Anion Ordering in Bichalcogenides

Abstract

This review contains recent developments and new insights in the research on inorganic, crystalline compounds with two different chalcogenide ions (bichalcogenides). Anion ordering is used as a parameter to form structural dimensionalities as well as local- and global-electric polarities. The reason for the electric polarity is that, in the heterogeneous bichalcogenide lattice, the individual bond-lengths between cations and anions are different from those in a homogeneous anion lattice. It is also shown that heteroleptic tetrahedral and octahedral coordinations offer a multitude of new crystal fields and coordinations for involved cations. This coordination diversity in bichalcogenides seems to be one way to surpass electro-chemical redox potentials: three oxidation states of a single transition metal can be stabilized, e.g., Ba₁₅V₁₂S₃₄O₃. A new type of disproportionation, related to coordination, is presented and results from chemical pressure on the bichalcogenide lattices of (La,Ce)CrS₂O, transforming doubly [CrS_3/3S_2/2O_1/1]³⁻ (5+1) into singly [CrS_4/2S_2/3]^7/3− (6+0) and [CrS_4/3O_2/1]^11/3− (4+2) coordinations. Also, magnetic anisotropy is imposed by the anion ordering in BaCoSO, where magnetic interactions via S or O occur along two different crystallographic directions. Further, the potential of the anion lattice is discussed as a parameter for future materials design.

1. Introduction

In solid-state inorganic chemistry, the anion lattice is usually mentioned as a matrix where the cations dwell. The latter, positively charged, ions are chiefly in the research focus because their valence electrons are responsible for physical properties, like magnetism, optic activity, and conductivity. As a result, the fundamental aspects of the potentially interesting anion lattice receives relatively little attention. In this review, the elements in main group 16, the chalcogenides, will be used to display the possibilities of the anion lattice and how its design is related to new chemical situations that eventually lead to desirable properties. Focus is placed on describing the ordering of two anions, so solid-solutions will be disregarded.

According to Hume-Rothery [1], if the size difference of two atoms/ions, composing a common lattice, is larger than ~10%, an ordered superstructure is formed rather than a solid solution. Hence, by considering the sizes of the two-fold negatively charged chalcogenide ions (r(O²⁻) = 1.26 Å, r(S²⁻) = 1.70 Å, r(Se²⁻) = 1.84 Å, and r(Te²⁻) = 2.07 Å) [2], anion ordering is most probable for sulfide-oxides, selenide-oxides, telluride-oxides, and perhaps telluride-sulfides. These chemical prerequisites are chosen in this review to keep the focus on the phenomenon (anion superstructures) instead of on its vast possibilities.

Below, causes and consequences of involving two chalcogenides into one crystal lattice are presented. Each case is briefly introduced and subsequently discussed on the basis of existing compounds. At the end of this review, further possibilities are given, but only with a few practical examples.

So far, there are several known examples of bichalcogenides, but many of them were obtained by chance, often admitted in honesty by the discoverers themselves. By comparing existing compounds, this review aims to initiate an understanding in this research field.

2. Causes and Consequences of Chalcogenide Ordering

2.1. Partial Anionic Substitution

Despite a significant size difference between two anions, a stoichiometric composition of two anions might build up a common lattice with great similarities to that of an anion homogeneous one. For example, the ternary La₂SO₂ [3] is isostructural to the binary La₂O₃ [4], but exhibits an anion superstructure, i.e., S−O ordering. Also, by replacing half of O²⁻ in SrZnO₂ [5] by S²⁻ and at the same time substitute Sr²⁺ for Ba²⁺, the quaternary compound BaZnSO results [6]. As both compounds are structurally very similar, the latter sulfide oxide can be described as an anionic superstructure of the former. These kinds of anion substitutions are also expected to work both ways: for example, partly replacing S for O converts the anion lattice of La₃CuSiS₇ [7] (or Ce₆Al_10/3S₁₄ [8]) into that of Ba₃V₂S₄O₃ [9,10] and the latter is isostructural with the former, having even the same crystal symmetry. This means that there might be rational solubility of one chalcogenide in the matrix of another: These partial substitutions are possible if the anions in a candidate compound occupy two crystallographically unique sites, with preferably different environments.

