Zirconium di­hydroxide chromate

The crystal structure of the title compound, Zr(OH)₂CrO₄, has been reinvestigated [Mark (1972). Acta Chem. Scand. 26, 3744-3756]. It is composed of ordered layers whose stacking in the c direction is disordered. The symmetry of the superposition structure is tetragonal, space group I4₁/amd with a = 6.8709 (1) and c = 29.0432 (2) Å. The true 0D structure has ordered layers of the dimensions a_L = b_L = 2a and c₀ = c/4, where c₀ is the spacing between adjacent layers. The Zr atoms are joined by double hydroxide bridges and the structure consists of infinite nets with the composition [Zr₃(OH)₆CrO₄]_n⁴ⁿ⁺, joined together in c direction by chromate groups. The zirconium polyhedra are not influenced by the 0D phenomenon.

S1. Comment

%T Investigations of the xZrO$_{2}$,yCrO$_{3}$,zH$_{2}$O system were carried out by Lundgren (1958) and Mark (1972, 1973). They showed that three different phases can be obtained by hydro\-thermal hydro\-lysis and indicated that two phases have similar structures, while the third structure, Zr(OH)$_{2}$CrO$_{4}$, is essentially different. In the title compound, the zirconium is more highly polymerized than in the other phases. This phase is obtained at lower chromium trioxide concentration and higher temperature than the others. The Zr(OH)$_{2}$CrO$_{4}$ crystallizes as small red square plates with a tetragonal shape.

The structure of zirconium di\-hydroxide chromate has been redetermined. In accordance with the earlier investigation (Mark, 1972) of this compound, this structure is an OD structure (Dornberger-Shiff, 1956, 1982) consisting of ordered layers whose stacking in {ιt c} direction is disordered. The space group of the superposition structure is tetragonal I4$_{1}$/amd with a = 6.8709κern2pt(1)κern2ptσmash{AA{}} and {ιt c} = 29.0432κern2pt(2)κern2ptσmash{AA{}} and Z = 12. There are four equivalent layers L$_{0}$, L$_{1}$, L$_{2}$ and L$_{4}$ in the true structure. The space group of the superposition structure implies consecutive layers L to be linked by the operation:

$$λeft (µatrix {x_{Ln+1}χr y_{Ln+1}χr z_{Ln+1}χr} ρight) = λeft (µatrix {0 & 1 & 0 χr −1 & 0 & 0 χr 0 & 0 & 1 χr} ρight) λeft (µatrix {x_{Ln} χr y_{Ln} χr z_{Ln} χr} ρight) + λeft (µatrix {σcriptstyle{3 οver 4} χr σcriptstyle{−1 οver 4} χr σcriptstyle{1 οver 4} χr} ρight) $$

The superposition structure, $ρho$$_{S}$(x,{ιt y},{ιt z}) is related to the true structure, $ρho$(x,{ιt y},{ιt z}) by the relation: $ρho$$_{S}$(x,{ιt y},{ιt z}) = 1/4[$ρho$(x,{ιt y},{ιt z}) + $ρho$(x + 1/2,{ιt y},{ιt z}) + $ρho$(x,{ιt y} + 1/2,{ιt z}) + $ρho$(x + 1/2,{ιt y} + 1/2,{ιt z})] (Mark, 1972)

There are two structurally non-equivalent Zr atoms in the structure; one with eightfold coordination forming a dodecahedron, ZrO$_{8}$, and one with sevenfold coordination forming a pentagonal bipyramid, ZrO$_{7}$. There also are two structurally non-equivalent chromate groups. The zirconium polyhedra are well described by the space group symmetry of the superposition structure. The disorder in the structure is, in accordance with the earlier structure determination (Mark, 1972), due to the chromate groups. One particular chromate tetrahedron (Cr1) may be situated either above or below the edge sharing ZrO$_{8}$ dodecadron, thus affecting the available positions for the (Cr2) chromate tetrahedron. The only atoms affected by the disorder are the Cr1, O6, Cr2, O5 and the O2 bonded H atoms. The OD-grupoids associated to the disordered atoms was formulated by Mark (1972) as follows:

Starting from layer L$_{0}$ or L$_{2}$: $$ κern-15ptP κern2ptm κern2ptm κern6pt(n)_{1,1/2} κern10pt1 κern22pt1$$ $$λeft \ {κern6pt1 κern6pt1 κern8ptπmatrix {οverline{4} χr 4_{4}} {2_{1/2} οver n_{1/4, 2}} {2 οver n_{1/4, 2}} ρight \} $$

