NaSr(AsO₄)(H₂O)₉: the (Sr,As) analogue of nabaphite and nastrophite

The crystal structure of the title compound, sodium strontium orthoarsenate(V) nona­hydrate, is isotypic with NaSr(PO₄)(H₂O)₉ and the minerals nabaphite [NaBa(PO₄)(H₂O)₉] and nastrophite [Na(Sr,Ba)(PO₄)(H₂O)₉]. The Na and Sr atoms are located on threefold rotation axes and are in the centres of slightly distorted Na(H₂O)₆ octa­hedra and Sr(H₂O)₉ tricapped trigonal prisms, respectively. A framework structure is established via edge-sharing of these polyhedra. Disordered AsO₄ tetra­hedra (with threefold symmetry) are situated in the inter­stitial space of the framework. Although reasonable H-atom positions of the water mol­ecules were not established, close O⋯O contacts between the disordered AsO₄ tetra­hedra and the water mol­ecules suggest strong O—H⋯O hydrogen bonding.

Related literature

For a previous study of the title compound that revealed cubic symmetry and the lattice parameters, see: Ariguib-Kbir & Guerin (1973). Isotypic structures have been reported for synthetic NaSr(PO₄)(H₂O)₉ (Takagi et al., 1982), nabaphite [NaBa(PO₄)(H₂O)₉] (Baturin et al., 1982) and nastrophite [Na(Sr,Ba)(PO₄)(H₂O)₉] (Baturin et al., 1981). For crystal structures in the Sr—As—O—(H) system, see: Mihajlovic & Effenberger (2006); Weil et al. (2009). As—O bond-length data for tetra­hedrally coordinated arsenic were compiled and computed by Baur (1981) and Schwendtner (2008). For ionic radii, see: Shannon (1976).

Experimental

Crystal data

• NaSr(AsO₄)(H₂O)₉

• M_r = 411.67

• Cubic, P 2₁ 3

• a = 10.6435 (1) Å

• V = 1205.74 (2) ų

• Z = 4

• Mo Kα radiation

• μ = 7.29 mm⁻¹

• T = 296 K

• 0.36 × 0.24 × 0.24 mm

Data collection

• Bruker APEXII CCD diffractometer

• Absorption correction: multi-scan (SADABS; Bruker, 2008) T_min = 0.179, T_max = 0.274

• 41355 measured reflections

• 3435 independent reflections

• 3272 reflections with I > 2σ(I)

• R_int = 0.037

Refinement

• R[F² > 2σ(F²)] = 0.023

• wR(F²) = 0.056

• S = 1.07

• 3435 reflections

• 60 parameters

• H-atom parameters not refined

• Δρ_max = 1.73 e Å⁻³

• Δρ_min = −1.66 e Å⁻³

• Absolute structure: Flack (1983), 1537 Friedel pairs

• Flack parameter: −0.005 (6)

Table 1
Selected interatomic distances (Å)

Sr—O1^i	2.6326 (10)
Sr—O2	2.6558 (10)
Sr—O3^ii	2.6994 (10)
Na—O3^iii	2.3926 (12)
Na—O2^iv	2.4086 (12)

O1⋯O5^v	2.558 (7)
O1⋯O5	2.612 (8)
O1⋯O9^vi	2.623 (8)
O1⋯O6^vii	2.6640 (17)
O1⋯O4	2.7667 (14)
O1⋯O7	2.829 (5)
O1⋯O7^vi	2.919 (5)
O2⋯O9^vi	2.515 (9)
O2⋯O6^vii	2.7488 (17)
O3⋯O8^vi	2.562 (9)
O3⋯O6^vi	2.6949 (17)
O3⋯O9^vi	2.732 (9)
O3⋯O6	2.7492 (17)
O3⋯O5	2.757 (7)
O3⋯O7	2.776 (5)
O3⋯O7^vi	2.930 (5)
Symmetry codes: (i) ; (ii) ; (iii) ; (iv) ; (v) y, z, x; (vi) ; (vii) .

