A novel crystal polymorph of volborthite, Cu₃V₂O₇(OH)₂·2H₂O

A new polymorph of volborthite [tricopper(II) divanadium(V) hepta­oxide dihydroxide dihydrate], Cu₃V₂O₇(OH)₂·2H₂O, has been discovered in a single crystal prepared by hydro­thermal synthesis. X-ray analysis reveals that the monoclinic structure has the space group C2/c at room temperature, which is different from that of the previously reported C2/m structure. Both structures have Cu₃O₆(OH)₂ layers composed of edge-sharing CuO₄(OH)₂ octa­hedra, with V₂O₇ pillars and water mol­ecules between the layers. The Cu atoms occupy two and three independent crystallographic sites in the C2/m and C2/c structures, respectively, likely giving rise to different magnetic inter­actions between Cu^II spins in the kagome lattices embedded in the Cu₃O₆(OH)₂ layers.

S1. Comment

Kagome antiferromagnets have been extensively studied to search for exotic magnetic phenomena. It is believed that an unknown ground state, such as a spin liquid, can be realized instead of the conventional Néel order, due to geometric frustration of spins residing on triangle-based lattices. Several Cu minerals comprising kagome lattices formed by Cu^II ions have been targeted as model compounds for the spin-1/2 kagome antiferromagnet: herbertsmithite ZnCu₃(OH)₆Cl₂ (Shores et al., 2005), volborthite Cu₃V₂O₇(OH)₂ 2H₂O (Hiroi et al., 2001), vesignieite BaCu₃V₂O₈(OH)₂ (Okamoto et al., 2009), haydeeite Cu₃Mg(OH)₆Cl₂ (Colman et al., 2010) and kapellasite Cu₃Zn(OH)₆Cl₂ (Colman et al., 2008). However, the true ground state of the spin-1/2 kagome antiferromagnet is still a mystery because of experimental obstacles posed by real compounds: distortion, defects and other deviations from the ideal kagome model tend to hinder the characterization of low-temperature properties.

Volborthite is a mineral found in nature as yellow–green crystals of sub-millimetre size, and has been known since the 18th century. Its chemical and physical properties were described by Guillemin (1956). The compound has recently been studied as a candidate for the spin-1/2 kagome antiferromagnet (Hiroi et al., 2001). A high-quality powder sample of volborthite was synthesized hydrothermally and found to exhibit anomalous magnetic transitions at temperatures near 1 K (Bert et al., 2005; Yoshida, Okamoto et al., 2009; Yoshida, Takigawa et al., 2009).

The crystal structure of volborthite at room temperature has been examined by several groups and still remains controversial. Leonardsen & Petersen (1974) described a monoclinic unit cell with a = 10.604, b = 5.879 and c = 7.202 Å, and β = 94.81°. Kashaev & Vasil'ev (1974) reported space group C2/c or Cc. Later, Basso et al. (1988) reported another monoclinic structure in space group C2/m by X-ray diffraction (XRD) measurements on a natural single crystal; this had the same unit cell as that observed by Leonardsen & Petersen (1974). A similar crystal structure in space group C2/m and the same unit cell was found by Lafontaine et al. (1990) through X-ray and neutron diffraction measurements using a synthetic powder sample. However, Kashaev et al. (2008) gave a different monoclinic structural model in space group Ia. Thus, the crystal system is monoclinic in all cases, but it seems that more than one polymorph exists at room temperature. Very recently, Yoshida et al. (2012) successfully prepared a single crystal of sub-millimetre size and found a first-order structural phase transition at 310 K from a C2/m phase at high temperature to an I2/a phase at low temperature, as characterized by X-ray diffraction. The previous discrepancies regarding the structure may be partly related to the presence of this transition near room temperature. Although there are minor differences between these crystal structures, they commonly comprise Cu₃O₆(OH)₂ layers built of edge-sharing CuO₄(OH)₂ octahedra, which are separated by V₂O₇ pillars and unligated water molecules, as depicted in Fig. 1(a). In the Cu₃O₆(OH)₂ layer, Cu^II ions form distorted kagome lattices, and V^V ions are located above and below the centres of the hexagons of the kagome lattice (Fig. 1b). To date, the magnetic properties of volborthite have been discussed on the basis of the C2/m structure reported by Lafontaine et al.

