Wadsley vanadium oxides

Abstract

Wadsley vanadium oxides form a homologous series V_nO_2n+1 between the end members α-V₂O₅ and VO₂(B). They exhibit a variety of crystal structures due to different polyhedra around the V⁴⁺ and V⁵⁺ cations and polyhedral connectivity. Their structural features as well as transport and magnetic properties are reviewed here. The Wadsley vanadium oxides are oxygen deficient with different ordered vacancies in the oxygen cubic close-packing array. The rutile-type structure, with the oxygen hexagonal close packing, is found in V₆O₁₃ (n = 6) obtained at high pressures and high temperatures, which unlike its α polymorph stable at atmospheric conditions, does not undergo a metal–insulator phase transition. This finding opens a possibility of synthesizing new materials with unexpected properties in the system V₂O₅–VO₂ by varying compositions and exerting extreme conditions.

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Andrzej Grzechnik

Andrzej Grzechnik studied geology (MSc) at the University of Warsaw and chemistry (PhD) at Arizona State University, where he was a Fulbright scholar. His work is focused on solid state research at extreme conditions.

Karen Friese

Karen Friese studied mineralogy (Diploma) at the University of Hamburg, where she also obtained her PhD. Her work is focused on crystal structure determination of functional materials.

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Introduction

Experimentally determined equilibrium phases in the central part of the V–O phase diagram (VO_x, 1.5 ≤ x ≤ 2.5) at atmospheric pressure are V₂O₃, V_nO_2n−1 (n = 3 ÷ 8), VO₂, V₃O₇, V₆O₁₃, and V₂O₅, with V₂O₃, VO₂, and V₂O₅ exhibiting very narrow composition ranges.¹ The theoretically calculated phase diagram includes only V₂O₃, V₃O₅, VO₂, V₃O₇, and V₂O₅.² The synthesis, functionalities, and applications of the VO_x oxides are extensively reviewed in ref. 2–5.

The oxides V_nO_2n−1 (n = 3 ÷ 9) form a Magnéli homologous series, V_nO_2n−1 = V₂O₃ + (n − 2) VO₂.^6,7 The end members of this series are corundum-type V₂O₃ and rutile-type VO₂.⁸ The corundum structure (R3̄c, Z = 6) is a hexagonal close-packed array of oxygen atoms, in which the V³⁺ cations occupy two-thirds of the octahedral sites. It is built of pairs of VO₆ octahedra sharing faces along the c direction. Such pairs form chains by edge-sharing in the plane perpendicular to c. These chains are linked to others by edge sharing in a three-dimensional network. The rutile structure (phase R, P4₂/mnm, Z = 2) is a distorted hexagonal close-packed oxygen array with the V⁴⁺ cations occupying one half of the octahedral sites. Chains of edge-sharing VO₆ octahedra along the c direction connect with each other in a three-dimensional network. Magnéli phases could be derived from the parent rutile structure by removing an oxygen layer at every nth vanadium layer in the direction perpendicular to the (211) plane of the parent rutile structure.⁸ With respect to the composition of vanadium dioxide, they are anion deficient and can be expressed as VO_2−y. They order antiferromagnetically and, apart from V₇O₁₃, undergo metal–insulator phase transitions (MIT) accompanied by structural transformations.^6–10 Magnéli phases are also known for titanium, niobium, and tungsten oxides.¹¹

The emphasis of this article is on the homologous series of vanadium oxides V_nO_2n+1 predicted by A. D. Wadsley¹² in the system V₂O₅–VO₂. Its formula can be written as V_nO_2n+1 = V₂O₅ + (n − 2) VO₂ for 2 ≤ n. The end members of this homologous series are α-V₂O₅ (Pmmn, Z = 2) and VO₂(B) (C2/m, Z = 8).⁸ With respect to the chemical composition of VO₂, the Wadsley oxides are cation deficient, V_1−zO₂. They exhibit a variety of crystal structures due to different coordination polyhedra around the V atoms (tetrahedra, trigonal prisms, square pyramids, or octahedra) and different polyhedral connectivities. The V⁵⁺ cations favor the polyhedra with low coordination numbers, while the V⁴⁺ cations are five- or six-fold coordinated to the oxygen atoms.¹³ Compared to the Magnéli phases, the polymorphism in the Wadsley series is altogether richer at ambient pressure. It offers a possibility to study the structure–property relationship in correlation with phase transitions including those induced at extreme conditions. In the following, the crystal structures and physical properties of the Wadsley homologous series V_nO_2n+1 and of the relevant polymorphs of vanadium dioxide are reviewed. It is then indicated how high-pressure phase transitions and synthesis could lead to new materials in the V₂O₅–VO₂ system.

