Zn2P2O7 crystallizes in a thortveitite-like structure and features temperature-dependent polymorphism. At high temperatures (T > 500 K), the aristotype phase β-Zn2P2O7 (C2/m, Z = 2, a ≃ 6.60, b ≃ 8.28, c ≃ 4.53 Å, β ≃ 105.4°) is stable. At lower temperatures the lock-in phase α1-Zn2P2O7 [at 350 K: I2/c, Z = 12, a = 20.1131 (13), b = 8.2769 (6), c = 9.109 (3) Å, β = 106.338 (16)°], a sixfold superstructure with commensurate modulation vector q = (1/3, 0, 1/2), is stable. Between the stability ranges of the α1- and β-phases exists the intermediate, incommensurately modulated α2-Zn2P2O7 phase with modulation wavevector q ≃ (0.33, 0, 0.40) and C2/m(α, 0, γ)0s superspace group symmetry. The α1 → α2 lock-in phase transition at TL = 408 K is of first-order and features virtually no hysteresis. It is immediately followed by the second-order α2 → β transition to the non-modulated phase at TI ≃ 430 K. This transformation is sluggish and even at T = 500 K very weak satellite reflections of the α2-phase were observed. Both phase transitions were analyzed with differential scanning calorimetry and high-temperature powder and single-crystal X-ray diffraction. The crystal structures of the α1- and α2-phases were refined from single crystal data collected at T = 350, 400, 405, 410, 415, 420, 425, 430, 450 and 500 K. Different models describing the slow transition from the incommensurately modulated α2- to the non-modulated β-phase were tested. In the model resulting in the best residuals, the bridging O atom of the [P2O7] group, which is located on a 2/m position in the basic structure, is described as an overlap of an atom ordered in internal space and one atom disordered around the mirror plane. The occupancy of the ordered atom decreases with temperature until at T = 500 K virtually only the disordered atom remains. Simultaneously, the amplitude of the modulation functions of the remaining atoms decreases, so that the T = 500 K structure can be considered as the C2/m aristotype structure, although the diffraction pattern still features satellite reflections of first order with very low intensities.
Supporting information
B-IncStrDB reference: 9142Ec1aK6
CCDC references: 1001705; 1001706; 1001707; 1001708; 1001709; 1001710; 1001711; 1001712; 1001713
Data collection: APEX2 (Bruker, 2012) for alpha2_zn2p2o7_400, alpha2_zn2p2o7_405, alpha2_zn2p2o7_410, alpha2_zn2p2o7_415, alpha2_zn2p2o7_420, alpha2_zn2p2o7_430, alpha2_zn2p2o7_450, alpha2_zn2p2o7_500. Cell refinement: SAINT-Plus (Bruker, 2012) for alpha2_zn2p2o7_400, alpha2_zn2p2o7_405, alpha2_zn2p2o7_410, alpha2_zn2p2o7_415, alpha2_zn2p2o7_420, alpha2_zn2p2o7_430, alpha2_zn2p2o7_450, alpha2_zn2p2o7_500. Data reduction: SAINT-Plus (Bruker, 2012) for alpha2_zn2p2o7_400, alpha2_zn2p2o7_405, alpha2_zn2p2o7_410, alpha2_zn2p2o7_415, alpha2_zn2p2o7_420, alpha2_zn2p2o7_430, alpha2_zn2p2o7_450, alpha2_zn2p2o7_500. Program(s) used to solve structure: by isomorphous structure methods for alpha2_zn2p2o7_400, alpha2_zn2p2o7_405, alpha2_zn2p2o7_410, alpha2_zn2p2o7_415, alpha2_zn2p2o7_420, alpha2_zn2p2o7_430, alpha2_zn2p2o7_450, alpha2_zn2p2o7_500. Program(s) used to refine structure: JANA2006 (Petříček, et al., 2006) for alpha2_zn2p2o7_400, alpha2_zn2p2o7_405, alpha2_zn2p2o7_410, alpha2_zn2p2o7_415, alpha2_zn2p2o7_420, alpha2_zn2p2o7_430, alpha2_zn2p2o7_450, alpha2_zn2p2o7_500. Molecular graphics: ATOMS (Dowty, 2006) for alpha2_zn2p2o7_400, alpha2_zn2p2o7_405, alpha2_zn2p2o7_410, alpha2_zn2p2o7_415, alpha2_zn2p2o7_420, alpha2_zn2p2o7_430, alpha2_zn2p2o7_450, alpha2_zn2p2o7_500.