In this study, we report a new polymorph of volborthite in a synthetic single crystal of millimetre size, probably of higher quality than those studied previously. This sample has another monoclinic structure, in space group C2/c at room temperature, further illustrating the richness of the crystal chemistry of volborthite.

The C2/c structure found in the present study is a 2c superstructure of the C2/m system (Basso et al., 1988; Lafontaine et al., 1990). We observed 1543 supercell reflections that would not have integer indices for the C2/m cell, out of a total of 4212 reflections found for our cell in C2/c. The average I and I/σ(I) are 12752.3/43.2 for the principal reflections and 661.0/21.8 for the supercell reflections. This structure may be identical to the C2/c or Cc structure given by Kashaev & Vasil'ev (1974), for which atomic coordinates are not available. Since there is no objective reason to question the veracity of the C2/m phase reported by Basso et al. (1988) and Lafontaine et al. (1990), we conclude that at least two polymorphs of volborthite exist at room temperature.

By way of comparison, there are two and three crystallographic sites for Cu in the C2/m and C2/c structures, respectively, as depicted in Figs. 1(c) and 2. In C2/m, atoms Cu1 and Cu2 occupy the 2a and 4e positions with site symmetries 2/m and 1, respectively. In contrast, in the present C2/c phase atom Cu1 has lower site symmetry with 1 at the 4a position, and atom Cu2 splits into Cu21 and Cu22 at the 4c and 4d positions, both with inversion symmetry. Irrespective of these differences at the Cu sites, the kagome lattices in both structures consist of isosceles triangles formed by Cu1 and either Cu2 (C2/m) or Cu21/Cu22 (C2/c).

The two structures clearly differ in the environment of the Cu1 sites. The Cu—O bond lengths are compared in Table 1. In the C2/m structure, atom Cu1 is coordinated by six oxide ligands, with two short Cu1—O2 and four long Cu1—O3 bonds. (The `long' bonds are intermediate in length between what is commonly found for short and long Cu—L distances in a Jahn–Teller compound; see below for an alternative explanation of this geometry.) In contrast, in the C2/c structure, there are four short bonds (two Cu1—O2 and two Cu1—O32) and two long bonds (Cu1—O31). The difference between short and long bonds is large in the C2/c structure. In contrast, the coordination environments around Cu2 (C2/m) and Cu21/Cu22 (C2/c) are nearly equal: in both structures there are four short bonds (two Cu2—O2 and two Cu2—O4 in the C2/m structure, and two Cu21/Cu22—O2 and two Cu21/Cu22—O4 in the C2/c structure) and two long bonds (two Cu2—O3 and two Cu21/Cu22—O31/O32, respectively).

The details of the Jahn–Teller distortion of an octahedron about Cu^II are important for understanding the magnetic properties of copper minerals, because the distortion determines the orbital state of the Cu^II ion, and thus the magnetic interactions between neighbouring Cu spins. For an octahedron consisting of two short and four long Cu—O bonds, i.e. (2+4) coordination, an unpaired electron should occupy the d_z2 orbital, while the d_x2-y2 orbital is occupied in the case of four short and two long bonds, i.e. (4+2) coordination. At the Cu1 site of the C2/m structure, the d_z2 orbital is apparently selected (but see below), while the d_x2-y2 orbital is occupied by an unpaired electron in the C2/c structure. Such a difference in the orbital occupancies must give rise to a substantial difference in magnetic interactions between Cu spins in the kagome lattice. In particular, the magnetic interactions via Cu—O superexchange pathways between Cu1 and Cu2 spins are identical in the C2/m structure, while those between Cu1···Cu21 and Cu1···Cu22 must be different in the C2/c structure. It would be interesting to study the influence of this distortion on the magnetic properties of volborthite.