Rutile-type and VO₂(S) vanadium dioxides

The first-order MIT in stoichiometric vanadium dioxide occurs at T_MIT ≈ 341 K.^14–17 It is associated with a magnetic susceptibility drop and a change in thermochromic properties. The V³⁺ and V⁵⁺ cations co-exist in the high-temperature metallic phase R due to charge fluctuations of the V⁴⁺ cations.¹⁶ The V–V distance in the octahedral chains is equal to the c lattice parameter (Fig. 1). The low-temperature insulating phase M1 (P2₁/c, Z = 4) is made of VO₆ chains but with V–V dimers in a zigzag pattern due to displacement of the V atoms from the ideal-rutile positions.¹⁸

Fig. 1 Interatomic connectivity in VO₂ polymorphs. The V–V distances in the octahedral chains are drawn as thick green, blue, and cyan lines.

Doping with low-valence cations (e.g., Al³⁺, Cr³⁺, Fe³⁺) stabilizes additional insulating polymorphs M2 (C2/m, Z = 8) and T (P1̄, Z = 4). In M2, there are alternating short and long V–V distances in the linear octahedral chain and equidistant V–V distances in the zigzag octahedral chain (Fig. 1).^19,20 T is a distorted variant of M2 due to linearity breaking and pairing of the V atoms in the zigzag chain.²⁰ M1 and M2 can transform into each other, with T as an intermediate.¹⁹ M2 can also be an intermediate in the M1 → R transition.^21–23 The three insulating phases may coexist and form domains.²⁴ Their stabilities are affected by electric field, strain, or pressure.^14,16,25,26 The high-valence dopants (e.g., Nb⁵⁺, Mo⁶⁺, W⁶⁺) lower T_MIT, while the low-valence dopants (e.g., Al³⁺, Cr³⁺, Fe³⁺) increase it.^14–16 The charge is compensated by the presence of the V³⁺ or V⁵⁺ cations, respectively. In non-stoichiometric undoped vanadium dioxide, T_MIT decreases in VO_2−y with increasing y, while it increases in V_1−zO₂ with increasing z.^15–17 The crystallographic data across MIT for different non-stoichiometries are lacking.¹⁶

In addition to the R and M1 polymorphs, insulating M1′ (monoclinic), metallic X (triclinic) and O (Pnnm, Z = 4) phases are identified in the pressure–temperature phase diagram of VO₂.²⁷ At room temperature, M1 transforms to isostructural M1′ at 13.9 GPa.²⁶ At 383 K, R undergoes a phase transition to O above 13.7 GPa.²⁸ Upon further compression, both M1′ and O transform into X above 34.3 and 38.3 GPa at room temperature and 383 K, respectively. X, which is postulated to be metallic above about 35 GPa,^28–31 co-exists with M1′ in the pressure range 32–42 GPa.

Insulating VO₂(S) (P3, Z = 7), synthesized from a mixture of V₂O₃ and V₂O₅ at 2–7 GPa and 873–1173 K, is built of isolated and strongly distorted edge-sharing octahedral VO₆ trimers arranged in two different layers.³² The trimers in every second layer are linked via edge-sharing with another octahedron. Upon heating, the product transforms to M1 below 4 GPa and to M2 at higher pressures.