2.2. Structural Dimensionality

The anion lattice dimensionality (D) is often inherited by the crystal structure as a whole. Decisive is the relative abundance of the two anions: the closer this ratio is to unity, the higher is the dimensionality. Hence, a 1:1 ration could constitute a 3-D lattice, a 2:1 ratio most likely a 2-D stacking, and a 6:1 probably leads to a 0-D structure e.g. a single anion surrounded by the other type of anion. For example, the sulfide–oxide Eu₅V₃S₆O₇ [11] contains a weaved net of O and S rows (O/S = 7/6 ≈ 1) and is best described as a 3-D lattice. Two-dimensional layers of Se and O are found in La₂Fe₂Se₂O₃ [12] where the ratio O/Se = 1.5. In Bi₂SO₂, stacked square layers of either O or S are observed [13] (Figure 1), with the ratio O/S = 2. Quasi 1-D chains of Se ions penetrate the crystal structure of Sr₂Mn₂SeO₄ [14], in correspondence to the composition O/Se = 4. Single O ions are separated by S in La₄MnS₆O [15], which is a representative of a 0-D oxygen anionic order and the ratio S/O = 6.

2.3. Charge Ordering

By combining the concepts of anion superstructures with that of hard–soft-acid–base (HSAB), which is often used for ions in solutions [16], it becomes apparent that a charge ordering might accompany an anion ordering. This means that higher (lower) oxidation states would be found close to anions with higher (lower) electronegativity. Assuming that the hypothetical compound TM₃TeO₃ (TM = transition metal), with TM^2.67+ on average, exists and is charge ordered, it is most probable that TM²⁺ coordinates mainly to Te²⁻ and TM³⁺ to O²⁻. In Eu₅V₃S₆O₇, a charge order is proposed due to semiconducting behavior although the mean valence of V is +11/3 (+3.67) [11] and corresponds to 1 × V³⁺ and 2 × V⁴⁺. As the crystal structure contains two V sites, it is possible to order the charges although the authors chose differently: both sites are in first approximation octahedrally coordinated, [VS_4/2O_2/1]^13/3−, with similar interatomic distances, making it difficult to see any preference for the charges. However, the sites have different multiplicities, according to the Wyckoff definition (4f and 2b), and probably should be divided as V⁴⁺ (4f) and V³⁺ (2b). In contrast, it can be expected from the stoichiometry that V is +4 in Ba₃V₂S₄O₃ [9,10], but the observations correspond to a charge disproportionation: V³⁺ is found in an octahedral [VS_6/2]³⁻ coordination and V⁵⁺ in a [VSO₃]³⁻ tetrahedron [10], agreeing with the HSAB principle. Similarly, tetrahedrally coordinated V⁵⁺ and an intermediate valence of V^26/7+ in [VS_6/3]^2/7−-octahedra were reported in Sr₆V₉S₂₂O₂ but no magnetic moment was observed, agreeing with a lack of true charge ordering [17]. However, in Ba₁₅V₁₂S₃₄O₃ three oxidation states (V³⁺, V⁴⁺, V⁵⁺) were proven experimentally and a suggested charge ordering was presented (Figure 2), as based on the existence of a short vandyl bond, (V=O)²⁺, the HSAB principle, and Coulombic repulsion forces [18]. Obviously, the anion superstructure offers several different coordination environments for the transition metal, which seems to be an important prerequisite for the ordering of multiple oxidation states of one element on neighboring sites in a mutual crystal structure. In metal oxides, similar situations were suggested in La₄Mn₅Si₄O₂₂ [19] (Mn²⁺, Mn³⁺, and Mn⁴⁺) and in Ba₃Co₁₀O₁₇ (Co²⁺, Co³⁺, and Co⁴⁺) [20]. However, only the former was supported by spectroscopic data [19].

These, still rare, crystal structures prove that the lattice energy can surpass the electrochemical potential of redox pairs, which has to be studied further. Having several oxidation states of one element in one compound might induce novel optic and electronic properties.

