The solid solution Co3.6Mg1.4Cl2(TeO3)4

Takagi, R.; Hjelmqvist, D.T.; Johnsson, M.

doi:10.1107/S1600536807024014

The solid solution Co_3.6Mg_1.4Cl₂(TeO₃)₄

R. Takagi, D. T. Hjelmqvist and M. Johnsson

Single crystals of the cobalt magnesium dichloride tetrakis[trioxotellurate(IV)] solid solution Co_5−yMg_y(TeO₃)₄Cl₂ [y = 1.4] were obtained from solid–gas phase reactions in sealed evacuated silica tubes. The crystal symmetry is monoclinic and the compound is isostructural with Co₅(TeO₃)₄X₂ and Ni₅(TeO₃)₄X₂ (X = Cl, Br). The layered structure comprises distorted MO₆ and MO₅Cl octahedra (M = statistically occupied Co and Mg sites) and TeO₃E tetrahedra (E = stereochemically active electron lone pair of Te^IV). Five face-sharing MO₆ octahedra make up claw-like [M₅O₁₆Cl₂] units which form layers by corner-sharing with four other such units and by corner- and edge-sharing with TeO₃E tetrahedra. The layers are held together only by weak van der Waals forces with a closest Te

Cl distance of 3.184 (2) Å between two layers.

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Supporting information

	Crystallographic Information File (CIF) https://doi.org/10.1107/S1600536807024014/wm2109sup1.cif Contains datablocks global, I
	Structure factor file (CIF format) https://doi.org/10.1107/S1600536807024014/wm2109Isup2.hkl Contains datablock I

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Key indicators

Single-crystal X-ray study
T = 292 K
Mean (e-O) = 0.004 Å
Disorder in main residue
R factor = 0.044
wR factor = 0.064
Data-to-parameter ratio = 30.1

checkCIF/PLATON results

No syntax errors found



Alert level B
PLAT029_ALERT_3_B _diffrn_measured_fraction_theta_full Low .......       0.95

Alert level C
DIFMN02_ALERT_2_C  The minimum difference density is < -0.1*ZMAX*0.75
            _refine_diff_density_min given =     -3.940
            Test value =     -3.900
DIFMN03_ALERT_1_C  The minimum difference density is < -0.1*ZMAX*0.75
            The relevant atom site should be identified.
REFLT03_ALERT_3_C  Reflection count < 95% complete
           From the CIF: _diffrn_reflns_theta_max           36.83
           From the CIF: _diffrn_reflns_theta_full          36.26
           From the CIF: _reflns_number_total               3245
           TEST2: Reflns within _diffrn_reflns_theta_max
           Count of symmetry unique reflns         3523
           Completeness (_total/calc)             92.11%
PLAT041_ALERT_1_C Calc. and Rep. SumFormula Strings    Differ ....          ?
PLAT042_ALERT_1_C Calc. and Rep. MoietyFormula Strings Differ ....          ?
PLAT045_ALERT_1_C Calculated and Reported Z Differ by ............       0.25 Ratio
PLAT076_ALERT_1_C Occupancy       0.50 less than 1.0 for Sp.pos  .        CO1
PLAT076_ALERT_1_C Occupancy       0.50 less than 1.0 for Sp.pos  .        MG1
PLAT077_ALERT_4_C Unitcell contains non-integer number of atoms ..          ?
PLAT098_ALERT_2_C Minimum (Negative) Residual Density ............      -3.94 e/A   
PLAT301_ALERT_3_C Main Residue  Disorder .........................      17.00 Perc.
PLAT711_ALERT_1_C BOND    Unknown or Inconsistent Label ..........         M1
                    M1     O1
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                    M2     MG3
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                    M2     CL1
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                    M2     O1
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                    O4     M1     O4
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                    O5     M1     O5
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                    O5     M1     O5
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                    CL1    M2     O1
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                    CL1    M2     O3
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                    CL1    M2     O4
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                    CL1    M2     O5
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                    CL1    M2     O6
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                    O3     M2     O4
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                    O1     M3     O2
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                    O1     M3     O5
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                    O2     M3     O3
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                    O2     M3     O5
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                    O2     M3     O6
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                    O3     M3     O4
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                    O3     M3     O5
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                    O3     M3     O6
PLAT712_ALERT_1_C ANGLE   Unknown or Inconsistent Label ..........         M3
                    O4     M3     O5
PLAT712_ALERT_1_C ANGLE   Unknown or Inconsistent Label ..........         M3
                    O4     M3     O6
PLAT712_ALERT_1_C ANGLE   Unknown or Inconsistent Label ..........         M3
                    O5     M3     O6