Cation-deficient V_1−zO₂ phases with a distorted rutile structure (P2/m, Z = 2) are synthesized at 6.5 GPa and 1273 K by substituting 2 wt% and 10 wt% of V₂O₅ into VO₂.^33,34 Their compositions could also be written as V_0.995O₂ and V_0.976O₂, respectively. The V–V distances in both octahedral chains are equidistant. The resistivity data show that V_0.995O₂ and V_0.976O₂ undergo MIT at 353 K and 361 K, respectively.³³ No structural details of the metallic phases in both materials are provided.

A summary of the compounds discussed in this section, including their space group symmetries, synthesis methods, V–V distances, and properties, is provided in Table S1 in the SI. Further details on polymorphism and physical properties of vanadium dioxide can be found in the ref. 2–5 and 14–17.

α-V₂O₅ and VO₂(B) end members of the Wadsley homologous series V_nO_2n+1

α-V₂O₅

α-V₂O₅ (Pmmn, Z = 2) is built of ribbons of edge-sharing VO₅ square pyramids or very distorted VO₆ octahedra when an additional long V–O distance is considered (Fig. 2).¹³ The smallest building block in the idealized octahedral structure is a doublet of edge-sharing octahedra in the ribbons along the a axis. These ribbons are linked with the adjacent ones by corners to form layers. In each ribbon, there is a zigzag chain of equidistant V–V atoms.³⁵ The layers share corners in a three-dimensional structure.

Fig. 2 Octahedral connectivity in the idealized α-V₂O₅ structure with distorted VO₆ octahedra, single layer in VO₂(B), and high-temperature phase of VO₂(A).

α-V₂O₅ amorphizes above about 7.3 GPa.^36,37 The polymorph that crystallizes from the amorphous material at high pressures and high temperatures is δ-V₂O₅ (C2/c, Z = 4) as evidenced by in situ angle-dispersive synchrotron powder diffraction in large-volume multi-anvil press.³⁷ It is built of slabs connected with each other by octahedral corners.^36–39 Each slab is made of edge-sharing VO₆ doublets linked with the others by corners. The single slab is in fact a building block of the rutile type (Fig. 3). In β-V₂O₅ (P2₁/m, Z = 2), obtained at lower pressures than δ-V₂O₅,^38,39 there are two symmetry non-equivalent V positions V1 and V2. The octahedra V1O₆ form isolated stripes of the α-V₂O₅ type along the b direction. The V2O₆ octahedra are linked by corners to form chains along b. The stripes and chains share edges within one layer. The phase boundaries between α-V₂O₅ and the recovered β-V₂O₅ and δ-V₂O₅ products from high pressures and temperatures are drawn in ref. 39.

Fig. 3 High-pressure high temperature phases of V₂O₅. The V1O₆ and V2O₆ octahedra in β-V₂O₅ are drawn yellow and cyan, respectively.

VO₂(B)

VO₂(B) is synthesized by reducing V₂O₅ in a sulphur or hydrogen atmosphere.⁴¹ Its crystal structure (C2/m, Z = 8) consists of sheets of edge- and corner-sharing distorted VO₆ octahedra. It could be derived from the one of α-V₂O₅ by a crystallographic shear when every second oxygen plane is removed, and the adjacent blocks are shifted by the vector ⅙[103]. In an alternative description, each sheet in VO₂(B) could be separated into two layers of the idealized α-V₂O₅ type,¹³ which share octahedral edges with each other (Fig. 2).

VO₂(B) as a bulk, nanorod, or thin film material undergoes a first-order isostructural phase transition in the range 180–300 K (ref. 42–46) with co-existing low-temperature (insulating and magnetically ordered), intermediate-temperature (insulating), and high-temperature (presumably metallic) phases.⁴⁵ The transition is associated with partial V⁴⁺–V⁴⁺ pairing.⁴² When heated in argon, it transforms to R.⁴³ When heated under reducing conditions, it turns into corundum. Annealing in vacuum yields M1.⁴⁷

Under uniaxial tensile strain, VO₂(B) undergoes MIT at room temperature.⁴⁸ The transition along the b axis is gradual, while it is abrupt along the a axis. Insulating domains develop with increasing tensile strain along the b axis. They are due to the V–V dimerization within the distorted zigzag chains of vanadium atoms in the octahedral ribbons (Fig. 2).

