Phase transitions in rutile-related V_0.92O₂ synthesized at high pressures and tem­per­a­tures

Structural phase transitions in metastable rutile-related V_0.92O₂ synthesized at 10 GPa and 1273 K were studied with single-crystal X-ray diffraction in the tem­per­a­ture range 110–500 K and at pressures up to 9.2 GPa. V_0.92O₂ starts to decom­pose at 470 K and atmospheric pressure. When heated to tem­per­a­tures above about 350 K, the material transforms to an incommensurate phase. The oxygen sublattice is essentially rigid and it is mostly the V atoms that are affected by the modulation. An anharmonic description of the displacement parameters and their corresponding modulation is used for the V atoms to reach satisfactory agreement factors for main and first-order satellite reflections, indicating substantial disorder in the modulated structure. Measurements of electronic transport properties provide evidence that the incommensurate phase is insulating. On com­pression at room tem­per­a­ture, V_0.92O₂ reaches the ideal rutile structure at about 5.0 GPa. Both structural and electronic phase transitions are of the first-order character. The results of this work demonstrate that the structural and electronic behaviour of V_0.92O₂ at extreme conditions is distinctly different from that of stoichiometric VO₂.

1. Introduction

Vanadium dioxide (VO₂) undergoes a first-order metal–insulator phase transition (MIT) from the rutile (phase R, P4₂/mnm, Z = 2) to the monoclinic (phase M1, P2₁/c, Z = 4) polymorphs at about T_MIT = 341 K (Qazilbash et al., 2007; Shao et al., 2018; Liu et al., 2020; Pouget, 2021; Xue & Yin, 2022; Joshi et al., 2023). The metallic R phase is built of chains of edge-sharing VO₆ octa­hedra connected by common corners. The V—V distance of 2.85 Å along the chains is equal to the c lattice parameter. The structure of the insulating M1 phase is also made of two VO₆ chains, but with V–V dimers in a zigzag pattern due to displacement of the V atoms from the ideal rutile positions (Longo et al., 1970). The R→M1 structural instability gives rise to pre-transitional diffuse scattering (Pouget, 2021). MIT, which is an improper ferroelastic phase transition, is associated with a magnetic susceptibility drop (Pouget, 2021) and a change in thermochromic properties (Mamakhel et al., 2022).

Doping with low-valence cations (e.g. Al³⁺, Cr³⁺ and Fe³⁺) stabilizes two additional insulating polymorphs, which are monoclinic (phase M2, C2/m, Z = 8) and triclinic (phase T, P, Z = 4). In M2, there are alternate short and long distances in the linear V—V chain, while the V atoms are equidistant in the other zigzag V—V chain (Marezio et al., 1972; Ghedira et al., 1977). The distortion in T with respect to M2 is mainly due to breaking of the linearity and pairing of the V atoms in the zigzag chain (Ghedira et al., 1977). The stabilities of phases R, M1, M2 and T are affected by stoichiometry, electric field, strain or pressure (Marezio et al., 1972, Ghedira et al., 1977; Atkin et al., 2012; Liu et al., 2018; Pouget, 2021; Wilson et al., 2022; Bouvier et al., 2023; Joshi et al., 2023). M1 and M2 can transform into one another, with T as an inter­mediate (Marezio et al., 1972). M2 could also be an inter­mediate in the M1→R transformation (Liu et al., 2020; Bleu et al., 2023). The three insulating phases may co-exist and form domains (Lu et al., 2014). The high-valence dopants (e.g. Nb⁵⁺, Mo⁶⁺ and W⁶⁺) lower the T_MIT, while the low-valence dopants (e.g. Al³⁺, Cr³⁺ and Fe³⁺) increase it (Pouget, 2021; Xue & Yin, 2022; Joshi et al., 2023). In the first case, the charge is com­pensated by the presence of the V³⁺ cations. In the latter, it is com­pensated by the V⁵⁺ cations.

⁵¹V NMR studies of the metallic and insulating phases of VO₂ provide contradictory results. Boyarsky et al. (2000) suggested that MIT is accom­panied by the change of the electronic state 2V⁴⁺ ↔ V³⁺ + V⁵⁺, with the presence of two structurally and chemically different vanadium cations V³⁺ and V⁵⁺ in M1. On the other hand, the data by Gro Nielsen et al. (2002) show the presence of only V⁴⁺ cations in the insulating phase. Electrical and photoemission investigations by Joshi et al. (2023) demonstrated that the V³⁺ and V⁵⁺ cations co-exist in the metallic state of stoichiometric VO₂ due to charge fluctuations of the V⁴⁺ cations. The insulating phase is sup­pressed in VO_2–x, while the metallic phase is suppressed in VO_2+y. However, Joshi et al. (2023) did not present structural data for any of the VO_2–x and VO_2+y phases across MIT.

The pressure–tem­per­a­ture phase diagram of VO₂ was determined by Chen et al. (2017). In addition to the R and M1 polymorphs, one insulating M1′ (monoclinic) phase and two metallic phases X (triclinic) and O (ortho­rhom­bic) were identified. When M1 is com­pressed at room tem­per­a­ture, it transforms to M1′ at 13.9 GPa (Bouvier et al., 2023). X co-exists with M1′ in the pressure range 32–42 GPa. Upon decom­pression, X transforms to another (unidentified) phase between 20 and 3 GPa. The sequence of phase transitions in VO₂ under strong com­pression was examined by Xie et al. (2018).

Apart from VO₂, the 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), V₃O₇, V₆O₁₃ and V₂O₅ (Wriedt, 1989). The calculated phase diagram for 1.5 ≤ x ≤ 2.5 includes only V₂O₃, V₃O₅, VO₂, V₃O₇ and V₂O₅ (Hu et al., 2023). The oxides V_nO_2n–1 (n = 3 ÷ 9) form a Magnéli homologous series (Schwingenschlögl & Eyert, 2004; Allred & Cava, 2013) according to the formula V_nO_2n–1 = V₂O₃ + (n − 2)VO₂. With respect to the com­position of vanadium dioxide, they are anion deficient and can also be expressed as VO_2–y. The end members of this series are corundum V₂O₃ (Rc, Z = 6) and rutile VO₂ (phase R), both with a hexa­gonal close-packed array of O atoms (Katzke et al., 2003). One oxygen layer is removed at every nth vanadium layer in the direction perpendicular to the (211) plane of the parent rutile structure. Magnéli phases are also known for the titanium, niobium and tungsten oxides (Wu et al., 2023).