We have also carried out structural analyses at low temperatures and found a transition at 290 K to an I2/a structure, which will be reported elsewhere. This low-temperature structure is essentially the same as the I2/a structure reported by Yoshida et al. (2012). Thus, volborthite takes the I2/a structure at low temperatures, but there are two polymorphs in the vicinity of room temperature. This may be the main reason for the discrepancies among previous reports of the crystal structure at room temperature. The thermal history of a crystal might result in different structures, because the first-order transition to the I2/a structure occurs with a thermal hysteresis of ΔT = 10 K at around room temperature (296 K upon cooling and 306 K upon heating for Yoshida's crystal). In addition, another factor that may influence the structure is the presence of impurities or nonstoichiometry; a natural crystal contains some degree of alien elements, such as other transition metals at the Cu or V site, while a synthetic crystal assumes no contamination.

Burns & Hawthorne (1996) point out that the (2+4) coordination for Cu1 in the C2/m structure of volborthite can be attributed to a dynamic Jahn–Teller effect, rather than to static order. In other words, two orthogonal (4+2) coordinations are dynamically swapped with each other, so that an apparent (2+4) coordination is observed in the average structure. If so, the present C2/c and the low-temperature I2/a structures could be considered as frozen states with one of two (4+2) coordinations being selected. On the other hand, Yoshida et al. suggest that the structural transition from C2/m to I2/a is related to an order–disorder transition involving the water molecules between the kagome layers. It is likely that ordering of these water molecules occurs in more than one way and also causes the structural differences between the C2/m and C2/c phases near room temperature. Alternatively, a subtle difference in the amount of water present could in principle result in two different structures. Further experiments are in progress to examine these possibilities.

Related literature

For related literature, see: Basso et al. (1988); Bert et al. (2005); Burns & Hawthorne (1996); Colman et al. (2008, 2010); Guillemin (1956); Hiroi et al. (2001); Kashaev & Vasil'ev (1974); Kashaev et al. (2008); Lafontaine et al. (1990); Leonardsen & Petersen (1974); Okamoto et al. (2009); Shores et al. (2005); Yoshida et al. (2012); Yoshida, Okamoto, Tayama, Sakakibara, Tokunaga, Matsuo, Narumi, Kindo, Yoshida, Takigawa & Hiroi (2009); Yoshida, Takigawa, Yoshida, Okamoto & Hiroi (2009).

S2. Experimental

CuO (99.9%; 0.5727 g, 7.200 mmol) and V₂O₅ (99.99%; 0.4365 g, 2.400 mmol) powders were mixed (Cu:V 3:2 stoichiometric ratio) and, together with 1% nitric acid (15 ml), were place in a Teflon container which was in turn placed in a stainless steel vessel. The vessel was sealed, heated to 443 K for 10 d, and furnace-cooled to room temperature. Transparent yellow–green single crystals of volborthite were obtained, along with a polycrystalline powder. The crystals are arrow-head shaped and typically 1 × 0.5 × 0.05 mm in size. Several fractured crystals were used for single-crystal XRD measurements, all of which gave the same monoclinic C2/c structure.

S3. Refinement

Atomic positions were determined by the charge-flipping method. Occupational deficiency was not observed for the interstitial water molecules. Atom H2 was assumed to be present as part of an OH group (with O2), as found in the neutron diffraction refinement of the C2/m structure by Lafontaine et al. Atom H2 was placed at a calculated position and refined as riding. The water H atoms could not be located.

Computing details

Data collection: APEX (Bruker, 2000); cell refinement: SAINT (Bruker, 2000); data reduction: SAINT (Bruker, 2000); program(s) used to solve structure: SUPERFLIP (Palatinus & Chapuis, 2007); program(s) used to refine structure: SHELXL97 (Sheldrick, 2008); molecular graphics: CrystalMaker (Palmer, 2005); software used to prepare material for publication: TEXSAN (Rigaku, 1999).