Data collection: APEX2 (Bruker, 2008); cell refinement: SAINT (Bruker, 2008); data reduction: SAINT; program(s) used to solve structure: SHELXS97 (Sheldrick, 2008); program(s) used to refine structure: SHELXL97 (Sheldrick, 2008); molecular graphics: ATOMS for Windows (Dowty, 2006); software used to prepare material for publication: SHELXL97.

Supporting information

S1. Comment

A previous study of NaSr(AsO₄)(H₂O)₉ reports cubic symmetry and the lattice parameter as a = 10.70 Å (Ariguib-Kbir & Guerin, 1973). Moreover, isotypism with NaSr(PO₄)(H₂O)₉ (Takagi et al., 1982) was also revealed. Besides the synthetic phosphate analogue, NaSr(AsO₄)(H₂O)₉ is also isotypic with the minerals nabaphite [NaBa(PO₄)(H₂O)₉] (Baturin et al., 1982) and nastrophite [Na(Sr,Ba)(PO₄)(H₂O)₉] (Baturin et al., 1981).

The crystal structures consist of slightly distorted Na(OH₂)₆ octahedra (3 symmetry) and M(OH₂)₉ tricapped trigonal prisms (3 symmetry), where M = Sr, Ba. These polyhedra share edges and establish a framework structure. Disordered XO₄ tetrahedra (X = P, As; 3 symmetry) are situated in the interstitial space of the framework (Fig. 1).

The Na(H₂O)₆ octahedron is slightly distorted. The corresponding Na—O bond lenghts are in the usual range with an average of 2.40 Å, conform with the values in the isotypic compounds (NaSr(PO₄)(H₂O)₉: 2.41 Å; nabaphite: 2.42 Å; nastrophite: 2.42 Å) and the sum of the ionic radii of 2.41 Å, as calculated for six-coordinated Na (Shannon, 1976).

The Sr²⁺ ion is surrounded by 9 oxygen atoms with an average Sr—O distance of 2.663 Å, in good agreement with the phosphate analogue (2.668 Å; Takagi et al., 1982) and the sum of the ionic radii of 2.67 Å, as calculated for nine-coordinated Sr (Shannon, 1976).

The environment of the disordered AsO₄ group consists of 16 water molecules with donor (D) — acceptor (A) distances between 2.5 and 3.0 Å (see Table 2). The overcrowding of water molecules (only 12 surrounding O atoms are expected, considering an ordered tetrahedral configuration for the arsenate unit with three donator atoms) may be the reason for the disorder of the AsO₄ group. The average As—O bond length for the disordered AsO₄ group is 1.685 Å, a value in very good agreement with those of 1.682 Å (Baur, 1981) and 1.686 Å (Schwendtner, 2008).

Related literature

For a previous study of the title compound that revealed cubic symmetry and the lattice parameters, see: Ariguib-Kbir & Guerin (1973). Isotypic structures have been reported for synthetic NaSr(PO₄)(H₂O)₉ (Takagi et al., 1982), nabaphite [NaBa(PO₄)(H₂O)₉] (Baturin et al., 1982) and nastrophite [Na(Sr,Ba)(PO₄)(H₂O)₉] (Baturin et al., 1981). For crystal structures in the Sr—As—O—(H) system, see: Mihajlovic & Effenberger (2006); Weil et al. (2009). As—O bond-length data for tetrahedrally coordinated arsenic were compiled and computed by Baur (1981) and Schwendtner (2008). For ionic radii, see: Shannon (1976).

S2. Experimental

Crystals of the title compound were obtained during phase formation studies in the system Sr—As—O (Weil et al., 2009) from hydrous solutions. All chemicals used were of analytical grade and employed without further purification. To a saturated Sr(OH)₂^.8H₂O solution a diluted arsenic acid solution was dropwise added which resulted in a flocculent white precipitate (pH ca. 9). A concentrated NaOH solution was then added until a pH of 12 was reached. The resulting suspension was boiled for an hour. Then the precipitate was filtered off and the remaining solution was left to stand for several days. Besides few crystals of SrHAsO₄ (Mihajlovic & Effenberger, 2006), colourless columnar crystals of the title compound up to several mm in length were obtained after complete evaporation of water.