The homologous series of vanadium oxides V_nO_2n+1 in the V₂O₅–VO₂ system was predicted by Wadsley (1957). Its formula can be written as V_nO_2n+1 = V₂O₅ + (n − 2)VO₂ for 2 ≤ n. With respect to the chemical com­position of VO₂, the Wadsley oxides are cation deficient, i.e. V_1–xO₂. The end members of this series are α-V₂O₅ and VO₂(B) (Katzke et al., 2003). These materials have structures derived from VO_x (Fmm, Z = 4), where x ≃ 1, by introducing different ordered vacancies in the oxygen cubic close-packing array. Shear deformations break symmetry and cause the collapse of the face-centred cubic layers along the cubic c axis. The cations partially fill out the available voids in the oxygen sublattice in a commensurate way.

Metal-deficient V_1–xO₂ material, synthesized at 6.5 GPa and 1273 K by substituting V⁵⁺ into VO₂ (Chamberland, 1973), has a distorted rutile structure (P2/m, Z = 2), with the V—V distances in both chains equal to the b lattice parameter (Galy & Miehe, 1999). Up to 10 wt% of V₂O₅ was accommodated in V_1–xO₂ at these conditions. Based on the resistivity data, the tem­per­a­tures for MIT depend on the actual com­position (Chamberland, 1973). They increase from 353 to 361 K for 2 wt% (V_0.995O₂) and 10 wt% of V₂O₅ (V_0.976O₂), respectively. No structural details of the metallic phase were provided.

Recently, we have grown single crystals of rutile-related V_0.92O₂ at 10 GPa and 1273 K from a polycrystalline starting material of the Wadsley phase V₆O₁₃ (Grzechnik et al., 2024) corresponding in terms of its com­position to V_1–xO₂ (Chamberland, 1973) or VO_2+y (Joshi et al., 2023) with 35 wt% of V₂O₅. In situ synchrotron measurements revealed that this new phase forms above 500 K in the pressure range 4–17.5 GPa and can be 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 the two split-atom positions V1 and V2. The V1 atoms in one of the octa­hedral chains are displaced along the b axis, while the V2 atoms in the other are fourfold split in the bc plane. This results in two zigzag V—V chains, one with equidistant V1 atoms and the other with short and long V2—V2 distances. Disregarding the split V-atom positions, the average structure (P2/m, Z = 2) of this new phase (Fig. 1) is like that for the V_1–xO₂ material (Chamberland, 1973; Galy & Miehe, 1999). Pseudosymmetry considerations (Grzechnik et al., 2024) indicate that it is the ordered variant of M2. The transformation of the Wadsley phase V₆O₁₃ into rutile-related V_0.92O₂ involves the transition from cubic to hexa­gonal close-packing of the O atoms.

Figure 1 The average crystal structure in the space group P2/m (Z = 2), as well as the tem­per­a­ture dependence of its lattice parameters and unit-cell volumes. The octa­hedra around the V1 and V2 atoms are drawn in yellow and cyan, respectively. The O1 and O2 atoms are labelled. The symbols in the plots of the lattice parameters and unit-cell volumes are larger than the estimated standard deviations.

The physical properties of different structural forms of V_1–xO₂ are closely correlated with the formation and spatial arrangement of the short V—V distances (Liu et al., 2018; Joshi et al., 2023). Detailed experimental characterization of new types of structural ordering, such as the (in)commensurate long- or short-range order, are a necessary step towards the better understanding of structure–property relationships and the further control of the physical properties of vanadium oxides. While browsing the literature on (non)stoichiometric vanadium dioxides, one can readily see that most of the articles are somewhat incom­plete in the sense that either the structural or electronic properties and transformations of VO_2±x are investigated. In this article, we combine both approaches (i) to determine whether metastable V_0.92O₂ undergoes any tem­per­a­ture- or pressure-induced phase transitions using single-crystal X-ray diffraction, and (ii) to examine its electronic transport properties at atmospheric pressure for further elucidation of the structure–property relationships in vanadium dioxides.

2. Experimental methods

Single-crystal growth of V_0.92O₂ from the Wadsley phase V₆O₁₃ was described previously (Grzechnik et al., 2024).

Synchrotron single-crystal diffraction measurements (λ = 0.72044 Å) were performed on the BM01 station of the Swiss–Norwegian Beamlines (SNBL) at the European Synchrotron Radiation Facility (Grenoble, France) (Dyadkin et al., 2016). The data (a full rotation of 360°) were collected using a Pilatus 2M detector. After several tests on various crystals at room tem­per­a­ture to check for their quality and for any radiation damage (Grzechnik et al., 2023), our data collection strategy was to measure frames with a fine angular slicing of 0.1° and the exposure time of 0.1 s/frame. The chosen crystal was mounted on a glass pin and placed in the stream of nitro­gen from an Oxford Cryostream 700+. It was cooled to 100 K and the data were collected on heating to 500 K with a step of 10 K.

High-pressure single-crystal X-ray data at room tem­per­a­ture were measured on a STOE IPDS-II (Stoe & Cie GmbH, Darmstadt, Germany; λ = 0.71073 Å) equipped with an image plate, as well as on a 4-circle Huber diffractometer with an Ag microfocus Incoatec source (λ = 0.5608 Å) and a Pilatus 300k detector. A crystal of V_0.92O₂ was loaded into the Ahsbahs diamond anvil cell (Ahsbahs, 2012), together with a 4:1 (v/v) methanol–ethanol pressure medium and a ruby ball as a pressure marker (Mao et al., 1986).

All the laboratory and synchrotron data collected with the Pilatus detectors were analysed with the program CrysAlis PRO (Rigaku Oxford Diffraction, 2024). The data from the IPDS-II diffractometer were processed with the program X-AREA (Stoe & Cie, 1998). Solution and refinement of the structures were carried out with the programs JANA2006 (Petříček et al., 2014) and JANA2020 (Petříček et al., 2023).