2.4. Low Formal Oxidation States of Cations

A typical feature for the heavier chalcogens is the chemical non-stoichiometry towards reduced oxidation states of involved metals, exemplified by the non-stoichiometric Fe_1+xTe having an α-PbO type structure but with an additional partly occupied Fe site [21]. This is naturally also a consequence of the more covalent bonding character of Te—as compared to O, for example—and of the electronic itinerancy. Hence, to reach low formal oxidations states of transition metals, a combination of heavier chalcogenides with lighter ones can be the right strategy. Recently, the layered compound CsV₂S₂O was reported with V having the formally intermediate charge +2.5 [22]. However, metallic properties were observed, meaning that new systems have to be found for the study of the low oxidation states. Still, it is fair to assume that the combination of hard and soft anions (i.e., according to HSAB) might stabilize rare charges of cations.

2.5. Polar Coordinations

A cation in a homogeneous anion lattice will bond similarly to its next neighbors, with a predictable coordination number (CN), as estimated from its ionic size relative to the anion size. However, within lattices consisting of two different anions, it is more challenging to make similar predictions. So far, no one has tried to settle any rules for the cations coordination in a heterogeneous anion lattice.

It is well established that the amount of covalency in the bonding nature between two elements is dependent on their differences in electronegativities. By introducing two different anions in the coordination of a common cation, the bonding will obtain irregularities (Figure 3). The bond distance between two specific atoms, e.g., Zn and O, varies somewhat depending on the other neighboring anions. Examples of this effect can be found in ternary bichalcogenides of actinides or lanthanides, like Gd₂Se₂O [23] and Ce₂TeO₂ [24], but also in ZrSO [25], and Ba₂TeO [26]. These four compounds—Gd³⁺, Ce³⁺, Zr⁴⁺, and Ba²⁺—have heteroleptic coordinations, and the bonding to either chalcogenide is clearly different from those in a homogeneous anion lattice (see

Table 1. Comparisons of average bond lengths (in Å) for cations in homo- or heteroleptic coordination. Average distances are normalized by site multiplicities. The reference materials might contain two cations, but the cation of interest is chosen to have the same oxidation state and similar coordination number (CN) to validate the comparison. Bold fonts in formulas indicate the cations (M) in focus and Ch signifies chalcogens.

M−Ch−O	CN 1 × M−O	CN 1 × M−S	CN 1 × M−Se	CN 1 × M−Te
Gd2Se2O [23]	2 × 2.30		5 × 2.98
Gd2Ti2O7 [34], Gd2Se3 [35]	8 × 2.46		7.5 × 2.98
Ce2TeO2 [24]	4 × 2.37			4 × 3.51
Ce2Zr2O7 [36], Ce8/3Te4 [37]	8 × 2.47			8 × 3.31
ZrSO [25]	3 × 2.13	4 × 2.63
ZrO2 [38], Er2ZrS5 [39]	8 × 2.21	7 × 2.59
Ba2TeO [26]	1 × 2.45			5 × 3.59
BaO [40], Ba2MnTe3 [41]	6 × 2.76			7 × 3.54

¹ Average coordination number.

). More specifically, heteroleptic coordination induces shorter M−O (M = metal) and longer M−Ch (Ch = chalcogen) distances in comparison to the corresponding bonds in homoleptic coordinations. This is also valid for ions of lighter elements like Fe²⁺ in the more complex compounds AEFe₂Ch₂O (AE = Ba²⁺, Sr²⁺, Ch = S²⁻, Se²⁻) [27,28,29,30], where Fe²⁺ has a quasi-tetrahedral [FeS_3/3O_1/2]⁻ coordination and the Fe−S distance is surprisingly large, whereas Fe−O is correspondingly short in comparison to bonds in pure sulfides and oxides, respectively [30]. Naturally, this has strong influence on the involved magnetic coupling strengths, local electric polarizations, and crystal fields (see below). Similar situations can be observed in metal–organic complexes but those crystal structures are usually based on finite transition metal entities separated by organic molecules. On the contrary, in superstructures of anions, the lattices are extended and will cause global effects, so far, with unpredictable consequences.