Figures

Fig. 1. (a) Axial view, (b) plane view and (c) displacement ellipsoid plot including the asymmetric unit, of the C2/c phase of volborthite. Octahedral and tetrahedral polyhedra coordinated to Cu and V atoms, respectively, are displayed. CuO6 octahedra form kagome layers separated by V2O7 pillars and solvent water molecules. The layer contains a distorted kagome lattice made up of Cu^II ions, as represented by thick lines in (b). Displacement ellipsoids are drawn at the 50% probability level in (c). [Symmetry codes: (i) -x + 1/2, -y + 1/2, -z; (ii) -x, -y, -z; (iii) x - 1/2, y - 1/2, z; (iv) x, y - 1, z, (v) -x, -y + 1, -z; (vi) -x + 1/2, -y + 3/2, -z.]

Fig. 2. The coordination around the Cu atoms in (a) the C2/m structure and (b) the C2/c structure. Thin solid lines indicate Cu—Cu bonds, with lengths in Å. Short and long Cu—O bonds are displayed by thick solid lines and thin broken lines, respectively. [Symmetry codes: (i) x + 1/2, y + 1/2, z; (ii) -x + 1/2, -y + 1/2, -z; (iii) -x + 1/2, -y + 3/2, -z.]

tricopper(II) divanadium(V) heptaoxide dihydroxide dihydrate

Crystal data

Cu3V2O7(OH)2·2H2O	F(000) = 908
Mr = 474.55	Dx = 3.523 Mg m^−3
Monoclinic, C2/c	Mo Kα radiation, λ = 0.71073 Å
Hall symbol: -C 2yc	Cell parameters from 8424 reflections
a = 10.6118 (4) Å	θ = 2.8–29.7°
b = 5.8708 (2) Å	µ = 9.08 mm^−1
c = 14.4181 (6) Å	T = 293 K
β = 95.029 (1)°	Plate, green
V = 894.79 (6) Å^3	0.11 × 0.06 × 0.02 mm
Z = 4

Data collection

Bruker APEX CCD area-detector diffractometer	1030 independent reflections
Radiation source: rotating anode	954 reflections with I > 2σ(I)
Graphite monochromator	Rint = 0.026
ω scans	θmax = 27.5°, θmin = 2.8°
Absorption correction: multi-scan (SADABS; Bruker, 2001)	h = −13→13
Tmin = 0.689, Tmax = 0.901	k = 0→7
8424 measured reflections	l = 0→18

Refinement

Refinement on F^2	Secondary atom site location: difference Fourier map
Least-squares matrix: full	Hydrogen site location: inferred from neighbouring sites
R[F^2 > 2σ(F^2)] = 0.025	H-atom parameters constrained
wR(F^2) = 0.085	w = 1/[σ^2(Fo^2) + (0.0338P)^2 + 2.9193P] where P = (Fo^2 + 2Fc^2)/3
S = 1.46	(Δ/σ)max < 0.001
1030 reflections	Δρmax = 0.79 e Å^−3
79 parameters	Δρmin = −0.78 e Å^−3
0 restraints	Extinction correction: SHELXL97 (Sheldrick, 2008), Fc^*=kFc[1+0.001xFc^2λ^3/sin(2θ)]^-1/4
Primary atom site location: structure-invariant direct methods	Extinction coefficient: 0.0011 (2)

Special details

Geometry. All esds (except the esd in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell esds are taken into account individually in the estimation of esds in distances, angles and torsion angles; correlations between esds in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell esds is used for estimating esds involving l.s. planes.

Refinement. Refinement of F² against ALL reflections. The weighted R-factor wR and goodness of fit S are based on F², conventional R-factors R are based on F, with F set to zero for negative F². The threshold expression of F² > σ(F²) is used only for calculating R-factors(gt) etc. and is not relevant to the choice of reflections for refinement. R-factors based on F² are statistically about twice as large as those based on F, and R-factors based on ALL data will be even larger.