Electronic transport measurements were carried out between 250 and 400 K inside a Quantum Design PPMS system, employing the electrical transport option (ETO). We used a standard four-wire measurement technique with a low AC excitation current of 100 µA to avoid parasitic sample heating and a frequency around 57 Hz. Good electronic contacts were made by attaching 10 µm Au wires to a single crystal of approximate dimensions 0.15 mm × 0.10 mm × 0.08 mm using an Ag paint. We confirmed a negligible phase angle of less than 1° over the tem­per­a­ture range.

3. Results and discussion

3.1. Single-crystal X-ray diffraction in the tem­per­a­ture range 110–500 K and under ambient pressure

On heating from 110 K to about 460 K, all the main reflections in the synchrotron data are indexed and integrated with the primitive monoclinic lattice corresponding to the average structure (P2/m, Z = 2) determined previously (Galy & Miehe, 1999; Grzechnik et al., 2024). Metastable V_0.92O₂ starts to collapse at above 460 K as the reflections become smeared out. Also, new additional reflections appear. Above 470 K, the observed reflections cannot be indexed as originating from a single phase, indicating decom­position of the V_0.92O₂ material.

From the abrupt changes of the lattice parameters and unit-cell volumes (Fig. 1), it is seen that the material undergoes a first-order iso-symmetrical P2/m→P2/m phase transition at about 350 K. The b lattice parameter of the high-tem­per­a­ture phase is smaller than that for the low-tem­per­a­ture phase. The drop in this lattice parameter at the phase transition is correlated with an abrupt shortening of the V—V distances in the octa­hedral chains. The a and c lattice parameters exhibit the same evolution in the entire tem­per­a­ture range studied here. The β angle, which is a measure of a monoclinic distortion of the tetra­gonal rutile structure, increases with elevated tem­per­a­ture and has a drastic change of slope at about 350 K. It is remarkable that the tem­per­a­ture of the phase transition observed in V_0.92O₂ is very similar to that observed in V_1–xO₂, depending on the com­positional variable x (Chamberland, 1973; Qazilbash et al., 2007; Liu et al., 2020; Pouget, 2021; Joshi et al., 2023).

The V—O distances in the average structure of V_0.92O₂ (P2/m, Z = 2) as a function of tem­per­a­ture are shown in Fig. 2. There is no obvious anomaly that could be associated with the phase transition at about 350 K. However, the O—O distances in both chains of octa­hedra exhibit clear changes in their tem­per­a­ture dependencies at the phase transition (Fig. 3). The equatorial planes of the octa­hedra are defined by the atoms involved in edge sharing in the chains. The apical atoms in V1O₆ and V2O₆ are O1 and O2, respectively. The shortest and longest O—O distances are in the equatorial planes of both polyhedra, i.e. the O2—O2 distances in the V1O₆ octa­hedra and the O1—O1 distances in the V2O₆ octa­hedra. The shortest distances correspond to the shared edges of the octa­hedra. The most affected O—O distances at the phase transition are those in the respective equatorial planes. The average O—O distances abruptly change at the phase transition – they increase in V1O₆, while they decrease in V2O₆ (Fig. 4). The octa­hedron around the V1 atom at the site with the higher occupancy is less distorted than that around the V2 atom and becomes more regular above the phase transition.

Figure 2 Temperature dependence of the V—O distances in the V1O6 (full symbols) and V2O6 (open symbols) octa­hedra in the average structure (P2/m, Z = 2).

Figure 3 Temperature dependence of the O—O distances in the average structure (P2/m, Z = 2). The error bars are shown when larger than the symbols.

Figure 4 Average O—O distances and Δ〈O—O〉 deviation parameter in the V1O6 (full symbols) and V2O6 (open symbols) octa­hedra of the average structure (P2/m, Z = 2). The deviation parameter is defined as Δ〈O—O〉 = .

Diffuse scattering is not observed in the laboratory data measured either on the IPDS-II diffractometer (image plate, Mo Kα radiation) or on the 4-circle diffractometer (Pilatus 300k detector, Ag microfocus source). However, the analysis of the reconstructions of the reciprocal space based on the synchrotron measurements reveals the presence of diffuse scattering at all tem­per­a­tures (Figs. 5 and 6). The intensity of the diffuse scattering increases close to the transition tem­per­a­ture. Above the phase transition, the diffuse features start to condense to well-defined satellite reflections. The strongest diffuse scattering is between the nearest satellites, which could be indexed with one incommensurate wave vector q = (, β, ), where β ≃ 0.234. This vector, which is essentially constant as a function of tem­per­a­ture, can only be precisely determined above 400 K (Fig. 7).¹ All these observations indicate that metastable V_0.92O₂ does not transform to the ideal rutile structure (R) at high tem­per­a­tures and ambient pressure.

Figure 5 Reconstructions of the reciprocal space in the (0kl) and (kl) planes (the upper and lower row, respectively) from the synchrotron data at selected tem­per­a­tures.

Figure 6 Reconstructions of the reciprocal space in the (hk0) and (hk) planes (the upper and lower row, respectively) from the synchrotron data at selected tem­per­a­tures.

Figure 7 Temperature dependence of the qβ com­ponent of the incommensurate vector.

All the main and satellite reflections in the diffraction pattern at 460 K can be indexed and integrated with monoclinic lattice parameters a = 4.5995 (4), b = 2.8746 (2), c = 4.6014 (4) Å and β = 92.49 (1)° in combination with the vector q = [, 0.2328 (9), ]. Only first-order satellites were detected. Satellites of the second order do not show any significant intensity in the integration and are also not visible in the reconstructions of reciprocal space. For all the refinements, the overall stoichiometry and occupancies for V1 and V2 were fixed to the values reported by Grzechnik et al. (2024), as a free refinement of the occupation parameters showed only minor deviations from this stoichiometry.

The refinement of the average structure at 460 K was carried out in the space groups P2/m, P2, Pm, P and P1. For the triclinic space groups, additional twinning via a twofold axis in the direction [010] was included. For none of the last four space groups were the overall agreement factors significantly better than for P2/m, considering the higher number of parameters in the refinements.