S3. Refinement

The oxygen atoms O4 and O6 of the arsenate group were clearly discernible from Fourier maps. Consideration of full occupancy of these sites resulted in high electron densities of ca 4 e ų at a distance of ca 1.7 Å from As, indicating other disordered oxygen atoms. Therefore four additional O atoms were considered in the final model. Free refinement of the site occupancy factors (s.o.f.) of all six O atoms attached to arsenic resulted in a composition very close to the theoretical value. In the last refinement cycles the s.o.f.'s were constrained to meet the criterion for electroneutrality. The six disordered O atoms were finally refined with isotropic displacement parameters. No reasonable positions of the H atoms attached to the water molecules (O1, O2, O3) could be found in difference Fourier maps which may be due to the disorder of the AsO₄ tetrahedron and the resulting complex hydrogen bonding scheme. Therefore all H atoms were excluded from the refinement. The highest remaining peak in the final difference Fourier map is 0.49 Å from As and the deepest hole is 0.43 Å from the same atom.

Computing details

Data collection: APEX2 (Bruker, 2008); cell refinement: SAINT (Bruker, 2008); data reduction: SAINT (Bruker, 2008); program(s) used to solve structure: SHELXS97 (Sheldrick, 2008); program(s) used to refine structure: SHELXL97 (Sheldrick, 2008); molecular graphics: ATOMS for Windows (Dowty, 2006); software used to prepare material for publication: SHELXL97 (Sheldrick, 2008).

Figures

Fig. 1. The crystal structure of NaSr(PO4)(H2O)9 in a projection approximately along [001]. Sr atoms are represented as blue spheres and O atoms as white spheres; NaO6 octahedra are given in yellow and AsO4 tetrahedra in red. For clarity, Sr—O bonds are omitted and only one orientation of the disordered AsO4 group is given. Ellipsoids are drawn at the 90% probability level.

sodium strontium orthoarsenate(V) nonahydrate

Crystal data

NaSr(AsO4)(H2O)9	Dx = 2.268 Mg m^−3
Mr = 411.67	Mo Kα radiation, λ = 0.71073 Å
Cubic, P213	Cell parameters from 9782 reflections
Hall symbol: P 2ac 2ab 3	θ = 5.8–45.2°
a = 10.6435 (1) Å	µ = 7.29 mm^−1
V = 1205.74 (2) Å^3	T = 296 K
Z = 4	Fragment, colourless
F(000) = 816	0.36 × 0.24 × 0.24 mm

Data collection

Bruker APEXII CCD diffractometer	3435 independent reflections
Radiation source: fine-focus sealed tube	3272 reflections with I > 2σ(I)
Graphite monochromator	Rint = 0.037
ω and φ scans	θmax = 45.7°, θmin = 5.4°
Absorption correction: multi-scan (SADABS; Bruker, 2008)	h = −21→21
Tmin = 0.179, Tmax = 0.274	k = −20→21
41355 measured reflections	l = −17→17

Refinement

Refinement on F^2	H-atom parameters not refined
Least-squares matrix: full	w = 1/[σ^2(Fo^2) + (0.0274P)^2 + 0.5628P] where P = (Fo^2 + 2Fc^2)/3
R[F^2 > 2σ(F^2)] = 0.023	(Δ/σ)max = 0.001
wR(F^2) = 0.056	Δρmax = 1.73 e Å^−3
S = 1.07	Δρmin = −1.66 e Å^−3
3435 reflections	Extinction correction: SHELXL97 (Sheldrick, 2008), Fc^*=kFc[1+0.001xFc^2λ^3/sin(2θ)]^-1/4
60 parameters	Extinction coefficient: 0.0147 (10)
0 restraints	Absolute structure: Flack (1983), 1537 Friedel pairs
Primary atom site location: structure-invariant direct methods	Absolute structure parameter: −0.005 (6)
Secondary atom site location: difference Fourier map

