion but yet does not significantly lower the voltage.

Thermoelectric materials Thermoelectric materials enable direct conversion between thermal and electrical energy. Optimal materials with a high figure of merit ZT have a high Seebeck coefficient and electronic conductivity in combination with a low-thermal conductivity. BiCuSeO with (Cu 2 Se 2 ) 2− layers alternately stacked with (Bi 2 O 2 ) 2+ layers (Fig. 1g ), is a promising thermoelectric material, where one layer is responsible for electric conduction, while another lowers thermal conductivity 78 .

Nanostructuring which may be based on local segregation of anions is another effective means to reduce phonon thermal conductivity. The PbTe–PbS system exhibits phase separation (spinodal decomposition), owing to a large difference in the anion sizes (Hume-Rothery rules) 79 . The resultant PbTe-rich and PbS-rich regions form dissimilar nanostructures with interphase boundaries that act as effective scattering centers for short-wavelength phonons (Fig. 5d ). A nominal composition of PbTe 0.7 S 0.3 doped with 2.5% K achieved a figure-of-merit ZT of > 2 over a wide temperature range from 400 to 650 °C 80 . On contrary, a complete solid solution is formed in the PbTe–PbSe system. By tuning the anionic composition in Pb(Te 1– x Se x ), the electronic band structure exhibits high-valley degeneracy (Fig. 5d ), leading to an optimized ZT value of 1.8 at 577 °C 81 .