2.6. Structural Polarity

A local polarity, as induced by heterogeneous (heteroleptic) coordination can result in a global polarity, if the crystal structure is described with a non-centrosymmetric space group. For example, BaGeSe₂O contains GeSe₂O₂ tetrahedra, where the highly charged Ge⁴⁺ is found far from the tetrahedral center due to the obvious size difference between Se and O [42]; the non-linear optic response from non-centrosymmetric BaGeSe₂O (P2₁2₁2₁) is surprisingly large. Another example is CaZnSO (P6₃mc) with strong electric polarity for tetrahedrally coordinated Zn²⁺ ([ZnS_3/3O]²⁻, Figure 3) [32]; Although the measured sample was polycrystalline, the second harmonic generation (SHG) effect is about 100 times stronger in CaZnSO than in α-SiO₂. By replacing the non-magnetic Zn²⁺ with the S = 2 entity high-spin Fe²⁺, the isostructural CaFeSO was formed [43], where a magneto-electric coupling might result, although only a weak orbital moment is expected for a high-spin d⁶ electronic configuration in tetrahedral coordination. However, according to the first report on this compound, a collinear anti-ferromagnetic long range order in each crystal structure layer was observed, which is further surprising because of the geometrical frustration from the hexagonal symmetry.

An indirect electric polarity is induced by non-magnetic [VSO₃]³⁻ units on a quasi-1-D magnetic (S = 1) system in Ba₃V₂S₄O₃ (Figure 4): the trigonal packing of columns consisting of face-sharing [VS_6/3]³⁻ octahedra are separated by Ba²⁺ and polar [VSO₃]³⁻ tetrahedra that all have a common polar direction [9,10]. The first investigations on its physical properties reveal two broad magnetic anomalies without long ranged spin-order, which might indicate thermal excitations of states that are induced by magneto-electric couplings [10].

A similar 1-D magnetic sublattice is found in La₃WTMS₃O₆ (TM = Cr, Mn, Fe, Co, Ni) [44]. By replacing Ba²⁺ by La³⁺ and the polar [VSO₃]³⁻ unit by the non-polar [WO₆]⁶⁻ trigonal prism, the quasi-1-D magnetic lattices can be obtained with (P6₃) or without (P6₃/m) structural polarity. To emphasize this, the compounds can be written as Ba₃[VSO₃][TMS_6/2] and La₃[WO₆][TMS_6/2], where the [TMS_6/2]³⁻ columns are very similar even with the same +3 oxidation state of TM. This offers the unique situation to check the influence of the structural polarity on the material properties (magnetism, conductivity) on basically identical TM sublattices. While this is not necessarily a result of anion ordering, the significant electric polarity in non-centrosymmetric Ba₃[VSO₃][TMS_6/2] is assured by the heteroleptically coordinated V⁵⁺ (Figure 4).

2.7. Coordination Configurations and Crystal Field Effects

The valence electrons of the first row TMs (Sc−Zn) are strongly affected by the surrounding crystal field, which has consequences for energy differences between possible spin-states. With two different coordinating anions, there are more possibilities to design the crystal field strength and resulting relative energy of the orbitals on the TM. If the energy difference between two spin-states is relatively small, a transition between them can be achieved by means of temperature change and/or magnetic fields change (metamagnetism). The spin-state change is normally accompanied by a change in electrical conductivity, which is highly interesting for fundamental and applied science. For example, the spin-state transition in Sr_2−xLa_xCoO₄ is related to the metal-insulator transition [45]. On the other hand, the spin-states of transition metals in compound with heterogeneous anionic lattice are far from understood.