Starting from layer L$_{1}$ or L$_{3}$: $$ κern-15ptP κern2ptm κern2ptm κern6pt(n)_{1/2,1} κern10pt1 κern22pt1$$ $$λeft \ {κern6pt1 κern6pt1 κern8ptπmatrix {οverline{4} χr 4_{4}} {2 οver n_{1/4, 2}} {2_{1/2} οver n_{1/4, 2}} ρight \} $$

The main structural feature in zirconium and related hydro\-xide salts (Lundgren, 1958; Mark, 1972, 1973; Hansson, 1973{ιt b}; El Brahimi {ιt et al.}. 1988), is the forming of infinite parallel chains with the formula [Zr(OH)$_{2}$]$_{{ιt n}}$$^{{2{ιt n}+}$, all running in the same direction. The coordination numbers of the metal atoms seem to be of importance for the type of chains adopted by the compounds. In structures containing parallel linear chains (Hansson 1969; Hansson \& Lundgren 1968; Hansson \& Mark, 1973; Mark, 1973) the metal atoms are 7-coordinated to O atoms, while in the structures containing parallel zigzag chains (Lundgren, 1950; Hansson, 1973{ιt a},{ιt b}; El Brahimi, 1988), with the metal atoms situated at alternate sides of the rows of hydro\-xide ions, the metal atoms are 8-coordinated.}

In every layer of the title compound, the Zr atoms form parallel linear and intersecting chains. There are two kinds of layers, containing chains of zirconium polyhedra either along the {^{ιt a} axis or along the {ιt b} axis. The layers alternate, creating nets with the composition [Zr$_{3}$(OH)$_{6}$CrO$_{4}$]$_{{ιt n}}$$}{4{ιt n}+}$, joined together in {ιt c} direction by chromate groups. The most important interatomic distances and angles in the structure are given in Table 1. One third of the Zr atoms (Zr1, Wyckoff position 4a) exhibit eight fold oxy\-gen coordination while the remaining two thirds (Zr2, Wyckoff position 8 e) are coordinated to seven O atoms. Each Zr1 atom is joined by double hydro\-xide bridges to four Zr2 atoms. Each ZrO$_{7}$ pentagonal bipyramid shares two edges with ZrO$_{8}$ dodecahedra. One third of the Cr atoms (Cr1, Wyckoff position 8 e, site occupancy 1/8) are included in the infinite nets while the others (Cr2, Wyckoff position 16 h, site occupancy 1/4) are net-connecting. The net-included chromate group shares one of its tetrahedral edges with an edge of a ZrO$_{8}$ dodecahedron, in this case the two bridging hydro\-xide ions have been displaced by two chromate O atoms (Fig. 2). The net-connecting chromate group shares three vertices with three different ZrO$_{7}$ polyhedra, two belonging to the same net and one belonging to a net above or below. The extent of distortion of the cromate groups from ideal tetrahedral symmetry is in accordance with the one expected from calculation by the bond valence sum method (Brown \& Kung, 1976; Brown \& Altermatt, 1985). The positions of the H atoms were not located.

S2. Experimental

Zirconium compounds of the system xZrO₂,yCrO₃,zH₂O was prepared by hydrothermal hydrolysis, according to a method originally described by Briggs (1929). The synthesis has been performed in two steps. First an amorphous product has been prepared (Lundgren, 1958), which then was converted to crystals by hydrothermal hydrolysis as described ealier by Mark (1972).

S3. Refinement

The well diffracting crystal produced a regular pattern of sharp and intense reflections. A visual exploration of the frames was performed and several frames showed continuous streaks between rows of sharp reflections. The continuous lines were parallel to the c* direction and situated midway between neighbouring reflections in both a* and b* directions. This indicated, in accordance with the earlier structure determination (Mark, 1972) that the true structure is periodic in the a and b directions but lacks periodicity in the c direction.

The determination of the structure is more precise than the original one (Mark, 1972) making the stucture features well defined, s.u.'s beeing smaller by a factor of about 5.

Computing details

Data collection: SMART (Siemens, 1995); cell refinement: SAINT (Siemens, 1995); data reduction: SAINT (Siemens, 1995) and SADABS (Sheldrick, 1996); program(s) used to solve structure: SHELXTL (Bruker, 1997); program(s) used to refine structure: SHELXTL (Bruker, 1997); molecular graphics: SHELXTL (Bruker, 1997).