For the refinements of the incommensurate structure, the structure was transformed according to a′ = a + c, b′ = b and c′ = −a + c, with a resulting q vector of [0, 0.2328 (9), 0] to a pseudo-ortho­rhom­bic X-centred cell with X = (, 0, , ) and an angle of 90.02° (Table 1). Several trial refinements were performed in monoclinic and triclinic superspace groups. Considering the agreement factors and the number of parameters in the refinement, the best result was obtained in superspace group X2/m(0β0)s0. Additional twinning with a twofold axis in the direction [001] was included. The introduction of the twinning led to a significant decrease in the agreement factors for the satellite reflections. In this model, initially only the first harmonics of the Fourier coefficients of a displacive modulation of the V and O atoms were considered. This led to an unsatisfactory R(obs) agreement factor of approximately 25% for the satellite reflections and high difference density in the difference Fourier map around the V atoms. When the second harmonic of the displacive modulation function for the V atoms was added, a substantial decrease in the overall agreement factors for the satellite and main reflections was achieved, while introducing higher harmonics for oxygen or an occupational modulation wave for vanadium did not result in better agreement factors (while leading to an increased data-to-parameter ratio). However, a trial calculation of the intensities of the second-order satellites showed that, assuming this model, their intensities would be substantial so that they should be clearly observed. As this is not the case, it is obvious that this model cannot be the correct one. Also, an inspection of the de Wolff sections and the refined modulation functions around the V-atom positions clearly showed a very bad agreement. We therefore discarded the model with higher harmonics of the displacive modulation.

Table 1
Experimental and refinement details at 460 K (λ = 0.72044 Å)

Space group	X2/m(0β0)s0
Centring	X = , 0, ,
Z	4
a (Å)	6.6458 (6)
b (Å)	2.8746 (2)
c (Å)	6.3631 (6)
β (°)	90.024 (10)
V (Å^3)	121.562 (18)
q vector	0, 0.2328 (9), 0
ρ (g cm^−3)	4.3091
μ (mm^−1)	6.934
No. measured reflns	1297
Range of hkl	−8 ≤ h ≤ 8
	−4 ≤ k ≤ 4
	−8 ≤ l ≤ 84
	−1 ≤ m ≤ 1
θ (min/max)	3.53/32.52
No. symmetry independent reflns (all)	445
No. symmetry independent reflns (obs)^a	302
Rint(obs/all)	0.75/0.76
All reflns R(obs)/wR(all)^b	5.60/7.28
Main reflns R(obs)/wR(all)	5.08/6.44
Satellite reflns R(obs)/wR(all)	9.44/11.74
GoF (obs/all)	5.71/4.44
Twin law	(−100, 0−10, 001)
Twin volumes I/II	0.86 (4)/0.14 (4)
Δρmax, Δρmin (e Å^−3)	0.72, −0.79
No. parameters	92
Symmetry operations: (1) x1, x2, x3, x4; (2) −x1, x2, −x3, x4 + ; (3) −x1, −x2, −x3, −x4; (4) x1, −x2, x3, −x4 + . Notes: (a) criterion for the observed reflections is |F(obs)| > 3σ; (b) all agreement factors are given in percent (%) and the weighing scheme is 1/{σ^2F(obs) + [0.01F(obs)]^2}.

Instead, we started from the assumption of a modulation of the displacement parameters. The electron density around the V atoms in the average structure (Fig. S1 in the supporting information) was best described using an anharmonic tensor. As the com­ponents of the third-order tensor for V are fixed to zero by the symmetry, we introduced a fourth-order anharmonic tensor in the average structure. This led to a substantial decrease in the agreement factors for the main reflections. Introducing a modulation of the anharmonic displacement parameters also led to a significant decrease of the agreement factor for the satellite reflections of first order, while the intensities of the second-order satellites were very small, in accordance with our observations.²

According to an earlier chemical analysis, the overall com­position of the com­pound is V_0.92O₂ (Grzechnik et al., 2024), suggesting vacancies in the V sublattice. However, neither of the de Wolff sections showed any indication of a significant modulation of the height of maxima in the electron density, nor did the introduction and subsequent refinement of occupational modulation lead to better agreement factors. From these observations, we deduced that the V vacancies are randomly distributed within the V sublattice.

In the disordered room-tem­per­a­ture structure, the oxygen sublattice does not substanti­ally deviate from the ideal positions. This observation correlates very well with the fact that the O-atom positions and their displacement parameters are hardly affected by the modulation functions in the incommensurate structure (Table 2). Consequently, the O—O distances do not essentially vary as a function of the inter­nal parameter t if the standard deviations are considered (Table S1 in the supporting information). All these observations imply that the oxygen sublattice is nearly rigid (see animation S1 in the supporting information).

Table 2
Positional and isotropic displacement parameters of the atoms, as well as Fourier coefficients of the modulation amplitudes at 460 K

