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The title compound, lithium/aluminium dimagnesium tetra­kis­[orthomolybdate(VI)], was prepared by a solid-state reaction route. The crystal structure is built up from MgO6 octa­hedra and MoO4 tetra­hedra sharing corners and edges, forming two types of chains running along [100]. These chains are linked into layers parallel to (010) and finally linked by MoO4 tetra­hedra into a three-dimensional framework structure with channels parallel to [001] in which lithium and aluminium cations equally occupy the same position within a distorted trigonal-bipyramidal coordination environment. The title structure is isotypic with LiMgIn(MoO4)3, with the In site becoming an Mg site and the fully occupied Li site a statistically occupied Li/Al site in the title structure.

Supporting information

cif

Crystallographic Information File (CIF) https://doi.org/10.1107/S1600536813022046/wm2760sup1.cif
Contains datablock I

hkl

Structure factor file (CIF format) https://doi.org/10.1107/S1600536813022046/wm2760Isup2.hkl
Contains datablock I

Key indicators

  • Single-crystal X-ray study
  • T = 298 K
  • Mean [sigma](Mg-O) = 0.003 Å
  • Disorder in main residue
  • R factor = 0.021
  • wR factor = 0.053
  • Data-to-parameter ratio = 13.3

checkCIF/PLATON results

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Alert level C PLAT906_ALERT_3_C Large K value in the Analysis of Variance ...... 2.144 PLAT975_ALERT_2_C Positive Residual Density at 1.07A from O7 . 0.53 eA-3 PLAT975_ALERT_2_C Positive Residual Density at 0.73A from O12 . 0.43 eA-3 PLAT975_ALERT_2_C Positive Residual Density at 0.66A from O10 . 0.41 eA-3
Alert level G FORMU01_ALERT_1_G There is a discrepancy between the atom counts in the _chemical_formula_sum and _chemical_formula_moiety. This is usually due to the moiety formula being in the wrong format. Atom count from _chemical_formula_sum: Al0.5 Li0.5 Mg2 Mo3 O12 Atom count from _chemical_formula_moiety:Al2 Li2 Mg8 Mo4 O12 PLAT004_ALERT_5_G Info: Polymeric Structure Found with Dimension . 3 PLAT005_ALERT_5_G No _iucr_refine_instructions_details in the CIF ? Do ! PLAT042_ALERT_1_G Calc. and Reported MoietyFormula Strings Differ ? Check PLAT045_ALERT_1_G Calculated and Reported Z Differ by ............ 0.50 Ratio PLAT232_ALERT_2_G Hirshfeld Test Diff (M-X) Mg1 -- O4 .. 6.4 su PLAT232_ALERT_2_G Hirshfeld Test Diff (M-X) Mg1 -- O11 .. 6.2 su PLAT232_ALERT_2_G Hirshfeld Test Diff (M-X) Mg1 -- O10_d .. 7.8 su PLAT232_ALERT_2_G Hirshfeld Test Diff (M-X) Mg1 -- O2_j .. 9.2 su PLAT232_ALERT_2_G Hirshfeld Test Diff (M-X) Mg1 -- O8_j .. 5.1 su PLAT301_ALERT_3_G Note: Main Residue Disorder ................... 3 %
0 ALERT level A = Most likely a serious problem - resolve or explain 0 ALERT level B = A potentially serious problem, consider carefully 4 ALERT level C = Check. Ensure it is not caused by an omission or oversight 11 ALERT level G = General information/check it is not something unexpected 3 ALERT type 1 CIF construction/syntax error, inconsistent or missing data 8 ALERT type 2 Indicator that the structure model may be wrong or deficient 2 ALERT type 3 Indicator that the structure quality may be low 0 ALERT type 4 Improvement, methodology, query or suggestion 2 ALERT type 5 Informative message, check