Zirconium dihydroxide chromate

Crystal data

Zr(OH)2CrO4	Dx = 3.506 Mg m^−3
Mr = 241.23	Mo Kα radiation, λ = 0.71073 Å
Tetragonal, I41/amd[originatcentre(2/m)]	Cell parameters from 5231 reflections
a = 6.8709 (1) Å	θ = 2–33°
c = 29.0432 (2) Å	µ = 4.59 mm^−1
V = 1371.11 (3) Å^3	T = 293 K
Z = 12	Square plate, red
F(000) = 1331	0.10 × 0.10 × 0.04 mm

Data collection

Siemens SMART CCD diffractometer	731 independent reflections
Radiation source: fine-focus sealed tube	638 reflections with I > 2σ(I)
Graphite monochromator	Rint = 0.035
ω scans	θmax = 33.0°, θmin = 2.8°
Absorption correction: multi-scan (Sheldrick, 1996)	h = −7→10
Tmin = 0.657, Tmax = 0.838	k = −10→9
4914 measured reflections	l = −43→35

Refinement

Refinement on F^2	Primary atom site location: structure-invariant direct methods
Least-squares matrix: full	Secondary atom site location: difference Fourier map
R[F^2 > 2σ(F^2)] = 0.025	w = 1/[σ^2(Fo^2) + (0.0379P)^2 + 5.9927P] where P = (Fo^2 + 2Fc^2)/3
wR(F^2) = 0.070	(Δ/σ)max < 0.001
S = 1.04	Δρmax = 0.80 e Å^−3
731 reflections	Δρmin = −1.02 e Å^−3
52 parameters	Extinction correction: SHELXL97, Fc^*=kFc[1+0.001xFc^2λ^3/sin(2θ)]^-1/4
0 restraints	Extinction coefficient: 0.00063 (15)

Special details

Geometry. All e.s.d.'s (except the e.s.d. in the dihedral angle between two l.s. planes)

are estimated using the full covariance matrix. The cell e.s.d.'s are taken into account individually in the estimation of e.s.d.'s in distances, angles and torsion angles; correlations between e.s.d.'s in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell e.s.d.'s is used for estimating e.s.d.'s 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	Occ. (<1)
Zr1	0.0000	0.7500	0.125000	0.01240 (15)
Zr2	0.5000	0.7500	0.082939 (14)	0.00889 (13)
Cr1	0.0000	0.7500	0.02349 (5)	0.0129 (3)	0.50
Cr2	0.43089 (15)	0.2500	0.04577 (3)	0.00839 (18)	0.50
O1	0.5000	0.4492 (4)	0.07498 (8)	0.0182 (5)
O2	0.1937 (3)	0.7500	0.06262 (8)	0.0152 (4)
O3	0.5000	0.7500	0.00595 (13)	0.0296 (10)
O4	0.6933 (3)	0.7500	0.14003 (8)	0.0149 (4)
O5	0.2010 (8)	0.2500	0.03892 (18)	0.0217 (10)	0.50
O6	0.0000	0.5637 (9)	−0.0086 (2)	0.0308 (13)	0.50

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Zr1	0.00641 (18)	0.00641 (18)	0.0244 (3)	0.000	0.000	0.000
Zr2	0.00658 (19)	0.0074 (2)	0.0127 (2)	0.000	0.000	0.000
Cr1	0.0121 (6)	0.0144 (7)	0.0121 (6)	0.000	0.000	0.000
Cr2	0.0100 (4)	0.0065 (4)	0.0086 (4)	0.000	0.0013 (3)	0.000
O1	0.0280 (13)	0.0084 (10)	0.0182 (10)	0.000	0.000	−0.0019 (8)
O2	0.0103 (10)	0.0222 (12)	0.0131 (9)	0.000	0.0003 (8)	0.000
O3	0.056 (3)	0.024 (2)	0.0092 (14)	0.000	0.000	0.000
O4	0.0076 (10)	0.0244 (12)	0.0128 (9)	0.000	−0.0003 (8)	0.000
O5	0.013 (2)	0.032 (3)	0.020 (2)	0.000	0.0005 (18)	0.000
O6	0.042 (3)	0.026 (3)	0.024 (3)	0.000	0.000	−0.012 (2)

Geometric parameters (Å, º)