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:   Cl2 Co3.617 Mg1.383 O12 Te4
            Atom count from _chemical_formula_moiety:

   0 ALERT level A = In general: serious problem
   1 ALERT level B = Potentially serious problem
  79 ALERT level C = Check and explain
   1 ALERT level G = General alerts; check

  75 ALERT type 1 CIF construction/syntax error, inconsistent or missing data
   2 ALERT type 2 Indicator that the structure model may be wrong or deficient
   3 ALERT type 3 Indicator that the structure quality may be low
   1 ALERT type 4 Improvement, methodology, query or suggestion
   0 ALERT type 5 Informative message, check

Comment top

The aim of this study was to introduce Mg^II into the Co^II—Te^IV—O—Cl system. Some few transition metal oxohalides comprising both Te^IV and an alkaline earth element have been described before, e.g. Ba₂Cu₄Te₄O₁₁Cl₄ (Feger & Kolis, 1998), Ca₂CuTe₄O₁₀Cl₂ (Takagi & Johnsson, 2005), Sr₂Cu₂TeO₆Br₂ (Takagi & Johnsson, 2006) and SrCu₂(TeO₃)₂Cl₂ (Takagi et al., 2006). In this communication we report the synthesis and crystal structure of the new compound Co_3.6Mg_1.4(TeO₃)₄Cl₂ (I). The refinement proved (I) to be isostructural to Co₅(TeO₃)₄X₂ (X = Cl, Br) (Becker, Prester, Berger, Johnsson et al., 2007) and Ni₅(TeO₃)₄X₂ (Johnsson et al., 2003). The corresponding Se-compounds are, however, not isostructural and the four compounds Co₅(SeO₃)₄X₂ and Ni₅(SeO₃)₄X₂ (X=Cl, Br) are all triclinic and crystallize in two different structure types (Becker, Prester, Berger, Hui Lin et al., 2007; Jiang & Mao, 2006; Shen et al., 2005).

There are two crystallographic distinct Te positions that both have a TeO₃E tetrahedral coordination (E = lone pair electrons of Te^IV). The Te(1)O₃E tetrahedron is quite regular while the Te(2)O₃E tetrahedron is more distorted. Te(1) has a fourth neighbouring oxygen atom located at 2.706 (5) Å, however, a distance that is too long to be considered as belonging to the primary coordination sphere. Geometrically placing the lone pairs under assumption of a Te - E distance (radius) of 1.25 Å (Galy et al., 1975) gives the fractional coordinates for E(1) with x = 0.3149, y = 0.1870, z = 0.2989, and for E(2) with x = 0.2073, y = 0.2878, z = 0.4325, respectively. The metal positions, M, are statistically occupied by Co and Mg. The M(1) and M(3) sites have a distorted MO₆ octahedral coordination with M—O distances ranging from 2.019 (3) Å to 2.397 (6) Å). The M(2) site has a MO₅Cl distorted octahedral coordination with M—O distances ranging from 2.020 (5) to 2.270 (3) Å, while the M—Cl distance is 2.4616 (16) Å (Table 1).

The structural arrangement of (I) is layered, see Figure 1. The layers extend parallel to (100) and consist of TeO₃E, MO₆ and MO₅Cl polyhedra. The M-polyhedra make up building blocks constituting five MO₆ octahedra which, by face sharing, make up a claw-like [M₅O₁₆Cl₂] unit. These units form layers by corner-sharing to four other such units and by corner- and edge-sharing to the TeO₃E tetrahedra. The halides and the electron lone-pairs (E) of Te^IV protrude from the layers to the empty space. The closest Te—Cl distance between two layers is 3.184 (2) Å. This distance is substantially shorter than the expected van der Waals distance of 3.81 Å (Bondi, 1964) indicating that there is a stronger interaction between two layers.

