One-dimensional composite host–guest structure in BaVS₃

A detailed synchrotron X-ray diffraction (XRD) study performed with a single crystal of BaVS₃ (barium vanadium trisulfide) in the temperature range between 10 and 295 K is reported. Aside from the known tetragonal–orthorhombic (240 K) and orthorhombic–monoclinic (69 K) phase transitions, in the 130 < T ≤ 295 K range the overall structure can be viewed as a host–guest (H–G) composite. The BaS₃ matrix is the host, while the V-chains form the guest. The two subsystems lock in at T_LOCK = 130 ± 20 K. This temperature is marked by a symmetry change from orthorhombic to monoclinic. This results in the formation of twins, implying a structural phase transition identified here for the first time. From the refined structural data, it is possible to follow, starting already at 295 K downwards, the stepwise transformation of VS₆ octahedra into VS₅ tetragonal pyramids as the origin of the structure evolution. The new findings will yield a better understanding of the complex electronic phase diagram of BaVS₃.

1. Introduction

The crystal structure of BaVS₃ can be described as consisting of hexagonal close packed (hcp) Ba and S atoms with V-chains located in the hexagonal channels formed by S atoms (Fig. 1). The short V–V distances of 2.8 Å along the V-chains, compared to the distance of more than 6 Å between them, was the reason to consider BaVS₃ as an electronically quasi-one-dimensional (quasi-1D) system, expected to exhibit strong on-chain correlations. Indeed, BaVS₃ undergoes a metal–insulator (MI) transition at T_MI = 69 K (Gardner et al., 1969; Takano et al., 1977; Massenet et al., 1978; Graf et al., 1995; Kuriyaki et al., 1995; Imada et al., 1998; Forró et al., 2000; Mihály et al., 2000; Inami et al., 2002; Fagot et al., 2005; Sanna et al., 2004; Choi et al., 2009), followed by magnetic ordering below T_N = 31 K (Heidemann & Takano, 1980; Leininger et al., 2011; Sugiyama et al., 2020). However, the anisotropy of the conductivity for T > T_MI of σ_c/σ_a = 3–4 is surprisingly low (Mihály et al., 2000; Barišić, 2004; Kézsmárki et al., 2006). Therefore, its remarkable and intriguing electrical and magnetic properties have been extensively studied starting from 1969 (Gardner et al., 1969) to very recently (Sugiyama et al., 2020). Besides the MI transition and magnetic ordering, numerous measurements of other physical properties are reported in the literature, such as: (i) electrical resistivity (Gardner et al., 1969; Kuriyaki et al., 1995; Graf et al., 1995; Booth et al., 1999; Mihály et al., 2000; Kézsmárki et al., 2006), (ii) Hall coefficient (Booth et al., 1999), (iii) Raman response with in-chain polarization (Choi et al., 2009), (iv) V L-edge X-ray absorption spectroscopy (Ilakovac et al., 2012), (v) specific heat (Imai et al., 1996), (vi) thermopower (Barišić, 2004). These studies show anomalies at 130 ± 20 K, as do some theoretical models (Jiang & Guo, 2004). This temperature can be associated with an increase of the 1D electronic fluctuations towards the Peierls transition at 69 K (Foury-Leylekian et al., 2012). From the observation of diffuse scattering lines, it appears that the onset of these fluctuations (Fagot et al., 2003) already occurs at 170 K.

Figure 1 Schematic representation of the BaVS3 crystal structure. The ab projection (top) and perspective view (bottom) are shown. Ba and S together form a hexagonal close packing (hcp). V-chains are located in the hexagonal channels formed by S atoms. Relationships between the unit-cell parameters are indicated for the hexagonal, orthorhombic and monoclinic settings: ahex = bhex ≃ 6.7 Å, chex ≃ corth ≃ cmono ≃ 5.6 Å; aorth = amono ≃ × ahex ≃ 11.6 Å, borth ≃ ahex ≃ bmono ≃ 6.7Å. V-chains acquire a zigzag configuration (dashed green line) in the orthorhombic and monoclinic phases. The crosses on one of the c axes show the different origins for the BaS3-hcp (black) and V-chain (green), which are considered in the present study.

Two structural transitions have been well documented in the 5–300 K temperature range (Gardner et al., 1969; Imada et al., 1998; Inami et al., 2002; Fagot et al., 2005; Foury-Leylekian et al., 2012). In the first at T_S = 240 K, the higher-temperature hexagonal metallic phase transforms to orthorhombic. The second transition is associated with T_MI = 69 K, where the orthorhombic phase converts to monoclinic with a doubling of the translation along the c axis. No noticeable structural changes have been detected for the magnetic transitions at T_N = 31 K (Fagot et al., 2005). Although the hexagonal and orthorhombic symmetries have commonly been described by the space groups P6₃/mmc and Ccm2₁, respectively, observations of a series of extra X-ray diffraction reflections violate both of them (Inami et al., 2002; Girard et al., 2019). Some doubts with regard to these space-group attributions also arose from neutron diffraction studies (Ghedira et al., 1981). Finally, the interplay between the structural and electronic phase transformations is still not entirely clear, in particular since the symmetry determination raises some questions for both the hexagonal and orthorhombic phases.

Here we report synchrotron XRD experiments performed on a single crystal of BaVS₃ at ten different temperatures in the range 10–295 K. We show that the mismatch between the space groups P6₃/mmc and Ccm2₁, and the presence of extra reflections that violate them, can be resolved by a host–guest (H–G) composite model. Accordingly, we consider the BaVS₃ structure as a 1D commensurate composite, which consists of a host (H) BaS₃ matrix and guest (G) V-chains for T > 130 K. H and G change their symmetry individually up to 295 K. The space groups mentioned above are correct, but they relate only to H, while the symmetry of G is systematically lower, which leads to the appearance of the extra reflections. Unlike in the classical approach, this host–guest concept allows us to identify a structural phase transition at T_LOCK = 130 ± 20 K. At this temperature, the H and G subsystems lock together, ceasing to behave independently. The low-temperature step-by-step transformation of the VS₆ octahedra into VS₅ pyramids is an essential consequence of the whole set of structural transformations that starts at T < 295 K. Finally, our findings related to structural properties should have a counterpart in the electronic and spin sector, and will thus help the interpretation of the intriguing electronic properties and states observed in BaVS₃.

2. Experimental

2.1. Synthesis and crystallization

All details of the synthesis and crystallization of high-quality single crystals have been described by Kuriyaki et al. (1995).

2.2. Single-crystal synchrotron XRD experiments

Single-crystal XRD data were collected at the Swiss–Norwegian Beamline BM01A (ESRF, Grenoble) at the following temperatures: 10, 40, 70, 100, 110, 150, 200, 220, 250 and 295 K (before and after cooling). The wavelength of λ = 0.7 Å was selected for the measurements. The CrysAlis PRO software (Agilent, 2014) was used for the systematic investigation of the reciprocal space. Absorption was corrected for by multi-scan methods (CrysAlis PRO; Agilent, 2014). An empirical absorption correction using spherical harmonics was implemented in the SCALE3 ABSPACK scaling algorithm. Crystal structure studies were performed using the JANA2006 program package (Petříček et al., 2014). Experimental details are shown in Table 1 for five structures selected from different representative temperature ranges and in Table S1 (see supporting information) for the remaining temperatures.

Table 1
Experimental details for the representative structures of BaVS₃

For all structures: M_r = 284.5. Absorption was corrected for by multi-scan methods (CrysAlis PRO; Agilent, 2014). A new multipurpose diffractometer PILATUS@SNBL (Dyadkin et al., 2016) was used for the data collections.

	250 K	220 K	100 K	70 K	150 K
Crystal data
Crystal system, space group	Hexagonal, P63/mmc (for BaS3)	Orthorhombic, Ccm21 (for BaS3)	Monoclinic, Cm	Monoclinic, Cm	Monoclinic, Im
	Trigonal, Pm1 (for V)*	Monoclinic, Cm (for V)*
a, b, c (Å)	6.7164 (2), 6.7164 (2), 5.6088 (2)	11.593 (7), 6.708 (5), 5.604 (3)	11.485 (7), 6.751 (5), 5.597 (3)	11.496 (9), 6.742 (7), 5.597 (5)	11.456 (1), 6.764 (1), 11.188 (1)
α, β, γ (°)	90, 90, 120	90, 90.00 (1), 90	90, 90.011 (5), 90	90, 90.012 (6), 90	90, 90.048 (9), 90
V (Å^3)	219.12 (1)	435.8 (5)	434.0 (5)	433.8 (7)	866.94 (9)
Z	2	4	4	4	8
Radiation type, λ (Å)	Synchrotron, 0.70814	Synchrotron, 0.70814	Synchrotron, 0.70000	Synchrotron, 0.70814	Synchrotron, 0.70814
μ (mm^−1)	12.05	12.12	11.79	12.17	12.18
Crystal size (mm)	0.05 × 0.03 × 0.02	0.05 × 0.03 × 0.02	0.05 × 0.03 × 0.02	0.05 × 0.03 × 0.02	0.05 × 0.03 × 0.02
Data collection
Tmin, Tmax	0.649, 1.000	0.606, 1.000	0.628, 1.000	0.529, 1.000	0.671, 1.000
No. of measured, independent and observed [I > 3σ(I)] reflections	2069, 196, 196	3944, 1464, 1464	3199, 1935, 1934	1782, 770, 769	4005, 1187, 1186
Rint	0.034	0.014	0.031	0.025	0.030
(sin θ/λ)max (Å^−1)	0.675	0.676	0.752	0.674	0.673
Refinement
R[F > 3σ(F)], wR(F), S	0.034, 0.146, 1.67	0.019, 0.040, 2.83	0.032, 0.045, 3.27	0.048, 0.065, 5.44	0.016, 0.027, 1.16
No. of reflections	196	1464	1935	770	1187
No. of parameters	13	32	59	53	110
Δρmax, Δρmin (e Å^−3)	1.67, −1.94	0.96, −0.72	1.39, −1.76	2.26, −1.77	0.37, −0.42
Absolute structure		668 of Friedel pairs used in the refinement	806 of Friedel pairs used in the refinement	367 of Friedel pairs used in the refinement	587 of Friedel pairs used in the refinement
Absolute structure parameter		0.28 (2)	0.05 (4)	0.05 (5)	0.097 (19)
Computer programs: CrysAlis PRO (Agilent, 2014) and JANA2006 (Petříček et al., 2014). Note: (*) the structure is considered as a 1D commensurate composite consisting of the BaS3 matrix and V-chains located in its hexagonal channels (Fig. 1).

2.2.1. Reciprocal space observations at different tem­per­atures

Our observations of systematic extra reflections shown in Fig. 2 contradict the generally accepted space group P6₃/mmc for the hexagonal phase and Ccm2₁ for the orthorhombic phase, and, in this respect, confirm the observations reported earlier by Imani et al. (2002) and Girard et al. (2019). The clearly observed hhl reflections with l = 2n+1 are incompatible with the c-glide plane of the P6₃/mmc space group, which was expected at T > T_S = 240 K. Reflections of this type are also clearly visible in the 0kl section with l = 2n+1 in the 70–220 K temperature range, where the orthorhombic phase is expected. These reflections are not compatible with the c-glide plane of the orthorhombic space group Ccm2₁.

Figure 2 Selected sections of the experimental reciprocal space for BaVS3 in the 70–295 K temperature range. (a) In the hk3 and 0kl sections taken for the hexagonal phase at 295 K, the red circles highlight 00l and hhl reflections with l = 2n+1, which violate the hexagonal space group P63/mmc. The symmetry of the patterns indicates the 6/mmm Laue class. (b) In the 0kl section taken at different temperatures between 70 and 220 K, the red arrows point to rows of 0kl reflections with l = 2n+1, which violate the orthorhombic space group Ccm21.

New and surprising observations occur in the temperature range between T_S = 240 K and T_MI = 69 K. The splitting of reflections, which is expected below T_S = 240 K due to the hex­ag­onal–orthorhombic symmetry reduction, changes sharply between 150 and 110 K (Fig. 3). The predicted maxi­mum reflection splitting is determined by the order relationship between the hexagonal and orthorhombic Laue classes, i.e. 24/8 = 3. This is what is indeed observed in the temperature range from 150 to 220 K. However, the observed splitting is of a much higher order at 110 K and below (Fig. 3), and it is similar to the monoclinic splitting that is typical for temperatures below T_MI = 69 K. The observed splitting evol­ution is completely reversible with respect to temperature. This new observation is corroborated by observations of anomalies in the above-mentioned physical properties, which indicate a remarkable electronic transition at about 130 K. It should be emphasized that in parallel, starting around 170 K, diffuse scattering lines were observed by Fagot et al. (2003). Their intensity and sharpness increase upon cooling, being a signature of 1D structural fluctuations. They are accompanied by a change in electrical resistivity which increases strongly from about 130 K down to T_MI (Gardner et al., 1969; Kuriyaki et al., 1995; Kézsmárki et al., 2006; Barišić, 2004; see also Fig. S2 in the supporting information).

Figure 3 The hk0 sections of the reciprocal space showing a correlation between the splitting of reflections and the published electrical properties of BaVS3. In the insets, framed with red squares, one of the reflections is enlarged for each temperature.

It is worth mentioning one more observation related to the structure below T_S = 69 K. Some systematic reflections could possibly but mistakenly be indexed with the new modulation vector q′ = 0.5a + 0.5b + 0.5c_hex. However, these reflections originate from three twin components related by the threefold axis, as illustrated in Fig. S1 (see supporting information).

Summarizing the analysis of the reciprocal space at different temperatures, we establish with certainty that the symmetry of BaVS₃ needs to be revised in the temperature range 69–295 K.

2.2.2. Revising the BaVS₃ space-group symmetry down to T_MI = 69 K

The 6/mmm Laue class of the hexagonal phase (Fig. 2a) and the presence of the extra reflections in the hexagonal and orthorhombic phases leads to the space group Pm2 (instead of P6₃/mmc) for the hexagonal phase and its subgroup Cmm2 (instead of Ccm2₁) for the orthorhombic phase, in agreement with the reported symmetries by Inami et al. (2002). However, down to 130 K, structure refinements based on about 3000 experimental single-crystal reflections (which includes about 200 extra reflections) show that Ba and S atoms can only be correctly fitted within the commonly used space groups: P6₃/mmc for the hexagonal phase and Ccm2₁ for the orthorhombic phase. This implies that the BaS₃ substructure does not contribute to the intensity of the extra reflections. These weak reflections arise from a small difference in two V–V distances along the c axis. The difference can only be achieved with lower V-chain symmetry: the space group Pm1 (instead of P6₃/mmc for BaS₃) and its monoclinic subgroup C2/m (instead of the orthorhombic Ccm2₁ for BaS₃), with a shift of about (but not identical to) 0.25c between origins (inversion centers in the hexagonal phase) characterizing the BaS₃ hcp matrix and the V-chain (Fig. 1). Here we face a discrepancy in the description of the symmetry of the two parts of the same structure.