Zr1—O4^i	2.152 (2)	O2—O6^v	2.774 (5)
Zr1—O4^ii	2.152 (2)	O2—O6	2.774 (5)
Zr1—O4^iii	2.152 (2)	O2—O4^ii	2.847 (2)
Zr1—O4^iv	2.152 (2)	O2—O4^i	2.847 (2)
Zr1—O2^v	2.248 (2)	O3—Cr2^ix	1.575 (4)
Zr1—O2	2.248 (2)	O3—Cr2^xi	1.575 (4)
Zr1—O2^vi	2.248 (2)	O3—O5^ix	2.433 (6)
Zr1—O2^vii	2.248 (2)	O3—O5^xi	2.433 (6)
Zr2—O1	2.080 (2)	O3—O2^iii	2.672 (3)
Zr2—O1^iii	2.080 (2)	O3—O1^xi	2.720 (4)
Zr2—O4	2.124 (2)	O3—O1^ix	2.720 (4)
Zr2—O4^iii	2.124 (2)	O3—O1^iii	2.880 (4)
Zr2—O2^iii	2.186 (2)	O4—Zr1^xii	2.152 (2)
Zr2—O2	2.186 (2)	O4—O2^iii	2.378 (3)
Zr2—O3	2.236 (4)	O4—O4^iii	2.656 (5)
Cr1—O6^v	1.584 (6)	O4—O5^vi	2.816 (5)
Cr1—O6	1.584 (6)	O4—O5^xiii	2.816 (5)
Cr1—O2	1.750 (2)	O4—O2^xiv	2.847 (2)
Cr1—O2^v	1.750 (2)	O4—O2^xiii	2.847 (2)
Cr1—O6^viii	2.198 (6)	O5—O6^xv	2.078 (7)
Cr1—O6^ix	2.198 (6)	O5—O6^viii	2.078 (7)
Cr1—O5^viii	2.279 (5)	O5—Cr1^viii	2.279 (5)
Cr1—O5^ix	2.279 (5)	O5—O3^xi	2.433 (6)
Cr2—Cr2^x	0.950 (2)	O5—O1^x	2.681 (5)
Cr2—O3^xi	1.575 (4)	O5—O5^xvi	2.762 (10)
Cr2—O5	1.592 (5)	O5—O4^i	2.816 (5)
Cr2—O1	1.679 (2)	O5—O4^vii	2.816 (5)
Cr2—O1^x	1.679 (2)	O5—O6	2.909 (6)
O1—Cr2^x	1.679 (2)	O5—O6^xvi	2.909 (6)
O1—O5^x	2.681 (5)	O6—O6^viii	1.009 (12)
O1—O5	2.681 (5)	O6—O5^ix	2.078 (7)
O1—O3^xi	2.720 (4)	O6—O5^viii	2.078 (7)
O1—O1^x	2.737 (5)	O6—Cr1^viii	2.198 (6)
O1—O3	2.880 (4)	O6—O6^v	2.560 (12)
O2—O4^iii	2.379 (3)	O6—O2^v	2.774 (5)
O2—O2^v	2.662 (5)	O6—O5^xvi	2.909 (6)
O2—O3	2.672 (3)
O4^i—Zr1—O4^ii	156.60 (12)	Zr2—O3—O2^iii	51.97 (8)
O4^i—Zr1—O4^iii	92.36 (2)	O5^ix—O3—O2^iii	174.35 (19)
O4^ii—Zr1—O4^iii	92.36 (2)	O5^xi—O3—O2^iii	70.42 (13)
O4^i—Zr1—O4^iv	92.36 (2)	O2—O3—O2^iii	103.93 (16)
O4^ii—Zr1—O4^iv	92.36 (2)	Cr2^ix—O3—O1^xi	34.51 (7)
O4^iii—Zr1—O4^iv	156.59 (12)	Cr2^xi—O3—O1^xi	34.51 (7)
O4^i—Zr1—O2^v	80.59 (5)	Zr2—O3—O1^xi	149.79 (7)
O4^ii—Zr1—O2^v	80.59 (5)	O5^ix—O3—O1^xi	62.43 (13)
O4^iii—Zr1—O2^v	138.01 (8)	O5^xi—O3—O1^xi	62.43 (13)
O4^iv—Zr1—O2^v	65.40 (9)	O2—O3—O1^xi	122.17 (5)
O4^i—Zr1—O2	80.59 (5)	O2^iii—O3—O1^xi	122.17 (5)
O4^ii—Zr1—O2	80.59 (5)	Cr2^ix—O3—O1^ix	34.51 (7)
O4^iii—Zr1—O2	65.40 (9)	Cr2^xi—O3—O1^ix	34.51 (7)
O4^iv—Zr1—O2	138.01 (8)	Zr2—O3—O1^ix	149.79 (7)