Physical properties Ordering of two anions within a material often leads to low dimensionality in structural and physical properties. Layering of different anion types (Fig. 1g ) is common and leads to 2D conductivity or magnetic correlations when cations with unpaired electrons are present. The ZrCuSiAs structure type is a flexible arrangement that allows two different anions and cations to segregate into distinct layers according to HSAB (hard and soft acids and bases) principles. Many mixed-anionterm·key materials adopt the ZrCuSiAs type, notably the LnFeAsO family of layered magnetic conductors and (when suitably doped) high- T c superconductors (Fig. 6a ), the p-type semiconductor LaCuSO, the ferromagnetic Kondo material CeRuPO, and the Ag-ion conductor LaAgSO 82 . Layered order of nitride and halide anions in MNX materials (M = Ti, Zr, and Hf; X = Cl, Br, and I) results in X-M-N-N-M-X slabs separated by van der Waals gaps (Fig. 6a ) into which cations such as lithium are intercalated, leading to conductivity and superconductivity 83 . Fig. 6 Mixed-anionterm·key driven physical functions. a Superconducting transition temperatures as a function of the year of discovery, where symbols of mixed-anion compoundsterm·dom are highlighted in color. Layered structures of parent high- T c superconductors HfNCl 83 , LaOFeAs 104 and Sr 2 CuO 2 Cl 2 89 are shown (Fig. 1g ). b (Top) Geometrical frustration in ZnCu 3 (OH) 6 Cl 2 , Cu 3 V 2 O 7 (OH) 2 ·2H 2 O and BaCu 3 V 2 O 8 (OH) 2 with the S = 1/2 kagomé lattice 85 , 87 . A Cu-triangle unit is formed by the chlorine anion of three trans -Cu(OH) 4 Cl 2 octahedra in the former, while sharing the OH anion of three trans -CuO 4 (OH) 2 octahedra in the latter two compounds. Different orbital-ordering patterns appear in these compounds, leading to various exotic quantum states. (Bottom) A spin liquid ground state and inelastic neutron scattering on ZnCu 3 (OH) 6 Cl 2 showing fractionalized excitations 86 . c (Upper) Crystal and electronic structures of SrV III O 2 H with trans -VO 4 H 2 octahedra 9 . H – 1 s orbitals, orthogonal with V t 2g orbitals act as orbital scissors (or π-blockers), resulting in 2D electronic structures (Fig. 2c ). (Lower) 2D-to-1D crossover in serial n -legged spin ladders, Sr n +1 V n O 2 n +1 H n (Fig. 1g ) 90 . d (Upper left) Band dispersions of the cation/anion co-substituted (Bi,Sb) 2 (Te,Se) 3 with a tunable Dirac cone 91 . (Upper right) Topological surface state quantum Hall effect in the intrinsic topological insulator (Bi,Sb) 2 (Te,Se) 3 92 . (Lower left) Giant bulk Rashba effect in BiTeI with polar facial -BiTe 3 I 3 octahedral layers (Fig. 1d ) 93 . (Lower right) Spectroscopic imaging scanning tunneling microscopy of BiTeI evidencing the ambipolar 2D carriers at the surface, indicating the formation of lateral p – n junctions 94 . Some data shown here are reproduced with permission from each journal Multiple anions and their ratios may be used to control dimensionality and connectivity of magnetic interactions. V 4+ and Cu 2+ both have spin S = 1/2 and so are of interest for quantum magnetic and superconducting properties, especially in low-dimensional structures that are often found in mixed-anionterm·key materials. In the early copper oxideterm·dom superconductor studies, two copper oxyhalides, Sr 2 CuO 2 F 2+δ 84 and (Ca,Na) 2 CuO 2 Cl 2 85 , played a role in understanding the superconducting mechanism (Fig. 6a ). Although, these compounds possess F – and Cl – ions instead of O 2– ions at the apical site above and below the Cu 2+ ions, they are superconducting with T c = 46 and 26 K, respectively. This fact challenged the theoretical models proposing a vital role of the apical oxygen in the superconducting mechanism. Now it is well established that the high- T c superconductivity occurs within the CuO 2 sheet having a strong covalency between the Cu d x 2 - y 2 and O 2 p σ states, while the apical-site anions (oxideterm·dom ions) are more ionic (Fig. 1e ), resulting in the 2D electronic state. In V 4+ oxyfluoridesterm·dom, the V = O vanadyl oxideterm·dom anions do not link to other cations whereas fluorides readily form V–F–V bridges, enabling many structural topologies to be achieved. DQVOF (Diammonium Quinuclidinium Vanadium OxyFluorideterm·dom; [NH 4 ] 2 [C 7 H 14 N][V 7 O 6 F 18 ]) is notable as a geometrically frustrated kagomé bilayer material with a gapless spin liquid ground state, instead of the conventional Néel order (Fig. 6b ) 86 . Various synthetic copper minerals with Cu 2+ ( S = 1/2 ion) and mixed anions have been studied as geometrically frustrated quantum magnets that can also show exotic ground states. A good example is herbertsmithite, ZnCu 3 (OH) 6 Cl 2 (Fig. 6b ), in which the Cu 2+ ion is coordinated by two axial Cl – ions and four equatorial OH – ions with its spin residing on the d x 2 - y 2 orbital 87 . The Cu 2+ spins form a 2D kagomé lattice and are coupled to each other by strong superexchange interactions only via the OH – ions. The compound exhibits no long-range order down to 50 mK with fractionalized excitations (Fig. 6b ) 88 , owing to the strong frustration on the kagomé lattice. Volborthite Cu 3 V 2 O 7 (OH) 2 ·2H 2 O and vesignieite BaCu 3 V 2 O 8 (OH) 2 with trans -CuO 4 (OH) 2 octahedra having different orbital arrangements composed of d x 2 - y 2 / d z 2 and d z 2 orbitals, respectively, enrich the phase diagram of the kagomé antiferromagnet 89 .

The lack of p orbitals in the valence shell of H – (1 s ) effectively blocks the π-symmetry exchange pathways (Fig. 2c ), a situation occurring in SrV III O 2 H with ( t 2g ) 2 , where the in-plane exchange via V dπ –O pπ –V dπ is much greater than the out-of-plane one via V dπ –H 1s –V dπ interactions (Fig. 6c ) 9 . The application of pressure to the Mott insulator drives a transition to a metal at ~50 GPa. Interestingly, despite the enormous compressibility of hydrideterm·key (Fig. 2a), which is twice as compressible as oxideterm·dom (Fig. 2a ), the electronic structure of the metallic phase is quasi-2D, meaning that the hydrideterm·key ligand acts as a ‘π-blocker’. The dimensional control from 2D to 1D is possible in the n -legged spin ladder oxyhydridesterm·key Sr n +1 V n O 2 n +1 H n ( n = 1, 2,.., ∞) (Fig. 1g ) 90 .