This controversy could be resolved by applying an approach called the host–guest commensurate composite structure (Arakcheeva et al., 2002; Höhn et al., 2006; McMahon & Nelmes, 2006). This type of crystal structure assumes different symmetries for the host (usually a 3D matrix) and the guest (usually a chain inside a 3D matrix) with the same lattice parameters. Similarly, we consider the BaS₃ hcp matrix as the host (H) and V-chains as the guest (G). Consequently, to refine the hexagonal phase (at 295 and 250 K), we use the space group P3m1, which is common for H and G, and additional pairwise restrictions for Ba, S and V sites according to their true symmetry. For the orthorhombic phase (at 220, 200 and 150 K), the C1m1 space group, which is common for H and G, was used with the corresponding pairwise restrictions for Ba, V and two S sites. Examples of atomic sites and the applied restrictions are available in the supporting information. The host–guest approach perfectly fits our diffraction experiments down to 150 K. It should be mentioned that the contribution of quasi-elastic scattering to the intensities of the extra reflections (Girard et al., 2019) cannot be excluded since their calculated intensities are systematically somewhat lower than those observed.

Starting from 110 K and down to T_MI = 69 K, both H and G adopt the common monoclinic symmetry C1m1 in agreement with the above-described observations of the monoclinic splitting for diffraction reflections below 130 K (Fig. 3).

Our study confirms the space group I1m1 with a double unit-cell c parameter, which has been reported numerous times for the structure below T_MI after the initial publication by Fagot et al. (2005).

The summary of the structure symmetry reconsideration is presented in Fig. 4, which shows a scheme of the group–subgroup relationships found for BaVS₃ in the 10–295 K temperature range.

Figure 4 The group–subgroup relationships for BaVS3 between 10 and 295 K. The bold black arrows indicate the relationships within the host (H) and the guest (G) components of the structure. Below TLOCK, both components acquire the same (equilibrium) monoclinic symmetry. The lowering to monoclinic symmetry at TMI is due to a doubling of the unit-cell c parameter.

3. Results and discussion

3.1. Structural phase transition at T_LOC at 130 ± 20 K

The first important result of the present study follows directly from the symmetry revision of BaVS₃ at different temperatures above T_MI (Figs. 3 and 4). It appears that the structural phase transition observed at 130 ± 20 K correlates remarkably well with the change in the slope of the electrical resistivity from negative to positive at about 130 K (Kézsmárki et al., 2006; see also Fig. S2 in the supporting information). As already mentioned in the Introduction, other properties also show changes/anomalies in the behaviour at this temperature. This structural transition consists of a monoclinic transformation of the entire BaVS₃ structure and the loss of the inversion centre in the V-chains. This leads to a locking of the two structural subsystems, H and G, so that we denote the transition temperature as T_LOCK = 130 ± 20 K. It is important to emphasize that, at this temperature, instead of one V site, two independent crystallographic V sites appear with monoclinic (m) local symmetry. This novel insight should be carefully considered theoretically with respect to the 1D electronic instability which is clearly visible below T_LOCK.

3.2. Analysis of the temperature-dependent geometric characteristics

Another set of important information is obtained from the analysis of the T-dependent geometric characteristics of the BaVS₃ structure (Fig. 5). Namely, we analyze here the evolution of: (i) intra-chain V–V–V angles; (ii) V–V and V–S interatomic distances, which are then related to (iii) the bond valence sum (BVS) of V⁴⁺. BVS is calculated for each V site in its octahedral (VS₆) and pyramidal (VS₅) environment and compared to the nominal BVS = 4 for V⁴⁺.

Figure 5 Structural characteristics of BaVS3 between 10 and 295 K. (a) The VS6 chain represents ranges separated by the transformation temperatures. VS5 tetragonal pyramids (green) and VS6 octahedra (blue), highlighted according to (b) V–S distances and (c) the bond valence sum of V. For each V polyhedron, the equatorial (orange) and apical (brown) V–S contacts are shown; dashed brown lines specify the longest apical contacts. (b) Geometry characteristics: V–V–V angles and V–V and V–S distances. The markers indicate experimental values; the lines are guides for the eyes. (c) Bond valence sums (BVSs) calculated for each V atom in its octahedral (V^4+S6, blue rhombuses) and pyramidal (V^4+S5, green triangles) environment. The choice of polyhedron (dashed blue and green lines) is confirmed by the calculations, which are very close to the nominal BVS = 4. The colour coding is identical in all panels.

In agreement with the previously published studies, the essential change of the V–V–V angle (from 180 to 165.4°) is observed at T_S, and the difference in the V–V distances varies within the range of about 0.2 Å below T_MI.

The new experimental data characterize the host–guest structure at temperatures above T_LOCK and the monoclinic structure between T_MI and T_LOCK. Unlike in all previously published studies, the difference between the intra-chain V–V distances is observed even in the hexagonal phase, i.e. above the temperature of the structural transition at T_S. This difference, of about 0.1 Å at 295 K, increases to about 0.2 Å at 250 K. The zigzag deformation of the V-chain arising at T_S reduces the difference to 0.07 Å at 220 K and then to 0.04 Å at 150 K. This small difference is maintained almost down to T_MI. The small increase of this value up to 0.07 Å is observed at 70 K, i.e. immediately before the MI transition.

The analysis of the V–S distances points to a remarkable difference between the equatorial (yellow dots/lines in Fig. 5) and apical (brown dots/lines in Fig. 5) interatomic contacts in the temperature-dependent VS₆ octahedra. The equatorial V–S distances are more of less stable within 2.35 ± 0.05 Å at any temperature, while the apical contacts are strongly temperature dependent. At temperatures above T_S (295 and 250 K), there are no differences between them. However, below T_S, the difference appears and increases systematically to about 0.6 Å at 10 K. This is the main tendency of the BaVS₃ structure evolution between 295 and 10 K (Fig. 5). This observation leads us to consider an optimal number of S²⁻ ions, i.e. six in a V⁴⁺S₆ octahedron or five in a V⁴⁺S₅ pyramid, which can exactly fit the expecting oxidation state of V⁴⁺. The BVS presented in Fig. 5(c) indicates that the V⁴⁺S₆ octahedron is preferable down to T_LOCK. Two different polyhedra, i.e. a V⁴⁺S₆ octahedron and a V⁴⁺S₅ pyramid, can be recognized between T_LOCK and T_MI, and only the V⁴⁺S₅ pyramid has the exact characteristics of the structure below T_MI.

This analysis allows us to propose a scenario for the temperature-dependent structure transformations of BaVS₃.

3.3. A possible scenario for the temperature-dependent structure transformations of BaVS₃ below 295 K

The analysis described above indicates the existence of a unique mechanism causing the evolution of the BaVS₃ structure with decreasing temperature. This mechanism manifests itself as a successive deformation of regular V⁴⁺S₆ octahedra stable at room temperature, towards the stabilization of the V⁴⁺S₅ pyramids, which is completed at temperatures below T_LOCK. This deformation of the octahedra is realized by successive contraction of one of the apical V–S contacts and the corresponding increase of the other one, while maintaining the equatorial V–S contacts in the VS₆ octahedra, as illustrated in Figs. 5 and 6. In the hexagonal phase, the contraction of the apical V–S contact is possible only if the V atoms move closer together along the V-chain. Even a slight compression of this contact (e.g. 0.03 Å at 250 K) leads to the formation of an unstable short V–V contact (e.g. 2.70 Å at 250 K), which causes the first structural phase transition at T_S (Fig. 6a). As a result of this transition, the apical V–S contacts decrease essentially due to the appearance of a V–V–V angle of about 165°, which in turn recovers the stable V–V distances. The structure remains practically unchanged down to 150 K with short apical contacts of about 2.23 Å and a V⁴⁺S₆ octahedron for two V atoms connected by a centre of inversion within the V-chain. An additional temperature decrease induces further contraction of the V–S apical contacts. A significant shortening of one of them occurs at T_LOCK, stabilizing its V⁴⁺S₅ pyramid, while the V⁴⁺S₆ octahedron is still stable for the second V atom (Figs. 5c and 6b). The loss of the inversion centre in the V-chain leads to a significant distortion in the short V–S apical contacts (2.19 versus 2.26 Å) and the corresponding polyhedra characteristic of two V atoms. The distortions are completely eliminated at T_MI due to the doubling of the unit-cell c parameters (Figs. 5c and 6c). At T < T_MI, the structure becomes stable with respect to charge compensation within the V⁴⁺S₅ pyramids for the whole set of V atoms. However, this is accompanied by a significant difference (2.94 versus 2.78 Å) in V–V distances in the V-chain, in agreement with most of the previous studies. It is important to note that each described structural transition can be considered as initiated by the displacement of V atoms, as shown in Fig. 6. This indicates the electronic instability of V as the main cause of structural transformations, which already manifest themselves as diffusion scattering at temperatures below 170 K (Fagot et al., 2003).

Figure 6 Illustration of the transformation of VS6 octahedra into VS5 pyramids as a general underlying principle for changes in the BaVS3 structure as a function of temperature. The interatomic distances are given in Å. Arched arrows point to the transformation of short apical V–S contacts in VS6 octahedra. The numerical values of the distances are highlighted in red, which change as a result of the corresponding structural phase transitions. Straight red arrows show displacements of V atoms, which initiate the transformation of the structure. (a) Compression of the apical V–S contacts in the hexagonal phase results in a too-short V–V contact, indicated in brown. During the TS transition, this contact relaxes due to its increase as a result of the V-atom displacement, which leads to a zigzag deformation of the V-chain. (b) At the TLOCK phase transition, further compression of the apical V–S contact for one V atom occurs due to its predominant displacement, which leads to the loss of the inversion centre (black crosses) in the V-chain. This results in two sites, V1 and V2, for the V atom instead of one. (c) During the TMI structural transition, the uniformly compressed apical V–S contact for each V atom is realized due to different displacements of the V atoms along the c axis. As a consequence, the number of V sites increases from two to four (V1, V2, V3 and V4). A side effect is a significant difference of the intra-chain V–V distances, indicated in brown.

4. Summary

Using single-crystal X-ray synchrotron diffraction experiments, we reveal that, upon decreasing the temperature, the series of structural phase transitions in the complex quasi-1D metallic system BaVS₃ satisfies the group–subgroup symmetry relationships only if its structure is considered as a 1D commensurate composite, which consists of the host (H), the BaS₃ hcp matrix and the guest (G) V-chains. The host–guest structure model reveals a structural phase transition at T_LOCK = 130 ± 20 K, which was not previously observed and which can be considered as a prerequisite for the metal–insulator transformation. The refined structural characteristics obtained in the 10–295 K temperature range indicate the presence of a unique ingredient required for the correct description of the structural evolution with temperature. It is associated with the VS₆ octahedra that characterize the structure at room temperature, which successively transform upon decreasing the temperature into VS₅ tetragonal pyramids, characteristic of the structure below T_MI = 69 K. We are convinced that our findings will yield a better understanding of the low-temperature driven electronic transformations of the BaVS₃ quasi-1D electronic system.

Supporting information

Computing details

For all structures, data collection: CrysAlis PRO (Agilent, 2014); cell refinement: CrysAlis PRO (Agilent, 2014); data reduction: CrysAlis PRO (Agilent, 2014); program(s) used to refine structure: JANA2006 (Petčíček et al., 2014).

(I)

Crystal data

BaVS3	F(000) = 1016
Mr = 284.5	Dx = 4.359 Mg m^−3
Monoclinic, Im	Synchrotron radiation, λ = 0.70814 Å
Hall symbol: I -2y	Cell parameters from 4005 reflections
a = 11.456 (1) Å	θ = 2.5–28.4°
b = 6.764 (1) Å	µ = 12.18 mm^−1
c = 11.188 (1) Å	T = 10 K
β = 90.048 (9)°	Irregular, grey
V = 866.94 (9) Å^3	0.05 × 0.03 × 0.02 mm
Z = 8

Data collection

Dectris-CrysAlisPro-abstract goniometer imported dectris images diffractometer	1186 reflections with I > 3σ(I)
Radiation source: synchrotron	Rint = 0.030
Synchrotron monochromator	θmax = 28.4°, θmin = 2.5°
Absorption correction: multi-scan (CrysAlis PRO; Agilent, 2014)	h = −15→15
Tmin = 0.671, Tmax = 1.000	k = −8→8
4005 measured reflections	l = −11→11
1187 independent reflections

Refinement

Refinement on F	Weighting scheme based on measured s.u.'s w = 1/(σ^2(F) + 0.0001F^2)
R[F > 3σ(F)] = 0.016	(Δ/σ)max = 0.028
wR(F) = 0.027	Δρmax = 0.37 e Å^−3
S = 1.16	Δρmin = −0.42 e Å^−3
1187 reflections	Extinction correction: B-C type 1 Gaussian isotropic (Becker & Coppens, 1974)
110 parameters	Extinction coefficient: 70 (30)
0 restraints	Absolute structure: 587 of Friedel pairs used in the refinement
0 constraints	Absolute structure parameter: 0.097 (19)

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

	x	y	z	Uiso*/Ueq
Ba1	0.336486	0	0.123603	0.0108 (3)
Ba2	−0.33423 (6)	0	0.37488 (10)	0.0121 (4)
Ba3	0.34143 (4)	0	0.62323 (4)	0.0114 (3)
Ba4	−0.33819 (7)	0	0.86942 (10)	0.0099 (2)
V2	−0.0250 (3)	0	0.23737 (18)	0.0070 (6)
V3	0.0235 (3)	0	0.4968 (2)	0.0125 (7)
V1	−0.0235 (3)	0	0.73899 (19)	0.0078 (6)
V4	0.0234 (3)	0	0.9872 (2)	0.0100 (5)
S1	0.8264 (7)	0	0.1185 (6)	0.0132 (11)
S2	−0.8301 (8)	0	0.3752 (6)	0.0122 (10)
S3	0.8276 (7)	0	0.6207 (6)	0.0129 (10)
S4	−0.8297 (8)	0	0.8658 (6)	0.0142 (11)
S5	0.0814 (7)	0.2429 (5)	0.1271 (5)	0.0111 (7)
S6	−0.0859 (7)	−0.2440 (5)	0.3793 (5)	0.0107 (7)
S7	0.0801 (7)	0.2463 (5)	0.6282 (5)	0.0108 (8)
S8	−0.0848 (7)	−0.2451 (5)	0.8773 (5)	0.0103 (7)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Ba1	0.0071 (6)	0.0193 (3)	0.0060 (5)	0	−0.0029 (5)	0
Ba2	0.0075 (7)	0.0193 (3)	0.0095 (8)	0	−0.0010 (6)	0
Ba3	0.0090 (8)	0.0193 (3)	0.0058 (5)	0	−0.0018 (5)	0
Ba4	0.0055 (5)	0.0196 (3)	0.0048 (5)	0	−0.0036 (4)	0
V2	0.0015 (11)	0.0151 (4)	0.0043 (14)	0	−0.0018 (10)	0
V3	0.0048 (12)	0.0234 (5)	0.0094 (15)	0	0.0001 (9)	0
V1	0.0027 (11)	0.0125 (4)	0.0080 (15)	0	−0.0015 (10)	0
V4	0.0049 (12)	0.0217 (4)	0.0034 (10)	0	−0.0032 (12)	0
S1	0.004 (2)	0.0210 (11)	0.0149 (19)	0	−0.0058 (13)	0
S2	0.012 (2)	0.0174 (9)	0.0072 (15)	0	0.0019 (14)	0
S3	0.002 (2)	0.0225 (11)	0.0141 (18)	0	−0.0030 (13)	0
S4	0.017 (3)	0.0154 (8)	0.0100 (17)	0	−0.0051 (15)	0
S5	0.0058 (18)	0.0203 (8)	0.0072 (9)	−0.0045 (8)	0.0030 (14)	0.0008 (10)
S6	0.0069 (17)	0.0166 (7)	0.0087 (11)	0.0044 (8)	0.0061 (14)	0.0015 (8)
S7	0.0046 (19)	0.0198 (7)	0.0080 (10)	−0.0030 (8)	0.0030 (14)	0.0006 (10)
S8	0.0090 (17)	0.0158 (7)	0.0062 (9)	0.0027 (8)	0.0046 (14)	0.0016 (8)