O2^v—Zr1—O2	72.61 (12)	O5^ix—O3—O1^ix	62.43 (13)
O4^i—Zr1—O2^vi	138.01 (8)	O5^xi—O3—O1^ix	62.43 (13)
O4^ii—Zr1—O2^vi	65.40 (9)	O2—O3—O1^ix	122.17 (5)
O4^iii—Zr1—O2^vi	80.59 (5)	O2^iii—O3—O1^ix	122.17 (5)
O4^iv—Zr1—O2^vi	80.59 (5)	O1^xi—O3—O1^ix	60.41 (13)
O2^v—Zr1—O2^vi	130.50 (7)	Cr2^ix—O3—O1	131.59 (6)
O2—Zr1—O2^vi	130.50 (7)	Cr2^xi—O3—O1	131.59 (6)
O4^i—Zr1—O2^vii	65.40 (9)	Zr2—O3—O1	45.87 (7)
O4^ii—Zr1—O2^vii	138.01 (8)	O5^ix—O3—O1	111.89 (9)
O4^iii—Zr1—O2^vii	80.59 (5)	O5^xi—O3—O1	111.89 (9)
O4^iv—Zr1—O2^vii	80.59 (5)	O2—O3—O1	64.60 (7)
O2^v—Zr1—O2^vii	130.50 (7)	O2^iii—O3—O1	64.60 (7)
O2—Zr1—O2^vii	130.50 (7)	O1^xi—O3—O1	103.92 (6)
O2^vi—Zr1—O2^vii	72.61 (12)	O1^ix—O3—O1	164.33 (12)
O1—Zr2—O1^iii	167.24 (14)	Cr2^ix—O3—O1^iii	131.59 (6)
O1—Zr2—O4	94.98 (5)	Cr2^xi—O3—O1^iii	131.59 (6)
O1^iii—Zr2—O4	94.97 (5)	Zr2—O3—O1^iii	45.87 (7)
O1—Zr2—O4^iii	94.98 (5)	O5^ix—O3—O1^iii	111.89 (9)
O1^iii—Zr2—O4^iii	94.97 (5)	O5^xi—O3—O1^iii	111.89 (9)
O4—Zr2—O4^iii	77.38 (12)	O2—O3—O1^iii	64.60 (7)
O1—Zr2—O2^iii	88.28 (2)	O2^iii—O3—O1^iii	64.60 (7)
O1^iii—Zr2—O2^iii	88.28 (2)	O1^xi—O3—O1^iii	164.33 (12)
O4—Zr2—O2^iii	66.97 (9)	O1^ix—O3—O1^iii	103.92 (6)
O4^iii—Zr2—O2^iii	144.35 (8)	O1—O3—O1^iii	91.75 (14)
O1—Zr2—O2	88.28 (2)	Zr2—O4—Zr1^xii	116.99 (10)
O1^iii—Zr2—O2	88.28 (2)	Zr2—O4—O2^iii	57.75 (8)
O4—Zr2—O2	144.35 (8)	Zr1^xii—O4—O2^iii	59.25 (8)
O4^iii—Zr2—O2	66.98 (9)	Zr2—O4—O4^iii	51.31 (6)
O2^iii—Zr2—O2	148.68 (12)	Zr1^xii—O4—O4^iii	168.30 (6)
O1—Zr2—O3	83.62 (7)	O2^iii—O4—O4^iii	109.06 (8)
O1^iii—Zr2—O3	83.62 (7)	Zr2—O4—O5^vi	106.10 (10)
O4—Zr2—O3	141.31 (6)	Zr1^xii—O4—O5^vi	127.62 (9)
O4^iii—Zr2—O3	141.31 (6)	O2^iii—O4—O5^vi	147.85 (12)
O2^iii—Zr2—O3	74.34 (6)	O4^iii—O4—O5^vi	61.86 (7)
O2—Zr2—O3	74.34 (6)	Zr2—O4—O5^xiii	106.10 (10)
O6^v—Cr1—O6	107.8 (4)	Zr1^xii—O4—O5^xiii	127.62 (9)
O6^v—Cr1—O2	112.50 (13)	O2^iii—O4—O5^xiii	147.85 (12)
O6—Cr1—O2	112.50 (13)	O4^iii—O4—O5^xiii	61.86 (7)
O6^v—Cr1—O2^v	112.50 (13)	O5^vi—O4—O5^xiii	58.7 (2)
O6—Cr1—O2^v	112.50 (13)	Zr2—O4—O2^xiv	147.12 (7)
O2—Cr1—O2^v	99.01 (16)	Zr1^xii—O4—O2^xiv	51.17 (6)
O6^v—Cr1—O6^viii	132.59 (13)	O2^iii—O4—O2^xiv	102.41 (10)