The structural phase transition VO₂(B) → VO₂(A) is induced by uniaxial compressing and grinding VO₂(B) powders at room temperature and by subsequent heat treatment.^49,50 In nanobelts, the sequence of the phase transitions is VO₂(B) → VO₂(A)_HT → VO₂(A)_LT, where VO₂(A)_LT and VO₂(A)_HT are the low- (P4/ncc, Z = 16) and high-temperature (I4/m, Z = 8) phases of VO₂(A), respectively.⁵¹ In the low-temperature structure below 435 K, the V atoms form zigzags with alternating short and long V–V distances in the c direction due to V⁴⁺–V⁴⁺ pairing. At higher temperatures, they form straight lines of equidistant V atoms. VO₂(A) has a lower formation energy compared to VO₂(B).⁵² On annealing, VO₂(A) transforms to M1.³

The difference between VO₂(B) and both phases of VO₂(A) is the connectivity of the VO₆ octahedra (Fig. 2). According to the structure interpretation in ref. 48–51, the ribbons in VO₂(B) are formed by octahedral doublets that share edges with the adjacent doublets. In VO₂(A), the neighbouring doublets are rotated by 90° with respect to each other and share edges. The resulting chains share corners in the three-dimensional framework. Our description of the low- and high-temperature VO₂(A) structures, which is an alternative to the one in ref. 49–51, is that they consist of slabs of edge-sharing octahedra stacked along the [110] or [11̄0] directions. Each slab is then formed by two edge-sharing layers that are formed by ribbons that are nearly exactly like those in α-V₂O₅ and VO₂(B) (Fig. 2). In other words, α-V₂O₅, VO₂(B), and VO₂(A) have the same building unit that is the single layer of the idealized α-V₂O₅ octahedral type.¹³ The differences arise from the stacking of these layers due to corner-sharing in α-V₂O₅ and different schemes of octahedral edge-sharing in VO₂(B) and VO₂(A).

At room temperature, VO₂(B) nanosheets and nanobelts become amorphous above 21 GPa (ref. 53) and 30 GPa,⁵⁴ respectively, due to a dynamically hindered transformation to M1.⁵³ When annealed at atmospheric pressure, the recovered material, produced during amorphization of the nanosheets, recrystallizes back to VO₂(B). VO₂(A) becomes metallic at about 28 GPa and amorphizes at 32 GPa at room temperature.⁵⁵

Wadsley homologous series V_nO_2n+1

Known Wadsley V_nO_2n+1 phases are V₃O₇ (V_0.86O₂), V₄O₉ (V_0.89O₂), and V₆O₁₃ (V_0.92O₂) (Fig. 4). The stable compounds in the experimentally determined V–O phase diagram are V₃O₇ and V₆O₁₃,¹ while thermodynamical calculations find only V₃O₇ as a stable phase.² The difficulty extending the series using various synthesis methods at ambient conditions is due to different chemical and structural characteristics of the V⁴⁺ and V⁵⁺ cations. The unifying description of the crystal structures for n = 2, 3, and 6 as well as for α-V₂O₅ and VO₂(B) is presented in ref. 8. These materials have oxygen-deficient structures deduced from VO_x (Fm3̄m, Z = 4), where x ≈ 1, by introducing different ordered vacancies in the oxygen close-packing array. Symmetry breaking and collapse of the fcc layers along the cubic c axis induces shear deformations. The considerations in ref. 8 do not include the analysis of the structures of V₄O₉ determined in ref. 56 and 57. A classification of the polyhedral connectivities is given in ref. 13. A summary of the compounds discussed in this section, including α-V₂O₅ as well as VO₂(B) and VO₂(A), is provided in Table S2 in the SI.

Fig. 4 Idealized crystal structures in the Wadsley homologous series.