Geometric parameters (Å, º)

Ba1—S2^i	3.403 (8)	V3—S6	2.453 (6)
Ba1—S3^ii	3.3837 (3)	V3—S6^v	2.453 (6)
Ba1—S3^iii	3.3837 (3)	V3—S7	2.314 (5)
Ba1—S4^iv	3.454 (7)	V3—S7^v	2.314 (5)
Ba1—S5	3.353 (7)	V1—V4	2.828 (3)
Ba1—S5^v	3.353 (7)	V1—S3^x	2.158 (8)
Ba1—S6^vi	3.356 (6)	V1—S4^i	2.635 (9)
Ba1—S6^vii	3.356 (6)	V1—S7	2.392 (6)
Ba1—S7^viii	3.277 (7)	V1—S7^v	2.392 (6)
Ba1—S7^ix	3.277 (7)	V1—S8	2.374 (5)
Ba1—S8^vi	3.441 (6)	V1—S8^v	2.374 (5)
Ba1—S8^vii	3.441 (6)	V4—S1^xx	2.695 (8)
Ba2—S1^x	3.409 (7)	V4—S4^i	2.163 (9)
Ba2—S3^x	3.315 (7)	V4—S5^xxiii	2.364 (5)
Ba2—S4^viii	3.3839 (2)	V4—S5^xxiv	2.364 (5)
Ba2—S4^vi	3.3839 (2)	V4—S8	2.407 (6)
Ba2—S5^xi	3.454 (6)	V4—S8^v	2.407 (6)
Ba2—S5^xii	3.454 (6)	S1—S5^i	3.353 (10)
Ba2—S6	3.289 (7)	S1—S5^xxv	3.353 (10)
Ba2—S6^v	3.289 (7)	S1—S6^i	3.499 (8)
Ba2—S7^ii	3.394 (6)	S1—S6^xxv	3.499 (8)
Ba2—S7^xiii	3.394 (6)	S1—S7^viii	3.304 (10)
Ba2—S8^iii	3.349 (7)	S1—S7^ix	3.304 (10)
Ba2—S8^xiv	3.349 (7)	S1—S8^iv	3.327 (8)
Ba3—S1^xi	3.3868 (4)	S1—S8^xxvi	3.327 (8)
Ba3—S1^xv	3.3868 (4)	S2—S5^x	3.381 (8)
Ba3—S2^i	3.399 (8)	S2—S5^xxvii	3.381 (8)
Ba3—S4^i	3.349 (8)	S2—S6^x	3.363 (11)
Ba3—S5^xvi	3.253 (7)	S2—S6^xxvii	3.363 (11)
Ba3—S5^xvii	3.253 (7)	S2—S7^x	3.442 (8)
Ba3—S6^xviii	3.449 (6)	S2—S7^xxvii	3.442 (8)
Ba3—S6^xix	3.449 (6)	S2—S8^iii	3.297 (11)
Ba3—S7	3.426 (7)	S2—S8^xiv	3.297 (11)
Ba3—S7^v	3.426 (7)	S3—S5^xvi	3.315 (10)
Ba3—S8^vi	3.356 (6)	S3—S5^xvii	3.315 (10)
Ba3—S8^vii	3.356 (6)	S3—S6^i	3.317 (8)
Ba4—S1^xx	3.364 (7)	S3—S6^xxv	3.317 (8)
Ba4—S2^xvi	3.3839 (3)	S3—S7^i	3.339 (10)
Ba4—S2^xviii	3.3839 (3)	S3—S7^xxv	3.339 (10)
Ba4—S3^x	3.371 (7)	S3—S8^i	3.464 (8)
Ba4—S5^xi	3.349 (6)	S3—S8^xxv	3.464 (8)
Ba4—S5^xii	3.349 (6)	S4—S6^xv	3.290 (11)
Ba4—S6^xv	3.326 (7)	S4—S6^xxi	3.290 (11)
Ba4—S6^xxi	3.326 (7)	S4—S7^x	3.303 (8)
Ba4—S7^xi	3.494 (6)	S4—S7^xxvii	3.303 (8)
Ba4—S7^xii	3.494 (6)	S4—S8^x	3.363 (11)
Ba4—S8	3.344 (7)	S4—S8^xxvii	3.363 (11)
Ba4—S8^v	3.344 (7)	S5—S5^v	3.286 (5)
V2—V3	2.955 (3)	S5—S5^xxviii	3.478 (5)
V2—V4^xxii	2.854 (3)	S5—S6^v	3.412 (9)
V2—S1^x	2.159 (8)	S5—S8^xxix	3.380 (9)
V2—S2^i	2.713 (9)	S6—S6^xxx	3.464 (4)
V2—S5	2.389 (6)	S6—S6^v	3.300 (4)
V2—S5^v	2.389 (6)	S6—S7^v	3.371 (9)
V2—S6	2.394 (5)	S7—S7^v	3.331 (5)
V2—S6^v	2.394 (5)	S7—S7^xxviii	3.433 (5)
V3—V1	2.763 (3)	S7—S8^v	3.369 (9)
V3—S2^i	2.161 (9)	S8—S8^xxx	3.448 (4)
V3—S3^x	2.638 (8)	S8—S8^v	3.316 (4)
V3—V2—V4^xxii	157.96 (16)	V3—V1—V4	157.80 (16)
S1^x—V2—S2^i	176.6 (3)	S3^x—V1—S4^i	174.8 (3)
S1^x—V2—S5	94.8 (2)	S3^x—V1—S7	94.3 (2)
S1^x—V2—S5^v	94.8 (2)	S3^x—V1—S7^v	94.3 (2)
S1^x—V2—S6	100.3 (3)	S3^x—V1—S8	99.6 (3)
S1^x—V2—S6^v	100.3 (3)	S3^x—V1—S8^v	99.6 (3)
S2^i—V2—S5	82.7 (2)	S4^i—V1—S7	82.0 (2)
S2^i—V2—S5^v	82.7 (2)	S4^i—V1—S7^v	82.0 (2)
S2^i—V2—S6	82.1 (2)	S4^i—V1—S8	84.2 (2)
S2^i—V2—S6^v	82.1 (2)	S4^i—V1—S8^v	84.2 (2)
S5—V2—S5^v	86.9 (2)	S7—V1—S7^v	88.3 (2)
S5—V2—S6	164.9 (3)	S7—V1—S8	166.2 (3)
S5—V2—S6^v	90.99 (18)	S7—V1—S8^v	89.93 (18)
S5^v—V2—S6	90.99 (18)	S7^v—V1—S8	89.93 (18)
S5^v—V2—S6^v	164.9 (3)	S7^v—V1—S8^v	166.2 (3)
S6—V2—S6^v	87.13 (18)	S8—V1—S8^v	88.57 (19)
V2—V3—V1	157.94 (16)	V2^xxiii—V4—V1	157.82 (16)
S2^i—V3—S3^x	172.7 (3)	S1^xx—V4—S4^i	174.2 (3)
S2^i—V3—S6	93.4 (2)	S1^xx—V4—S5^xxiii	82.7 (2)
S2^i—V3—S6^v	93.4 (2)	S1^xx—V4—S5^xxiv	82.7 (2)
S2^i—V3—S7	100.5 (3)	S1^xx—V4—S8	81.2 (2)
S2^i—V3—S7^v	100.5 (3)	S1^xx—V4—S8^v	81.2 (2)
S3^x—V3—S6	81.2 (2)	S4^i—V4—S5^xxiii	101.4 (3)
S3^x—V3—S6^v	81.2 (2)	S4^i—V4—S5^xxiv	101.4 (3)
S3^x—V3—S7	84.5 (2)	S4^i—V4—S8	94.6 (2)
S3^x—V3—S7^v	84.5 (2)	S4^i—V4—S8^v	94.6 (2)
S6—V3—S6^v	84.5 (2)	S5^xxiii—V4—S5^xxiv	88.04 (19)
S6—V3—S7	165.4 (3)	S5^xxiii—V4—S8	163.9 (3)
S6—V3—S7^v	89.95 (18)	S5^xxiii—V4—S8^v	90.21 (18)
S6^v—V3—S7	89.95 (18)	S5^xxiv—V4—S8	90.21 (18)
S6^v—V3—S7^v	165.4 (3)	S5^xxiv—V4—S8^v	163.9 (3)
S7—V3—S7^v	92.1 (2)	S8—V4—S8^v	87.1 (2)

Symmetry codes: (i) x+1, y, z; (ii) x−1/2, y−1/2, z−1/2; (iii) x−1/2, y+1/2, z−1/2; (iv) x+1, y, z−1; (v) x, −y, z; (vi) x+1/2, y+1/2, z−1/2; (vii) x+1/2, −y−1/2, z−1/2; (viii) x+1/2, y−1/2, z−1/2; (ix) x+1/2, −y+1/2, z−1/2; (x) x−1, y, z; (xi) x−1/2, y−1/2, z+1/2; (xii) x−1/2, −y+1/2, z+1/2; (xiii) x−1/2, −y+1/2, z−1/2; (xiv) x−1/2, −y−1/2, z−1/2; (xv) x−1/2, y+1/2, z+1/2; (xvi) x+1/2, y−1/2, z+1/2; (xvii) x+1/2, −y+1/2, z+1/2; (xviii) x+1/2, y+1/2, z+1/2; (xix) x+1/2, −y−1/2, z+1/2; (xx) x−1, y, z+1; (xxi) x−1/2, −y−1/2, z+1/2; (xxii) x, y, z−1; (xxiii) x, y, z+1; (xxiv) x, −y, z+1; (xxv) x+1, −y, z; (xxvi) x+1, −y, z−1; (xxvii) x−1, −y, z; (xxviii) x, −y+1, z; (xxix) x, −y, z−1; (xxx) x, −y−1, z.

(II)

Crystal data

BaVS3	F(000) = 1016
Mr = 284.5	Dx = 4.357 Mg m^−3
Monoclinic, Im	Synchrotron radiation, λ = 0.70814 Å
Hall symbol: I -2y	Cell parameters from 4010 reflections
a = 11.458 (1) Å	θ = 2.5–28.4°
b = 6.764 (1) Å	µ = 12.18 mm^−1
c = 11.190 (1) Å	T = 40 K
β = 90.045 (1)°	Irregular, grey
V = 867.25 (9) Å^3	0.05 × 0.03 × 0.02 mm
Z = 8

Data collection

Dectris-CrysAlisPro-abstract goniometer imported dectris images diffractometer	1185 reflections with I > 2σ(I)
Radiation source: synchrotron	Rint = 0.031
Synchrotron monochromator	θmax = 28.4°, θmin = 2.5°
Absorption correction: multi-scan (CrysAlis PRO; Agilent, 2014)	h = −15→15
Tmin = 0.632, Tmax = 1.000	k = −8→8
4010 measured reflections	l = −11→11
1185 independent reflections

Refinement

Refinement on F	Weighting scheme based on measured s.u.'s w = 1/(σ^2(F) + 0.0001F^2)
R[F > 3σ(F)] = 0.027	(Δ/σ)max = 0.043
wR(F) = 0.036	Δρmax = 0.87 e Å^−3
S = 1.45	Δρmin = −1.07 e Å^−3
1185 reflections	Extinction correction: B-C type 1 Gaussian isotropic (Becker & Coppens, 1974)
110 parameters	Extinction coefficient: 60 (40)
0 restraints	Absolute structure: 586 of Friedel pairs used in the refinement
0 constraints	Absolute structure parameter: 0.11 (2)

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

	x	y	z	Uiso*/Ueq
Ba1	0.336486	0	0.123603	0.0113 (3)
Ba2	−0.33472 (7)	0	0.37543 (11)	0.0136 (4)
Ba3	0.34085 (5)	0	0.62344 (5)	0.0130 (3)
Ba4	−0.33846 (8)	0	0.87039 (11)	0.0121 (3)
V2	−0.0272 (4)	0	0.2392 (2)	0.0110 (8)
V3	0.0216 (4)	0	0.4975 (3)	0.0118 (8)
V1	−0.0257 (4)	0	0.7411 (3)	0.0125 (8)
V4	0.0214 (4)	0	0.9889 (3)	0.0123 (8)
S1	0.8283 (7)	0	0.1184 (8)	0.0185 (10)
S2	−0.8285 (8)	0	0.3773 (7)	0.0131 (9)
S3	0.8293 (7)	0	0.6210 (8)	0.0179 (9)
S4	−0.8285 (8)	0	0.8692 (8)	0.0183 (12)
S5	0.0884 (9)	0.2413 (6)	0.1295 (6)	0.0122 (9)
S6	−0.0785 (8)	−0.2433 (5)	0.3789 (6)	0.0100 (9)
S7	0.0874 (9)	0.2457 (7)	0.6304 (7)	0.0122 (9)
S8	−0.0775 (8)	−0.2456 (5)	0.8771 (6)	0.0099 (9)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Ba1	0.0040 (6)	0.0224 (4)	0.0074 (4)	0	−0.0029 (4)	0
Ba2	0.0091 (9)	0.0224 (4)	0.0092 (8)	0	−0.0006 (5)	0
Ba3	0.0091 (8)	0.0231 (4)	0.0067 (4)	0	−0.0033 (5)	0
Ba4	0.0047 (7)	0.0225 (4)	0.0091 (5)	0	−0.0039 (4)	0
V2	0.0047 (17)	0.0216 (10)	0.0066 (14)	0	−0.0005 (14)	0
V3	0.0044 (17)	0.0244 (10)	0.0066 (12)	0	0.0039 (13)	0
V1	0.0069 (18)	0.0219 (10)	0.0085 (14)	0	0.0013 (15)	0
V4	0.0045 (17)	0.0240 (10)	0.0083 (14)	0	−0.0052 (14)	0
S1	0.002 (2)	0.0240 (13)	0.029 (3)	0	−0.0001 (1)	0
S2	0.014 (2)	0.0209 (13)	0.0048 (14)	0	0.0014 (14)	0
S3	0.003 (2)	0.0224 (13)	0.028 (2)	0	−0.0001 (1)	0
S4	0.013 (2)	0.0203 (13)	0.022 (3)	0	−0.0025 (16)	0
S5	0.007 (2)	0.0272 (10)	0.0024 (12)	0.0013 (12)	0.0024 (19)	0.0005 (11)
S6	0.005 (2)	0.0173 (9)	0.0075 (14)	−0.0044 (9)	0.0036 (17)	−0.0026 (10)
S7	0.008 (2)	0.0280 (9)	0.0005 (13)	0.0013 (12)	0.0015 (19)	0.0006 (11)
S8	0.006 (2)	0.0169 (8)	0.0071 (13)	−0.0037 (10)	0.0041 (16)	−0.0025 (9)