As a consequence of (at least) two different coordinating anions, new coordination situations can be expected with novel crystal fields. Especially for the TM ions, it is interesting to explore and to identify new electronic environments that influence the local polarity and the distribution of electrons among the d-orbitals. For tetrahedra, 3+1 and 2+2 coordinations are possible (Figure 3), of which a distorted type of the former is seen for Fe²⁺ (HS, d⁶) in AEFe₂Ch₂O (AE = Ba²⁺, Sr²⁺, Ch = S²⁻, Se²⁻) [38,39,40,41] and in CaFeSO [43]. The latter 2+2 coordination is found for TM²⁺ in BaTMSO (TM = Zn²⁺ [8], Co²⁺ HS, d⁷ [46]) and Fe²⁺ (HS, d⁶) in CaFeSeO [47]. Cis and trans 2+2 distorted square planar coordinations of two electronically noble-gas-like anions have not been reported in bulk material to date, but should be possible. Numerous different five-fold coordinations are possible, but the two heteroleptic 4+1 and 3+2 configurations are most reasonable. A square pyramidal version of 4+1 is known for Mn³⁺ (HS, d⁴) in Sr₂Mn₂SeO₄ [14]. The 3+2 coordination has not been reported yet for bichalcogenides, but holds at least the possible cis and trans configurations that result in obviously different crystal fields. Moreover, a hypothetical trigonal bipyramidal trans coordination is likely to occur when the plane is constituted by the relatively smaller anions. The six-fold coordination has even more possibilities, namely 5+1, 4+2, and 3+3, of which all have several configurational names (Figure 5). So far, 5+1 has been reported for Cr³⁺ (d³) in LaCrS₂O [48], for Ti³⁺ (d¹) in La₄Ti₂Se₅O₄ [49], and for Ti⁴⁺ (d⁰) in La₆Ti₃Se₉O₅ [49]. A 4+2 coordination can be either cis, at least known for Ti⁴⁺ (d⁰) in Pr₆Ti₂S₇O₆ [50], or trans as for Fe²⁺ (HS, d⁶) in La₂Fe₂Se₂O₃ [12]. The facial (fac) and the meridional (mer) 3+3 coordinations are still very rare and were almost solely reported for metal-organic complexes, where polydental ligands make it possible to control the fac and mer isomerism. However, in extended crystals structure with monoatomic anions, the mer coordination in bichalcogenides only exists for non-magnetic Ti⁴⁺ (d⁰) in La₆Ti₂S₇O₆ [51]. Higher coordination numbers than six are mainly reported for lanthanides, actinides, and larger main group metals, see for example Gd₂Se₂O [23], Ce₂TeO₂ [24], USeO [52], and BiCuSO [53]. Seven-fold capped trigonal antiprismatic coordinations are known for Zr⁴⁺ (d⁰) in ZrSO and Nb⁵⁺ (d⁰) in Gd₃NbS₃O₄. Further seven-fold (or higher) coordination might be possible at least for Mn or for TMs of later periods (4d or 5d).

Clearly, the coordination flexibility is at hand, but a spin-state transition (HS−LS) has not been fully proven yet, although it was suggested for Co³⁺ (d⁶) in La₃WCoS₃O₆ [44], where Co is trigonal antiprismatically coordinated by S²⁻ solely.

2.8. Coordination Disproportionation

LaCrS₂O is a quasi-1-D system with zig-zag chains of [CrS_3/3S_2/2O_1/1]³⁻ edge-sharing octahedra (Figure 6, left), where La³⁺ ions separate the chains. By introducing the slightly smaller lanthanide ion Ce³⁺ instead of La³⁺, the lattice experiences a so-called "chemical pressure". As a result, the crystal structure of CeCrS₂O consists of layers (Figure 6, right) built from two different octahedra that are edge- and vertex-sharing and are separated by Ce³⁺ ions. The structural difference between the two chemically similar systems can be described as a coordination disproportionation: LaCrS₂O contains only [CrS_3/3S_2/2O_1/1]³⁻ entities [48] and CeCrS₂O contains equal amount of [CrS_4/2S_2/3]^7/3− and [CrS_4/3O_2/1]^11/3− octahedra in an ordered fashion [54] (Figure 6). As it is clearly not a charge ordering phenomenon, this might be related to coordination order entropy that is rarely taken into consideration. An alternative explanation would be that the 5+1 coordination in LaCrS₂O is relatively unstable, as indicated by the fact that the highly symmetrical electron distribution on Cr³⁺ in an octahedron (3t_2g0e_g) does not agree with the relatively low symmetry of the Cr-site, i.e., four different bond lengths are found in the structure (Figure 6). Coordination disproportionation is also found in CeCrSe₂O and even in LaCrSe₂O [55], leaving LaCrS₂O as only example, so far, with homogeneous 5+1 coordination of Cr³⁺.

This type of polymorphism is probably described for the first time here and has to be studied further to understand its origin: The complex anionic lattice might be an ideal starting point for finding further examples of this phenomenon.

