Li₃Sc(MoO₄)₃: substitutional disorder on three (Li,Sc) sites

Li₃Sc(MoO₄)₃, trilithium scandium trimolybdate(VI), is isotypic with its Fe^III analogue and a number of Li₃M^III(MoO₄)₃ and Li₂M^II₂(MoO₄)₃ compounds. It contains three substitutionally disordered (Li,Sc) sites; two of these show octahedral coordination and contain about 42 and 25% Sc, whereas the third site has a trigonal-prismatic environment and contains only about 8% Sc. The average (Li,Sc)-O bond lengths are 2.092, 2.129, and 2.195 Å, respectively. The (Li,Sc)O₆ polyhedra share either faces or edges with equivalent polyhedra to form columns and zigzag chains, all running parallel to [100]. These building units are connected, via two non-equivalent MoO₄ tetrahedra (average Mo-O bond length 1.771 Å), into a three-dimensional framework.

Key indicators

• Single-crystal X-ray study
• T = 293 K
• Mean [sigma](Mo-O) = 0.002 Å
• R factor = 0.023
• wR factor = 0.058
• Data-to-parameter ratio = 14.9

checkCIF results

No syntax errors found

ADDSYM reports no extra symmetry

General Notes



CELLZ_01
         From the CIF: _cell_formula_units_Z    4
         From the CIF: _chemical_formula_sum  Li3 Mo3 O12 Sc1
         TEST: Compare cell contents of formula and atom_site data

         atom    Z*formula  cif sites diff
         Li        12.00     12.03   -0.03
         Mo        12.00     12.00    0.00
         O         48.00     48.00    0.00
         Sc         4.00      3.97    0.03
          Difference between formula and atom_site contents detected.
          ALERT: check formula stoichiometry or atom site occupancies.

---

S1. Comment

During flux-growth preparation in air of compounds in the system Sc₂O₃–Al₂O₃–TiO₂–SiO₂, the title compound was obtained as a by-product from an Li-rich molybdate flux. Li₃Sc(MoO₄)₃ crystallizes in space group Pnma and is isotypic with Li₃Fe(MoO₄)₃ (Klevtsova & Magarill, 1970). The pale-green Fe^III member forms a solid solution series with black Li₂Fe^II₂(MoO₄)₃ (Klevtsov, 1970; Klevtsova & Magarill, 1970). In fact, a number of isotypic (space group Pnma) Li₃M^III(MoO₄)₃ and Li₂M^II₂(MoO₄)₃ compounds are known, although the crystal structures of the M^III members have only been refined for the above-mentioned Fe^III representative.

Li₃M^III(MoO₄)₃ members with M^III = Fe, Al, Sc, Ga, In, and Cr were prepared by Klevtsov (1970) and Trunov & Efremov (1971). The In member has also been studied by Velikodnyi et al. (1970). Li₃Cr(MoO₄)₃ has been further characterized by Butukhanov et al. (1972), Trunov & Velikodnyi (1972), and Mokhosoev et al. (1973), and the members for M^III = Al and In were described by Kozhevnikova et al. (1980). Li₃Ga(MoO₄)₃ was observed by Alekseev et al. (1982) as one of the products of the reaction between Li₂MoO₄ and Ga₂(SO₄)₃. Porotnikov et al. (1982) prepared Li₃Sc(MoO₄)₃ and stated that it melts congruently at 1109 K, and decomposes to Li₂MoO₄ and LiSc(MoO₄)₂ at less than 810 K. IR spectroscopic studies of Li₃M^III(MoO₄)₃ members with M^III = Al, In, Cr, Fe, and Co were reported by Juri et al. (1984, 1992).