Geometric parameters (Å, º)

Ba1—S2^i	3.412 (9)	V3—S6	2.405 (7)
Ba1—S3^ii	3.3831 (2)	V3—S6^v	2.405 (7)
Ba1—S3^iii	3.3831 (2)	V3—S7	2.353 (7)
Ba1—S4^iv	3.416 (9)	V3—S7^v	2.353 (7)
Ba1—S5	3.279 (9)	V1—V4	2.825 (4)
Ba1—S5^v	3.279 (9)	V1—S3^x	2.135 (9)
Ba1—S6^vi	3.386 (7)	V1—S4^i	2.675 (10)
Ba1—S6^vii	3.386 (7)	V1—S7	2.445 (8)
Ba1—S7^viii	3.351 (9)	V1—S7^v	2.445 (8)
Ba1—S7^ix	3.351 (9)	V1—S8	2.330 (6)
Ba1—S8^vi	3.460 (7)	V1—S8^v	2.330 (6)
Ba1—S8^vii	3.460 (7)	V4—S1^xx	2.645 (9)
Ba2—S1^x	3.431 (9)	V4—S4^i	2.180 (10)
Ba2—S3^x	3.329 (9)	V4—S5^xxiii	2.393 (7)
Ba2—S4^viii	3.3835 (3)	V4—S5^xxiv	2.393 (7)
Ba2—S4^vi	3.3835 (3)	V4—S8	2.368 (7)
Ba2—S5^xi	3.453 (7)	V4—S8^v	2.368 (7)
Ba2—S5^xii	3.453 (7)	S1—S5^i	3.399 (12)
Ba2—S6	3.366 (9)	S1—S5^xxv	3.399 (12)
Ba2—S6^v	3.366 (9)	S1—S7^viii	3.256 (11)
Ba2—S7^ii	3.357 (7)	S1—S7^ix	3.256 (11)
Ba2—S7^xiii	3.357 (7)	S1—S8^iv	3.350 (10)
Ba2—S8^iii	3.271 (8)	S1—S8^xxvi	3.350 (10)
Ba2—S8^xiv	3.271 (8)	S2—S5^x	3.355 (10)
Ba3—S1^xi	3.3855 (4)	S2—S5^xxvii	3.355 (10)
Ba3—S1^xv	3.3855 (4)	S2—S6^x	3.304 (12)
Ba3—S2^i	3.367 (9)	S2—S6^xxvii	3.304 (12)
Ba3—S4^i	3.367 (9)	S2—S7^x	3.422 (10)
Ba3—S5^xvi	3.333 (9)	S2—S7^xxvii	3.422 (10)
Ba3—S5^xvii	3.333 (9)	S2—S8^iii	3.351 (11)
Ba3—S6^xviii	3.469 (7)	S2—S8^xiv	3.351 (11)
Ba3—S6^xix	3.469 (7)	S3—S5^xvi	3.270 (11)
Ba3—S7	3.347 (9)	S3—S5^xvii	3.270 (11)
Ba3—S7^v	3.347 (9)	S3—S6^i	3.342 (10)
Ba3—S8^vi	3.382 (7)	S3—S6^xxv	3.342 (10)
Ba3—S8^vii	3.382 (7)	S3—S7^i	3.393 (11)
Ba4—S1^xx	3.368 (9)	S3—S7^xxv	3.393 (11)
Ba4—S2^xvi	3.3848 (4)	S3—S8^i	3.479 (11)
Ba4—S2^xviii	3.3848 (4)	S3—S8^xxv	3.479 (11)
Ba4—S3^x	3.390 (9)	S4—S5^xx	3.472 (10)
Ba4—S5^xi	3.321 (7)	S4—S5^xxviii	3.472 (10)
Ba4—S5^xii	3.321 (7)	S4—S6^xv	3.351 (12)
Ba4—S6^xv	3.254 (8)	S4—S6^xxi	3.351 (12)
Ba4—S6^xxi	3.254 (8)	S4—S7^x	3.291 (10)
Ba4—S7^xi	3.486 (7)	S4—S7^xxvii	3.291 (10)
Ba4—S7^xii	3.486 (7)	S4—S8^x	3.302 (12)
Ba4—S8	3.422 (9)	S4—S8^xxvii	3.302 (12)
Ba4—S8^v	3.422 (9)	S5—S5^v	3.264 (6)
V2—V3	2.944 (4)	S5—S6^v	3.384 (11)
V2—V4^xxii	2.857 (4)	S5—S8^xxix	3.403 (11)
V2—S1^x	2.136 (9)	S6—S6^xxx	3.472 (5)
V2—S2^i	2.751 (9)	S6—S6^v	3.292 (5)
V2—S5	2.435 (8)	S6—S7^v	3.395 (11)
V2—S5^v	2.435 (8)	S7—S7^v	3.323 (6)
V2—S6	2.345 (6)	S7—S7^xxxi	3.441 (6)
V2—S6^v	2.345 (6)	S7—S8^v	3.347 (11)
V3—V1	2.779 (4)	S8—S8^xxx	3.441 (5)
V3—S2^i	2.183 (9)	S8—S8^v	3.323 (5)
V3—S3^x	2.602 (9)
V3—V2—V4^xxii	157.80 (19)	V3—V1—V4	157.7 (2)
S1^x—V2—S2^i	174.9 (3)	S3^x—V1—S4^i	173.4 (3)
S1^x—V2—S5	95.9 (3)	S3^x—V1—S7	95.4 (3)
S1^x—V2—S5^v	95.9 (3)	S3^x—V1—S7^v	95.4 (3)
S1^x—V2—S6	103.1 (3)	S3^x—V1—S8	102.3 (3)
S1^x—V2—S6^v	103.1 (3)	S3^x—V1—S8^v	102.3 (3)
S2^i—V2—S5	80.4 (3)	S4^i—V1—S7	79.9 (3)
S2^i—V2—S5^v	80.4 (3)	S4^i—V1—S7^v	79.9 (3)
S2^i—V2—S6	80.4 (3)	S4^i—V1—S8	82.3 (3)
S2^i—V2—S6^v	80.4 (3)	S4^i—V1—S8^v	82.3 (3)
S5—V2—S5^v	84.2 (2)	S7—V1—S7^v	85.6 (3)
S5—V2—S6	160.6 (4)	S7—V1—S8	162.0 (4)
S5—V2—S6^v	90.1 (2)	S7—V1—S8^v	89.0 (2)
S5^v—V2—S6	90.1 (2)	S7^v—V1—S8	89.0 (2)
S5^v—V2—S6^v	160.6 (4)	S7^v—V1—S8^v	162.0 (4)
S6—V2—S6^v	89.2 (2)	S8—V1—S8^v	90.9 (2)
V2—V3—V1	157.8 (2)	V2^xxiii—V4—V1	157.7 (2)
S2^i—V3—S3^x	174.0 (3)	S1^xx—V4—S4^i	175.3 (3)
S2^i—V3—S6	92.0 (3)	S1^xx—V4—S5^xxiii	84.7 (3)
S2^i—V3—S6^v	92.0 (3)	S1^xx—V4—S5^xxiv	84.7 (3)
S2^i—V3—S7	97.9 (3)	S1^xx—V4—S8	83.6 (3)
S2^i—V3—S7^v	97.9 (3)	S1^xx—V4—S8^v	83.6 (3)
S3^x—V3—S6	83.7 (3)	S4^i—V4—S5^xxiii	98.7 (3)
S3^x—V3—S6^v	83.7 (3)	S4^i—V4—S5^xxiv	98.7 (3)
S3^x—V3—S7	86.3 (3)	S4^i—V4—S8	93.0 (3)
S3^x—V3—S7^v	86.3 (3)	S4^i—V4—S8^v	93.0 (3)
S6—V3—S6^v	86.4 (2)	S5^xxiii—V4—S5^xxiv	86.0 (2)
S6—V3—S7	169.8 (4)	S5^xxiii—V4—S8	168.2 (3)
S6—V3—S7^v	91.0 (2)	S5^xxiii—V4—S8^v	91.3 (2)
S6^v—V3—S7	91.0 (2)	S5^xxiv—V4—S8	91.3 (2)
S6^v—V3—S7^v	169.8 (4)	S5^xxiv—V4—S8^v	168.2 (3)
S7—V3—S7^v	89.8 (2)	S8—V4—S8^v	89.1 (2)

Symmetry codes: (i) x+1, y, z; (ii) x−1/2, y−1/2, z−1/2; (iii) x−1/2, y+1/2, z−1/2; (iv) x+1, y, z−1; (v) x, −y, z; (vi) x+1/2, y+1/2, z−1/2; (vii) x+1/2, −y−1/2, z−1/2; (viii) x+1/2, y−1/2, z−1/2; (ix) x+1/2, −y+1/2, z−1/2; (x) x−1, y, z; (xi) x−1/2, y−1/2, z+1/2; (xii) x−1/2, −y+1/2, z+1/2; (xiii) x−1/2, −y+1/2, z−1/2; (xiv) x−1/2, −y−1/2, z−1/2; (xv) x−1/2, y+1/2, z+1/2; (xvi) x+1/2, y−1/2, z+1/2; (xvii) x+1/2, −y+1/2, z+1/2; (xviii) x+1/2, y+1/2, z+1/2; (xix) x+1/2, −y−1/2, z+1/2; (xx) x−1, y, z+1; (xxi) x−1/2, −y−1/2, z+1/2; (xxii) x, y, z−1; (xxiii) x, y, z+1; (xxiv) x, −y, z+1; (xxv) x+1, −y, z; (xxvi) x+1, −y, z−1; (xxvii) x−1, −y, z; (xxviii) x−1, −y, z+1; (xxix) x, −y, z−1; (xxx) x, −y−1, z; (xxxi) x, −y+1, z.

(III)

Crystal data

BaS3V	F(000) = 508
Mr = 284.5	Dx = 4.364 Mg m^−3
Monoclinic, Cm	Synchrotron radiation, λ = 0.70814 Å
Hall symbol: C -2y	Cell parameters from 1782 reflections
a = 11.496 (9) Å	θ = 3.5–28.5°
b = 6.742 (7) Å	µ = 12.17 mm^−1
c = 5.597 (5) Å	T = 70 K
β = 90.012 (6)°	Irregular, grey
V = 433.8 (7) Å^3	0.05 × 0.03 × 0.02 mm
Z = 4

Data collection

Dectris-CrysAlisPro-abstract goniometer imported dectris images diffractometer	769 reflections with I > 3σ(I)
Radiation source: synchrotron	Rint = 0.025
Synchrotron monochromator	θmax = 28.5°, θmin = 3.5°
Absorption correction: multi-scan (CrysAlis PRO; Agilent, 2014)	h = −14→15
Tmin = 0.529, Tmax = 1.000	k = 0→8
1782 measured reflections	l = −5→5
770 independent reflections

Refinement

Refinement on F	2 constraints
R[F > 3σ(F)] = 0.048	Weighting scheme based on measured s.u.'s w = 1/(σ^2(F) + 0.0001F^2)
wR(F) = 0.065	(Δ/σ)max = 0.035
S = 5.44	Δρmax = 2.26 e Å^−3
770 reflections	Δρmin = −1.77 e Å^−3
53 parameters	Absolute structure: 367 of Friedel pairs used in the refinement
0 restraints	Absolute structure parameter: 0.05 (5)

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

	x	y	z	Uiso*/Ueq
Ba1	0.336053	0	−0.000303	0.0131 (4)
Ba2	−0.33852 (10)	0	0.5010 (5)	0.0120 (4)
V1	−0.0205 (5)	0	−0.2417 (14)	0.0164 (11)
V2	0.0238 (6)	0	0.2635 (12)	0.0093 (10)
S1	−0.1730 (15)	0	0.014 (3)	0.013 (2)
S2	0.0833 (13)	0.2459 (8)	0.000 (3)	0.0148 (12)
S3	0.1689 (15)	0	0.506 (3)	0.0117 (19)
S4	−0.0836 (12)	−0.2427 (7)	0.495 (3)	0.0132 (11)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Ba1	0.0170 (8)	0.0143 (4)	0.0079 (9)	0	0.0003 (12)	0
Ba2	0.0130 (6)	0.0145 (5)	0.0084 (8)	0	0.0016 (11)	0
V1	0.0164 (17)	0.0118 (9)	0.021 (3)	0	−0.003 (3)	0
V2	0.0094 (14)	0.0165 (10)	0.002 (3)	0	−0.003 (2)	0
S1	0.015 (5)	0.0205 (18)	0.005 (4)	0	0.000 (4)	0
S2	0.021 (3)	0.0151 (12)	0.008 (2)	0.0047 (16)	0.002 (3)	0.003 (2)
S3	0.016 (4)	0.0109 (15)	0.008 (3)	0	0.002 (3)	0
S4	0.0136 (18)	0.0124 (11)	0.014 (2)	−0.0067 (16)	0.002 (3)	0.0021 (18)

Geometric parameters (Å, º)