Comment top

In recent years, great attention has been devoted to the examination of metal oxides containing mobile lithium ions due to their potential application in the fields of energy and electronics, such as LiMO2 materials (M= Mn, Fe, Co, Ni) (Whittingham & Silbernagel, 1976; Mizushima et al., 1980; Kanno et al., 1994) which allowed to construct electrochemical generators with a high energy density. In our field of research we are interested especially to doubles molybdates of alkali and divalent metals, and we tried to explore systems like Li2O—MO—MoO3. For such systems, the compounds Li3Fe(MoO4)3 and Li2Fe2(MoO4)3 are already known, the crystal structures of which have been determined by Klevtsova & Magarill (1970) and the structural similarity to NaCo2.31(MoO4)3 and to other framework oxides is noted. These compounds include Li2M2(MoO4)3 (M = Mg, Mn, Co, Ni, Cu, Zn) (Efremov & Trunov, 1972; Ozima & Zoltai, 1976), Li3M3+(MoO4)3 (M=Al, Cr, Ga, Sc, In, Co) (Klevtsov, 1970; Kolitsch & Tillmanns, 2003) and Li2M4+(MoO4)3 (M = Ti, Zr, Hf) (Klevtsov & Zolotova, 1973; Klevtsova et al., 1979). During our examinations we now have serendipitously obtained a new molybdenum oxide crystal with composition Li0.5Al0.5Mg2(MoO4)3, (I).

The asymmetric unit of compound (I) is composed of two MgO6 octahedra and three MoO4 tetrahedra sharing corners, as well as a (li/Al) site (Fig. 1). The structure of (I) can be described as being composed of two types of infinite chains expanding parallel to [100]. The first chain is built up from Mg2O6 octahedra and Mo1O4 tetrahedra sharing corners, forming double chains with composition (Mg2Mo2O14)n and with a cis arrangement of the MoO4 tetrahedra relative to the MgO6 octahedra (Fig. 2a). The second type of chain is formed by Mg1O6 octahedra and Mo2O4 tetrahedra, also linked by corners but in a trans arrangement. Single chains of the second type are linked by sharing edges between two adjacent Mg1O6 octahedra (Fig. 2b). The linkage between the two types of chains leads to a layer-like arrangement parallel to (010) (Fig. 3), whereas the linkage into a three-dimensional framework is provided by Mo3O4 tetrahedra by sharing corners. In this framework channels are present where the mixed-occupied Li+/Al3+ sites are located (Fig. 4). The Mg2O6 octahedron has an almost regular coordination sphere with five nearly equal Mg—O distances (d(Mg—O) = 2.04 Å) with the sixth slightly longer. Each Mg12O10 double octahedron is surrounded by ten MoO4 tetrahedra forming Mg12Mo10O40 units. The Mg—O distances vary from 1.968 (3) Å to 2.104 (3) Å which are close to those found for related systems (Nord & Kierkegaard, 1984). The Mo—O distances vary from 1.719 (3) Å to 1.812 (3) Å with the average Mo—O distance of 1.762 Å, closed to literature values (Solodovnikov et al., 1997). The (Li/Al) site has a distorted trigonal-bipyramidal coordination environment.

The structure of compound (I) is isotypic with LiMgIn(MoO4)3 (Khazheeva et al., 1985). The In3+ site becomes Mg2 in the title structure, and the Li site in LiMgIn(MoO4)3 has full occupation, whereas in the title structure it is a mixed-occupied (Li/Al) site with half-occupancy for each of the metal ions. In fact, charge compensation can only be ensured by insertion of Al3+ in the same site as Li+ ((Mg2+ + In3+ + Li+) = (2Mg2+ + (Al3+/Li+)) (Fig. 5).

The unit-cell parameters of triclinic Li0.5Al0.5Mg2(MoO4)3 indicate some resemblance to the structures of Ag2M2(MoO4)3 (M = Zn, Mg, Co) (Tsyrenova et al., 2004, 2001; Gicquel-Mayer et al., 1981), but a close comparison of the structures reveals some differences. The latter have mixed frameworks of MoO4 tetrahedra and pairs of MO6 octahedra sharing common edges, whereas in structure (I) MO6 octahedra and also Mg2O10 units surrounded by MoO4 tetrahedra are present. A further comparison of the structure of compound (I) with the Li2M2(MoO4)3 family (M=Mg, Mn, Co, Ni, Cu, Zn) (Efremov & Trunov, 1972; Ozima & Zoltai, 1976) reveals that the substitution of some of the lithium ions by aluminium has changed the crystal structure. The latter family adopts the lyonsite structure type, space group Pnma, and their general formula can be written as A16B12O48. Generally, the A site is statistically occupied by Li+ and a M2+ ion.