The highest fraction of Mg is present at the M(1) and M(3) sites that both coordinate solely to oxygen atoms. The shortest M—M distance between two layers is 5.832 (2) Å, which is slightly longer than in the structure of Co₅(TeO₃)₄Cl₂ (5.690 (7) Å).

Related literature top

For isostructural compounds, see: Johnsson et al., 2003; Becker, Prester, Berger, Johnsson et al., 2007; for compounds with the same formula type but different structures, see: Becker, Prester, Berger, Hui Lin et al., 2007; Jiang & Mao, 2006; Shen et al., 2005; for related Te^IV containing compounds with transition and alkaline earth metals, see: Feger & Kolis, 1998; Takagi & Johnsson, 2005, 2006; Takagi et al., 2006; for structural peculiarities of Te^IV compounds, see: Galy et al. 1975; Bondi, 1964.

Experimental top

Single crystals of compound (I) were synthesized from MgO (Merck, 99.99%), CoCl₂ (Aldrich, +97%), CoO (Alfa Aesar, +99%), and TeO₂ (ABCR, +99%) in the molar ratio 1:1:1:2. The components were mixed in a mortar and placed in a silica tube (length ~5 cm) which was then evacuated. The sample tube was heated at 920 K for 70 h in a muffle furnace to allow for solid-gas phase reactions. The final non-hygroscopic product consisted of a mixture of a purple powder, a brown powder, and blue transparent prismatic single crystals of (I). Analysis by energy dispersive spectrometry (EDS, LINK AN10000) of the crystal used for the diffraction experiment gave (at-%): 36.3% Te, 33.0% Co, 12.5% Mg, and 18.1% Cl. The Co:Mg ratio was thus found to be 73:27 = 2.7 which is in very good agreement with the composition determined from structure refinement (ratio 2.6).

Structure description top

Computing details top

Data collection: CrysAlis CCD (Oxford Diffraction, 2006); cell refinement: CrysAlis RED (Oxford Diffraction, 2006); data reduction: CrysAlis RED; program(s) used to solve structure: SHELXS97 (Sheldrick, 1997); program(s) used to refine structure: JANA2000 (Petříček et al., 2000); molecular graphics: DIAMOND (Bergerhoff, 1996); software used to prepare material for publication: JANA2000.

Figures top

Fig. 1. The crystal structure of (I) in projection along [010].

cobalt magnesium dichloride tetrakis[trioxotellurate(IV)] top

Crystal data top

Co_3.617Mg_1.383Cl₂(TeO₃)₄	F(000) = 1809
M_r = 1020.08	D_x = 4.832 Mg m⁻³
Monoclinic, C2/c	Mo Kα radiation, λ = 0.71069 Å
Hall symbol: -C 2yc	Cell parameters from 5897 reflections
a = 19.8551 (11) Å	θ = 3.9–36.8°
b = 5.2584 (2) Å	µ = 12.87 mm⁻¹
c = 16.4637 (10) Å	T = 292 K
β = 125.3607 (7)°	Prism, blue
V = 1401.81 (13) Å³	0.11 × 0.10 × 0.08 mm
Z = 4

Data collection top

Oxford Diffraction Xcalibur3 diffractometer	3246 independent reflections
Radiation source: fine-focus sealed tube	2376 reflections with I > 3σ(I)
Graphite monochromator	R_int = 0.056
Detector resolution: 6.7 pixels mm^-1	θ_max = 36.8°, θ_min = 4.1°
φ–scan	h = −33→33
Absorption correction: numerical [X-RED (Stoe & Cie, 1999) and X-SHAPE (Stoe & Cie, 2001)]	k = −6→8
T_min = 0.145, T_max = 0.220	l = −23→27
8065 measured reflections

Refinement top

Refinement on F	108 parameters
R[F > 3σ(F)] = 0.044	Weighting scheme based on measured s.u.'s w = 1/(σ²(F) + 0.0004F²)
wR(F) = 0.064	(Δ/σ)_max = 0.018
S = 1.48	Δρ_max = 3.82 e Å⁻³
3246 reflections	Δρ_min = −3.94 e Å⁻³