	Occupancy	x	y	z	Uiso
V1	0.492 (4)	0.0	0.0	0.0	0.0318 (11)
V2	0.428 (4)	0.0	0.5	0.5	0.0283 (13)
O1	0.5	−0.2003 (2)	0.0	0.5002 (4)	0.0155 (7)
O2	0.5	0.0005 (3)	0.5	0.2000 (2)	0.0128 (6)
	xsin1	ysin1	zsin1	xcos1	ycos1	zcos1
V1	0.0065 (4)	0.0	0.0003 (6)	0.0	0.0	0.0
V2	−0.0059 (4)	0.0	0.0001 (6)	0.0	0.0	0.0
O1	−0.0004 (3)	0.0	−0.0004 (6)	0.0	−0.0039 (8)	0.0
O2	0.0008 (3)	0.0	0.0001 (5)	0.0	0.0003 (10)	0.0
	u11	u22	u33	u12	u13	u23
V1	0.0693 (14)	0.0155 (18)	0.010 (2)	0.0	0.0068 (16)	0.0
V2	0.051 (2)	0.027 (2)	0.007 (3)	0.0	0.0025 (18)	0.0
O1	0.0147 (11)	0.0171 (9)	0.0147 (14)	0.0	0.0009 (12)	0.0
O2	0.0186 (13)	0.0112 (8)	0.0085 (12)	0.0	0.0059 (16)	0.0
V1/V2	uijsin1 = 0.0
	u11sin1	u22sin1	u33sin1	u12sin1	u13sin1	u23sin1
O1	−0.0009 (11)	−0.0002 (10)	−0.0004 (13)	0.0	0.0012 (15)	0.0
O2	0.0006 (17)	−0.0001 (13)	0.0020 (17)	0.0	−0.0004 (9)	0.0
	u11cos1	u22cos1	u33cos1	u12cos1	u13cos1	u23cos1
V1	For i = j uijcos1 = 0.0			0.0007 (9)	0.0	0.0012 (14)
V2				−0.0001 (11)	0.0	−0.0004 (16)
O1				0.0012 (7)	0.0	−0.0024 (15)
O2				−0.0008 (7)	0.0.	−0.0005 (12)
	D1111	D1113	D1122	D1133	D1223	D1333
V1	−0.0975 (13)	0.0019 (12)	−0.006 (3)	−0.0009 (8)	−0.005 (3)	−0.0007 (19)
V2	−0.019 (2)	−0.0022 (18)	−0.017 (3)	0.0017 (12)	−0.007 (3)	−0.003 (2)
	D2222	D2233	D3333	D1112 = D1123 = D1222 = D1233 = D2223 = D2333 = 0.0
V1	0.07 (4)	−0.009 (3)	0.000 (3)
V2	−0.10 (4)	−0.012 (3)	−0.002 (3)
	C111sin1	C113sin1	C122sin1	C133sin1	C223sin1	C333sin1
V1	−0.048 (2)	0.006 (2)	−0.015 (4)	−0.0037 (13)	−0.000 (5)	0.002 (3)
V2	0.022 (3)	−0.004 (2)	0.016 (5)	0.0020 (12)	0.000 (6)	0.000 (4)
V1/V2	C112sin1 = C123sin1 = C222sin1 = C233sin1 = 0.0
V1/V2	Cijkcos1 = 0.0
	D1112cos1	D1123cos1	D1222cos1	D1233cos1	D2223cos1	D2333cos1
V1	−0.000 (3)	0.002 (2)	0.008 (9)	−0.0002 (12)	0.007 (11)	−0.000 (4)
V2	0.006 (3)	−0.002 (3)	−0.004 (10)	0.0004 (15)	0.005 (13)	−0.002 (4)
V1/V2	D1111cos1 = D1113cos1 = D1122cos1 = D1133cos1 = D1223cos1 = D1333cos1 = D2222cos1 = D2233cos1 = D3333cos1 = 0.0
V1/V2	Dijklsin1 = 0.0

Amplitudes of the displacive modulation of the V atoms are also hardly significant and V—V distances are almost constant in the modulated structure (Table S2). We attribute the absence of significant displacements to the fact that the atoms are disordered over several split atom positions. In our structural model, the anharmonic displacement parameters and their corresponding modulations describe such a disorder of the atoms. While it is thus difficult to qu­antify the absolute displacements of the V atoms from their average positions, an inspection of the anharmonic displacement parameters reveals that the largest displacements are in the direction of a (animation S1). This is also clearly visible in animations S2 and S3, which show the joint probability density function (j.p.d.f.) around the V-atom positions in the modulated structure. Animations S4 and S5 show the j.p.d.f. around the O atoms. A complete animation of the incommensurate phase, including the j.p.d.f. for all the atoms in the unit cell, is in animation S6.

In the disordered room-tem­per­a­ture structure, the V1 atoms are arranged in a zigzag pattern, with a V1—V1 dis­tance of 2.9020 (2) Å. In the modulated structure, the average V1—V1 and V2—V2 distances are slightly smaller at 2.87489 (3) and 2.87484 (3) Å, respectively. Thus, surprisingly, the V—V distances are smaller at higher tem­per­a­tures. How­ever, the true positions of vanadium in the modulated structure are difficult to determine due to the additional disorder modelled by the anharmonic displacement parameters and their modulation.

Considering the V1O₆ octa­hedra, in the modulated structures there are four shorter V—O bonds, plus two longer ones (Table S3). On the other hand, within the V2O₆ octa­hedra, the situation is reversed and there are four longer and two shorter V—O bonds (Table S3).

In the disordered structure at room tem­per­a­ture, the bond valence sums (BVSs) of V1 and V2 are basically equal and amount to about 4.0 v.u. (with the BVS parameters for V⁴⁺) or about 4.4 v.u. (with the BVS parameters for V⁵⁺). In the modulated structure, the bond valence sums are smaller, with values of around 3.80 for both V atoms assuming a bond valence parameter of V⁴⁺ and 4.15 for a bond-valence parameter of V⁵⁺. Again, one must consider that these parameters are based on the average V-atom coordinates and do not really reflect the deviations from these average positions described by the anharmonic parameters.

3.2. Measurements of electronic transport properties at atmospheric pressure

Fig. 8 shows qualitatively the evolution of resistance measured on a single crystal of V_0.92O₂ on heating and cooling in the range 275–400 K. The onset of a first-order phase transition is at about 330 K. A hysteresis of about 10 K is observed on cooling the crystal from 400 K to room tem­per­a­ture. The data clearly show that both phases are non-metallic. V_0.92O₂ becomes even more insulating above the phase transition. Such a behaviour is different from that of (nearly) stoichiometric VO₂, in which the high-tem­per­a­ture phases are metallic (Chamberland, 1973; Joshi et al., 2023).

Figure 8 Resistance versus tem­per­a­ture on heating (black line) and cooling (red line) in the range 275–400 K.

3.3. Single-crystal X-ray diffraction to 9.2 GPa at room tem­per­a­ture

The high-pressure single-crystal data measured on both laboratory diffractometers up to 9.2 GPa at room tem­per­a­ture were analyzed in the average structure in P2/m (Z = 2). The β angle decreases on com­pression, and it becomes equal to 90° at 4.9 GPa (Fig. 9). All the reflections at this and higher pressures can be indexed with the tetra­gonal lattice: a ≃ 4.5 Å and c ≃ 2.8 Å. There is also a discontinuity in the lattice parameters b_m ↔ c_t, which are determined by the V—V distances in the octa­hedral chains. This implies a first-order phase transition from the monoclinic to tetra­gonal phases at about 3.7–4.9 GPa. The data measured at 6.35 GPa and room tem­per­a­ture on the 4-circle diffractometer could be integrated and refined with the ideal rutile structure (Tables S4–S6). The P2/m ↔ P4₂/mnm phase transition is reversible on decom­pression. All these observations agree with our previous observations about the fact that, on quenching to ambient conditions, rutile V_0.92O₂ transforms to a range of its distorted variants depending on the actual highest pressure and tem­per­a­ture reached during the synthesis (Grzechnik et al., 2024). The behaviour of metal-deficient V_0.92O₂ at high pressures and room tem­per­a­ture is therefore different from that of the M1 phase of stoichiometric VO₂, which transforms to a series of low-symmetry polymorphs but not to ideal rutile (Chen et al., 2017; Bouvier et al., 2023).