During the last decade, there has been remarkable progress in physics involving topological phases of matter, for which mixed-anion compoundsterm·dom play crucial roles in advancing this field. Binary chalcogenides Bi 2 Se 3 and Bi 2 Te 3 were thought to be potential three-dimensional topological insulators, but both suffered from native point defects and unintentional carrier doping. Alloying with these two compounds along with Sb-for-Bi substitution has established a highly insulating bulk and accessible Dirac carriers, accompanied by the observation of a sign change of the Dirac carriers (holes vs electrons) with chemical potential (Fig. 6d ) 91 . The precise carrier control has been also utilized to achieve a topological surface state quantum Hall effect (Fig. 6d ) 92 .

The layered polar semiconductor BiTeI shows a huge bulk Rashba-type spin splitting (Fig. 6d ) that arises from the strong inversion asymmetry along the trigonal c -axis induced by distinct covalent Bi-Te and ionic Bi-I bonds in the facial -BiTe 3 I 3 coordination (Fig. 1d ) 93 . This built-in bulk polarity induces 2D electronic surface structures with heavy depleted (I-termination) and accumulated (Te-termination) electrons forming p – n junctions (Fig. 6d ) 94 . Although BiTeI is a nontopological insulator at ambient pressure, it is proposed that the strong spin-orbit interaction allows a pressure-induced transition to a strong topological insulator, where, due to the broken inversion symmetry, a Weyl semimetal emerges between the two insulating phases 95 .

Outlook Increasing interest in solids based on mixed anions is expected to lead to new materials, some of which will make significant contributions to catalysisterm·key, energy conversion, and electronic devices, and will ultimately benefit industry in the coming decades. Functionality based on the earth-abundant, light elements usually present as anionic species (O, N, H, S, Cl, and so on) also offers the advantage of avoiding the inherent scarcity problems of metals, such as lanthanides. The metastabilityterm·dom of mixed-anion compoundsterm·dom increases the complexity of synthesisterm·dom and can limit the ways in which these materials can be used in devices. Therefore, chemically stabilizing these phases has to be considered when they are adapted for applications.

Synthetically, there will still be much room to develop methodologies. For example, multiple synthetic tools are used together (e.g., topochemical reaction under high pressure) or in a multistep process (e.g., solvothermal reaction followed by electrochemical reaction), both providing further platforms to manipulate multiple anions in extended solids. One of the important challenges is how to control anion order/disorderterm·var—one idea may be to utilize the size flexibility of hydrideterm·key (Fig. 2a ) to induce an order-disorder transition by (chemical) pressure. Furthermore, exploratory synthesis can be joined with computational tools ranging from DFT calculations to machine learning to expedite the screening process.

Regarding catalysisterm·key, this reviewterm·mth has focused on visible-light-driven water splittingterm·key, but we believe that mixed-anion compoundsterm·dom can offer a variety of new possibilities, which would provide a large impact on chemical industry. In fact, an oxyhydrideterm·key BaTiO 2.5 H 0.5 has been very recently found to be an active catalyst for ammonia synthesis, which is remarkable given that Ti has been regarded as a ‘dead’ element in terms of heterogeneous catalysisterm·key 96 . The lability of hydrideterm·key (Fig. 1f ) may be responsible for this catalytic activity. Introduction of a new anion, not limited to hydrideterm·key, into oxidesterm·dom will therefore be a useful strategy to explore a new catalytic function of ‘inert’ oxidesterm·dom. In situ and in operando analytic techniques will benefit and improve our understanding of these functions arising from mixed anionterm·key materials. The integration of DFT and machine learning and experiment can lead to the most likely reaction mechanism, and also provide new concepts or guiding principles to be added in Figs. 1 and 2 .