Crystal data top

Co_3.617Mg_1.383Cl₂(TeO₃)₄	V = 1401.81 (13) Å³
M_r = 1020.08	Z = 4
Monoclinic, C2/c	Mo Kα radiation
a = 19.8551 (11) Å	µ = 12.87 mm⁻¹
b = 5.2584 (2) Å	T = 292 K
c = 16.4637 (10) Å	0.11 × 0.10 × 0.08 mm
β = 125.3607 (7)°

Data collection top

Oxford Diffraction Xcalibur3 diffractometer	3246 independent reflections
Absorption correction: numerical [X-RED (Stoe & Cie, 1999) and X-SHAPE (Stoe & Cie, 2001)]	2376 reflections with I > 3σ(I)
T_min = 0.145, T_max = 0.220	R_int = 0.056
8065 measured reflections

Refinement top

R[F > 3σ(F)] = 0.044	108 parameters
wR(F) = 0.064	Δρ_max = 3.82 e Å⁻³
S = 1.48	Δρ_min = −3.94 e Å⁻³
3246 reflections

Special details top

Refinement. Single crystal X-ray data was collected on an Oxford Diffraction Xcalibur3 diffractometer using graphite-monochromated Mo Kα radiation, λ = 0.71073 Å. The intensities of the reflections were integrated using the supplied software CrysAlis (Oxford Diffraction, 2006) by the manufacturer. Numerical absorption correction was performed with the programs X-RED (Stoe & Cie, 1999) and X-SHAPE (Stoe & Cie, 2001). The structure was solved by direct methods: SHELXS97 (Sheldrick, 1997) and refined by full matrix least squares on F using the program JANA2000 (Petříček et al., 2000). All atoms including the mixed Co and Mg positions were refined with anisotropic temperature parameters. Molecular graphics were prepared with the program DIAMOND (Brandenburg, 1996).

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å²) top

	x	y	z	U_iso*/U_eq	Occ. (<1)
Te1	0.37266 (2)	0.19170 (7)	0.36070 (2)	0.01174 (14)
Te2	0.14654 (2)	0.28795 (7)	0.37921 (2)	0.01156 (13)
Co1	0	−0.2441 (3)	0.25	0.0193 (7)	0.500 (10)
Mg1	0	−0.244 (3)	0.25	0.0193 (7)	0.500 (10)
Co2	0.09308 (5)	−0.22203 (15)	0.47692 (6)	0.0126 (3)	0.874 (7)
Mg2	0.09308 (5)	−0.22203 (15)	0.47692 (6)	0.0126 (3)	0.126 (7)
Co3	−0.01002 (6)	0.22050 (18)	0.38052 (6)	0.0129 (4)	0.685 (8)
Mg3	−0.01002 (6)	0.22050 (18)	0.38052 (6)	0.0129 (4)	0.315 (8)
Cl1	0.25953 (10)	−0.1767 (3)	0.40309 (12)	0.0252 (6)
O1	0.0661 (2)	0.5050 (7)	0.3715 (3)	0.0140 (14)
O2	0.1135 (3)	0.3485 (8)	0.2513 (3)	0.0199 (17)
O3	−0.0733 (2)	0.3903 (7)	0.4283 (3)	0.0144 (15)
O4	0.0777 (2)	0.0109 (7)	0.3549 (3)	0.0144 (15)
O5	−0.0432 (2)	−0.1600 (7)	0.3564 (3)	0.0142 (15)
O6	0.0971 (2)	0.1415 (8)	0.5224 (3)	0.0169 (16)