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)
Sr	0.055001 (8)	0.055001 (8)	0.055001 (8)	0.00459 (3)
As	0.421839 (11)	0.421839 (11)	0.421839 (11)	0.00709 (4)
Na	0.67077 (6)	0.67077 (6)	0.67077 (6)	0.01193 (15)
O1	0.39368 (12)	0.07909 (10)	0.35359 (10)	0.01687 (18)
O2	0.29270 (9)	0.13067 (11)	0.04892 (10)	0.01519 (16)
O3	0.60854 (10)	0.29633 (9)	0.14338 (10)	0.01243 (14)
O4	0.33000 (13)	0.33000 (13)	0.33000 (13)	0.0077 (3)*	0.60
O5	0.4046 (7)	0.3186 (7)	0.3016 (7)	0.0117 (10)*	0.13
O6	0.56151 (12)	0.44234 (13)	0.35120 (12)	0.00759 (17)*	0.60
O7	0.5256 (5)	0.3069 (5)	0.3904 (5)	0.0115 (7)*	0.20
O8	0.5623 (8)	0.3833 (8)	0.4407 (8)	0.0088 (11)*	0.10
O9	0.5627 (8)	0.3668 (8)	0.4973 (8)	0.0084 (11)*	0.10

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Sr	0.00459 (3)	0.00459 (3)	0.00459 (3)	0.00016 (2)	0.00016 (2)	0.00016 (2)
As	0.00709 (4)	0.00709 (4)	0.00709 (4)	−0.00024 (3)	−0.00024 (3)	−0.00024 (3)
Na	0.01193 (15)	0.01193 (15)	0.01193 (15)	0.00126 (17)	0.00126 (17)	0.00126 (17)
O1	0.0319 (5)	0.0088 (3)	0.0098 (3)	0.0043 (3)	−0.0045 (3)	−0.0005 (3)
O2	0.0109 (3)	0.0229 (4)	0.0118 (3)	−0.0039 (3)	0.0002 (3)	0.0007 (3)
O3	0.0130 (3)	0.0111 (3)	0.0132 (3)	0.0024 (3)	−0.0005 (3)	0.0015 (3)

Geometric parameters (Å, º)