Figure 9 Lattice parameters, β angles and unit-cell volumes for the monoclinic (m, full symbols) and tetra­gonal (t, open symbols) phases on com­pression at room tem­per­a­ture. The estimated standard deviations are smaller than the size of the symbols. The solid lines are the fits of the third-order Murnaghan equations of state.

The monoclinic phase is much more com­pressible than the tetra­gonal one. The P–V data up to 3.66 GPa can be fitted with the third-order Murnaghan equation of state (EoS): V₀ = 60.24 (2) ų, B₀ = 66 (3) GPa and B₀′ = 29 (3). Since the zero-pressure volume V₀ for the tetra­gonal polymorph cannot be determined from the EoS fit, a modified third-order Murnaghan EoS in terms of (P – P_tr), where P_tr = 4.91 GPa in the transition pressure, was used. Consequently, V_tr = 57.80 (2) ų, B_tr = 143 (13) GPa and B_tr′ = 16 (8) are obtained at P_tr = 4.91 GPa. The B₀/B_tr and B₀′/B_tr′ parameters can be com­pared with those for the different polymorphs of stoichiometric VO₂. The bulk modulus B₀ for the phase M1 determined theoretically (Dong & Liu, 2013) is 237 GPa, while the reported experimental values are 213 (2) (Bai et al., 2015) and 194 (7) GPa (Bouvier et al., 2023). The theoretical B₀ for M2 is 241 GPa (Dong & Liu, 2013). According to the calculations by Dong & Liu (2013), B₀ for rutile VO₂ is 243 GPa. The experimental B₀ for rutile at 383 K is 190 (2) GPa (Bai et al., 2015). The most com­pressible polymorph of stoichiometric vanadium dioxide is VO₂(B), with B₀ = 129 (4) GPa (Wang et al., 2016), which is com­parable to V_0.92O₂. The first derivatives of the bulk moduli for V_0.92O₂ are higher than all those for VO₂, which are in the range 4–7 (Dong & Liu, 2013; Bai et al., 2015; Wang et al., 2016; Bouvier et al., 2023).

4. Conclusions

Structural modulations are usually stabilized at low tem­per­a­tures as a disordered structure transforms into a more ordered one on cooling. Notable exceptions are brownmillerites Ca₂Fe₂O₅ (Krüger et al., 2005) and Ca₂Al₂O₅ (Lazic et al., 2008), as well as inter­metallic PdBi (Folkers et al., 2020). In the brownmillerites at about 1000 K, the modulation arises from the incommensurate sequence of enanti­omorphic left- and right-handed tetra­hedral BO₄ chains (B = Fe or Al). In PdBi with the structure related to TlI, the incommensurability on heating to above 473 K originates from the presence of nearly regular TlI-type slabs in a distorted TlI superstructure with Pd–Pd dimers. Folkers et al. (2020) inter­preted the TlI-type slabs as the regions of higher vibrational freedom that are entropically favoured at high tem­per­a­tures. Metastable V_0.92O₂, which is investigated in this study, undergoes a phase transition to an incommensurate phase above about 350 K. Our inter­pretation is that such behaviour is a consequence of an incommensurate way of disordering of V⁴⁺ and V⁵⁺ cations, which are chemically and structurally distinct with different ionic radii, in a rigid hexa­gonal close-packing oxygen sublattice. Eventually, V_0.92O₂ starts to decom­pose above 460 K at atmospheric pressure. In other words, decom­position is preceded by incommensurability. Such a phenomenon could possibly be found in other materials, not necessarily metastable and synthesized at high pressures.

V_0.92O₂, which contains 35 wt% of V₂O₅, is insulating. It demonstrates the capacity of the rutile-type framework to accommodate a wide series of VO₂–V₂O₅ com­positions. It also suggests that by varying stoichiometries and pressure–tem­per­a­ture conditions one would synthesize rutile-related V_1–xO₂ materials with transport properties ranging from metallic to insulating. Since the com­pound with 10 wt% of V₂O₅ (V_0.976O₂) is indeed metallic (Chamberland, 1973), it remains to be seen for which higher V₂O₅ contents V_1–xO₂ oxides become insulating. In addition, 35 wt% of V₂O₅ does not need to be a com­positional limit for the stability of the rutile-related structure that has one important feature common to all the known (non-)stochiometric VO₂ phases: the hexa­gonal close-packing oxygen sublattice is rigid, while the cation sublattice is flexible, allowing for various schemes of cation (dis)order. Therefore, incommensurate phases could also be expected for other V_1–xO₂ com­positions, apart from V_0.92O₂.

Metal-deficient V_0.92O₂ reversibly transforms to the ideal rutile structure (P4₂/mnm, Z = 2) at about 5 GPa and room tem­per­a­ture. Altogether, the results of this work demonstrate that its structural behaviour under extreme conditions is distinctly different from that of stoichiometric VO₂.

Our findings imply then that the structural and electronic (in)stabilities of the non-stoichiometric vanadium dioxides warrant detailed investigations since the occurrence of the metallic R phases (P4₂/mnm, Z = 2) in the mixed-valence VO_2±x materials for different x ≠ 0 is not certain. As our work was focused on Bragg diffraction, further insight into the mechanism of the unusual phase transition observed in V_0.92O₂ on increasing the tem­per­a­ture could be obtained by a future detailed investigation of the diffuse scattering, which seems to occur as a precursor effect to the formation of the modulated structure.