Atomic displacement parameters (Å²) top

	U¹¹	U²²	U³³	U¹²	U¹³	U²³
Te1	0.01354 (16)	0.01096 (16)	0.01182 (15)	0.00027 (11)	0.00798 (12)	0.00053 (10)
Te2	0.01231 (15)	0.01128 (16)	0.01157 (14)	0.00008 (11)	0.00718 (12)	−0.00018 (10)
Co1	0.0244 (9)	0.0110 (7)	0.0117 (7)	0	0.0041 (6)	0
Mg1	0.0244 (9)	0.0110 (7)	0.0117 (7)	0	0.0041 (6)	0
Co2	0.0178 (4)	0.0093 (4)	0.0134 (4)	0.0010 (3)	0.0107 (3)	0.0004 (3)
Mg2	0.0178 (4)	0.0093 (4)	0.0134 (4)	0.0010 (3)	0.0107 (3)	0.0004 (3)
Co3	0.0161 (5)	0.0106 (5)	0.0149 (4)	0.0008 (3)	0.0107 (4)	0.0006 (3)
Mg3	0.0161 (5)	0.0106 (5)	0.0149 (4)	0.0008 (3)	0.0107 (4)	0.0006 (3)
Cl1	0.0197 (6)	0.0307 (8)	0.0244 (7)	0.0018 (6)	0.0122 (5)	−0.0025 (6)
O1	0.0169 (17)	0.0094 (16)	0.0149 (15)	0.0027 (14)	0.0088 (13)	0.0015 (13)
O2	0.025 (2)	0.0213 (19)	0.0144 (16)	−0.0048 (17)	0.0123 (15)	0.0025 (15)
O3	0.0213 (18)	0.0119 (16)	0.0154 (15)	0.0028 (15)	0.0136 (14)	0.0039 (13)
O4	0.0169 (17)	0.0123 (16)	0.0173 (16)	−0.0040 (14)	0.0118 (14)	−0.0029 (13)
O5	0.0154 (17)	0.0096 (16)	0.0200 (17)	−0.0001 (14)	0.0116 (14)	0.0015 (13)
O6	0.0240 (19)	0.0121 (16)	0.0156 (16)	0.0012 (16)	0.0120 (15)	−0.0002 (14)

Geometric parameters (Å, º) top

Te1—O2ⁱ	2.706 (5)	M2—Mg3	2.8920 (7)
Te1—O3ⁱⁱ	1.876 (4)	M2—Cl1^viii	2.4616 (16)
Te1—O5ⁱⁱⁱ	1.881 (5)	M2—O1^v	2.069 (4)
Te1—O6^iv	1.870 (4)	M2—O3^ix	2.020 (5)
Te2—O1	1.907 (5)	M2—O4	2.218 (5)
Te2—O2	1.834 (5)	M2—O5	2.270 (3)
Te2—O4	1.876 (4)	M2—O6	2.037 (4)
M1—O1^v	2.104 (4)	M3—O1	2.191 (5)
M1—O1^vi	2.104 (4)	M3—O2^vii	2.056 (3)
M1—O4	2.019 (3)	M3—O3	2.035 (5)
M1—O4^vii	2.019 (3)	M3—O4	2.296 (5)
M1—O5	2.397 (6)	M3—O5	2.072 (4)
M1—O5^vii	2.397 (6)	M3—O6	2.098 (3)
M2—M3	2.8920 (12)