O6—Cr1—O6^viii	24.8 (4)	O4^iii—O4—O2^xiv	137.75 (5)
O2—Cr1—O6^viii	97.31 (10)	O5^vi—O4—O2^xiv	76.45 (7)
O2^v—Cr1—O6^viii	97.31 (10)	O5^xiii—O4—O2^xiv	102.97 (11)
O6^v—Cr1—O6^ix	24.8 (4)	Zr2—O4—O2^xiii	147.12 (7)
O6—Cr1—O6^ix	132.59 (13)	Zr1^xii—O4—O2^xiii	51.17 (6)
O2—Cr1—O6^ix	97.31 (10)	O2^iii—O4—O2^xiii	102.41 (10)
O2^v—Cr1—O6^ix	97.31 (10)	O4^iii—O4—O2^xiii	137.75 (5)
O6^viii—Cr1—O6^ix	157.4 (3)	O5^vi—O4—O2^xiii	102.97 (11)
O6^v—Cr1—O5^viii	62.05 (17)	O5^xiii—O4—O2^xiii	76.45 (7)
O6—Cr1—O5^viii	62.05 (18)	O2^xiv—O4—O2^xiii	55.75 (10)
O2—Cr1—O5^viii	167.80 (16)	Cr2—O5—O6^xv	135.4 (2)
O2^v—Cr1—O5^viii	93.19 (15)	Cr2—O5—O6^viii	135.4 (2)
O6^viii—Cr1—O5^viii	81.03 (12)	O6^xv—O5—O6^viii	76.0 (3)
O6^ix—Cr1—O5^viii	81.03 (12)	Cr2—O5—Cr1^viii	134.5 (3)
O6^v—Cr1—O5^ix	62.05 (17)	O6^xv—O5—Cr1^viii	42.33 (18)
O6—Cr1—O5^ix	62.05 (17)	O6^viii—O5—Cr1^viii	42.33 (18)
O2—Cr1—O5^ix	93.18 (15)	Cr2—O5—O3^xi	39.56 (14)
O2^v—Cr1—O5^ix	167.81 (16)	O6^xv—O5—O3^xi	109.6 (2)
O6^viii—Cr1—O5^ix	81.03 (12)	O6^viii—O5—O3^xi	109.6 (2)
O6^ix—Cr1—O5^ix	81.03 (12)	Cr1^viii—O5—O3^xi	94.9 (2)
O5^viii—Cr1—O5^ix	74.6 (3)	Cr2—O5—O1	36.01 (10)
Cr2^x—Cr2—O3^xi	72.46 (5)	O6^xv—O5—O1	171.4 (2)
Cr2^x—Cr2—O5	172.83 (19)	O6^viii—O5—O1	111.11 (14)
O3^xi—Cr2—O5	100.4 (2)	Cr1^viii—O5—O1	140.81 (15)
Cr2^x—Cr2—O1	73.56 (4)	O3^xi—O5—O1	64.04 (14)
O3^xi—Cr2—O1	113.37 (9)	Cr2—O5—O1^x	36.01 (10)
O5—Cr2—O1	110.11 (10)	O6^xv—O5—O1^x	111.11 (14)
Cr2^x—Cr2—O1^x	73.56 (4)	O6^viii—O5—O1^x	171.4 (2)
O3^xi—Cr2—O1^x	113.37 (9)	Cr1^viii—O5—O1^x	140.81 (15)
O5—Cr2—O1^x	110.11 (10)	O3^xi—O5—O1^x	64.04 (14)
O1—Cr2—O1^x	109.21 (16)	O1—O5—O1^x	61.37 (15)
Cr2^x—O1—Cr2	32.87 (8)	Cr2—O5—O5^xvi	172.82 (19)
Cr2^x—O1—Zr2	150.03 (13)	O6^xv—O5—O5^xvi	48.35 (16)
Cr2—O1—Zr2	150.03 (13)	O6^viii—O5—O5^xvi	48.35 (16)
Cr2^x—O1—O5^x	33.88 (9)	Cr1^viii—O5—O5^xvi	52.69 (13)
Cr2—O1—O5^x	66.63 (11)	O3^xi—O5—O5^xvi	147.61 (14)
Zr2—O1—O5^x	123.41 (9)	O1—O5—O5^xvi	140.01 (10)
Cr2^x—O1—O5	66.63 (11)	O1^x—O5—O5^xvi	140.01 (10)
Cr2—O1—O5	33.88 (9)	Cr2—O5—O4^i	113.3 (2)
Zr2—O1—O5	123.41 (9)	O6^xv—O5—O4^i	105.9 (2)
O5^x—O1—O5	100.02 (19)	O6^viii—O5—O4^i	72.2 (2)
Cr2^x—O1—O3^xi	32.12 (7)	Cr1^viii—O5—O4^i	106.59 (18)