Ba1—S1^i	3.374 (7)	V1—S3^v	2.60 (2)
Ba1—S1^ii	3.374 (7)	V1—S4^v	2.318 (14)
Ba1—S2	3.346 (14)	V1—S4^xvi	2.318 (14)
Ba1—S2^i	3.319 (14)	V2—S1	2.658 (19)
Ba1—S2^iii	3.346 (14)	V2—S2	2.321 (14)
Ba1—S2^iv	3.319 (14)	V2—S2^iii	2.321 (14)
Ba1—S3^v	3.364 (19)	V2—S3	2.15 (2)
Ba1—S3	3.425 (19)	V2—S4	2.426 (14)
Ba1—S4^vi	3.440 (17)	V2—S4^iii	2.426 (14)
Ba1—S4^ii	3.399 (16)	S1—S2	3.38 (2)
Ba1—S4^vii	3.440 (17)	S1—S2^x	3.28 (2)
Ba1—S4^viii	3.399 (16)	S1—S2^iii	3.38 (2)
Ba2—S1	3.323 (18)	S1—S2^xii	3.28 (2)
Ba2—S1^ix	3.446 (18)	S1—S4^v	3.49 (2)
Ba2—S2^x	3.405 (17)	S1—S4	3.31 (2)
Ba2—S2^xi	3.399 (17)	S1—S4^xvi	3.49 (2)
Ba2—S2^xii	3.405 (17)	S1—S4^iii	3.31 (2)
Ba2—S2^xiii	3.399 (17)	S2—S2^iii	3.316 (10)
Ba2—S3^x	3.372 (7)	S2—S2^xvii	3.426 (10)
Ba2—S3^xiv	3.372 (7)	S2—S3^v	3.37 (2)
Ba2—S4	3.357 (13)	S2—S3	3.43 (2)
Ba2—S4^xiv	3.308 (13)	S2—S4^xvi	3.42 (2)
Ba2—S4^iii	3.357 (13)	S2—S4^iii	3.37 (2)
Ba2—S4^xv	3.308 (13)	S3—S4	3.33 (2)
V1—V2^v	2.816 (12)	S3—S4^ii	3.33 (2)
V1—V2	2.873 (12)	S3—S4^iii	3.33 (2)
V1—S1	2.264 (19)	S3—S4^viii	3.33 (2)
V1—S2	2.451 (14)	S4—S4^xviii	3.469 (10)
V1—S2^iii	2.451 (14)	S4—S4^iii	3.273 (9)
V2^v—V1—V2	159.3 (3)	V1—V2—V1^ix	159.3 (3)
S1—V1—S2	91.6 (6)	S1—V2—S2	85.3 (5)
S1—V1—S2^iii	91.6 (6)	S1—V2—S2^iii	85.3 (5)
S1—V1—S3^v	173.7 (7)	S1—V2—S3	172.5 (7)
S1—V1—S4^v	99.2 (5)	S1—V2—S4	81.2 (5)
S1—V1—S4^xvi	99.2 (5)	S1—V2—S4^iii	81.2 (5)
S2—V1—S2^iii	85.1 (5)	S2—V2—S2^iii	91.2 (5)
S2—V1—S3^v	83.8 (5)	S2—V2—S3	99.9 (6)
S2—V1—S4^v	168.8 (6)	S2—V2—S4	166.2 (6)
S2—V1—S4^xvi	91.5 (4)	S2—V2—S4^iii	90.4 (4)
S2^iii—V1—S3^v	83.8 (5)	S2^iii—V2—S3	99.9 (6)
S2^iii—V1—S4^v	91.5 (4)	S2^iii—V2—S4	90.4 (4)
S2^iii—V1—S4^xvi	168.8 (6)	S2^iii—V2—S4^iii	166.2 (6)
S3^v—V1—S4^v	85.2 (5)	S3—V2—S4	93.3 (6)
S3^v—V1—S4^xvi	85.2 (5)	S3—V2—S4^iii	93.3 (6)
S4^v—V1—S4^xvi	89.8 (5)	S4—V2—S4^iii	84.8 (4)

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

(IV)

Crystal data

BaS3V	F(000) = 508
Mr = 284.5	Dx = 4.354 Mg m^−3
Monoclinic, Cm	Synchrotron radiation, λ = 0.70000 Å
Hall symbol: C -2y	Cell parameters from 3199 reflections
a = 11.485 (7) Å	θ = 3.5–31.8°
b = 6.751 (5) Å	µ = 11.79 mm^−1
c = 5.597 (3) Å	T = 100 K
β = 90.011 (5)°	Irregular, grey
V = 434.0 (5) Å^3	0.05 × 0.03 × 0.02 mm
Z = 4

Data collection

Mar345 image plate diffractometer	1934 reflections with I > 3σ(I)
Radiation source: synchrotron	Rint = 0.031
Absorption correction: multi-scan (CrysAlis PRO; Agilent, 2014)	θmax = 31.8°, θmin = 3.5°
Tmin = 0.627, Tmax = 1.000	h = −17→17
3199 measured reflections	k = −9→9
1935 independent reflections	l = −8→8

Refinement

Refinement on F	0 constraints
R[F > 3σ(F)] = 0.032	Weighting scheme based on measured s.u.'s w = 1/(σ^2(F) + 0.0001F^2)
wR(F) = 0.045	(Δ/σ)max = 0.048
S = 3.27	Δρmax = 1.39 e Å^−3
1935 reflections	Δρmin = −1.76 e Å^−3
59 parameters	Absolute structure: 806 of Friedel pairs used in the refinement
0 restraints	Absolute structure parameter: 0.05 (4)

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

	x	y	z	Uiso*/Ueq
Ba1	−0.3351 (3)	0	0.4995 (9)	0.0094 (9)
Ba2	0.338683	0	0	0.0088 (9)
V1	−0.0225 (10)	0	−0.2424 (16)	0.007 (2)
V2	0.0211 (10)	0	0.2593 (15)	0.011 (2)
S1	−0.173 (2)	0	0.015 (3)	0.006 (3)
S2	0.0785 (19)	0.2431 (19)	0.000 (2)	0.009 (2)
S3	0.167 (2)	0	0.512 (2)	0.006 (3)
S4	−0.0861 (18)	−0.2462 (18)	0.493 (2)	0.007 (2)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Ba1	0.0116 (16)	0.0096 (19)	0.0070 (9)	0	−0.0016 (10)	0
Ba2	0.0113 (18)	0.007 (2)	0.0079 (9)	0	−0.0034 (11)	0
V1	0.004 (3)	0.011 (5)	0.007 (2)	0	−0.001 (3)	0
V2	0.015 (4)	0.009 (5)	0.010 (2)	0	0.000 (3)	0
S1	0.005 (5)	0.006 (6)	0.006 (4)	0	0.0016 (16)	0
S2	0.012 (5)	0.010 (4)	0.005 (2)	−0.002 (3)	−0.002 (3)	−0.001 (3)
S3	0.008 (6)	0.004 (6)	0.005 (4)	0	−0.004 (2)	0
S4	0.006 (4)	0.004 (5)	0.012 (3)	−0.001 (2)	−0.002 (3)	−0.002 (2)

Geometric parameters (Å, º)

Ba1—S1	3.291 (19)	V1—S2^vii	2.425 (17)
Ba1—S1^i	3.429 (19)	V1—S3^xii	2.58 (2)
Ba1—S2^ii	3.437 (14)	V1—S4^xii	2.343 (15)
Ba1—S2^iii	3.440 (14)	V1—S4^xvi	2.343 (15)
Ba1—S2^iv	3.437 (14)	V2—S1	2.62 (2)
Ba1—S2^v	3.440 (14)	V2—S2	2.288 (15)
Ba1—S3^ii	3.3763 (6)	V2—S2^vii	2.288 (15)
Ba1—S3^vi	3.3763 (6)	V2—S3	2.19 (2)
Ba1—S4	3.308 (19)	V2—S4	2.447 (17)
Ba1—S4^vi	3.354 (19)	V2—S4^vii	2.447 (17)
Ba1—S4^vii	3.308 (19)	S1—S2	3.33 (3)
Ba1—S4^viii	3.354 (19)	S1—S2^ii	3.34 (3)
Ba2—S1^ix	3.3792 (12)	S1—S2^vii	3.33 (3)
Ba2—S1^x	3.3792 (12)	S1—S2^iv	3.34 (3)
Ba2—S2	3.41 (2)	S1—S4	3.31 (2)
Ba2—S2^ix	3.26 (2)	S1—S4^vii	3.31 (2)
Ba2—S2^vii	3.41 (2)	S2—S2^vii	3.282 (19)
Ba2—S2^xi	3.26 (2)	S2—S2^xvii	3.469 (19)
Ba2—S3^xii	3.370 (18)	S2—S3^xii	3.345 (19)
Ba2—S3	3.478 (18)	S2—S3	3.454 (19)
Ba2—S4^xiii	3.426 (13)	S2—S4^xvi	3.41 (2)
Ba2—S4^x	3.361 (13)	S2—S4^vii	3.35 (2)
Ba2—S4^xiv	3.426 (13)	S3—S4	3.35 (3)
Ba2—S4^xv	3.361 (13)	S3—S4^x	3.32 (3)
V1—V2^xii	2.834 (12)	S3—S4^vii	3.35 (3)
V1—V2	2.852 (12)	S3—S4^xv	3.32 (3)
V1—S1	2.25 (2)	S4—S4^xviii	3.427 (17)
V1—S2	2.425 (17)	S4—S4^vii	3.324 (17)
V2^xii—V1—V2	159.7 (5)	V1—V2—V1^i	159.7 (5)
S1—V1—S2	90.6 (6)	S1—V2—S2	85.1 (6)
S1—V1—S2^vii	90.6 (6)	S1—V2—S2^vii	85.1 (6)
S1—V1—S3^xii	172.6 (8)	S1—V2—S3	171.4 (8)
S1—V1—S4^xii	99.5 (7)	S1—V2—S4	81.4 (6)
S1—V1—S4^xvi	99.5 (7)	S1—V2—S4^vii	81.4 (6)
S2—V1—S2^vii	85.2 (6)	S2—V2—S2^vii	91.6 (6)
S2—V1—S3^xii	83.9 (6)	S2—V2—S3	100.9 (7)
S2—V1—S4^xii	169.4 (8)	S2—V2—S4	166.2 (9)
S2—V1—S4^xvi	91.3 (5)	S2—V2—S4^vii	89.8 (5)
S2^vii—V1—S3^xii	83.9 (6)	S2^vii—V2—S3	100.9 (7)
S2^vii—V1—S4^xii	91.3 (5)	S2^vii—V2—S4	89.8 (5)
S2^vii—V1—S4^xvi	169.4 (8)	S2^vii—V2—S4^vii	166.2 (9)
S3^xii—V1—S4^xii	85.7 (6)	S3—V2—S4	92.3 (6)
S3^xii—V1—S4^xvi	85.7 (6)	S3—V2—S4^vii	92.3 (6)
S4^xii—V1—S4^xvi	90.4 (6)	S4—V2—S4^vii	85.6 (6)

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

(V)

Crystal data

BaVS3	F(000) = 508
Mr = 284.5	Dx = 4.336 Mg m^−3
Monoclinic, Cm	Synchrotron radiation, λ = 0.70814 Å
Hall symbol: C -2y	Cell parameters from 1319 reflections
a = 11.5839 (7) Å	θ = 3.5–28.7°
b = 6.7016 (5) Å	µ = 12.12 mm^−1
c = 5.5956 (3) Å	T = 150 K
β = 90°	Irregular, grey
V = 434.39 (5) Å^3	0.05 × 0.03 × 0.02 mm
Z = 4

Data collection

Dectris-CrysAlisPro-abstract goniometer imported dectris images diffractometer	1409 reflections with I > 3σ(I)
Radiation source: synchrotron	Rint = 0.023
Synchrotron monochromator	θmax = 28.7°, θmin = 3.5°
Absorption correction: multi-scan (CrysAlis PRO; Agilent, 2014)	h = −14→14
Tmin = 0.658, Tmax = 1.000	k = −8→8
3834 measured reflections	l = −5→5
1409 independent reflections

Refinement

Refinement on F	28 constraints
R[F > 3σ(F)] = 0.046	Weighting scheme based on measured s.u.'s w = 1/(σ^2(F) + 0.0001F^2)
wR(F) = 0.072	(Δ/σ)max = 0.018
S = 4.83	Δρmax = 2.16 e Å^−3
1409 reflections	Δρmin = −1.62 e Å^−3
30 parameters	Absolute structure: 653 of Friedel pairs used in the refinement
0 restraints	Absolute structure parameter: 0.02 (4)

Special details

Refinement. Structure is considered as a commensurate composite with Ccm21 space group for the BaS3 matrix and C2/m space group for the V-chain. The corresponding constrains are applied for the corresponding atomic sides.

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

	x	y	z	Uiso*/Ueq
Ba1a	−0.33666 (4)	0	0.507918	0.0127 (2)
Ba1b	0.33666 (4)	0	0.007918	0.0127 (2)
V1a	0.02090 (11)	0	−0.2505 (3)	0.0131 (4)
V1b	−0.02090 (11)	0	0.2505 (3)	0.0131 (4)
S1a	−0.16932 (16)	0	−0.0029 (7)	0.0126 (9)
S2a	0.08307 (13)	0.24518 (15)	0.0226 (6)	0.0102 (7)
S1b	0.16932 (16)	0	0.4971 (7)	0.0126 (9)
S2b	−0.08307 (13)	−0.24518 (15)	0.5226 (6)	0.0102 (7)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Ba1a	0.0150 (4)	0.0142 (3)	0.0091 (5)	0	−0.0005 (3)	0
Ba1b	0.0150 (4)	0.0142 (3)	0.0091 (5)	0	−0.0005 (3)	0
V1a	0.0137 (7)	0.0180 (6)	0.0074 (9)	0	0.0006 (5)	0
V1b	0.0137 (7)	0.0180 (6)	0.0074 (9)	0	0.0006 (5)	0
S1a	0.0109 (12)	0.0168 (13)	0.010 (2)	0	0.0001 (11)	0
S2a	0.0158 (10)	0.0140 (10)	0.0010 (15)	−0.0029 (5)	−0.0013 (10)	0.0000 (5)
S1b	0.0109 (12)	0.0168 (13)	0.010 (2)	0	0.0001 (11)	0
S2b	0.0158 (10)	0.0140 (10)	0.0010 (15)	−0.0029 (5)	−0.0013 (10)	0.0000 (5)

Geometric parameters (Å, º)