V₃O₇

V₃O₇ (C2/c, Z = 12), which is an insulator and uniaxial ferromagnet,^58,59 is synthesized from a mixture of V₂O₃ and V₂O₅.⁶⁰ The structure is built of distorted VO₆ octahedra and VO₅ polyhedra joined by corner- and edge-sharing to form a three-dimensional framework (Fig. 4). The VO₅ polyhedra could be interpreted either as distorted trigonal bipyramids or square pyramids. The V⁴⁺ cations are situated in the octahedra, while the V⁵⁺ cations are in the VO₅ polyhedra.

Related to VO₂(S)³² is the cation-deficient insulating oxide V_3.047O₇ (P3, Z = 2) obtained by reduction of V₂O₅ at 5 GPa and 1073 K.⁶¹ It has a composition very close to V₃O₇ and is reported to have the Al₄Ta₃O₁₃(OH) simpsonite-type structure. The structure of V_3.047O₇ is described as a stacking of two octahedral layers along the c direction. One of them has isolated triplets of edge-sharing VO₆ octahedra. In the other, the triplets are connected to each other via additional bridging octahedra around partially occupied vanadium sites. Zibrov et al.⁶¹ expected that a new phase of V₃O₇ with the simpsonite structure could also be synthesized from a mixture of V₂O₃ and V₂O₅ at the same pressure–temperature conditions. However, their synthesis was not successful.

V₄O₉

Three different V₄O₉ products, depending on the synthesis procedures, are reported in the literature. The phase prepared by decomposing V₃O₇ in supercritical water at 873 K and 0.2 GPa (Pnma, Z = 4) is built of highly distorted edge-sharing octahedra in zigzag ribbons running along the b direction (Fig. 4).⁵⁶ The ribbons are joined by corners to form a three-dimensional framework. V₄O₉ could also be grown topotactically on single crystals of α-V₂O₅ by reducing them in a sulphur atmosphere.⁵⁷ The resulting crystal structure can then be considered a distorted superstructure of α-V₂O₅. The third product (Cmcm, Z = 8) can be obtained with a soft chemistry method also by reducing V₂O₅ with sulphur.⁶² It is composed of pairs of distorted edge-sharing octahedra and square pyramids linked by corner sharing with tetrahedra. The V atoms in the octahedra and pyramids have the valence 4+, while they have the valence 5+ in the tetrahedra. Such a structure cannot be explained with the shear concept that relies on the presence of oxygen-plane faults. This product is a spin-½ one-dimensional antiferromagnetic system with a spin-gap ground state.⁶²

α-V₆O₁₃

α-V₆O₁₃ (C2/m, Z = 2), obtained by reacting a mixture of V₂O₃ and V₂O₅ in an evacuated quartz glass tube at 873 K,^63–65 is composed of single and double layers formed by edge- and corner-sharing distorted VO₆ octahedra. The crystal structure can be described as built of alternating VO₂(B)- and idealized α-V₂O₅-like layers stacked along the c axis (Fig. 2, 4, and 5). One of the sites for the vanadium atoms in the double layer is preferentially occupied by the V⁵⁺ cations.⁶⁶ In the idealized α-V₂O₅, the shear planes separate narrow slabs of the ReO₃ type.⁶⁵ The structure of α-V₆O₁₃ is formed when another set of shear planes, perpendicular to the first, is introduced in α-V₂O₅ resulting in the loss of oxygen. The relationship between α-V₂O₅ and α-V₆O₁₃ is also defined in ref. 67. Removing all the atoms on every third (001) oxygen-atom plane in α-V₂O₅ and introducing crystallographic shear ⅙[103̄] leads to the structure of α-V₆O₁₃. Such a mechanism of transformations yields the double layer of the VO₂(B) type. The shear in β-V₆O₁₃ (Cmma, Z = 4), which is obtained by exposure of α-V₆O₁₃ to an electron beam⁶⁷ and by hydrothermal synthesis,⁶⁸ is ½[01̄1̄]. The difference between the α and β phases of V₆O₁₃ is clearly visible in Fig. 5: the double layer in β is like the slab in VO₂(A) (Fig. 2). Worth noting is the fact that a pseudosymmetry search⁶⁹ in β-V₆O₁₃ with respect to the minimal supergroups of Cmma results in the structure with space group Fmmm (Z = 4). This transformation does not involve any atomic displacements indicating that the reported space group symmetry Cmma⁶⁷ is too low.