Cr2—O1—O3^xi	32.12 (7)	O3^xi—O5—O4^i	143.78 (15)
Zr2—O1—O3^xi	126.59 (12)	O1—O5—O4^i	81.31 (11)
O5^x—O1—O3^xi	53.53 (11)	O1^x—O5—O4^i	109.28 (18)
O5—O1—O3^xi	53.54 (11)	O5^xvi—O5—O4^i	60.63 (10)
Cr2^x—O1—O1^x	35.39 (8)	Cr2—O5—O4^vii	113.3 (2)
Cr2—O1—O1^x	35.40 (8)	O6^xv—O5—O4^vii	72.2 (2)
Zr2—O1—O1^x	173.62 (7)	O6^viii—O5—O4^vii	105.9 (2)
O5^x—O1—O1^x	59.32 (8)	Cr1^viii—O5—O4^vii	106.59 (18)
O5—O1—O1^x	59.32 (8)	O3^xi—O5—O4^vii	143.78 (15)
O3^xi—O1—O1^x	59.79 (7)	O1—O5—O4^vii	109.28 (18)
Cr2^x—O1—O3	103.49 (12)	O1^x—O5—O4^vii	81.31 (11)
Cr2—O1—O3	103.49 (12)	O5^xvi—O5—O4^vii	60.63 (10)
Zr2—O1—O3	50.51 (8)	O4^i—O5—O4^vii	56.27 (13)
O5^x—O1—O3	95.41 (10)	Cr2—O5—O6	122.03 (16)
O5—O1—O3	95.41 (10)	O6^xv—O5—O6	86.56 (17)
O3^xi—O1—O3	76.08 (6)	O6^viii—O5—O6	13.39 (18)
O1^x—O1—O3	135.88 (7)	Cr1^viii—O5—O6	48.28 (13)
Cr1—O2—Zr2	155.17 (13)	O3^xi—O5—O6	98.43 (15)
Cr1—O2—Zr1	94.19 (11)	O1—O5—O6	99.85 (10)
Zr2—O2—Zr1	110.64 (9)	O1^x—O5—O6	158.03 (19)
Cr1—O2—O4^iii	149.55 (15)	O5^xvi—O5—O6	61.65 (12)
Zr2—O2—O4^iii	55.28 (8)	O4^i—O5—O6	76.45 (13)
Zr1—O2—O4^iii	55.36 (8)	O4^vii—O5—O6	117.68 (19)
Cr1—O2—O2^v	40.50 (8)	Cr2—O5—O6^xvi	122.03 (16)
Zr2—O2—O2^v	164.33 (6)	O6^xv—O5—O6^xvi	13.39 (18)
Zr1—O2—O2^v	53.69 (6)	O6^viii—O5—O6^xvi	86.56 (17)
O4^iii—O2—O2^v	109.05 (8)	Cr1^viii—O5—O6^xvi	48.28 (13)
Cr1—O2—O3	101.47 (11)	O3^xi—O5—O6^xvi	98.43 (15)
Zr2—O2—O3	53.69 (8)	O1—O5—O6^xvi	158.03 (19)
Zr1—O2—O3	164.34 (12)	O1^x—O5—O6^xvi	99.85 (10)
O4^iii—O2—O3	108.98 (13)	O5^xvi—O5—O6^xvi	61.65 (12)
O2^v—O2—O3	141.97 (8)	O4^i—O5—O6^xvi	117.68 (19)
Cr1—O2—O6^v	31.85 (10)	O4^vii—O5—O6^xvi	76.45 (13)
Zr2—O2—O6^v	131.57 (10)	O6—O5—O6^xvi	95.6 (2)
Zr1—O2—O6^v	108.50 (11)	O6^viii—O6—Cr1	114.0 (7)
O4^iii—O2—O6^v	149.54 (14)	O6^viii—O6—O5^ix	138.14 (17)
O2^v—O2—O6^v	61.33 (7)	Cr1—O6—O5^ix	75.6 (2)
O3—O2—O6^v	85.31 (11)	O6^viii—O6—O5^viii	138.14 (16)
Cr1—O2—O6	31.85 (10)	Cr1—O6—O5^viii	75.6 (2)
Zr2—O2—O6	131.57 (10)	O5^ix—O6—O5^viii	83.3 (3)
Zr1—O2—O6	108.50 (11)	O6^viii—O6—Cr1^viii	41.2 (5)
O4^iii—O2—O6	149.54 (14)	Cr1—O6—Cr1^viii	155.2 (4)
O2^v—O2—O6	61.33 (7)	O5^ix—O6—Cr1^viii	121.4 (2)