Ba1a—S1a	3.454 (3)	V1a—S2a^vii	2.356 (3)
Ba1a—S1a^i	3.354 (3)	V1a—S1b^xii	2.225 (3)
Ba1a—S2a^ii	3.340 (3)	V1a—S2b^xii	2.401 (2)
Ba1a—S2a^iii	3.475 (3)	V1a—S2b^xvi	2.401 (2)
Ba1a—S2a^iv	3.340 (3)	V1b—S1a	2.228 (3)
Ba1a—S2a^v	3.475 (3)	V1b—S2a	2.403 (2)
Ba1a—S1b^ii	3.3521 (5)	V1b—S2a^vii	2.403 (2)
Ba1a—S1b^vi	3.3521 (5)	V1b—S1b	2.600 (3)
Ba1a—S2b	3.3669 (15)	V1b—S2b	2.353 (3)
Ba1a—S2b^vi	3.3272 (15)	V1b—S2b^vii	2.353 (3)
Ba1a—S2b^vii	3.3669 (15)	S1a—S2a	3.357 (2)
Ba1a—S2b^viii	3.3272 (15)	S1a—S2a^ii	3.341 (2)
Ba1b—S1a^ix	3.3521 (5)	S1a—S2a^vii	3.357 (2)
Ba1b—S1a^x	3.3521 (5)	S1a—S2a^iv	3.341 (2)
Ba1b—S2a	3.3669 (15)	S1a—S2b^xii	3.278 (4)
Ba1b—S2a^ix	3.3272 (15)	S1a—S2b^xvi	3.278 (4)
Ba1b—S2a^vii	3.3669 (15)	S2a—S2a^vii	3.2862 (15)
Ba1b—S2a^xi	3.3272 (15)	S2a—S2a^xvii	3.4154 (15)
Ba1b—S1b^xii	3.454 (3)	S2a—S1b	3.278 (4)
Ba1b—S1b	3.354 (3)	S2a—S2b^xvi	3.396 (4)
Ba1b—S2b^xiii	3.340 (3)	S2a—S2b^vii	3.396 (4)
Ba1b—S2b^x	3.475 (3)	S1b—S2b	3.357 (2)
Ba1b—S2b^xiv	3.340 (3)	S1b—S2b^x	3.341 (2)
Ba1b—S2b^xv	3.475 (3)	S1b—S2b^vii	3.357 (2)
V1a—V1b^xii	2.834 (2)	S1b—S2b^xv	3.341 (2)
V1a—V1b	2.845 (2)	S2b—S2b^xviii	3.4154 (15)
V1a—S1a	2.603 (3)	S2b—S2b^vii	3.2862 (15)
V1a—S2a	2.356 (3)
V1b^xii—V1a—V1b	160.36 (6)	V1a—V1b—V1a^i	160.36 (6)
S1a—V1a—S2a	85.04 (9)	S1a—V1b—S2a	92.81 (10)
S1a—V1a—S2a^vii	85.04 (9)	S1a—V1b—S2a^vii	92.81 (10)
S1a—V1a—S1b^xii	172.76 (13)	S1a—V1b—S1b	172.55 (13)
S1a—V1a—S2b^xii	81.77 (9)	S1a—V1b—S2b	100.11 (9)
S1a—V1a—S2b^xvi	81.77 (9)	S1a—V1b—S2b^vii	100.11 (9)
S2a—V1a—S2a^vii	88.42 (9)	S2a—V1b—S2a^vii	86.26 (8)
S2a—V1a—S1b^xii	100.11 (9)	S2a—V1b—S1b	81.78 (9)
S2a—V1a—S2b^xii	166.80 (10)	S2a—V1b—S2b	166.93 (10)
S2a—V1a—S2b^xvi	91.09 (8)	S2a—V1b—S2b^vii	91.11 (8)
S2a^vii—V1a—S1b^xii	100.11 (9)	S2a^vii—V1b—S1b	81.78 (9)
S2a^vii—V1a—S2b^xii	91.09 (8)	S2a^vii—V1b—S2b	91.11 (8)
S2a^vii—V1a—S2b^xvi	166.80 (10)	S2a^vii—V1b—S2b^vii	166.93 (10)
S1b^xii—V1a—S2b^xii	92.97 (10)	S1b—V1b—S2b	85.17 (9)
S1b^xii—V1a—S2b^xvi	92.97 (10)	S1b—V1b—S2b^vii	85.17 (9)
S2b^xii—V1a—S2b^xvi	86.39 (8)	S2b—V1b—S2b^vii	88.58 (10)

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

(VI)

Crystal data

BaS3V	F(000) = 508
Mr = 284.5	Dx = 4.327 Mg m^−3
Monoclinic, Cm	Synchrotron radiation, λ = 0.693 Å
Hall symbol: C -2y	Cell parameters from 1653 reflections
a = 11.5729 (7) Å	θ = 3.5–28.7°
b = 6.7116 (5) Å	µ = 12.09 mm^−1
c = 5.6015 (3) Å	T = 200 K
β = 90°	Irregular, grey
V = 435.08 (5) Å^3	0.05 × 0.03 × 0.02 mm
Z = 4

Data collection

Dectris-CrysAlisPro-abstract goniometer imported dectris images diffractometer	2191 reflections with I > 3σ(I)
Radiation source: synchrotron	Rint = 0.021
Synchrotron monochromator	θmax = 32.0°, θmin = 3.4°
Absorption correction: multi-scan (CrysAlis PRO; Agilent, 2014)	h = −17→16
Tmin = 0.595, Tmax = 1.000	k = −9→9
3593 measured reflections	l = −8→8
2206 independent reflections

Refinement

Refinement on F	Weighting scheme based on measured s.u.'s w = 1/(σ^2(F) + 0.0001F^2)
R[F > 3σ(F)] = 0.021	(Δ/σ)max = 0.020
wR(F) = 0.026	Δρmax = 0.62 e Å^−3
S = 1.15	Δρmin = −0.80 e Å^−3
2206 reflections	Extinction correction: B-C type 1 Gaussian isotropic (Becker & Coppens, 1974)
31 parameters	Extinction coefficient: 510 (40)
0 restraints	Absolute structure: 974 of Friedel pairs used in the refinement
28 constraints	Absolute structure parameter: 0.17 (3)

Special details

Refinement. Structure is considered as a commensurate composite with Ccm21 space group for the BaS3 matrix and C2/m space group for the V-chain. The corresponding constrains are applied for the corresponding atomic sides.

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

	x	y	z	Uiso*/Ueq
Ba1a	−0.33533 (5)	0	0.504191	0.01417 (15)
Ba1b	0.33533 (5)	0	0.004191	0.01417 (15)
V1a	0.01585 (9)	0	−0.2520 (3)	0.0211 (3)
V1b	−0.01585 (9)	0	0.2520 (3)	0.0211 (3)
S1a	−0.16705 (13)	0	−0.0068 (6)	0.0123 (10)
S2a	0.08293 (11)	0.24686 (16)	0.0088 (10)	0.0133 (7)
S1b	0.16705 (13)	0	0.4932 (6)	0.0123 (10)
S2b	−0.08293 (11)	−0.24686 (16)	0.5088 (10)	0.0133 (7)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Ba1a	0.0150 (3)	0.0148 (3)	0.01268 (10)	0	0.0002 (3)	0
Ba1b	0.0150 (3)	0.0148 (3)	0.01268 (10)	0	0.0002 (3)	0
V1a	0.0186 (6)	0.0335 (8)	0.01127 (19)	0	0.0023 (5)	0
V1b	0.0186 (6)	0.0335 (8)	0.01127 (19)	0	0.0023 (5)	0
S1a	0.0141 (18)	0.0102 (18)	0.0125 (14)	0	0.0004 (15)	0
S2a	0.0180 (16)	0.0097 (14)	0.0122 (8)	−0.0020 (8)	−0.0008 (13)	0.0006 (6)
S1b	0.0141 (18)	0.0102 (18)	0.0125 (14)	0	0.0004 (15)	0
S2b	0.0180 (16)	0.0097 (14)	0.0122 (8)	−0.0020 (8)	−0.0008 (13)	0.0006 (6)

Geometric parameters (Å, º)

Ba1a—S1a	3.462 (3)	V1a—S1b^xii	2.258 (3)
Ba1a—S1a^i	3.361 (3)	V1a—S2b^xii	2.418 (3)
Ba1a—S2a^ii	3.388 (5)	V1a—S2b^xvi	2.418 (3)
Ba1a—S2a^iii	3.431 (5)	V1b—S1a	2.272 (3)
Ba1a—S2a^iv	3.388 (5)	V1b—S2a	2.430 (3)
Ba1a—S2a^v	3.431 (5)	V1b—S2a^vii	2.430 (3)
Ba1a—S1b^ii	3.3565 (5)	V1b—S1b	2.511 (3)
Ba1a—S1b^vi	3.3565 (5)	V1b—S2b	2.328 (4)
Ba1a—S2b	3.3582 (14)	V1b—S2b^vii	2.328 (4)
Ba1a—S2b^vi	3.3314 (14)	S1a—S2a	3.3350 (18)
Ba1a—S2b^vii	3.3582 (14)	S1a—S2a^ii	3.3566 (18)
Ba1a—S2b^viii	3.3314 (14)	S1a—S2a^vii	3.3350 (18)
Ba1b—S1a^ix	3.3565 (5)	S1a—S2a^iv	3.3566 (18)
Ba1b—S1a^x	3.3565 (5)	S1a—S2b^xii	3.325 (5)
Ba1b—S2a	3.3582 (14)	S1a—S2b	3.469 (5)
Ba1b—S2a^ix	3.3314 (14)	S1a—S2b^xvi	3.325 (5)
Ba1b—S2a^vii	3.3582 (14)	S1a—S2b^vii	3.469 (5)
Ba1b—S2a^xi	3.3314 (14)	S2a—S2a^vii	3.3137 (16)
Ba1b—S1b^xii	3.462 (3)	S2a—S2a^xvii	3.3979 (16)
Ba1b—S1b	3.361 (3)	S2a—S1b^xii	3.469 (5)
Ba1b—S2b^xiii	3.388 (5)	S2a—S1b	3.325 (5)
Ba1b—S2b^x	3.431 (5)	S2a—S2b^xvi	3.395 (6)
Ba1b—S2b^xiv	3.388 (5)	S2a—S2b^vii	3.395 (6)
Ba1b—S2b^xv	3.431 (5)	S1b—S2b	3.3350 (18)
V1a—V1b^xii	2.803 (2)	S1b—S2b^x	3.3566 (18)
V1a—V1b	2.847 (2)	S1b—S2b^vii	3.3350 (18)
V1a—S1a	2.523 (3)	S1b—S2b^xv	3.3566 (18)
V1a—S2a	2.341 (4)	S2b—S2b^xviii	3.3979 (16)
V1a—S2a^vii	2.341 (4)	S2b—S2b^vii	3.3137 (16)
V1b^xii—V1a—V1b	165.08 (5)	V1a—V1b—V1a^i	165.08 (5)
S1a—V1a—S2a	86.47 (10)	S1a—V1b—S2a	90.27 (11)
S1a—V1a—S2a^vii	86.47 (10)	S1a—V1b—S2a^vii	90.27 (11)
S1a—V1a—S1b^xii	173.78 (12)	S1a—V1b—S1b	172.92 (12)
S1a—V1a—S2b^xii	84.55 (10)	S1a—V1b—S2b	97.90 (10)
S1a—V1a—S2b^xvi	84.55 (10)	S1a—V1b—S2b^vii	97.90 (10)
S2a—V1a—S2a^vii	90.08 (13)	S2a—V1b—S2a^vii	85.96 (11)
S2a—V1a—S1b^xii	97.90 (10)	S2a—V1b—S1b	84.55 (10)
S2a—V1a—S2b^xii	170.87 (11)	S2a—V1b—S2b	171.31 (10)
S2a—V1a—S2b^xvi	91.01 (11)	S2a—V1b—S2b^vii	91.03 (11)
S2a^vii—V1a—S1b^xii	97.90 (10)	S2a^vii—V1b—S1b	84.55 (10)
S2a^vii—V1a—S2b^xii	91.01 (11)	S2a^vii—V1b—S2b	91.03 (11)
S2a^vii—V1a—S2b^xvi	170.87 (11)	S2a^vii—V1b—S2b^vii	171.31 (10)
S1b^xii—V1a—S2b^xii	90.93 (11)	S1b—V1b—S2b	87.05 (10)
S1b^xii—V1a—S2b^xvi	90.93 (11)	S1b—V1b—S2b^vii	87.05 (10)
S2b^xii—V1a—S2b^xvi	86.51 (11)	S2b—V1b—S2b^vii	90.76 (13)

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

(VII)

Crystal data

BaVS3	F(000) = 508
Mr = 284.5	Dx = 4.336 Mg m^−3
Monoclinic, Cm	Synchrotron radiation, λ = 0.70814 Å
Hall symbol: C -2y	Cell parameters from 1812 reflections
a = 11.593 (7) Å	θ = 3.5–28.6°
b = 6.708 (5) Å	µ = 12.12 mm^−1
c = 5.604 (3) Å	T = 220 K
β = 90°	Irregular, grey
V = 435.8 (5) Å^3	0.05 × 0.03 × 0.02 mm
Z = 4

Data collection

Dectris-CrysAlisPro-abstract goniometer imported dectris images diffractometer	1464 reflections with I > 3σ(I)
Radiation source: synchrotron	Rint = 0.014
Synchrotron monochromator	θmax = 28.6°, θmin = 3.5°
Absorption correction: multi-scan (CrysAlis PRO; Agilent, 2014)	h = −15→15
Tmin = 0.606, Tmax = 1.000	k = −8→8
3944 measured reflections	l = −5→5
1464 independent reflections

Refinement

Refinement on F	Weighting scheme based on measured s.u.'s w = 1/(σ^2(F) + 0.0001F^2)
R[F > 3σ(F)] = 0.019	(Δ/σ)max = 0.045
wR(F) = 0.040	Δρmax = 0.96 e Å^−3
S = 2.83	Δρmin = −0.72 e Å^−3
1464 reflections	Extinction correction: B-C type 1 Gaussian isotropic (Becker & Coppens, 1974)
32 parameters	Extinction coefficient: 580 (40)
0 restraints	Absolute structure: 668 of Friedel pairs used in the refinement
27 constraints	Absolute structure parameter: 0.28 (2)

Special details

Refinement. Structure is considered as a commensurate composite with Ccm21 space group for the BaS3 matrix and C2/m space group for the V-chain. The corresponding constrains are applied for the corresponding atomic sides.