Fig. 5 Crystal structures of the α and β phases of V₆O₁₃.

α-V₆O₁₃ is a paramagnetic metal at ambient conditions. It undergoes MIT at T_MIT = 150 K but remains paramagnetic down to 55 K.^70–75 T_MIT decreases to 100 K at 1.4 GPa.⁷⁴ The low-temperature crystal structure is disputed as C2 (ref. 74) and P2₁/a⁷⁶ space groups are initially proposed. The most recent study reports the structure in space group Pc.⁷⁰ All these models exhibit a high degree of pseudosymmetry with respect to space group C2/m and distortions from the parent phase are very small. In Pc, all the atoms are displaced from the mirror plane, but the structural changes appear mainly in the single layer. The charge transfer between the vanadium atoms in the single and double layers takes place during this phase transition. Some of the vanadium atoms in the single layer acquire more pentavalent character, while the others develop the tetravalent one. The model in space group Pc is then used to explain the changes of various physical properties across MIT in all subsequent studies.^71–74 At T_N ≈ 55 K, α-V₆O₁₃ becomes antiferromagnetically ordered.⁷⁴ However, the crystal and magnetic structures below T_N have not been reported yet.

At room temperature, α-V₆O₁₃ is structurally stable to at least 9.4 GPa.³⁷ Single-crystals of rutile-related V_0.92O₂ can be grown at 10 GPa and 1273 K from a polycrystalline α-V₆O₁₃ starting material.⁶⁵ In situ synchrotron measurements reveal that this new phase starts to crystallize above 500 K in the pressure range 4–17.5 GPa and is recovered to ambient conditions. The characteristic feature of its crystal structure (C2/m, Z = 4) is the presence of disorder affecting the V atoms, which occupy two split atom positions V1 and V2 (Fig. 6). The V1 atoms in one of the octahedral chains are displaced along the b axis, while the V2 atoms in the other are four-fold split in the (b, c) plane. This results in two zigzag V–V chains: one with equidistant V1 atoms and the other with short and long V2–V2 distances. There is no indication for V⁴⁺ and V⁵⁺ charge ordering and separation. Disregarding the V split positions, the average structure (P2/m, Z = 2) of this new phase is like the one for the V_1−zO₂ material obtained by Chamberland.^33,34 Pseudo-symmetry considerations⁶⁹ indicate that rutile-related V_0.92O₂ is a variant of insulating M2 (Fig. 1).⁶⁵

Fig. 6 Comparison of the ideal rutile and V_0.92O₂ crystal structures. The V1O₆ and V2O₆ octahedra are drawn yellow and cyan, respectively.

V_0.92O₂ is metastable when recovered to ambient conditions. It starts to decompose at 470 K and atmospheric pressure.⁷⁷ At about 350 K, the material undergoes a first-order phase transition, in which the low- and high-temperature phases have the same average structure (P2/m, Z = 2). The temperature for this transformation correlates well with those in V_0.995O₂ and V_0.976O₂.³³ V_0.92O₂ above the phase transition forms a modulated structure in super-space group X2/m(0β0)s0 (Z = 2) with the centering vector X(½, 0, ½, ½). The structure is remarkable as it is mainly the modulation of the displacement parameters of the vanadium atoms that dominate the incommensurate phase. Both structures of V_0.92O₂ have one important feature common to all the known (non-)stoichiometric VO₂ phases: the hexagonal close-packing oxygen sublattice is rigid while the cation sublattice is flexible, allowing for various schemes of cation (dis)order.