Related literature top

For complex oxides containing lithium ions, see: Whittingham & Silbernagel (1976); Mizushima et al. (1980); Kanno et al. (1994). For details of chemically and/or structurally related compounds, see: Efremov & Trunov (1972); Ozima & Zoltai (1976); Klevtsov (1970); Kolitsch & Tillmanns (2003); Tsyrenova et al. (2001, 2004); Gicquel-Mayer et al. (1981); Klevtsova & Magarill (1970); Klevtsov & Zolotova (1973); Klevtsova et al. (1979); Nord & Kierkegaard (1984); Solodovnikov et al. (1997). For the isotypic structure of LiMgIn(MoO4)3, see: Khazheeva et al. (1985).

Experimental top

The title compound, Li0.5Al0.5Mg2(MoO4)3, was obtained serendipitously by a solid state reaction from appropriate quantities of LiNO3 (Fluka, 62575), (NH4)2Mo4O13 (Fluka, 69858) and Mg(NO3)2.6H2O (Fluka, 63079) placed in a porcelain crucible, and slowly annealed in air at 623 K for 12 h, in order to eliminate volatile products. The resulting mixture was then heated to 853 K for 7 days before slowly cooling at 5 K/day to 773 K. Finally, the furnace was cooled at 50 K/day to room temperature. A qualitative EDX analysis of a selected crystal using a FEI Quanta 200 system revealed the presence of Al, Mo, Mg and O (Fig. 6). Aluminium was not present in the employed educts of the reaction mixture, but the incorporation of aluminium from the porcelain crucible is the most likely source of this element.

Refinement top

During the first stages of refinement the site in the channels was first attributed solely to Li. However, the refined composition did not satisfy electrical neutrality. After considering the presence of Al (see 'experimental part') on this site with an occupancy ratio of 1:1 for Li and Al, electrical neutrality was achieved. Both metals were refined with the same coordinates and the same anisotropic displacement parameters.

Computing details top

Data collection: CAD-4 EXPRESS (Duisenberg, 1992; Macíček & Yordanov, 1992); cell refinement: CAD-4 EXPRESS (Duisenberg, 1992; Macíček & Yordanov, 1992); data reduction: XCAD4 (Harms & Wocadlo, 1995); program(s) used to solve structure: SHELXS97 (Sheldrick, 2008); program(s) used to refine structure: SHELXL97 (Sheldrick, 2008); molecular graphics: DIAMOND (Brandenburg, 1998); software used to prepare material for publication: WinGX (Farrugia, 2012).