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

	x	y	z	Uiso*/Ueq
Cu1	0.0000	0.0000	0.0000	0.0092 (2)
Cu21	0.2500	0.2500	0.0000	0.00895 (19)
Cu22	0.2500	0.7500	0.0000	0.0097 (2)
V1	−0.00334 (5)	0.47640 (9)	0.12693 (4)	0.00689 (19)
O1	0.0000	0.4518 (7)	0.2500	0.0193 (8)
O2	0.3421 (2)	0.4987 (3)	0.05851 (18)	0.0089 (5)
H2	0.3499	0.4984	0.1267	0.011*
O4	0.1583 (3)	0.5054 (3)	−0.07583 (19)	0.0116 (5)
O5	0.3238 (5)	0.4842 (6)	0.2392 (2)	0.0445 (10)
O31	0.0697 (2)	0.2436 (4)	0.08605 (17)	0.0131 (5)
O32	0.0757 (2)	0.7067 (4)	0.10121 (16)	0.0140 (5)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Cu1	0.0076 (3)	0.0091 (3)	0.0111 (3)	−0.00098 (17)	0.0012 (2)	−0.00276 (16)
Cu21	0.0087 (3)	0.0066 (3)	0.0110 (3)	−0.00067 (18)	−0.0023 (2)	−0.00043 (18)
Cu22	0.0095 (3)	0.0067 (3)	0.0121 (3)	0.00068 (18)	−0.0037 (2)	−0.00037 (18)
V1	0.0073 (3)	0.0082 (3)	0.0050 (3)	−0.00026 (17)	−0.0004 (2)	−0.00033 (16)
O1	0.022 (2)	0.0276 (17)	0.0086 (16)	0.000	0.0018 (14)	0.000
O2	0.0086 (12)	0.0085 (11)	0.0095 (11)	−0.0007 (7)	0.0004 (9)	−0.0004 (7)
O4	0.0104 (13)	0.0109 (12)	0.0129 (12)	0.0002 (7)	−0.0021 (10)	−0.0001 (7)
O5	0.057 (3)	0.061 (3)	0.0148 (16)	0.0009 (16)	−0.0015 (16)	0.0009 (12)
O31	0.0118 (13)	0.0138 (12)	0.0135 (12)	0.0009 (8)	0.0002 (9)	−0.0025 (8)
O32	0.0134 (12)	0.0138 (10)	0.0142 (12)	−0.0016 (9)	−0.0015 (10)	0.0008 (9)

Geometric parameters (Å, º)