Li₂M^II₂(MoO₄)₃ compounds with M^II = Mg, Fe, Co, Ni, Cu, and Zn have been prepared by Efremov & Trunov (1975) and Penkova & Klevtsov (1977). Independently of the latter authors, the structure of Li₂Ni₂(MoO₄)₃ was reported by Ozima et al. (1977), who also presented a detailed discussion of the structure type. [Note that the z coordinate for the site designated `M1–Li' is misprinted in the original publication on Li₂Ni₂(MoO₄)₃ (Ozima et al., 1977), and also in the ICSD entry 1082 (Belsky et al., 2002) for this structure; the correct value, found by trial and error, must be 0.7568 (instead of 0.5568).] The crystal structure of Li_2–2xMn_{2 + x}(MoO₄)₃ (x = 1/5) was determined by Solodovnikov et al. (1994), and Li₂Co₂(MoO₄)₃ was structurally characterized by Wiesmann et al. (1995). Results from both studies confirm the previous results of Ozima et al. (1977).

Li₂Cu₂(MoO₄)₃ was reported to have the monoclinic space group P2₁/c (Wiesmann et al., 1994), but a close examination showed that the topology is identical to that of the Pnma-type Li₂M^II₂(MoO₄)₃ compounds, and a search for higher symmetry using PLATON (Spek, 2000, 2003) clearly suggested that the correct space group for Li₂Cu₂(MoO₄)₃ is probably also Pnma. A dimorph of Li₂Fe₂(MoO₄)₃, garnet-related and crystallizing in space group Pbcn, was structurally characterized by Torardi & Prince (1986) and Torardi et al. (1988). We also point out that `NaCo_2.31(MoO₄)₃' (Ibers & Smith, 1964; later shown to be rather Na₂Co^II₂(MoO₄)₃ by Klevtsova & Magarill, 1970) is isostructural with the Pnma-type Li₃M^III(MoO₄)₃ and Li₂M^II₂(MoO₄)₃ compounds listed above, and in fact represents the first solution of the common crystal structure.

The atomic arrangement in Li₃Sc(MoO₄)₃ is based on a three-dimensional framework of (Li,Sc)O₆ polyhedra linked to MoO₄ tetrahedra (Figs. 1–3). There are two distinct types of (Li,Sc)O₆ polyhedra: the first two (Li,Sc) sites, Li1 and Li2, show a nearly regular octahedral coordination (Table 1), whereas the third site, Li3, has a regular trigonal-prismatic environment (Figs. 1 and 2). The Li1 and Li2 sites contain about 42 and 25% Sc, whereas the trigonal-prismatic site (Li3) contains only about 8% Sc. The average (Li,Sc)—O bond lengths for the octahedrally coordinated Li1 and Li2 sites are 2.092 and 2.129 Å, respectively, whereas the corresponding value in the trigonal-prismatic (Li3,Sc)O₆ polyhedron is 2.195 Å. Thus, an increasing Li content on a specific sites causes a slight increase in average (Li,Sc)—O bond lengths, if the influences of the polyhedral geometry and distortion are neglected. This increase is in agreement with literature data on the size and geometry of LiO₆ and ScO₆ polyhedra; the average Li—O bond length for (more or less) octahedrally coordinated Li sites in a large number of oxidic Li compounds was calculated to be 2.15 Å (Wenger & Armbruster, 1991), whereas octahedrally coordinated Sc has an average Sc—O bond length of 2.105 Å (Baur, 1981). In Li₃Fe(MoO₄)₃ (Klevtsova & Magarill, 1970), the corresponding values for the (Li1,Fe), (Li2,Fe), and (Li3,Fe) sites are 2.046, 2.091, and 2.164 Å, respectively. Thus, the overall trend is identical.

A closer look at the connectivity within the framework structure of the title compound (Figs. 1 and 2) shows that it contains chains of face-sharing fairly regular (Li1,Sc)O₆ octahedra which run parallel to [100], zigzag chains of edge-sharing, somewhat distorted, (Li2,Sc)O₆ octahedra, which also run parallel to [100], and finally (Li3,Sc)O₆ regular trigonal prisms which share prism edges to form zigzag chains, again parallel to [100]. These three (Li,Sc)O₆ polyhedra share corners with two non-equivalent MoO₄ tetrahedra. The latter show relatively small angular distortions (Table 1) and similar average Mo—O bond lengths of 1.769 (Mo1) and 1.772 Å (Mo2), respectively. In Li₃Fe(MoO₄)₃ (Klevtsova & Magarill, 1970), the average Mo—O bond length is only slightly larger, 1.781 Å.