Figures top
[Figure 1] Fig. 1. Expanded asymmetric unit of Li0.5Al0.5Mg2(MoO4)3 showing the main building units. All atoms are represented as displacement ellipsoids at the 50% probability level. [Symmetry codes: (i) x, y+1, z; (ii) x+1, y, z; (iii) x, y, z+1.]
[Figure 2] Fig. 2. The two types of double chains with composition (Mg2Mo2O14)n, (a) in cis arrangement, (b) in trans arrangement.
[Figure 3] Fig. 3. The projection of the Li0.5Al0.5Mg2(MoO4)3 structure showing the layer parallel to (010).
[Figure 4] Fig. 4. Projection of Li0.5Al0.5Mg2(MoO4)3 along [001].
[Figure 5] Fig. 5. Projection of the isotypic structure of LiMgIn(MoO4)3 along [010].
[Figure 6] Fig. 6. Qualitative EDX analysis of Li0.5Al0.5Mg2(MoO4)3, showing the presence of Al.
Lithium aluminium dimagnesium tetrakismolybdate top
Crystal data top
Li0.5Al0.5Mg2(MoO4)3Z = 2
Mr = 545.40F(000) = 508
Triclinic, P1Dx = 3.606 Mg m3
Hall symbol: -P 1Mo Kα radiation, λ = 0.71073 Å
a = 6.8555 (7) ÅCell parameters from 25 reflections
b = 8.2910 (9) Åθ = 10–15°
c = 9.5760 (9) ŵ = 3.92 mm1
α = 96.032 (7)°T = 298 K
β = 106.743 (8)°Prism, colourless
γ = 101.824 (9)°0.2 × 0.18 × 0.11 mm
V = 502.27 (9) Å3
Data collection top
Enraf–Nonius CAD-4
diffractometer
2150 reflections with I > 2sσ(I)
Radiation source: fine-focus sealed tubeRint = 0.014
Graphite monochromatorθmax = 27.0°, θmin = 2.3°
ω/2θ scansh = 84
Absorption correction: ψ scan
(North et al., 1968)
k = 1010
Tmin = 0.520, Tmax = 0.648l = 1212
3450 measured reflections2 standard reflections every 120 min
2187 independent reflections intensity decay: 1.1%
Refinement top
Refinement on F2Primary atom site location: structure-invariant direct methods
Least-squares matrix: fullSecondary atom site location: difference Fourier map
R[F2 > 2σ(F2)] = 0.021 w = 1/[σ2(Fo2) + (0.0096P)2 + 2.5823P]
where P = (Fo2 + 2Fc2)/3
wR(F2) = 0.053(Δ/σ)max = 0.001
S = 1.29Δρmax = 0.57 e Å3
2187 reflectionsΔρmin = 0.81 e Å3
164 parametersExtinction correction: SHELXL97 (Sheldrick, 2008), Fc*=kFc[1+0.001xFc2λ3/sin(2θ)]-1/4
0 restraintsExtinction coefficient: 0.0123 (4)
Crystal data top
Li0.5Al0.5Mg2(MoO4)3γ = 101.824 (9)°
Mr = 545.40V = 502.27 (9) Å3
Triclinic, P1Z = 2
a = 6.8555 (7) ÅMo Kα radiation
b = 8.2910 (9) ŵ = 3.92 mm1
c = 9.5760 (9) ÅT = 298 K
α = 96.032 (7)°0.2 × 0.18 × 0.11 mm
β = 106.743 (8)°
Data collection top
Enraf–Nonius CAD-4
diffractometer
2150 reflections with I > 2sσ(I)
Absorption correction: ψ scan
(North et al., 1968)
Rint = 0.014
Tmin = 0.520, Tmax = 0.6482 standard reflections every 120 min
3450 measured reflections intensity decay: 1.1%
2187 independent reflections
Refinement top
R[F2 > 2σ(F2)] = 0.021164 parameters
wR(F2) = 0.0530 restraints
S = 1.29Δρmax = 0.57 e Å3
2187 reflectionsΔρmin = 0.81 e Å3
Special details top