2.9. Magnetic Anisotropy

On an extended lattice, the magnetic interactions via super-exchange paths will be affected by heteroleptic coordinations of magnetic ions. The S−O ordering in BaCoSO [46] constitutes a new type of parameter causing magnetic anisotropy (Figure 7). The extraordinary bonding situation results in two different super-exchange paths, Co−S−Co and Co−O−Co, that run parallel to two orthogonal crystallographic directions, a and c, respectively (Figure 7). The magnetic interactions between the S = 3/2 entities (Co²⁺) are dependent on inter-atomic distances, bonding type (hopping integral), and bridges angle (Co−S−Co (116°) or Co−O−Co (180°)). All of these parameters, being different for the super-exchange via S or O, cause the magnetic coupling strengths to differ. Hence, the magnetic system BaCoSO is not obviously 2-D, as even the layers are anisotropic and carry features of a 1-D lattice.

Moreover, the low-dimensional surrounding, as formed by different sizes of next-neighbor ions, allows for orbital moments of magnetic ions or for a coupling between spin and structural polarity to evolve (see above).

It is clear that the ordering of anions can be counted as additional parameters for designing magnetic anisotropy.

2.10. Band-Gap Optimization

The covalent bond character of heavier anions to cations will decrease the electronic correlation strengths locally and decrease the band-gap globally: ZnO is a typical electronic insulator, ZnS and ZnSe are semiconductors, and ZnTe is metallic. The electronic properties of hypothetical compositions Zn₂SO and Zn₂TeO are, thus, difficult to predict and can be affected by the dimensionality of the anionic lattice. As the band-gap is important for several applicable materials, like in thermoelectrics and for photocatalytic splitting of water, compounds including heavier chalcogenides are receiving more attention lately. BiCuSeO is a prominent example with exceptional thermoelectric properties [56]. Its band-gap of about 0.8 eV increases proportionally to the S content in BaCuSe_1−xS_xO up to about 1.1 eV [57], proving that this chalcogenide compound can be anion designed in a predictable way. The exceptional thermoelectric properties are naturally also a consequence of the low thermal conductivity, which is discussed as related to the 2-D layers of O and Se(S). Hence, the anion superstructure improves the applicable properties with its bonding anisotropy.

3. Further Notes

Anionic superstructures are only beginning to reveal their potential. In fact, there are several open problems in fundamental and applied sciences that might be solved by introducing the anionic superstructures as extra parameter in the design of related materials. For example, ionic conductors are often suffering from structural deterioration upon using the material, moving the ions; in cases where the moving ion is an anion, these compounds could be improved by introducing two anions, where one is moving and the other is holding the lattice together, perhaps in layers or in columns. On the other hand, if the moving ion is a cation, the anionic lattice can be designed with two ions to reach optimum diffusion paths. An already known example is Ag₃SI with a combined anionic lattice and extremely high cationic mobility [58].

Even more intricate anionic lattices are known: Ln₃SOF₅ (Ln = Nd, Sm, Gd–Ho) contain three different anions with only little mixing of F⁻ and O²⁻ [59]. The coordination is naturally more complex and the possibilities for the above mentioned parameters are extended. Heteroleptic coordinations by three anions in ordered layers of U₂Te₂PO result in two different surroundings for U: either UTe₅O₄ or UTe₅P₄ [60]. Although the charge ordering was not stated in that report, the HSAB principle [16] suggests U⁵⁺ in former and U⁴⁺ in latter.

4. Final Words

Several of the above-mentioned phenomena are induced by the ordering of anions and the examples, presented here, only contained the bichalcogenides. Pnictogens in combination with chalcogens are already making the head-lines due to LaFePO [61] and related materials, but in that case Fe is homoleptically coordinated and does not have the same parameters of freedom as the materials in this review. However, the pnictogenide halogenide ZrNCl [62] does connect to the topic of this review and also exhibits superconductivity upon electronic doping. By combining a chalcogen with complex anions, further possibilities are obvious, and thereof Bi₄(SO₄)S₂ is a prominent example, which is reported to be superconducting [63]. Hence, further systematic investigations of other anion superstructures are needed, which probably will be as rewarding as this preliminary one for the bichalcogenides.