Cu1—O2^i	1.941 (3)	Cu21—Cu22^iv	2.9354
Cu1—O2^ii	1.941 (3)	Cu21—Cu1^vi	3.0319
Cu1—O31	1.992 (2)	Cu22—O2	1.923 (2)
Cu1—O31^iii	1.992 (2)	Cu22—O2^vii	1.923 (2)
Cu1—O32^iv	2.353 (2)	Cu22—O4^vii	2.005 (2)
Cu1—O32^v	2.353 (2)	Cu22—O4	2.005 (2)
Cu1—Cu21	3.0319	Cu22—Cu21^viii	2.9354 (1)
Cu1—Cu21^i	3.0319	Cu22—Cu1^viii	3.0319
Cu1—Cu22^iv	3.0319	Cu22—Cu1^vi	3.0319
Cu1—Cu22^i	3.0319	V1—O32	1.651 (3)
Cu21—O2	1.912 (2)	V1—O31	1.702 (2)
Cu21—O2^ii	1.912 (2)	V1—O4^v	1.745 (3)
Cu21—O4^ii	2.050 (2)	V1—O1	1.7776 (6)
Cu21—O4	2.050 (2)	O1—V1^ix	1.7776 (6)
Cu21—O31	2.370 (3)	O2—Cu1^vi	1.941 (3)
Cu21—O31^ii	2.370 (3)	O4—V1^v	1.745 (3)
Cu21—Cu22	2.9354	O32—Cu1^viii	2.353 (2)
O2^i—Cu1—O2^ii	180.00 (13)	O4^ii—Cu21—Cu22^iv	43.01 (7)
O2^i—Cu1—O31	91.12 (9)	O4—Cu21—Cu22^iv	136.99 (7)
O2^ii—Cu1—O31	88.88 (9)	O31—Cu21—Cu22^iv	89.09 (5)
O2^i—Cu1—O31^iii	88.88 (9)	O31^ii—Cu21—Cu22^iv	90.91 (5)
O2^ii—Cu1—O31^iii	91.12 (9)	Cu22—Cu21—Cu22^iv	180.0
O31—Cu1—O31^iii	180.00 (12)	O2—Cu21—Cu1^vi	38.44 (8)
O2^i—Cu1—O32^iv	89.35 (9)	O2^ii—Cu21—Cu1^vi	141.56 (8)
O2^ii—Cu1—O32^iv	90.65 (9)	O4^ii—Cu21—Cu1^vi	88.83 (7)
O31—Cu1—O32^iv	92.93 (10)	O4—Cu21—Cu1^vi	91.17 (7)
O31^iii—Cu1—O32^iv	87.07 (10)	O31—Cu21—Cu1^vi	138.96 (6)
O2^i—Cu1—O32^v	90.65 (9)	O31^ii—Cu21—Cu1^vi	41.04 (6)
O2^ii—Cu1—O32^v	89.35 (9)	Cu22—Cu21—Cu1^vi	61.047 (1)
O31—Cu1—O32^v	87.07 (10)	Cu22^iv—Cu21—Cu1^vi	118.953 (1)
O31^iii—Cu1—O32^v	92.93 (10)	O2—Cu21—Cu1	141.56 (8)
O32^iv—Cu1—O32^v	180.00 (15)	O2^ii—Cu21—Cu1	38.44 (8)
O2^i—Cu1—Cu21	142.24 (6)	O4^ii—Cu21—Cu1	91.17 (7)
O2^ii—Cu1—Cu21	37.76 (6)	O4—Cu21—Cu1	88.83 (7)
O31—Cu1—Cu21	51.36 (7)	O31—Cu21—Cu1	41.04 (6)
O31^iii—Cu1—Cu21	128.64 (7)	O31^ii—Cu21—Cu1	138.96 (6)
O32^iv—Cu1—Cu21	95.91 (6)	Cu22—Cu21—Cu1	118.953 (1)
O32^v—Cu1—Cu21	84.09 (6)	Cu22^iv—Cu21—Cu1	61.047 (1)
O2^i—Cu1—Cu21^i	37.76 (6)	Cu1^vi—Cu21—Cu1	180.0
O2^ii—Cu1—Cu21^i	142.24 (6)	O2—Cu22—O2^vii	180.0
O31—Cu1—Cu21^i	128.64 (7)	O2—Cu22—O4^vii	96.12 (10)
O31^iii—Cu1—Cu21^i	51.36 (7)	O2^vii—Cu22—O4^vii	83.88 (10)
O32^iv—Cu1—Cu21^i	84.09 (6)	O2—Cu22—O4	83.88 (10)
O32^v—Cu1—Cu21^i	95.91 (6)	O2^vii—Cu22—O4	96.12 (10)
Cu21—Cu1—Cu21^i	180.0	O4^vii—Cu22—O4	180.0
O2^i—Cu1—Cu22^iv	141.89 (6)	O2—Cu22—Cu21	39.91 (7)
O2^ii—Cu1—Cu22^iv	38.11 (6)	O2^vii—Cu22—Cu21	140.09 (7)