The topology of the structure type can also be described as close-packed sheets of O atoms, composed of three-square-wide bands of the No. 9 regular net of Wells (1952) held together by semi-regular single chains of triangles; regular and semi-regular voids between the O atoms are filled by the Li and M^III/M^IIcations (see Ozima et al., 1977, for further details).

The fact that the trigonal–prismatic site in Li₃Sc(MoO₄)₃, Li3, contains about 8% Sc seems to distinguish it from Li₃Fe(MoO₄)₃, for which the equivalent site was reported to be occupied by Li only (Klevtsova & Magarill, 1970). Comparable minor discrepancies were noted for Li₂Co₂(MoO₄)₃ by Wiesmann et al. (1995) who stated that three positions for Co were determined for their compound instead of two as reported by Penkova & Klevtsov (1977); all three positions are partially occupied by Co and Li with different site occupations, with the highest Li:Co ratio being 0.79:0.21 on the trigonal-prismatic site, and the lowest Li:Co ratio being 0.34:0.66 on the edge-sharing octahedral site. Nonetheless, in Li₂Ni₂(MoO₄)₃, the trigonal-prismatic site was found to be occupied by Li only (Ozima et al., 1977), and in `NaCo_2.31(MoO₄)₃' [= Na₂Co^II₂(MoO₄)₃; Klevtsova & Magarill, 1970], the same site hosted Na only (Ibers & Smith, 1964). Although modern data collections and refinements might reveal small amounts of M cations on the trigonal-prismatic site in all these structures, the respective occupancies may all be dependent on temperature of formation or kinetic influences, availability of cations, and also possible oxidation of M^II cations. The common framework structure type is relatively flexible in adapting to different Li:M ratios on the three different (Li/M) sites (Ozima et al., 1977).

By comparison with the isostructural Li₃Fe(MoO₄)₃ (Klevtsova & Magarill, 1970), all unit-cell parameters of the Sc member are enlarged, and the cell volume is increased by 2.56%. This is expected from the average M—O bond lengths of six-coordinated Sc and Fe^III (2.105 and 2.011 Å, respectively; Baur, 1981). The presently determined unit-cell parameters of the title compound are, except for the parameter a, slightly smaller than those refined earlier from X-ray powder diffraction data, a = 5.12 (10), b = 10.65 (7), c = 17.86 (5) Å and V = 974 ų (Klevtsov, 1970; note: s.u. values estimated from error bars given in Fig. 2 of Klevtsov's paper). Unit-cell parameters given for `LiSc(MoO₄)₂', a = 5.12 (1), b = 10.52 (2), c = 17.86 (2) Å and V = 962 ų (Porotnikov et al., 1982; ICDD-PDF 36–207), suggest that this compound is in fact more likely to be Li₃Sc(MoO₄)₃.

Although Li₃Al(MoO₄)₃ is known to exist (Klevtsov, 1970; Trunov & Efremov, 1971; Kozhevnikova et al., 1980), and the flux used for crystal growth contained dissolved Al^III ions, the chemical analyses showed that the crystals of the title compound contained no Al. Thus, Sc strongly partitions into Li₃Sc(MoO₄)₃, whereas Al was completely used up by (earlier?) crystallization of the accompanying LiAl₅O₈ octahedra (see Experimental).

S2. Experimental

The title compound crystallized as a very minor component from an Li-rich flux (experimental parameters: 0.6 g LiF, 1.67 g MoO₃, 0.1726 g Sc₂O₃, 0.1276 g A l₂O₃, 0.1999 g TiO₂; Pt crucible covered with a lid, T_max = 1423 K, holding time 6 h, cooling rate 1.5 K min^-1, T_min = 1173 K, slow cooling to room temperature after switching off furnace). Li₃Sc(MoO₄)₃ formed colourless-to-white acicular crystals (up to ca 0.5 mm in length), often in bundle-like subparallel intergrowths. The crystals were accompanied by large amounts of LiAl₅O₈ (colourless sharp octahedra), and minor amounts of an Al-rich member of the solid-solution series Sc₂TiO₅—Al₂TiO₅ (Kolitsch & Tillmanns, 2003). Chemical analyses of the title compound with standard semiquantitative SEM-EDS showed the presence of only Sc and Mo (Li cannot be detected under these conditions).