O2ⁱ—Te1—O3ⁱⁱ	65.95 (16)	Cl1^viii—M2—O4	108.86 (13)
O2ⁱ—Te1—O5ⁱⁱⁱ	78.97 (17)	Cl1^viii—M2—O5	174.24 (13)
O2ⁱ—Te1—O6^iv	156.31 (14)	Cl1^viii—M2—O6	97.62 (11)
O3ⁱⁱ—Te1—O5ⁱⁱⁱ	99.06 (19)	O1^v—M2—O3^ix	105.78 (17)
O3ⁱⁱ—Te1—O6^iv	93.00 (17)	O1^v—M2—O4	77.91 (16)
O5ⁱⁱⁱ—Te1—O6^iv	94.6 (2)	O1^v—M2—O5	76.57 (16)
O1—Te2—O2	95.2 (2)	O1^v—M2—O6	153.49 (16)
O1—Te2—O4	88.37 (19)	O3^ix—M2—O4	162.76 (17)
O2—Te2—O4	99.07 (18)	O3^ix—M2—O5	94.10 (17)
O1^v—M1—O1^vi	102.34 (15)	O3^ix—M2—O6	96.4 (2)
O1^v—M1—O4	81.71 (14)	O4—M2—O5	70.09 (17)
O1^v—M1—O4^vii	167.7 (2)	O4—M2—O6	76.70 (17)
O1^v—M1—O5	73.18 (17)	O5—M2—O6	87.68 (14)
O1^v—M1—O5^vii	121.38 (17)	O1—M3—O2^vii	90.70 (17)
O1^vi—M1—O1^v	102.34 (15)	O1—M3—O3	109.33 (18)
O1^vi—M1—O4	167.7 (2)	O1—M3—O4	71.91 (16)
O1^vi—M1—O4^vii	81.71 (14)	O1—M3—O5	143.3 (2)
O1^vi—M1—O5	121.38 (17)	O1—M3—O6	85.17 (16)
O1^vi—M1—O5^vii	73.18 (17)	O2^vii—M3—O3	78.53 (19)
O4—M1—O4^vii	96.75 (15)	O2^vii—M3—O4	111.34 (19)
O4—M1—O5	70.82 (18)	O2^vii—M3—O5	95.80 (15)
O4—M1—O5^vii	94.78 (18)	O2^vii—M3—O6	172.04 (17)
O4^vii—M1—O4	96.75 (15)	O3—M3—O4	170.13 (13)
O4^vii—M1—O5	94.78 (18)	O3—M3—O5	107.4 (2)
O4^vii—M1—O5^vii	70.82 (18)	O3—M3—O6	96.41 (18)
O5—M1—O5^vii	158.73 (15)	O4—M3—O5	72.10 (18)
O5^vii—M1—O5	158.73 (15)	O4—M3—O6	73.83 (17)
Cl1^viii—M2—O1^v	97.67 (12)	O5—M3—O6	91.56 (14)
Cl1^viii—M2—O3^ix	87.56 (12)

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

Experimental details

Crystal data
Chemical formula	Co_3.617Mg_1.383Cl₂(TeO₃)₄
M_r	1020.08
Crystal system, space group	Monoclinic, C2/c
Temperature (K)	292
a, b, c (Å)	19.8551 (11), 5.2584 (2), 16.4637 (10)
β (°)	125.3607 (7)
V (Å³)	1401.81 (13)
Z	4
Radiation type	Mo Kα
µ (mm⁻¹)	12.87
Crystal size (mm)	0.11 × 0.10 × 0.08

Data collection
Diffractometer	Oxford Diffraction Xcalibur3
Absorption correction	Numerical [X-RED (Stoe & Cie, 1999) and X-SHAPE (Stoe & Cie, 2001)]
T_min, T_max	0.145, 0.220
No. of measured, independent and observed [I > 3σ(I)] reflections	8065, 3246, 2376
R_int	0.056
(sin θ/λ)_max (Å⁻¹)	0.843

Refinement
R[F > 3σ(F)], wR(F), S	0.044, 0.064, 1.48
No. of reflections	3246
No. of parameters	108
No. of restraints	?
Δρ_max, Δρ_min (e Å⁻³)	3.82, −3.94

Computer programs: CrysAlis CCD (Oxford Diffraction, 2006), CrysAlis RED (Oxford Diffraction, 2006), CrysAlis RED, SHELXS97 (Sheldrick, 1997), JANA2000 (Petříček et al., 2000), DIAMOND (Bergerhoff, 1996), JANA2000.

Selected bond lengths (Å) top

Te1—O3ⁱ	1.876 (4)	M2—Cl1^vii	2.4616 (16)
Te1—O5ⁱⁱ	1.881 (5)	M2—O1^iv	2.069 (4)
Te1—O6ⁱⁱⁱ	1.870 (4)	M2—O3^viii	2.020 (5)
Te2—O1	1.907 (5)	M2—O4	2.218 (5)
Te2—O2	1.834 (5)	M2—O5	2.270 (3)
Te2—O4	1.876 (4)	M2—O6	2.037 (4)
M1—O1^iv	2.104 (4)	M3—O1	2.191 (5)
M1—O1^v	2.104 (4)	M3—O2^vi	2.056 (3)
M1—O4	2.019 (3)	M3—O3	2.035 (5)
M1—O4^vi	2.019 (3)	M3—O4	2.296 (5)
M1—O5	2.397 (6)	M3—O5	2.072 (4)
M1—O5^vi	2.397 (6)	M3—O6	2.098 (3)

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

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