Sr—O1^i	2.6326 (10)	As—O9^iv	1.799 (9)
Sr—O1^ii	2.6326 (10)	As—O9^v	1.799 (9)
Sr—O1^iii	2.6326 (10)	Na—O3^ix	2.3926 (12)
Sr—O2^iv	2.6558 (10)	Na—O3^x	2.3926 (12)
Sr—O2	2.6558 (10)	Na—O3^xi	2.3926 (12)
Sr—O2^v	2.6558 (10)	Na—O2^xii	2.4086 (12)
Sr—O3^vi	2.6994 (10)	Na—O2^xiii	2.4086 (12)
Sr—O3^vii	2.6994 (10)	Na—O2^xiv	2.4086 (12)
Sr—O3^viii	2.6994 (10)	O4—O5^iv	0.858 (7)
As—O8^iv	1.563 (8)	O4—O5	0.858 (7)
As—O8	1.563 (8)	O4—O5^v	0.858 (7)
As—O8^v	1.563 (8)	O5—O5^v	1.440 (13)
As—O6	1.6801 (13)	O5—O5^iv	1.440 (13)
As—O6^v	1.6801 (13)	O5—O7	1.602 (9)
As—O6^iv	1.6801 (13)	O6—O8	1.141 (9)
As—O7^iv	1.682 (5)	O6—O9^v	1.462 (9)
As—O7	1.682 (5)	O6—O7	1.549 (5)
As—O7^v	1.682 (5)	O6—O9	1.750 (8)
As—O4	1.693 (2)	O7—O8	1.049 (10)
As—O5^iv	1.697 (7)	O7—O9	1.362 (9)
As—O5	1.697 (7)	O8—O9	0.627 (11)
As—O5^v	1.697 (7)	O9—O6^iv	1.462 (9)
As—O9	1.799 (9)
O1···O5^iv	2.558 (7)	O2···O6^xvi	2.7488 (17)
O1···O5	2.612 (8)	O3···O8^xv	2.562 (9)
O1···O9^xv	2.623 (8)	O3···O6^xv	2.6949 (17)
O1···O6^xvi	2.6640 (17)	O3···O9^xv	2.732 (9)
O1···O4	2.7667 (14)	O3···O6	2.7492 (17)
O1···O7	2.829 (5)	O3···O5	2.757 (7)
O1···O7^xv	2.919 (5)	O3···O7	2.776 (5)
O2···O9^xv	2.515 (9)	O3···O7^xv	2.930 (5)
O1^i—Sr—O1^ii	80.79 (4)	O8^v—As—O5^iv	140.9 (4)
O1^i—Sr—O1^iii	80.79 (4)	O6—As—O5^iv	128.5 (3)
O1^ii—Sr—O1^iii	80.79 (4)	O6^v—As—O5^iv	113.1 (3)
O1^i—Sr—O2^iv	86.96 (4)	O6^iv—As—O5^iv	80.9 (3)
O1^ii—Sr—O2^iv	134.39 (3)	O7^iv—As—O5^iv	56.6 (3)
O1^iii—Sr—O2^iv	140.21 (3)	O7—As—O5^iv	81.6 (3)
O1^i—Sr—O2	140.21 (3)	O7^v—As—O5^iv	106.7 (3)
O1^ii—Sr—O2	86.96 (4)	O8^iv—As—O5	140.9 (4)
O1^iii—Sr—O2	134.39 (3)	O8—As—O5	91.7 (4)
O2^iv—Sr—O2	75.03 (4)	O8^v—As—O5	115.8 (4)
O1^i—Sr—O2^v	134.39 (3)	O6—As—O5	80.9 (3)
O1^ii—Sr—O2^v	140.21 (3)	O6^v—As—O5	128.5 (3)
O1^iii—Sr—O2^v	86.96 (4)	O6^iv—As—O5	113.1 (3)
O2^iv—Sr—O2^v	75.03 (4)	O7^iv—As—O5	106.7 (3)
O2—Sr—O2^v	75.03 (4)	O7—As—O5	56.6 (3)
O1^i—Sr—O3^vi	68.72 (3)	O7^v—As—O5	81.6 (3)
O1^ii—Sr—O3^vi	68.05 (3)	O5^iv—As—O5	50.2 (4)
O1^iii—Sr—O3^vi	138.94 (4)	O8^iv—As—O9	80.4 (4)
O2^iv—Sr—O3^vi	66.55 (3)	O8^v—As—O9	108.7 (4)
O2—Sr—O3^vi	71.58 (3)	O8—As—O9	19.9 (4)
O2^v—Sr—O3^vi	134.06 (3)	O6^v—As—O9	127.1 (3)
O1^i—Sr—O3^vii	68.05 (3)	O6—As—O9	60.3 (3)
O1^ii—Sr—O3^vii	138.94 (4)	O6^iv—As—O9	49.6 (3)
O1^iii—Sr—O3^vii	68.72 (3)	O7^iv—As—O9	104.4 (3)
O2^iv—Sr—O3^vii	71.58 (3)	O7—As—O9	45.9 (3)
O2—Sr—O3^vii	134.06 (3)	O7^v—As—O9	134.8 (3)
O2^v—Sr—O3^vii	66.55 (3)	O4—As—O9	123.4 (3)