S3. Refinement

A freely refined model gave Li:Sc occupancy ratios of 0.639 (3):0.361 (3), 0.751 (3):0.249 (3) and 0.925 (3):0.075 (3) for the Li1, Li2 and Li3 sites, respectively, which would correspond to 5.88 positive charges and 6.00 negative charges in the formula unit. However, the Li1 and, to a lesser extent, the Li3 site show somewhat anisotropic displacement parameters, an observation which indicates that refined Li:Sc occupancy ratios are certainly influenced by the anisotropic behavior of the atoms on these sites (neglecting all other possible influences). In the final refinement, the Li:Sc ratio on the Li1 site was slightly modified and fixed at 58:42, in order to achieve a charge-balanced formula.

Computing details

Data collection: COLLECT (Nonius, 2002); cell refinement: HKL SCALEPACK (Otwinowski & Mino, 1997); data reduction: HKL DENZO (Otwinowski & Mino, 1997) and SCALEPACK; program(s) used to solve structure: SHELXS97 (Sheldrick, 1997); program(s) used to refine structure: SHELXL97 (Sheldrick, 1997); molecular graphics: ATOMS (Shape Software, 1999) and ORTEP-3 for Windows (Farrugia, 1997); software used to prepare material for publication: SHELXL97.

Figures

	Fig. 1. Prespective view of the framework structure of Li3Sc(MoO4)3 along [100], the direction of the polyhedral columns and zigzag chains of the (Li1,Sc1)O6 and (Li2,Sc2)O6 octahedra (grey), and (Li3,Sc3)O6 trigonal pyramids (blue). MoO4 tetrahedra are yellow and marked with crosses. The unit cell is outlined.
	Fig. 2. The structure of Li3Sc(MoO4)3 projected along [010], allowing a view perpendicular to the polyhedral columns and zigzag chains of the (Li1,Sc1)O6 and (Li2,Sc2)O6 octahedra (grey), and (Li3,Sc3)O6 trigonal pyramids (blue).
	Fig. 3. View of the atoms in the asymmetric unit of Li3Sc(MoO4)3, shown with anisotropic displacement ellipsoids at the 50% probability level. [Symmetry codes: (i) x + 1, y, z; (ii) x, -y + 1/2, z.]

trilithium scandium trimolybdate(VI)

Crystal data

Li3Mo3O12Sc	F(000) = 1008
Mr = 545.60	Dx = 3.770 Mg m^−3
Orthorhombic, Pnma	Mo Kα radiation, λ = 0.71073 Å
Hall symbol: -P 2ac 2n	Cell parameters from 1670 reflections
a = 5.130 (1) Å	θ = 2.0–30.0°
b = 10.560 (2) Å	µ = 4.56 mm^−1
c = 17.745 (4) Å	T = 293 K
V = 961.3 (3) Å^3	Fragment, colorless
Z = 4	0.10 × 0.05 × 0.05 mm

Data collection

Nonius KappaCCD diffractometer	1477 independent reflections
Radiation source: fine-focus sealed tube	1326 reflections with I > 2σ(I)
Graphite monochromator	Rint = 0.011
ψ and ω scans	θmax = 30.1°, θmin = 2.3°
Absorption correction: multi-scan (HKL SCALEPACK; Otwinowski & Minor, 1997)	h = −7→7
Tmin = 0.659, Tmax = 0.804	k = −14→14
2635 measured reflections	l = −24→24

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)] = 0.023	w = 1/[σ^2(Fo^2) + (0.024P)^2 + 2P] where P = (Fo^2 + 2Fc^2)/3
wR(F^2) = 0.058	(Δ/σ)max = 0.001
S = 1.12	Δρmax = 0.96 e Å^−3
1477 reflections	Δρmin = −0.84 e Å^−3
99 parameters	Extinction correction: SHELXL97, Fc^*=kFc[1+0.001xFc^2λ^3/sin(2θ)]^-1/4
2 restraints	Extinction coefficient: 0.0018 (3)