Supporting information

Computing details

Vanadium dioxide (V0.92O2tetragonal)

Crystal data

O2V0.92	Dx = 4.576 Mg m^−3
Mr = 78.9	Ag Kα radiation, λ = 0.5608 Å
Tetragonal, P42/mnm	Cell parameters from 127 reflections
Hall symbol: -P 4n;-2n	θ = 3.5–24.5°
a = 4.5050 (19) Å	µ = 3.73 mm^−1
c = 2.8200 (13) Å	T = 293 K
V = 57.23 (4) Å^3	Irregular, black
Z = 2	0.05 × 0.03 × 0.03 × 0.03 (radius) mm
F(000) = 74

Data collection

Esperanto-CrysAlisPro-abstract goniometer imported esperanto images diffractometer	45 independent reflections
Radiation source: X-ray tube	30 reflections with I > 3σ(I)
Synchrotron monochromator	Rint = 0.109
Detector resolution: 5.8140 pixels mm^-1	θmax = 25.0°, θmin = 5.0°
φ scans	h = −5→5
Absorption correction: multi-scan (CrysAlis PRO; Rigaku OD, 2024)	k = −6→6
Tmin = 0.937, Tmax = 1	l = −3→3
328 measured reflections

Refinement

Refinement on F	0 restraints
R[F^2 > 2σ(F^2)] = 0.060	0 constraints
wR(F^2) = 0.057	Weighting scheme based on measured s.u.'s w = 1/(σ^2(F) + 0.0001F^2)
S = 2.14	(Δ/σ)max = 0.0002
45 reflections	Extinction correction: B-C type 1 Gaussian isotropic (Becker & Coppens, 1974)
5 parameters	Extinction coefficient: 400 (200)

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Ų)

	x	y	z	Uiso*/Ueq	Occ. (<1)
V1	0.5	0.5	0	0.0280 (18)*	0.92
O1	0.2026 (11)	0.2026 (11)	0	0.009 (2)*

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
?	?	?	?	?	?	?

Geometric parameters (Å, º)

V1—V1^i	2.820 (3)	O1—O1^viii	2.582 (7)
V1—V1^ii	2.820 (3)	O1—O1^ix	2.691 (6)
V1—O1	1.895 (5)	O1—O1^x	2.691 (6)
V1—O1^iii	1.895 (5)	O1—O1^iv	2.691 (6)
V1—O1^iv	1.912 (4)	O1—O1^v	2.691 (6)
V1—O1^v	1.912 (4)	O1—O1^xi	2.691 (6)
V1—O1^vi	1.912 (4)	O1—O1^xii	2.691 (6)
V1—O1^vii	1.912 (4)	O1—O1^vi	2.691 (6)
O1—O1^i	2.820 (3)	O1—O1^vii	2.691 (6)
O1—O1^ii	2.820 (3)
V1^i—V1—V1^ii	180	V1^x—O1—O1^xi	93.6 (2)
V1^i—V1—O1	90	V1^x—O1—O1^xii	44.74 (13)
V1^i—V1—O1^iii	90	V1^x—O1—O1^vi	149.5 (2)
V1^i—V1—O1^iv	42.48 (11)	V1^x—O1—O1^vii	95.10 (11)
V1^i—V1—O1^v	137.52 (11)	O1^i—O1—O1^ii	180
V1^i—V1—O1^vi	42.48 (11)	O1^i—O1—O1^viii	90.00 (14)
V1^i—V1—O1^vii	137.52 (11)	O1^i—O1—O1^ix	58.41 (13)
V1^ii—V1—O1	90	O1^i—O1—O1^x	121.6 (2)
V1^ii—V1—O1^iii	90	O1^i—O1—O1^iv	58.41 (13)
V1^ii—V1—O1^iv	137.52 (11)	O1^i—O1—O1^v	121.6 (2)
V1^ii—V1—O1^v	42.48 (11)	O1^i—O1—O1^xi	58.41 (13)
V1^ii—V1—O1^vi	137.52 (11)	O1^i—O1—O1^xii	121.6 (2)
V1^ii—V1—O1^vii	42.48 (11)	O1^i—O1—O1^vi	58.41 (13)
O1—V1—O1^iii	180	O1^i—O1—O1^vii	121.6 (2)
O1—V1—O1^iv	90.00 (18)	O1^ii—O1—O1^viii	90.00 (14)
O1—V1—O1^v	90.00 (18)	O1^ii—O1—O1^ix	121.6 (2)
O1—V1—O1^vi	90.00 (18)	O1^ii—O1—O1^x	58.41 (13)
O1—V1—O1^vii	90.00 (18)	O1^ii—O1—O1^iv	121.6 (2)
O1^iii—V1—O1^iv	90.00 (18)	O1^ii—O1—O1^v	58.41 (13)
O1^iii—V1—O1^v	90.00 (18)	O1^ii—O1—O1^xi	121.6 (2)
O1^iii—V1—O1^vi	90.00 (18)	O1^ii—O1—O1^xii	58.41 (13)
O1^iii—V1—O1^vii	90.00 (18)	O1^ii—O1—O1^vi	121.6 (2)
O1^iv—V1—O1^v	95.05 (16)	O1^ii—O1—O1^vii	58.41 (13)
O1^iv—V1—O1^vi	84.95 (16)	O1^viii—O1—O1^ix	61.34 (17)
O1^iv—V1—O1^vii	180	O1^viii—O1—O1^x	61.34 (17)
O1^v—V1—O1^vi	180	O1^viii—O1—O1^iv	134.74 (19)
O1^v—V1—O1^vii	84.95 (16)	O1^viii—O1—O1^v	134.74 (19)
O1^vi—V1—O1^vii	95.05 (16)	O1^viii—O1—O1^xi	61.34 (17)
V1—O1—V1^ix	132.48 (11)	O1^viii—O1—O1^xii	61.34 (17)
V1—O1—V1^x	132.48 (11)	O1^viii—O1—O1^vi	134.74 (19)
V1—O1—O1^i	90.00 (14)	O1^viii—O1—O1^vii	134.74 (19)
V1—O1—O1^ii	90.00 (14)	O1^ix—O1—O1^x	63.19 (14)
V1—O1—O1^viii	180	O1^ix—O1—O1^iv	113.63 (11)
V1—O1—O1^ix	118.7 (2)	O1^ix—O1—O1^v	161.8 (3)
V1—O1—O1^x	118.7 (2)	O1^ix—O1—O1^xi	89.48 (17)
V1—O1—O1^iv	45.26 (13)	O1^ix—O1—O1^xii	122.7 (2)
V1—O1—O1^v	45.26 (13)	O1^ix—O1—O1^vi	74.07 (17)
V1—O1—O1^xi	118.7 (2)	O1^ix—O1—O1^vii	105.9 (2)
V1—O1—O1^xii	118.7 (2)	O1^x—O1—O1^iv	161.8 (3)
V1—O1—O1^vi	45.26 (13)	O1^x—O1—O1^v	113.63 (11)
V1—O1—O1^vii	45.26 (13)	O1^x—O1—O1^xi	122.7 (2)
V1^ix—O1—V1^x	95.0 (2)	O1^x—O1—O1^xii	89.48 (17)
V1^ix—O1—O1^i	42.48 (10)	O1^x—O1—O1^vi	105.9 (2)
V1^ix—O1—O1^ii	137.5 (2)	O1^x—O1—O1^vii	74.07 (17)
V1^ix—O1—O1^viii	47.52 (11)	O1^iv—O1—O1^v	63.19 (14)
V1^ix—O1—O1^ix	44.74 (13)	O1^iv—O1—O1^xi	74.07 (17)
V1^ix—O1—O1^x	93.6 (2)	O1^iv—O1—O1^xii	105.9 (2)
V1^ix—O1—O1^iv	95.10 (11)	O1^iv—O1—O1^vi	57.33 (17)
V1^ix—O1—O1^v	149.5 (2)	O1^iv—O1—O1^vii	90.5 (2)
V1^ix—O1—O1^xi	44.74 (13)	O1^v—O1—O1^xi	105.9 (2)
V1^ix—O1—O1^xii	93.6 (2)	O1^v—O1—O1^xii	74.07 (17)
V1^ix—O1—O1^vi	95.10 (11)	O1^v—O1—O1^vi	90.5 (2)
V1^ix—O1—O1^vii	149.5 (2)	O1^v—O1—O1^vii	57.33 (17)
V1^x—O1—O1^i	137.5 (2)	O1^xi—O1—O1^xii	63.19 (14)
V1^x—O1—O1^ii	42.48 (10)	O1^xi—O1—O1^vi	113.63 (11)
V1^x—O1—O1^viii	47.52 (11)	O1^xi—O1—O1^vii	161.8 (3)
V1^x—O1—O1^ix	93.6 (2)	O1^xii—O1—O1^vi	161.8 (3)
V1^x—O1—O1^x	44.74 (13)	O1^xii—O1—O1^vii	113.63 (11)
V1^x—O1—O1^iv	149.5 (2)	O1^vi—O1—O1^vii	63.19 (14)
V1^x—O1—O1^v	95.10 (11)