O31—Cu1—Cu22^iv	94.04 (7)	O4^vii—Cu22—Cu21	135.77 (7)
O31^iii—Cu1—Cu22^iv	85.96 (7)	O4—Cu22—Cu21	44.23 (7)
O32^iv—Cu1—Cu22^iv	52.72 (6)	O2—Cu22—Cu21^viii	140.09 (7)
O32^v—Cu1—Cu22^iv	127.28 (6)	O2^vii—Cu22—Cu21^viii	39.91 (7)
Cu21—Cu1—Cu22^iv	57.906 (2)	O4^vii—Cu22—Cu21^viii	44.23 (7)
Cu21^i—Cu1—Cu22^iv	122.094 (2)	O4—Cu22—Cu21^viii	135.77 (7)
O2^i—Cu1—Cu22^i	38.11 (6)	Cu21—Cu22—Cu21^viii	180.0
O2^ii—Cu1—Cu22^i	141.89 (6)	O2—Cu22—Cu1^viii	141.48 (8)
O31—Cu1—Cu22^i	85.96 (7)	O2^vii—Cu22—Cu1^viii	38.52 (8)
O31^iii—Cu1—Cu22^i	94.04 (7)	O4^vii—Cu22—Cu1^viii	92.06 (8)
O32^iv—Cu1—Cu22^i	127.28 (6)	O4—Cu22—Cu1^viii	87.94 (8)
O32^v—Cu1—Cu22^i	52.72 (6)	Cu21—Cu22—Cu1^viii	118.953 (1)
Cu21—Cu1—Cu22^i	122.094 (2)	Cu21^viii—Cu22—Cu1^viii	61.047 (1)
Cu21^i—Cu1—Cu22^i	57.906 (2)	O2—Cu22—Cu1^vi	38.52 (8)
Cu22^iv—Cu1—Cu22^i	180.0	O2^vii—Cu22—Cu1^vi	141.48 (8)
O2—Cu21—O2^ii	180.00 (16)	O4^vii—Cu22—Cu1^vi	87.94 (8)
O2—Cu21—O4^ii	97.05 (10)	O4—Cu22—Cu1^vi	92.06 (8)
O2^ii—Cu21—O4^ii	82.95 (10)	Cu21—Cu22—Cu1^vi	61.047 (1)
O2—Cu21—O4	82.95 (10)	Cu21^viii—Cu22—Cu1^vi	118.953 (1)
O2^ii—Cu21—O4	97.05 (10)	Cu1^viii—Cu22—Cu1^vi	180.0
O4^ii—Cu21—O4	180.00 (7)	O32—V1—O31	108.91 (14)
O2—Cu21—O31	100.73 (10)	O32—V1—O4^v	109.50 (11)
O2^ii—Cu21—O31	79.27 (10)	O31—V1—O4^v	110.12 (12)
O4^ii—Cu21—O31	94.38 (10)	O32—V1—O1	108.96 (14)
O4—Cu21—O31	85.62 (10)	O31—V1—O1	108.09 (14)
O2—Cu21—O31^ii	79.27 (10)	O4^v—V1—O1	111.22 (10)
O2^ii—Cu21—O31^ii	100.73 (10)	V1^ix—O1—V1	170.7 (3)
O4^ii—Cu21—O31^ii	85.62 (10)	Cu21—O2—Cu22	99.89 (12)
O4—Cu21—O31^ii	94.38 (10)	Cu21—O2—Cu1^vi	103.80 (11)
O31—Cu21—O31^ii	180.00 (11)	Cu22—O2—Cu1^vi	103.37 (11)
O2—Cu21—Cu22	40.20 (7)	V1^v—O4—Cu22	125.49 (12)
O2^ii—Cu21—Cu22	139.80 (7)	V1^v—O4—Cu21	130.96 (12)
O4^ii—Cu21—Cu22	136.99 (7)	Cu22—O4—Cu21	92.76 (11)
O4—Cu21—Cu22	43.01 (7)	V1—O31—Cu1	129.54 (15)
O31—Cu21—Cu22	90.91 (5)	V1—O31—Cu21	125.56 (12)
O31^ii—Cu21—Cu22	89.09 (5)	Cu1—O31—Cu21	87.60 (9)
O2—Cu21—Cu22^iv	139.80 (7)	V1—O32—Cu1^viii	125.88 (13)
O2^ii—Cu21—Cu22^iv	40.20 (7)

Symmetry codes: (i) x−1/2, y−1/2, z; (ii) −x+1/2, −y+1/2, −z; (iii) −x, −y, −z; (iv) x, y−1, z; (v) −x, −y+1, −z; (vi) x+1/2, y+1/2, z; (vii) −x+1/2, −y+3/2, −z; (viii) x, y+1, z; (ix) −x, y, −z+1/2.