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

	x	y	z	Uiso*/Ueq
Ba1a	−0.33471 (3)	0	0.5046 (4)	0.01489 (16)
Ba1b	0.33471 (3)	0	0.0046 (4)	0.01489 (16)
V1a	0.01545 (6)	0	−0.25311 (9)	0.0213 (2)
V1b	−0.01545 (6)	0	0.25311 (9)	0.0213 (2)
S1a	−0.16657 (9)	0	0.0040 (15)	0.0162 (6)
S2a	0.08293 (7)	0.24697 (8)	0.0193 (13)	0.0114 (5)
S1b	0.16657 (9)	0	0.5040 (15)	0.0162 (6)
S2b	−0.08293 (7)	−0.24697 (8)	0.5193 (13)	0.0114 (5)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Ba1a	0.0146 (3)	0.0141 (3)	0.0160 (3)	0	−0.0008 (2)	0
Ba1b	0.0146 (3)	0.0141 (3)	0.0160 (3)	0	−0.0008 (2)	0
V1a	0.0212 (4)	0.0301 (5)	0.0125 (4)	0	0.0011 (4)	0
V1b	0.0212 (4)	0.0301 (5)	0.0125 (4)	0	0.0011 (4)	0
S1a	0.0107 (9)	0.0153 (9)	0.0226 (13)	0	−0.0003 (9)	0
S2a	0.0142 (8)	0.0110 (7)	0.0089 (10)	−0.0017 (3)	−0.0003 (9)	0.0000 (3)
S1b	0.0107 (9)	0.0153 (9)	0.0226 (13)	0	−0.0003 (9)	0
S2b	0.0142 (8)	0.0110 (7)	0.0089 (10)	−0.0017 (3)	−0.0003 (9)	0.0000 (3)

Geometric parameters (Å, º)

Ba1a—S1a	3.416 (8)	V1a—S1b^xii	2.218 (6)
Ba1a—S1a^i	3.411 (8)	V1a—S2b^xii	2.382 (5)
Ba1a—S2a^ii	3.345 (7)	V1a—S2b^xvi	2.382 (5)
Ba1a—S2a^iii	3.480 (7)	V1b—S1a	2.240 (6)
Ba1a—S2a^iv	3.345 (7)	V1b—S2a	2.400 (5)
Ba1a—S2a^v	3.480 (7)	V1b—S2a^vii	2.400 (5)
Ba1a—S1b^ii	3.354 (5)	V1b—S1b	2.536 (5)
Ba1a—S1b^vi	3.354 (5)	V1b—S2b	2.363 (5)
Ba1a—S2b	3.357 (3)	V1b—S2b^vii	2.363 (5)
Ba1a—S2b^vi	3.342 (3)	S1a—S2a	3.334 (3)
Ba1a—S2b^vii	3.357 (3)	S1a—S2a^ii	3.365 (3)
Ba1a—S2b^viii	3.342 (3)	S1a—S2a^vii	3.334 (3)
Ba1b—S1a^ix	3.354 (5)	S1a—S2a^iv	3.365 (3)
Ba1b—S1a^x	3.354 (5)	S1a—S2b^xii	3.326 (10)
Ba1b—S2a	3.357 (3)	S1a—S2b	3.468 (10)
Ba1b—S2a^ix	3.342 (3)	S1a—S2b^xvi	3.326 (10)
Ba1b—S2a^vii	3.357 (3)	S1a—S2b^vii	3.468 (10)
Ba1b—S2a^xi	3.342 (3)	S2a—S2a^vii	3.313 (5)
Ba1b—S1b^xii	3.416 (8)	S2a—S2a^xvii	3.395 (5)
Ba1b—S1b	3.411 (8)	S2a—S1b^xii	3.468 (10)
Ba1b—S2b^xiii	3.345 (7)	S2a—S1b	3.326 (10)
Ba1b—S2b^x	3.480 (7)	S2a—S2b^xvi	3.398 (9)
Ba1b—S2b^xiv	3.345 (7)	S2a—S2b^vii	3.398 (9)
Ba1b—S2b^xv	3.480 (7)	S1b—S2b	3.334 (3)
V1a—V1b^xii	2.790 (3)	S1b—S2b^x	3.365 (3)
V1a—V1b	2.859 (3)	S1b—S2b^vii	3.334 (3)
V1a—S1a	2.555 (5)	S1b—S2b^xv	3.365 (3)
V1a—S2a	2.385 (5)	S2b—S2b^xviii	3.395 (5)
V1a—S2a^vii	2.385 (5)	S2b—S2b^vii	3.313 (5)
V1b^xii—V1a—V1b	165.43 (4)	V1a—V1b—V1a^i	165.43 (4)
S1a—V1a—S2a	84.83 (15)	S1a—V1b—S2a	91.80 (17)
S1a—V1a—S2a^vii	84.83 (15)	S1a—V1b—S2a^vii	91.80 (17)
S1a—V1a—S1b^xii	176.5 (2)	S1a—V1b—S1b	175.1 (2)
S1a—V1a—S2b^xii	84.64 (16)	S1a—V1b—S2b	97.73 (16)
S1a—V1a—S2b^xvi	84.64 (16)	S1a—V1b—S2b^vii	97.73 (16)
S2a—V1a—S2a^vii	88.00 (17)	S2a—V1b—S2a^vii	87.29 (14)
S2a—V1a—S1b^xii	97.68 (16)	S2a—V1b—S1b	84.68 (16)
S2a—V1a—S2b^xii	169.47 (15)	S2a—V1b—S2b	170.37 (14)
S2a—V1a—S2b^xvi	90.96 (16)	S2a—V1b—S2b^vii	91.03 (16)
S2a^vii—V1a—S1b^xii	97.68 (16)	S2a^vii—V1b—S1b	84.68 (16)
S2a^vii—V1a—S2b^xii	90.96 (16)	S2a^vii—V1b—S2b	91.03 (16)
S2a^vii—V1a—S2b^xvi	169.47 (15)	S2a^vii—V1b—S2b^vii	170.37 (14)
S1b^xii—V1a—S2b^xii	92.84 (18)	S1b—V1b—S2b	85.72 (15)
S1b^xii—V1a—S2b^xvi	92.84 (18)	S1b—V1b—S2b^vii	85.72 (15)
S2b^xii—V1a—S2b^xvi	88.15 (14)	S2b—V1b—S2b^vii	89.04 (17)

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

(VIII)

Crystal data

BaVS3	F(000) = 508
Mr = 284.5	Dx = 4.324 Mg m^−3
Monoclinic, Cm	Synchrotron radiation, λ = 0.7 Å
Hall symbol: C -2y	Cell parameters from 2084 reflections
a = 11.585 (7) Å	θ = 3.5–32.4°
b = 6.724 (5) Å	µ = 11.71 mm^−1
c = 5.610 (2) Å	T = 240 K
β = 90°	Irregular, grey
V = 437.0 (4) Å^3	0.05 × 0.03 × 0.02 mm
Z = 4

Data collection

Mar345 image plate diffractometer	1724 reflections with I > 3σ(I)
Radiation source: synchrotron	Rint = 0.018
Synchrotron monochromator	θmax = 32.4°, θmin = 3.5°
Absorption correction: multi-scan (CrysAlis PRO; Agilent, 2014)	h = −17→17
Tmin = 0.623, Tmax = 1.000	k = −10→10
2084 measured reflections	l = −7→8
1751 independent reflections

Refinement

Refinement on F	Weighting scheme based on measured s.u.'s w = 1/(σ^2(F) + 0.0001F^2)
R[F > 3σ(F)] = 0.021	(Δ/σ)max = 0.002
wR(F) = 0.033	Δρmax = 1.27 e Å^−3
S = 2.02	Δρmin = −0.98 e Å^−3
1751 reflections	Extinction correction: B-C type 1 Gaussian isotropic (Becker & Coppens, 1974)
32 parameters	Extinction coefficient: 510 (60)
0 restraints	Absolute structure: 573 of Friedel pairs used in the refinement
27 constraints	Absolute structure parameter: 0.20 (5)

Special details

Refinement. Structure is considered as a commensurate composite with Ccm21 space group for the BaS3 matrix and C2/m space group for the V-chain. The corresponding constrains are applied for the corresponding atomic sides.

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

	x	y	z	Uiso*/Ueq
Ba1a	−0.33427 (6)	0	0.5014 (8)	0.01674 (14)
Ba1b	0.33427 (6)	0	0.0014 (8)	0.01674 (14)
V1a	0.01168 (9)	0	−0.2553 (3)	0.0282 (4)
V1b	−0.01168 (9)	0	0.2553 (3)	0.0282 (4)
S1a	−0.16583 (15)	0	−0.005 (3)	0.0158 (8)
S2a	0.08287 (13)	0.24755 (18)	0.006 (3)	0.0153 (5)
S1b	0.16583 (15)	0	0.495 (3)	0.0158 (8)
S2b	−0.08287 (13)	−0.24755 (18)	0.506 (3)	0.0153 (5)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Ba1a	0.0153 (3)	0.0164 (3)	0.01850 (16)	0	−0.0006 (3)	0
Ba1b	0.0153 (3)	0.0164 (3)	0.01850 (16)	0	−0.0006 (3)	0
V1a	0.0254 (7)	0.0441 (10)	0.0152 (4)	0	0.0007 (7)	0
V1b	0.0254 (7)	0.0441 (10)	0.0152 (4)	0	0.0007 (7)	0
S1a	0.0100 (10)	0.0174 (12)	0.0200 (18)	0	0.0007 (10)	0
S2a	0.0134 (8)	0.0145 (9)	0.0179 (10)	−0.0023 (4)	0.0004 (9)	0.0004 (5)
S1b	0.0100 (10)	0.0174 (12)	0.0200 (18)	0	0.0007 (10)	0
S2b	0.0134 (8)	0.0145 (9)	0.0179 (10)	−0.0023 (4)	0.0004 (9)	0.0004 (5)

Geometric parameters (Å, º)

Ba1a—S1a	3.446 (13)	V1a—S1b^xii	2.269 (9)
Ba1a—S1a^i	3.388 (13)	V1a—S2b^xii	2.400 (8)
Ba1a—S2a^ii	3.395 (12)	V1a—S2b^xvi	2.400 (8)
Ba1a—S2a^iii	3.438 (12)	V1b—S1a	2.307 (10)
Ba1a—S2a^iv	3.395 (12)	V1b—S2a	2.434 (8)
Ba1a—S2a^v	3.438 (12)	V1b—S2a^vii	2.434 (8)
Ba1a—S1b^ii	3.362 (5)	V1b—S1b	2.457 (9)
Ba1a—S1b^vi	3.362 (5)	V1b—S2b	2.330 (9)
Ba1a—S2b	3.355 (4)	V1b—S2b^vii	2.330 (9)
Ba1a—S2b^vi	3.343 (4)	S1a—S2a	3.328 (4)
Ba1a—S2b^vii	3.355 (4)	S1a—S2a^ii	3.371 (4)
Ba1a—S2b^viii	3.343 (4)	S1a—S2a^vii	3.328 (4)
Ba1b—S1a^ix	3.362 (5)	S1a—S2a^iv	3.371 (4)
Ba1b—S1a^x	3.362 (5)	S1a—S2b^xii	3.350 (17)
Ba1b—S2a	3.355 (4)	S1a—S2b	3.451 (17)
Ba1b—S2a^ix	3.343 (4)	S1a—S2b^xvi	3.350 (17)
Ba1b—S2a^vii	3.355 (4)	S1a—S2b^vii	3.451 (17)
Ba1b—S2a^xi	3.343 (4)	S2a—S2a^vii	3.329 (5)
Ba1b—S1b^xii	3.446 (13)	S2a—S2a^xvii	3.395 (5)
Ba1b—S1b	3.388 (13)	S2a—S1b^xii	3.451 (17)
Ba1b—S2b^xiii	3.395 (12)	S2a—S1b	3.350 (17)
Ba1b—S2b^x	3.438 (12)	S2a—S2b^xvi	3.399 (17)
Ba1b—S2b^xiv	3.395 (12)	S2a—S2b^vii	3.399 (17)
Ba1b—S2b^xv	3.438 (12)	S1b—S2b	3.328 (4)
V1a—V1b^xii	2.758 (3)	S1b—S2b^x	3.371 (4)
V1a—V1b	2.878 (3)	S1b—S2b^vii	3.328 (4)
V1a—S1a	2.491 (9)	S1b—S2b^xv	3.371 (4)
V1a—S2a	2.367 (9)	S2b—S2b^xviii	3.395 (5)
V1a—S2a^vii	2.367 (9)	S2b—S2b^vii	3.329 (5)
V1b^xii—V1a—V1b	168.98 (5)	V1a—V1b—V1a^i	168.98 (5)
S1a—V1a—S2a	86.5 (3)	S1a—V1b—S2a	89.1 (3)
S1a—V1a—S2a^vii	86.5 (3)	S1a—V1b—S2a^vii	89.1 (3)
S1a—V1a—S1b^xii	176.3 (4)	S1a—V1b—S1b	173.9 (4)
S1a—V1a—S2b^xii	86.4 (3)	S1a—V1b—S2b	96.2 (3)
S1a—V1a—S2b^xvi	86.4 (3)	S1a—V1b—S2b^vii	96.2 (3)
S2a—V1a—S2a^vii	89.4 (3)	S2a—V1b—S2a^vii	86.3 (3)
S2a—V1a—S1b^xii	96.2 (3)	S2a—V1b—S1b	86.4 (3)
S2a—V1a—S2b^xii	172.8 (3)	S2a—V1b—S2b	173.99 (15)
S2a—V1a—S2b^xvi	91.0 (3)	S2a—V1b—S2b^vii	91.0 (3)
S2a^vii—V1a—S1b^xii	96.2 (3)	S2a^vii—V1b—S1b	86.4 (3)
S2a^vii—V1a—S2b^xii	91.0 (3)	S2a^vii—V1b—S2b	91.0 (3)
S2a^vii—V1a—S2b^xvi	172.8 (3)	S2a^vii—V1b—S2b^vii	173.99 (15)
S1b^xii—V1a—S2b^xii	90.9 (3)	S1b—V1b—S2b	88.0 (3)
S1b^xii—V1a—S2b^xvi	90.9 (3)	S1b—V1b—S2b^vii	88.0 (3)
S2b^xii—V1a—S2b^xvi	87.8 (3)	S2b—V1b—S2b^vii	91.2 (3)

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

(IX)

Crystal data

BaVS3	Dx = 4.312 Mg m^−3
Mr = 284.5	Synchrotron radiation, λ = 0.70814 Å
Trigonal, P3m1	Cell parameters from 1783 reflections
Hall symbol: P 3;-2"	θ = 3.5–28.6°
a = 6.7164 (2) Å	µ = 12.05 mm^−1
c = 5.6088 (2) Å	T = 250 K
V = 219.12 (1) Å^3	Irregular, grey
Z = 2	0.05 × 0.03 × 0.02 mm
F(000) = 254

Data collection

Dectris-CrysAlisPro-abstract goniometer imported dectris images diffractometer	196 reflections with I > 3σ(I)
Radiation source: synchrotron	Rint = 0.034
Synchrotron monochromator	θmax = 28.6°, θmin = 3.5°
Absorption correction: multi-scan (CrysAlis PRO; Agilent, 2014)	h = −8→8
Tmin = 0.649, Tmax = 1.000	k = −8→8
2069 measured reflections	l = −5→5
196 independent reflections

Refinement

Refinement on F	Weighting scheme based on measured s.u.'s w = 1/(σ^2(F) + 0.00034225F^2)
R[F > 3σ(F)] = 0.034	(Δ/σ)max = 0.018
wR(F) = 0.146	Δρmax = 1.67 e Å^−3
S = 1.67	Δρmin = −1.94 e Å^−3
196 reflections	Extinction correction: B-C type 1 Gaussian isotropic (Becker & Coppens, 1974)
13 parameters	Extinction coefficient: 600 (400)
0 restraints	Absolute structure: 0 of Friedel pairs used in the refinement
12 constraints

Special details

Refinement. Structure is considered as a commensurate composite with P63/mmc space group for the BaS3 matrix and P3/m space group for the V-chain. The corresponding constrains are applied for the corresponding atomic sides.