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 (Å2) top
xyzUiso*/UeqOcc. (<1)
Mo10.30272 (5)0.89586 (4)0.66046 (3)0.00921 (10)
Mo20.98153 (5)0.19503 (4)0.87863 (4)0.01148 (10)
Mo30.49457 (5)0.50622 (4)0.74760 (3)0.00964 (10)
Mg10.53871 (19)0.19031 (15)0.99366 (13)0.0071 (2)
Mg20.2478 (2)0.20149 (16)0.40750 (14)0.0096 (2)
Li10.0379 (4)0.6097 (3)0.7889 (3)0.0200 (5)0.50
Al10.0379 (4)0.6097 (3)0.7889 (3)0.0200 (5)0.50
O10.0505 (4)0.7660 (3)0.6386 (3)0.0131 (5)
O20.4454 (4)0.9765 (4)0.8546 (3)0.0147 (6)
O30.9874 (5)0.3666 (4)0.7886 (4)0.0252 (7)
O40.5435 (5)0.3564 (4)0.8579 (3)0.0212 (6)
O50.2586 (5)0.0618 (4)0.5726 (3)0.0197 (6)
O60.8558 (5)0.0118 (4)0.7493 (3)0.0212 (6)
O70.7368 (4)0.6232 (4)0.7376 (3)0.0138 (5)
O80.3563 (4)0.6386 (4)0.8234 (3)0.0151 (6)
O90.3363 (5)0.4040 (4)0.5737 (3)0.0165 (6)
O100.8481 (5)0.2198 (4)0.0140 (3)0.0180 (6)
O110.2432 (5)0.1911 (4)0.9700 (4)0.0226 (7)
O120.4468 (5)0.7896 (4)0.5776 (3)0.0177 (6)
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
Mo10.00817 (16)0.01051 (16)0.00822 (16)0.00090 (12)0.00288 (12)0.00056 (11)
Mo20.01273 (17)0.01071 (17)0.01133 (17)0.00244 (12)0.00502 (12)0.00086 (12)
Mo30.00894 (16)0.01052 (16)0.00917 (16)0.00232 (12)0.00293 (12)0.00046 (11)
Mg10.0077 (6)0.0069 (6)0.0065 (5)0.0020 (4)0.0020 (4)0.0006 (4)
Mg20.0088 (6)0.0097 (6)0.0094 (6)0.0014 (5)0.0027 (5)0.0008 (5)
Li10.0172 (10)0.0215 (11)0.0203 (11)0.0038 (9)0.0046 (9)0.0060 (9)
Al10.0172 (10)0.0215 (11)0.0203 (11)0.0038 (9)0.0046 (9)0.0060 (9)
O10.0111 (13)0.0137 (13)0.0147 (13)0.0028 (10)0.0041 (11)0.0044 (11)
O20.0121 (13)0.0172 (14)0.0128 (13)0.0036 (11)0.0025 (11)0.0018 (11)
O30.0305 (18)0.0179 (15)0.0298 (17)0.0038 (13)0.0127 (15)0.0103 (13)
O40.0207 (15)0.0250 (16)0.0204 (15)0.0089 (13)0.0064 (13)0.0084 (13)
O50.0244 (16)0.0160 (14)0.0180 (15)0.0025 (12)0.0064 (12)0.0054 (12)
O60.0240 (16)0.0198 (15)0.0170 (15)0.0020 (13)0.0071 (13)0.0033 (12)
O70.0124 (13)0.0158 (13)0.0140 (13)0.0050 (11)0.0047 (11)0.0024 (11)
O80.0136 (13)0.0153 (14)0.0175 (14)0.0030 (11)0.0081 (11)0.0004 (11)
O90.0187 (14)0.0140 (14)0.0126 (13)0.0001 (11)0.0028 (11)0.0011 (11)
O100.0222 (15)0.0206 (15)0.0150 (14)0.0092 (12)0.0084 (12)0.0040 (12)
O110.0200 (15)0.0275 (17)0.0219 (16)0.0080 (13)0.0079 (13)0.0031 (13)
O120.0147 (14)0.0219 (15)0.0157 (14)0.0038 (12)0.0056 (11)0.0016 (12)
Geometric parameters (Å, º) top
Mo1—O5i1.721 (3)Mg1—O41.992 (3)
Mo1—O121.745 (3)Mg1—O10iii2.033 (3)
Mo1—O11.781 (3)Mg1—O2v2.104 (3)
Mo1—O21.812 (3)Mg2—O12vi2.042 (3)
Mo2—O31.738 (3)Mg2—O1vii2.045 (3)
Mo2—O61.743 (3)Mg2—O92.046 (3)