The first-order phase transition to the incommensurate phase in V_0.92O₂ is also visible in the temperature-dependent resistivity data measured on a single crystal on heating and cooling in the range 275–400 K.⁷⁷ On heating, the onset of the phase transition is at about 330 K. A hysteresis of about 10 K is observed on cooling the crystal from 400 K down to room temperature. Both phases of V_0.92O₂ are insulating. Such a behaviour is different from that of (nearly) stoichiometric VO₂, in which the high-temperature phases are metallic.^16,32

On compression at room temperature, V_0.92O₂ reaches the ideal rutile structure at about 5.0 GPa.⁷⁷ This transformation is also of the first-order character. It demonstrates that the structural behavior of the cation deficient vanadium dioxide at extreme conditions is distinctly different from that of stoichiometric VO₂.^26–31

Conclusions and outlook

Ribbons of edge-sharing VO₆ octahedral doublets could be traced in the crystal structures along the Wadsley series at atmospheric pressure. They are a basic building unit in idealized α-V₂O₅, VO₂(B), and related VO₂(A). The connectivity of the rutile type, with chains of edge-sharing octahedra joined with each other by corners, can be found in the materials synthesized at high pressures. It is partially realized in δ-V₂O₅ (ref. 37–40) and fully achieved in V_0.92O₂ (ref. 65 and 77) obtained from V₆O₁₃. This could imply that vanadium oxides with the Wadsley stoichiometries V_nO_2n+1 and high VO₂ content (at least n ≥ 6) would tend to transform to the rutile type at extreme conditions. The crystal structures of the Magnéli phases at ambient are also derived from the rutile one. The rutile structure would then be an aristotype for both cation and anion deficient vanadium dioxides at various pressures and temperatures. The rigidity of the hexagonal close-packing oxygen sublattice and different occupational schemes of the V³⁺, V⁴⁺, and V⁵⁺ cations could also result in the occurrence of incommensurate phases in non-stoichiometric VO₂.

Metallic properties in all the rutile-type as well as Wadsley phases are observed in the compounds with no V–V dimerization along the octahedral chains (see also Tables S1 and S2 in the SI). The application of pressure in the synthesis could yield materials with shorter V–V distances but would not necessarily break the dimers. Based on the current data available for the V₂O₅–VO₂ system, it is not possible to establish any relation of the crystal structures and properties with the synthesis conditions without considering the compositional variations. V_0.92O₂, which is insulating, contains 35 wt% of V₂O₅.^65,77 It demonstrates the capacity of the rutile-type framework to accommodate a wide range of VO₂–V₂O₅ compositions. Varying stoichiometries and pressure–temperature conditions could then yield V_1−zO₂ materials with transport properties ranging from metallic to insulating. Since the compound with 10 wt% of V₂O₅ (V_0.976O₂) is indeed metallic,³³ it remains to be seen for which higher V₂O₅ contents V_1−zO₂ oxides would become insulating. In addition, 35 wt% of V₂O₅ does not need to be a compositional limit for the stability of the rutile-related structures. We conclude then that materials engineering by varying compositions in the system V₂O₅–VO₂ and exerting high pressures and temperatures offers a possibility to synthesize new materials with unexpected properties.

Previous studies show that T_MIT decreases in the anion-deficient VO_2−y, while it increases in the cation-deficient V_1−zO₂.^14,16,33 For small deviations from the exact VO₂ stoichiometry, the high-temperature phase is supposed to have the ideal rutile structure. However, this has not been clearly demonstrated either for the compounds synthesized at elevated pressures reported in ref. 33 nor for several materials, which can already be obtained at atmospheric conditions.¹⁶ Further detailed investigations of the structural and electronic (in)stabilities in the non-stoichiometric vanadium dioxides are then warranted as the occurrence of the ideal R and metallic phases in the V_1−zO₂ materials is not demonstrated.

Author contributions

Both authors contributed equally to this work.

Conflicts of interest

No conflicts of interest.

Data availability

All data discussed in the manuscript are available upon request.

Supplementary information (SI) is available. See DOI: https://doi.org/10.1039/d5ce01171j.

Acknowledgements

This work is supported by the Helmholtz InnoPool Project MATHIPE (MATerials under HIgh PrEssure).

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