O3—O2—O6	85.31 (11)	O5^viii—O6—Cr1^viii	121.4 (2)
O6^v—O2—O6	55.0 (3)	O6^viii—O6—O6^v	150.1 (6)
Cr1—O2—O4^ii	87.60 (8)	Cr1—O6—O6^v	36.1 (2)
Zr2—O2—O4^ii	108.65 (6)	O5^ix—O6—O6^v	51.98 (16)
Zr1—O2—O4^ii	48.23 (5)	O5^viii—O6—O6^v	51.98 (16)
O4^iii—O2—O4^ii	72.30 (7)	Cr1^viii—O6—O6^v	168.69 (15)
O2^v—O2—O4^ii	62.12 (5)	O6^viii—O6—O2	91.6 (6)
O3—O2—O4^ii	131.75 (5)	Cr1—O6—O2	35.66 (10)
O6^v—O2—O4^ii	78.14 (13)	O5^ix—O6—O2	73.3 (2)
O6—O2—O4^ii	118.54 (11)	O5^viii—O6—O2	110.5 (3)
Cr1—O2—O4^i	87.60 (8)	Cr1^viii—O6—O2	126.8 (2)
Zr2—O2—O4^i	108.65 (6)	O6^v—O6—O2	62.52 (13)
Zr1—O2—O4^i	48.23 (5)	O6^viii—O6—O2^v	91.6 (6)
O4^iii—O2—O4^i	72.31 (7)	Cr1—O6—O2^v	35.66 (10)
O2^v—O2—O4^i	62.12 (5)	O5^ix—O6—O2^v	110.5 (2)
O3—O2—O4^i	131.75 (5)	O5^viii—O6—O2^v	73.3 (2)
O6^v—O2—O4^i	118.54 (11)	Cr1^viii—O6—O2^v	126.8 (2)
O6—O2—O4^i	78.14 (13)	O6^v—O6—O2^v	62.52 (13)
O4^ii—O2—O4^i	95.52 (10)	O2—O6—O2^v	57.35 (14)
Cr2^ix—O3—Cr2^xi	35.09 (11)	O6^viii—O6—O5	28.47 (12)
Cr2^ix—O3—Zr2	162.46 (5)	Cr1—O6—O5	108.6 (2)
Cr2^xi—O3—Zr2	162.46 (5)	O5^ix—O6—O5	110.0 (2)
Cr2^ix—O3—O5^ix	40.07 (13)	O5^viii—O6—O5	166.61 (18)
Cr2^xi—O3—O5^ix	75.16 (17)	Cr1^viii—O6—O5	50.69 (15)
Zr2—O3—O5^ix	122.38 (14)	O6^v—O6—O5	137.81 (12)
Cr2^ix—O3—O5^xi	75.16 (17)	O2—O6—O5	76.10 (13)
Cr2^xi—O3—O5^xi	40.07 (13)	O2^v—O6—O5	102.4 (2)
Zr2—O3—O5^xi	122.38 (14)	O6^viii—O6—O5^xvi	28.47 (12)
O5^ix—O3—O5^xi	115.2 (3)	Cr1—O6—O5^xvi	108.6 (2)
Cr2^ix—O3—O2	110.49 (6)	O5^ix—O6—O5^xvi	166.61 (18)
Cr2^xi—O3—O2	145.58 (12)	O5^viii—O6—O5^xvi	110.0 (2)
Zr2—O3—O2	51.97 (8)	Cr1^viii—O6—O5^xvi	50.69 (15)
O5^ix—O3—O2	70.42 (13)	O6^v—O6—O5^xvi	137.81 (12)
O5^xi—O3—O2	174.35 (19)	O2—O6—O5^xvi	102.4 (2)
Cr2^ix—O3—O2^iii	145.58 (12)	O2^v—O6—O5^xvi	76.09 (13)
Cr2^xi—O3—O2^iii	110.49 (6)	O5—O6—O5^xvi	56.7 (2)

Symmetry codes: (i) −y+3/4, x−1/4, −z+1/4; (ii) y−3/4, −x+7/4, −z+1/4; (iii) −x+1, −y+3/2, z; (iv) x−1, y, z; (v) −x, −y+3/2, z; (vi) −y+3/4, x+3/4, −z+1/4; (vii) y−3/4, −x+3/4, −z+1/4; (viii) −x, −y+1, −z; (ix) x, y+1/2, −z; (x) −x+1, −y+1/2, z; (xi) −x+1, −y+1, −z; (xii) x+1, y, z; (xiii) y+1/4, −x+3/4, −z+1/4; (xiv) −y+7/4, x+3/4, −z+1/4; (xv) x, y−1/2, −z; (xvi) −x, −y+1/2, z.