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)
Mo1	0.27559 (5)	0.52755 (2)	0.156515 (13)	0.01468 (9)
Mo2	0.77812 (6)	0.2500	0.057110 (18)	0.01320 (10)
Li1	0.1048 (5)	0.2500	0.25027 (10)	0.0289 (4)	0.58
Sc1	0.1048 (5)	0.2500	0.25027 (10)	0.0289 (4)	0.42
Li2	0.7547 (3)	0.57420 (15)	0.02731 (9)	0.0129 (4)	0.751 (3)
Sc2	0.7547 (3)	0.57420 (15)	0.02731 (9)	0.0129 (4)	0.249 (3)
Li3	0.2446 (9)	0.7500	0.3018 (3)	0.0237 (13)	0.925 (3)
Sc3	0.2446 (9)	0.7500	0.3018 (3)	0.0237 (13)	0.075 (3)
O1	0.8588 (6)	0.2500	0.15432 (16)	0.0201 (6)
O2	0.0531 (6)	0.2500	−0.00495 (16)	0.0194 (6)
O3	0.5831 (4)	0.1167 (2)	0.03722 (11)	0.0201 (4)
O4	0.0838 (4)	0.4902 (2)	0.07587 (11)	0.0199 (4)
O5	0.0797 (4)	0.6233 (2)	0.21271 (12)	0.0240 (5)
O6	0.3528 (4)	0.38437 (19)	0.20513 (11)	0.0195 (4)
O7	0.5554 (4)	0.61262 (19)	0.12713 (12)	0.0208 (4)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Mo1	0.01428 (14)	0.01484 (14)	0.01493 (14)	0.00046 (8)	−0.00045 (8)	0.00130 (8)
Mo2	0.01243 (16)	0.01373 (17)	0.01345 (16)	0.000	0.00018 (11)	0.000
Li1	0.0522 (12)	0.0172 (7)	0.0172 (8)	0.000	0.0012 (8)	0.000
Sc1	0.0522 (12)	0.0172 (7)	0.0172 (8)	0.000	0.0012 (8)	0.000
Li2	0.0112 (7)	0.0150 (8)	0.0125 (8)	0.0003 (5)	0.0007 (5)	0.0022 (6)
Sc2	0.0112 (7)	0.0150 (8)	0.0125 (8)	0.0003 (5)	0.0007 (5)	0.0022 (6)
Li3	0.017 (2)	0.023 (3)	0.031 (3)	0.000	0.0049 (18)	0.000
Sc3	0.017 (2)	0.023 (3)	0.031 (3)	0.000	0.0049 (18)	0.000
O1	0.0230 (15)	0.0185 (14)	0.0189 (14)	0.000	−0.0035 (11)	0.000
O2	0.0171 (14)	0.0184 (13)	0.0227 (14)	0.000	0.0026 (11)	0.000
O3	0.0180 (10)	0.0219 (10)	0.0203 (10)	−0.0021 (8)	−0.0015 (8)	−0.0009 (8)
O4	0.0167 (10)	0.0240 (10)	0.0190 (9)	0.0011 (8)	−0.0006 (8)	0.0014 (8)
O5	0.0226 (11)	0.0256 (11)	0.0237 (10)	0.0031 (9)	0.0005 (8)	−0.0030 (9)
O6	0.0208 (10)	0.0196 (10)	0.0183 (9)	0.0005 (8)	−0.0006 (8)	0.0019 (8)
O7	0.0203 (10)	0.0209 (10)	0.0210 (10)	−0.0030 (8)	0.0007 (8)	−0.0005 (8)

Geometric parameters (Å, º)