Mo2—O11ii1.763 (3)Mg2—O52.049 (3)
Mo2—O10iii1.807 (3)Mg2—O6viii2.049 (3)
Mo3—O91.718 (3)Mg2—O7vi2.121 (3)
Mo3—O41.736 (3)Li1—O3ix1.974 (4)
Mo3—O71.777 (3)Li1—O7ix2.009 (4)
Mo3—O81.812 (3)Li1—O12.044 (4)
Mg1—O2iv1.968 (3)Li1—O82.070 (4)
Mg1—O111.974 (3)Li1—O10vi2.076 (4)
Mg1—O8v1.983 (3)
O5i—Mo1—O12108.83 (15)O11—Mg1—O2v94.31 (13)
O5i—Mo1—O1106.36 (14)O8v—Mg1—O2v82.89 (12)
O12—Mo1—O1111.36 (14)O4—Mg1—O2v176.13 (14)
O5i—Mo1—O2108.44 (14)O10iii—Mg1—O2v91.76 (12)
O12—Mo1—O2111.03 (13)O12vi—Mg2—O1vii166.46 (14)
O1—Mo1—O2110.64 (13)O12vi—Mg2—O991.79 (13)
O3—Mo2—O6109.58 (16)O1vii—Mg2—O986.88 (13)
O3—Mo2—O11ii108.05 (16)O12vi—Mg2—O592.20 (14)
O6—Mo2—O11ii109.67 (15)O1vii—Mg2—O5101.11 (13)
O3—Mo2—O10iii108.85 (15)O9—Mg2—O585.35 (13)
O6—Mo2—O10iii111.40 (15)O12vi—Mg2—O6viii91.25 (13)
O11ii—Mo2—O10iii109.23 (14)O1vii—Mg2—O6viii91.06 (13)
O9—Mo3—O4107.98 (15)O9—Mg2—O6viii175.12 (14)
O9—Mo3—O7109.75 (14)O5—Mg2—O6viii90.72 (14)
O4—Mo3—O7109.09 (14)O12vi—Mg2—O7vi85.67 (13)
O9—Mo3—O8108.76 (14)O1vii—Mg2—O7vi80.80 (12)
O4—Mo3—O8109.30 (14)O9—Mg2—O7vi86.40 (12)
O7—Mo3—O8111.88 (13)O5—Mg2—O7vi171.41 (13)
O2iv—Mg1—O1190.13 (14)O6viii—Mg2—O7vi97.64 (13)
O2iv—Mg1—O8v163.23 (14)O3ix—Li1—O7ix97.36 (16)
O11—Mg1—O8v92.29 (13)O3ix—Li1—O1137.17 (18)
O2iv—Mg1—O4102.01 (14)O7ix—Li1—O183.58 (14)
O11—Mg1—O488.75 (14)O3ix—Li1—O893.03 (16)
O8v—Mg1—O494.64 (14)O7ix—Li1—O8168.56 (17)
O2iv—Mg1—O10iii94.68 (13)O1—Li1—O885.55 (14)
O11—Mg1—O10iii172.82 (15)O3ix—Li1—O10vi121.05 (17)
O8v—Mg1—O10iii84.64 (13)O7ix—Li1—O10vi97.16 (15)
O4—Mg1—O10iii85.04 (13)O1—Li1—O10vi101.10 (15)
O2iv—Mg1—O2v80.38 (13)O8—Li1—O10vi81.44 (14)
Symmetry codes: (i) x, y+1, z; (ii) x+1, y, z; (iii) x, y, z+1; (iv) x, y1, z; (v) x+1, y+1, z+2; (vi) x+1, y+1, z+1; (vii) x, y+1, z+1; (viii) x+1, y, z+1; (ix) x1, y, z.
Selected bond lengths (Å) top
Mo1—O5i1.721 (3)Mg1—O41.992 (3)
Mo1—O121.745 (3)Mg1—O10iii2.033 (3)
Mo1—O11.781 (3)Mg1—O2v2.104 (3)
Mo1—O21.812 (3)Mg2—O12vi2.042 (3)
Mo2—O31.738 (3)Mg2—O1vii2.045 (3)
Mo2—O61.743 (3)Mg2—O92.046 (3)
Mo2—O11ii1.763 (3)Mg2—O52.049 (3)
Mo2—O10iii1.807 (3)Mg2—O6viii2.049 (3)
Mo3—O91.718 (3)Mg2—O7vi2.121 (3)
Mo3—O41.736 (3)Li1—O3ix1.974 (4)
Mo3—O71.777 (3)Li1—O7ix2.009 (4)
Mo3—O81.812 (3)Li1—O12.044 (4)
Mg1—O2iv1.968 (3)Li1—O82.070 (4)
Mg1—O111.974 (3)Li1—O10vi2.076 (4)
Mg1—O8v1.983 (3)
Symmetry codes: (i) x, y+1, z; (ii) x+1, y, z; (iii) x, y, z+1; (iv) x, y1, z; (v) x+1, y+1, z+2; (vi) x+1, y+1, z+1; (vii) x, y+1, z+1; (viii) x+1, y, z+1; (ix) x1, y, z.
 

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