Most functional mixed-anionterm·key materials known to date, and providing the focus of this reviewterm·mth, are oxideterm·dom based, although non-oxide mixed-anionterm·key systems may also provide novel phases and phenomena 83 , 97 – 99 . The additional inclusion of molecular anions (e.g., O 2 – , BH 4 – ) can give rise to new aspects of anion-based materials (Fig. 1h ) 100 – 102 . For instance, the use of anisotropic anionsterm·dom, such as O 2 2– or S 2 2– will result in local symmetry breakingterm·dom and alter the hybridization with coordinating cations. Furthermore, mixed anions in surface, 2D-sheet materials 99 , interfaces, porous and nano materials, and amorphous systems are an important area for both fundamental and applied research.

There is still much to discover about the scientific principles and technological applications of mixed-anionterm·key materials. It means that the future prospects of mixed-anionterm·key materials are largely unknown at this time and this is what precisely makes the field so interesting moving forward. P. W. Anderson famously proposed that ‘More is Different’; in the world of anion-based materials we analogously conclude that ‘Mixed is Different’.

Box 1. From oxidesterm·dom to mixed-anion compoundsterm·dom Applications of oxidesterm·dom date back to prehistoric times, when our ancestors found useful properties from natural stones including, e.g., arrowheads, magnets, pigments, gems, and even medicines. Subsequent efforts have been devoted to improvements and hunting for new functions. The 20th century was a prosperous era, with discoveries of synthetic oxidesterm·dom that sustain modern technology, as exemplified by the ferroelectric BaTiO 3 , yttria-stabilized zirconia (YSZ) for solid oxideterm·dom fuel cells, and Li x MnO 2 , a cathode material for lithium batteries. The successful story of oxidesterm·dom (and other single-anion compounds, such as fluorides, nitrides, and chlorides) is largely due to their stability and ease of synthesis, along with development of structural characterization techniques, such as X-ray diffraction. Numerous inorganic compounds (51,856 oxidesterm·dom, 1581 nitrides, 2978 fluorides in the Inorganic Crystal Structure Database (ICSDterm·key, https://icsdterm·key.fiz-karlsruhe.de ), as of 5 October 2017) have been reported, most of which can be prepared by high-temperature solid-state reactions over 1000 °C. A result of extensive research over the last century is that new materials accessible by ‘heat and beat’ exploration of new cation combinations may be exhausted soon.

Focusing on the anions within a compound offers a solution to this problem. This can enhance the possible combinations of elements, but also offers more diversity. Cation-based compounds are based on common coordination polyhedra as building units (e.g., CuO 4 square planes). However, if several oxideterm·dom anions are replaced with other anions, new and unusual coordination geometries may result. When these polyhedra, as new building blocks, are arranged to form an extended array, one can expect enhanced properties or fundamentally new phenomena. Since anions exhibit different characteristics (e.g., ionic radii, valence, polarizability, and electronegativity), selecting different anions can introduce a new dimension of flexibility for materials design and function. Despite such possibilities, the number of mixed-anion compoundsterm·dom available are limited: the number of recorded materials in ICSDterm·key are 1266 for oxyfluoridesterm·dom, 612 for oxynitridesterm·key, 47 for oxyhydridesterm·key, 655 oxychalcogenides, and 312 oxypnictides. Note that mixed-anion compoundsterm·dom do not necessarily possess a heterolepticterm·key coordination geometry around a transition metal. For example, a number of structures are comprised of alternating layers, each with a homoleptic coordination by a different anion, as found in Sr 2 MnO 2 Cu 1.5 S 2 with alternating Sr 2 MnO 2 and Cu 1.5 S 2 layers 102 .

Although some excellent overviews of mixed anionterm·key compounds have been provided 2 , 5 , 12 , 16 , 81 , 82 , 102 , each covers relatively narrow range of materials and disciplines. This reviewterm·mth article is attempting to capture the broader fundamentals of these materials and draw new insights among materials classes.