Mo1—O5	1.740 (2)	Li1—O1^iv	2.136 (4)
Mo1—O7	1.772 (2)	Li2—O7	2.085 (3)
Mo1—O4	1.781 (2)	Li2—O4^ii	2.093 (3)
Mo1—O6	1.785 (2)	Li2—O4^vi	2.122 (3)
Mo2—O3	1.762 (2)	Li2—O3^vii	2.125 (2)
Mo2—O3^i	1.762 (2)	Li2—O2^vi	2.139 (2)
Mo2—O1	1.774 (3)	Li2—O3^i	2.207 (3)
Mo2—O2^ii	1.790 (3)	Li3—O7^viii	2.153 (4)
Li1—O6	2.067 (3)	Li3—O7^iv	2.153 (4)
Li1—O6^i	2.067 (3)	Li3—O5^ix	2.193 (4)
Li1—O6^iii	2.076 (3)	Li3—O5^x	2.193 (4)
Li1—O6^iv	2.076 (3)	Li3—O5	2.237 (5)
Li1—O1^v	2.119 (4)	Li3—O5^xi	2.237 (5)
O5—Mo1—O7	109.99 (10)	O4^ii—Li2—O4^vi	84.51 (10)
O5—Mo1—O4	105.68 (10)	O7—Li2—O3^vii	90.97 (10)
O7—Mo1—O4	108.86 (10)	O4^ii—Li2—O3^vii	165.77 (12)
O5—Mo1—O6	110.09 (10)	O4^vi—Li2—O3^vii	85.48 (10)
O7—Mo1—O6	113.08 (10)	O7—Li2—O2^vi	102.40 (11)
O4—Mo1—O6	108.87 (9)	O4^ii—Li2—O2^vi	94.14 (11)
O3—Mo2—O3^i	105.98 (14)	O4^vi—Li2—O2^vi	86.46 (11)
O3—Mo2—O1	109.10 (9)	O3^vii—Li2—O2^vi	95.31 (11)
O3^i—Mo2—O1	109.10 (9)	O7—Li2—O3^i	85.10 (9)
O3—Mo2—O2^ii	108.92 (9)	O4^ii—Li2—O3^i	84.36 (10)
O3^i—Mo2—O2^ii	108.92 (9)	O4^vi—Li2—O3^i	86.08 (10)
O1—Mo2—O2^ii	114.49 (14)	O3^vii—Li2—O3^i	84.89 (10)
O6—Li1—O6^i	86.70 (14)	O2^vi—Li2—O3^i	172.49 (12)
O6—Li1—O6^iii	179.42 (14)	O7^viii—Li3—O7^iv	84.7 (2)
O6^i—Li1—O6^iii	93.54 (9)	O7^viii—Li3—O5^ix	90.64 (12)
O6—Li1—O6^iv	93.54 (9)	O7^iv—Li3—O5^ix	146.4 (3)
O6^i—Li1—O6^iv	179.42 (15)	O7^viii—Li3—O5^x	146.4 (3)
O6^iii—Li1—O6^iv	86.21 (14)	O7^iv—Li3—O5^x	90.64 (12)
O6—Li1—O1^v	93.16 (11)	O5^ix—Li3—O5^x	75.16 (18)
O6^i—Li1—O1^v	93.16 (11)	O7^viii—Li3—O5	130.3 (2)
O6^iii—Li1—O1^v	86.29 (11)	O7^iv—Li3—O5	80.82 (12)
O6^iv—Li1—O1^v	86.29 (11)	O5^ix—Li3—O5	125.3 (2)
O6—Li1—O1^iv	86.09 (11)	O5^x—Li3—O5	81.30 (13)
O6^i—Li1—O1^iv	86.09 (11)	O7^viii—Li3—O5^xi	80.82 (12)
O6^iii—Li1—O1^iv	94.46 (10)	O7^iv—Li3—O5^xi	130.3 (2)
O6^iv—Li1—O1^iv	94.46 (10)	O5^ix—Li3—O5^xi	81.30 (13)
O1^v—Li1—O1^iv	178.97 (18)	O5^x—Li3—O5^xi	125.3 (2)
O7—Li2—O4^ii	97.36 (10)	O5—Li3—O5^xi	73.4 (2)
O7—Li2—O4^vi	170.75 (12)

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