O3^vi—Sr—O3^vii	119.992 (1)	O5^iv—As—O9	110.0 (4)
O1^i—Sr—O3^viii	138.94 (4)	O5—As—O9	102.5 (4)
O1^ii—Sr—O3^viii	68.72 (3)	O5^v—As—O9	152.0 (4)
O1^iii—Sr—O3^viii	68.05 (3)	O8^iv—As—O9^iv	19.9 (4)
O2^iv—Sr—O3^viii	134.06 (3)	O8^v—As—O9^iv	80.4 (4)
O2—Sr—O3^viii	66.55 (3)	O8—As—O9^iv	108.7 (4)
O2^v—Sr—O3^viii	71.58 (3)	O6^v—As—O9^iv	49.6 (3)
O3^vi—Sr—O3^viii	119.992 (1)	O6—As—O9^iv	127.1 (3)
O3^vii—Sr—O3^viii	119.992 (1)	O6^iv—As—O9^iv	60.3 (3)
O8^iv—As—O8	99.3 (4)	O7^iv—As—O9^iv	45.9 (3)
O8^iv—As—O8^v	99.3 (4)	O7—As—O9^iv	134.8 (3)
O8—As—O8^v	99.3 (4)	O7^v—As—O9^iv	104.4 (3)
O8^iv—As—O6	130.1 (3)	O4—As—O9^iv	123.4 (3)
O8^v—As—O6	69.2 (3)	O5^iv—As—O9^iv	102.5 (4)
O8^iv—As—O6^v	69.2 (3)	O5—As—O9^iv	152.0 (4)
O8—As—O6^v	130.1 (3)	O5^v—As—O9^iv	110.0 (4)
O6—As—O6^v	109.83 (4)	O9—As—O9^iv	92.6 (4)
O8—As—O6^iv	69.2 (3)	O8^iv—As—O9^v	108.7 (4)
O8^v—As—O6^iv	130.1 (3)	O8^v—As—O9^v	19.9 (4)
O6—As—O6^iv	109.83 (4)	O8—As—O9^v	80.4 (4)
O6^v—As—O6^iv	109.83 (4)	O6^v—As—O9^v	60.3 (3)
O8—As—O7^iv	124.0 (4)	O6—As—O9^v	49.6 (3)
O8^v—As—O7^iv	117.1 (3)	O6^iv—As—O9^v	127.1 (3)
O6—As—O7^iv	164.45 (18)	O7^iv—As—O9^v	134.8 (3)
O6^v—As—O7^iv	76.41 (17)	O7—As—O9^v	104.4 (3)
O6^iv—As—O7^iv	54.87 (18)	O7^v—As—O9^v	45.9 (3)
O8^iv—As—O7	117.1 (3)	O4—As—O9^v	123.4 (3)
O8^v—As—O7	124.0 (4)	O5^iv—As—O9^v	152.0 (4)
O6—As—O7	54.87 (18)	O5—As—O9^v	110.0 (4)
O6^v—As—O7	164.45 (18)	O5^v—As—O9^v	102.5 (4)
O6^iv—As—O7	76.41 (17)	O9—As—O9^v	92.6 (4)
O7^iv—As—O7	117.62 (9)	O9^iv—As—O9^v	92.6 (4)
O8^iv—As—O7^v	124.0 (4)	O3^ix—Na—O3^x	89.64 (5)
O8—As—O7^v	117.1 (3)	O3^ix—Na—O3^xi	89.65 (5)
O6—As—O7^v	76.41 (17)	O3^x—Na—O3^xi	89.64 (5)
O6^v—As—O7^v	54.87 (18)	O3^ix—Na—O2^xii	75.47 (4)
O6^iv—As—O7^v	164.45 (18)	O3^x—Na—O2^xii	155.21 (3)
O7^iv—As—O7^v	117.62 (9)	O3^xi—Na—O2^xii	109.62 (4)
O7—As—O7^v	117.62 (9)	O3^ix—Na—O2^xiii	109.62 (4)
O8^iv—As—O4	118.4 (3)	O3^x—Na—O2^xiii	75.47 (4)
O8—As—O4	118.4 (3)	O3^xi—Na—O2^xiii	155.21 (3)
O8^v—As—O4	118.4 (3)	O2^xii—Na—O2^xiii	90.76 (5)
O6—As—O4	109.11 (5)	O3^ix—Na—O2^xiv	155.21 (3)
O6^v—As—O4	109.11 (5)	O3^x—Na—O2^xiv	109.62 (4)
O6^iv—As—O4	109.11 (5)	O3^xi—Na—O2^xiv	75.47 (4)
O7^iv—As—O4	81.04 (17)	O2^xii—Na—O2^xiv	90.76 (5)
O7—As—O4	81.04 (17)	O2^xiii—Na—O2^xiv	90.76 (5)
O7^v—As—O4	81.04 (17)	Na^xvi—O2—Sr	103.37 (4)
O8^iv—As—O5^iv	91.7 (4)	Na^xvii—O3—Sr^xviii	102.52 (4)
O8—As—O5^iv	115.8 (4)

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