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

	x	y	z	Uiso*/Ueq
Ba1a	0.333333	0.666667	0.5	0.0170 (13)
Ba1b	−0.333333	−0.666667	0	0.0170 (13)
V1a	0	0	−0.2593 (16)	0.0339 (19)
V1b	0	0	0.2598 (16)	0.0339 (19)
S1a	0.16378 (19)	−0.16378 (19)	0	0.018 (3)
S1b	−0.16378 (19)	0.163783	0.5	0.018 (3)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Ba1a	0.0149 (15)	0.0149 (15)	0.021 (3)	0.0074 (7)	0	0
Ba1b	0.0149 (15)	0.0149 (15)	0.021 (3)	0.0074 (7)	0	0
V1a	0.040 (2)	0.040 (2)	0.021 (4)	0.0201 (11)	0	0
V1b	0.040 (2)	0.040 (2)	0.021 (4)	0.0201 (11)	0	0
S1a	0.018 (3)	0.018 (3)	0.025 (6)	0.013 (2)	0.0002 (7)	−0.0002 (7)
S1b	0.018 (3)	0.018 (3)	0.025 (6)	0.013 (2)	0.0002 (7)	−0.0002 (7)

Geometric parameters (Å, º)

Ba1a—S1a^i	3.4286 (9)	V1a—V1b	2.912 (13)
Ba1a—S1a^ii	3.4286 (9)	V1a—S1a	2.397 (6)
Ba1a—S1a^iii	3.4286 (9)	V1a—S1a^iii	2.397 (6)
Ba1a—S1a^iv	3.4286 (9)	V1a—S1a^x	2.397 (6)
Ba1a—S1a^v	3.4286 (9)	V1a—S1b^xxi	2.335 (5)
Ba1a—S1a^vi	3.4286 (9)	V1a—S1b^xviii	2.335 (5)
Ba1a—S1b	3.3584 (7)	V1a—S1b^xxii	2.335 (5)
Ba1a—S1b^vii	3.3584 (7)	V1b—S1a	2.399 (5)
Ba1a—S1b^viii	3.3584 (7)	V1b—S1a^iii	2.399 (5)
Ba1a—S1b^ix	3.3584 (7)	V1b—S1a^x	2.399 (5)
Ba1a—S1b^x	3.3584 (15)	V1b—S1b	2.333 (5)
Ba1a—S1b^xi	3.3584 (15)	V1b—S1b^iii	2.333 (5)
Ba1b—S1a^xii	3.3584 (10)	V1b—S1b^x	2.333 (5)
Ba1b—S1a	3.3584 (10)	S1a—S1a^xiv	3.416 (2)
Ba1b—S1a^xiii	3.3584 (16)	S1a—S1a^iii	3.300 (2)
Ba1b—S1a^xiv	3.3584 (16)	S1a—S1a^x	3.300 (2)
Ba1b—S1a^xv	3.3584 (16)	S1a—S1a^xxiii	3.416 (2)
Ba1b—S1a^x	3.3584 (16)	S1a—S1b^xviii	3.3904 (7)
Ba1b—S1b^xvi	3.4286 (7)	S1a—S1b^iii	3.3904 (7)
Ba1b—S1b^xvii	3.4286 (7)	S1a—S1b^xxii	3.3904 (9)
Ba1b—S1b^xviii	3.4286 (7)	S1a—S1b^x	3.3904 (9)
Ba1b—S1b^iii	3.4286 (7)	S1b—S1b^iii	3.3001 (15)
Ba1b—S1b^xix	3.4286 (7)	S1b—S1b^viii	3.4163 (15)
Ba1b—S1b^xx	3.4286 (7)	S1b—S1b^xxiv	3.416 (2)
V1a—V1b^xxi	2.697 (13)	S1b—S1b^x	3.300 (2)
V1b^xxi—V1a—V1b	180	V1a—V1b—V1a^xxv	180
S1a—V1a—S1a^iii	87.0 (3)	S1a—V1b—S1a^iii	86.9 (2)
S1a—V1a—S1a^x	87.0 (3)	S1a—V1b—S1a^x	86.9 (2)
S1a—V1a—S1b^xxi	178.0 (4)	S1a—V1b—S1b	177.9 (3)
S1a—V1a—S1b^xviii	91.52 (3)	S1a—V1b—S1b^iii	91.52 (3)
S1a—V1a—S1b^xxii	91.52 (4)	S1a—V1b—S1b^x	91.52 (4)
S1a^iii—V1a—S1a^x	87.0 (3)	S1a^iii—V1b—S1a^x	86.9 (2)
S1a^iii—V1a—S1b^xxi	91.52 (4)	S1a^iii—V1b—S1b	91.52 (4)
S1a^iii—V1a—S1b^xviii	178.0 (4)	S1a^iii—V1b—S1b^iii	177.9 (3)
S1a^iii—V1a—S1b^xxii	91.52 (3)	S1a^iii—V1b—S1b^x	91.52 (3)
S1a^x—V1a—S1b^xxi	91.52 (5)	S1a^x—V1b—S1b	91.52 (5)
S1a^x—V1a—S1b^xviii	91.52 (2)	S1a^x—V1b—S1b^iii	91.52 (2)
S1a^x—V1a—S1b^xxii	178.0 (4)	S1a^x—V1b—S1b^x	177.9 (3)
S1b^xxi—V1a—S1b^xviii	89.9 (3)	S1b—V1b—S1b^iii	90.0 (2)
S1b^xxi—V1a—S1b^xxii	89.9 (3)	S1b—V1b—S1b^x	90.0 (3)
S1b^xviii—V1a—S1b^xxii	89.9 (3)	S1b^iii—V1b—S1b^x	90.0 (2)

Symmetry codes: (i) x, y+1, z; (ii) x, y+1, z+1; (iii) −y, x−y, z; (iv) −y, x−y, z+1; (v) −x+y+1, −x+1, z; (vi) −x+y+1, −x+1, z+1; (vii) x+1, y+1, z; (viii) −y, x−y+1, z; (ix) −y+1, x−y+1, z; (x) −x+y, −x, z; (xi) −x+y, −x+1, z; (xii) x−1, y−1, z; (xiii) −y−1, x−y−1, z; (xiv) −y, x−y−1, z; (xv) −x+y, −x−1, z; (xvi) x, y−1, z−1; (xvii) x, y−1, z; (xviii) −y, x−y, z−1; (xix) −x+y−1, −x−1, z−1; (xx) −x+y−1, −x−1, z; (xxi) x, y, z−1; (xxii) −x+y, −x, z−1; (xxiii) −x+y+1, −x, z; (xxiv) −x+y−1, −x, z; (xxv) x, y, z+1.

(X)

Crystal data

BaVS3	Dx = 4.305 Mg m^−3
Mr = 284.5	Synchrotron radiation, λ = 0.6622 Å
Trigonal, P3m1	Cell parameters from 2946 reflections
Hall symbol: P 3;-2"	θ = 3.3–24.4°
a = 6.7180 (5) Å	µ = 10.01 mm^−1
c = 5.6150 (2) Å	T = 295 K
V = 219.46 (2) Å^3	Irregular, grey
Z = 2	0.05 × 0.03 × 0.02 mm
F(000) = 254

Data collection

Dectris-CrysAlisPro-abstract goniometer imported dectris images diffractometer	168 reflections with I > 2σ(I)
Radiation source: synchrotron	Rint = 0.038
Synchrotron monochromator	θmax = 24.4°, θmin = 3.3°
Absorption correction: multi-scan (CrysAlis PRO; Agilent, 2014)	h = −8→8
Tmin = 0.556, Tmax = 1.000	k = −8→8
2946 measured reflections	l = −6→6
173 independent reflections

Refinement

Refinement on F	Weighting scheme based on measured s.u.'s w = 1/(σ^2(F) + 0.00034225F^2)
R[F > 3σ(F)] = 0.028	(Δ/σ)max = 0.001
wR(F) = 0.063	Δρmax = 0.76 e Å^−3
S = 3.13	Δρmin = −0.73 e Å^−3
173 reflections	Extinction correction: B-C type 1 Gaussian isotropic (Becker & Coppens, 1974)
13 parameters	Extinction coefficient: 2700 (700)
0 restraints	Absolute structure: 0 of Friedel pairs used in the refinement
12 constraints	Absolute structure parameter: not applicable for the particular case

Special details

Refinement. Structure is considered as a commensurate composite with P63/mmc space group for the BaS3 matrix and P3/m space group for the V-chain. The corresponding constrains are applied for the corresponding atomic sides.

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

	x	y	z	Uiso*/Ueq
Ba1a	0.333333	0.666667	0.5	0.0183 (7)
Ba1b	−0.333333	−0.666667	0	0.0183 (7)
V1a	0	0	−0.2540 (9)	0.0337 (9)
V1b	0	0	0.2558 (9)	0.0337 (9)
S1a	0.16500 (10)	−0.16500 (10)	0	0.0171 (13)
S1b	−0.16500 (10)	0.164998	0.5	0.0171 (13)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Ba1a	0.0171 (9)	0.0171 (9)	0.0206 (10)	0.0086 (4)	0	0
Ba1b	0.0171 (9)	0.0171 (9)	0.0206 (10)	0.0086 (4)	0	0
V1a	0.0410 (12)	0.0410 (12)	0.0192 (14)	0.0205 (6)	0	0
V1b	0.0410 (12)	0.0410 (12)	0.0192 (14)	0.0205 (6)	0	0
S1a	0.0187 (15)	0.0187 (15)	0.017 (2)	0.0117 (10)	0.0000 (3)	0.0000 (3)
S1b	0.0187 (15)	0.0187 (15)	0.017 (2)	0.0117 (10)	0.0000 (3)	0.0000 (3)

Geometric parameters (Å, º)

Ba1a—S1a^i	3.4233 (5)	V1a—V1b	2.862 (7)
Ba1a—S1a^ii	3.4233 (5)	V1a—S1a	2.392 (3)
Ba1a—S1a^iii	3.4233 (5)	V1a—S1a^iii	2.392 (3)
Ba1a—S1a^iv	3.4233 (5)	V1a—S1a^x	2.392 (3)
Ba1a—S1a^v	3.4233 (5)	V1a—S1b^xxi	2.365 (3)
Ba1a—S1a^vi	3.4233 (5)	V1a—S1b^xviii	2.365 (3)
Ba1a—S1b	3.3591 (8)	V1a—S1b^xxii	2.365 (3)
Ba1a—S1b^vii	3.3591 (8)	V1b—S1a	2.398 (3)
Ba1a—S1b^viii	3.3591 (6)	V1b—S1a^iii	2.398 (3)
Ba1a—S1b^ix	3.3591 (6)	V1b—S1a^x	2.398 (3)
Ba1a—S1b^x	3.3591 (9)	V1b—S1b	2.359 (3)
Ba1a—S1b^xi	3.3591 (9)	V1b—S1b^iii	2.359 (3)
Ba1b—S1a^xii	3.3591 (9)	V1b—S1b^x	2.359 (3)
Ba1b—S1a	3.3591 (9)	S1a—S1a^xiv	3.3926 (13)
Ba1b—S1a^xiii	3.3591 (9)	S1a—S1a^iii	3.3254 (13)
Ba1b—S1a^xiv	3.3591 (9)	S1a—S1a^x	3.3254 (13)
Ba1b—S1a^xv	3.3591 (9)	S1a—S1a^xxiii	3.3926 (13)
Ba1b—S1a^x	3.3591 (9)	S1a—S1b^xviii	3.4012 (4)
Ba1b—S1b^xvi	3.4233 (4)	S1a—S1b^iii	3.4012 (4)
Ba1b—S1b^xvii	3.4233 (4)	S1a—S1b^xxii	3.4012 (5)
Ba1b—S1b^xviii	3.4233 (4)	S1a—S1b^x	3.4012 (5)
Ba1b—S1b^iii	3.4233 (4)	S1b—S1b^iii	3.3254 (9)
Ba1b—S1b^xix	3.4233 (4)	S1b—S1b^viii	3.3926 (9)
Ba1b—S1b^xx	3.4233 (4)	S1b—S1b^xxiv	3.3926 (11)
V1a—V1b^xxi	2.753 (7)	S1b—S1b^x	3.3254 (11)
V1b^xxi—V1a—V1b	180	V1a—V1b—V1a^xxv	180
S1a—V1a—S1a^iii	88.09 (15)	S1a—V1b—S1a^iii	87.81 (14)
S1a—V1a—S1a^x	88.09 (15)	S1a—V1b—S1a^x	87.81 (14)
S1a—V1a—S1b^xxi	179.1 (2)	S1a—V1b—S1b	178.7 (2)
S1a—V1a—S1b^xviii	91.287 (16)	S1a—V1b—S1b^iii	91.281 (17)
S1a—V1a—S1b^xxii	91.29 (2)	S1a—V1b—S1b^x	91.28 (2)
S1a^iii—V1a—S1a^x	88.09 (15)	S1a^iii—V1b—S1a^x	87.81 (14)
S1a^iii—V1a—S1b^xxi	91.29 (2)	S1a^iii—V1b—S1b	91.28 (2)
S1a^iii—V1a—S1b^xviii	179.1 (2)	S1a^iii—V1b—S1b^iii	178.7 (2)
S1a^iii—V1a—S1b^xxii	91.287 (17)	S1a^iii—V1b—S1b^x	91.281 (17)
S1a^x—V1a—S1b^xxi	91.29 (2)	S1a^x—V1b—S1b	91.28 (2)
S1a^x—V1a—S1b^xviii	91.287 (13)	S1a^x—V1b—S1b^iii	91.281 (13)
S1a^x—V1a—S1b^xxii	179.1 (2)	S1a^x—V1b—S1b^x	178.7 (2)
S1b^xxi—V1a—S1b^xviii	89.33 (15)	S1b—V1b—S1b^iii	89.61 (15)
S1b^xxi—V1a—S1b^xxii	89.33 (15)	S1b—V1b—S1b^x	89.61 (15)
S1b^xviii—V1a—S1b^xxii	89.33 (15)	S1b^iii—V1b—S1b^x	89.61 (15)

Symmetry codes: (i) x, y+1, z; (ii) x, y+1, z+1; (iii) −y, x−y, z; (iv) −y, x−y, z+1; (v) −x+y+1, −x+1, z; (vi) −x+y+1, −x+1, z+1; (vii) x+1, y+1, z; (viii) −y, x−y+1, z; (ix) −y+1, x−y+1, z; (x) −x+y, −x, z; (xi) −x+y, −x+1, z; (xii) x−1, y−1, z; (xiii) −y−1, x−y−1, z; (xiv) −y, x−y−1, z; (xv) −x+y, −x−1, z; (xvi) x, y−1, z−1; (xvii) x, y−1, z; (xviii) −y, x−y, z−1; (xix) −x+y−1, −x−1, z−1; (xx) −x+y−1, −x−1, z; (xxi) x, y, z−1; (xxii) −x+y, −x, z−1; (xxiii) −x+y+1, −x, z; (xxiv) −x+y−1, −x, z; (xxv) x, y, z+1.