Symmetry codes: (i) x, y, z−1; (ii) x, y, z+1; (iii) −x+1, −y+1, z; (iv) −y+1/2, x+1/2, z−1/2; (v) −y+1/2, x+1/2, z+1/2; (vi) y+1/2, −x+1/2, z−1/2; (vii) y+1/2, −x+1/2, z+1/2; (viii) −x, −y, z; (ix) −y+1/2, x−1/2, z−1/2; (x) −y+1/2, x−1/2, z+1/2; (xi) y−1/2, −x+1/2, z−1/2; (xii) y−1/2, −x+1/2, z+1/2.

(V0.92O2modulated)

Crystal data

O2V0.92	V = 121.56 (2) Å^3
Mr = 78.9	Z = 4
Monoclinic,	F(000) = 149
a = 6.6458 (6) Å	Dx = 4.309 Mg m^−3
b = 2.8746 (2) Å	X-ray radiation, λ = 0.72044 Å
c = 6.3631 (6) Å	µ = 6.93 mm^−1
β = 90.024 (10)°	T = 293 K

Data collection

1297 measured reflections	θmax = 35.4°, θmin = 3.5°
445 independent reflections	h = −8→8
302 reflections with I > 3σ(I)	k = −4→4
Rint = 0.007	l = −8→8

Refinement

Refinement on F	1 constraint
R[F^2 > 2σ(F^2)] = 0.056	Weighting scheme based on measured s.u.'s w = 1/(σ^2(F) + 0.01F^2)
wR(F^2) = 0.073	(Δ/σ)max = 0.006
S = 4.44	Δρmax = 0.72 e Å^−3
445 reflections	Δρmin = −0.78 e Å^−3
92 parameters	Extinction correction: B-C type 1 Gaussian isotropic (Becker & Coppens, 1974)
0 restraints	Extinction coefficient: 3800 (400)

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Ų)

	x	y	z	Uiso*/Ueq	Occ. (<1)
V1	0	0	0	0.0318 (11)	0.983 (8)
V2	0	0.5	0.5	0.0283 (13)	0.857 (8)
O1	−0.2003 (2)	0	0.5002 (4)	0.0155 (7)
O2	0.0005 (3)	0.5	0.2000 (2)	0.0128 (6)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
V1	0.0693 (14)	0.0155 (18)	0.010 (2)	0	0.0068 (16)	0
V2	0.051 (2)	0.027 (2)	0.007 (3)	0	0.0025 (18)	0
O1	0.0147 (11)	0.0171 (9)	0.0147 (14)	0	0.0008 (12)	0
O2	0.0186 (13)	0.0112 (8)	0.0085 (12)	0	0.0059 (16)	0

 

Footnotes

¹The incommensurate vector would be q = (0, 0, γ), where γ ≈ 0.234, in the pseudo-ortho­rhom­bic C-centred cell derived from the primitive monoclinic one using the transformation a′ = a + c, b′ = −a + c and c′ = −b.

²It is noteworthy that part of the elements of the anharmonic tensor and the coefficients of the modulation function of the anharmonic tensor elements refined to values below 3σ. If one restricts these parameters to 0, the overall number of parameters is halved (approximately 40). At the same time, the agreement factors for the satellite reflections increase by approximately 2% [R(obs) = 11.54% and wR(all) = 13.84%].