Crystal data top
O7P2Zn2 | F(000) = 1752 |
Mr = 304.7 | Dx = 4.171 Mg m−3 |
Monoclinic, I2/c | Mo Kα radiation, λ = 0.71073 Å |
Hall symbol: -I 2yc | Cell parameters from 9829 reflections |
a = 20.1131 (13) Å | θ = 3.4–35.0° |
b = 8.2769 (6) Å | µ = 10.53 mm−1 |
c = 9.109 (3) Å | T = 350 K |
β = 106.338 (16)° | Triangular fragment, clear colourless |
V = 1455.2 (5) Å3 | 0.45 × 0.33 × 0.03 mm |
Z = 12 | |
Data collection top
Bruker KAPPA APEX II CCD diffractometer | 3215 independent reflections |
Radiation source: X-ray tube | 2822 reflections with I > 3σ(I) |
Graphite monochromator | Rint = 0.037 |
ω and φ scans | θmax = 35.0°, θmin = 2.1° |
Absorption correction: multi-scan SADABS | h = −32→32 |
Tmin = 0.022, Tmax = 0.73 | k = −13→13 |
46498 measured reflections | l = −14→14 |
Refinement top
Refinement on F | 0 constraints |
R[F2 > 2σ(F2)] = 0.016 | Weighting scheme based on measured s.u.'s w = 1/(σ2(F) + 0.0001F2) |
wR(F2) = 0.023 | (Δ/σ)max = 0.002 |
S = 1.47 | Δρmax = 0.82 e Å−3 |
3215 reflections | Δρmin = −0.87 e Å−3 |
151 parameters | Extinction correction: B-C type 1 Gaussian isotropic (Becker & Coppens, 1974) |
0 restraints | Extinction coefficient: 4210 (70) |
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top | x | y | z | Uiso*/Ueq | |
Zn1 | 0.318103 (6) | 0.189033 (13) | 0.023504 (13) | 0.00927 (4) | |
Zn2 | 0.512812 (6) | −0.311694 (13) | 0.477093 (13) | 0.00847 (4) | |
Zn3 | 0.336359 (5) | −0.183166 (14) | −0.001330 (12) | 0.00808 (4) | |
P1 | 0.433584 (11) | 0.01883 (3) | 0.29562 (3) | 0.00537 (6) | |
P2 | 0.261362 (11) | 0.48226 (3) | −0.20166 (3) | 0.00510 (6) | |
P3 | 0.398295 (12) | 0.49306 (3) | −0.28479 (3) | 0.00592 (6) | |
O31 | 0.44822 (4) | −0.13908 (9) | 0.37880 (9) | 0.0138 (2) | |
O32 | 0.41750 (4) | 0.15581 (9) | 0.39221 (8) | 0.00823 (18) | |
O33 | 0.26469 (4) | 0.64249 (9) | −0.11770 (8) | 0.00883 (18) | |
O34 | 0.24690 (4) | 0.34051 (8) | −0.10924 (8) | 0.00868 (18) | |
O35 | 0.38337 (4) | 0.64524 (9) | −0.37560 (9) | 0.0165 (2) | |
O36 | 0.40633 (4) | 0.34861 (9) | −0.38204 (8) | 0.00815 (18) | |
O21 | 0.5 | 0.08403 (13) | 0.25 | 0.0134 (3) | |
O22 | 0.33546 (4) | 0.44334 (10) | −0.21952 (9) | 0.0158 (2) | |
O11 | 0.37651 (4) | 0.00583 (8) | 0.14465 (8) | 0.00797 (17) | |
O12 | 0.21052 (4) | 0.49030 (8) | −0.36065 (7) | 0.00839 (17) | |
O13 | 0.45958 (4) | 0.50579 (8) | −0.14125 (7) | 0.00795 (17) | |
Atomic displacement parameters (Å2) top | U11 | U22 | U33 | U12 | U13 | U23 |
Zn1 | 0.01028 (6) | 0.00581 (6) | 0.00959 (6) | 0.00013 (3) | −0.00070 (4) | −0.00005 (3) |
Zn2 | 0.00869 (6) | 0.00575 (6) | 0.00966 (6) | −0.00011 (3) | 0.00044 (4) | −0.00010 (3) |
Zn3 | 0.00808 (6) | 0.00605 (6) | 0.00953 (6) | 0.00048 (3) | 0.00154 (5) | 0.00005 (3) |
P1 | 0.00512 (9) | 0.00516 (9) | 0.00538 (9) | 0.00050 (7) | 0.00075 (8) | −0.00052 (7) |
P2 | 0.00533 (9) | 0.00520 (9) | 0.00475 (9) | 0.00028 (7) | 0.00140 (7) | −0.00006 (7) |
P3 | 0.00591 (9) | 0.00550 (9) | 0.00550 (9) | 0.00145 (7) | 0.00022 (7) | −0.00097 (7) |
O31 | 0.0176 (3) | 0.0076 (3) | 0.0130 (3) | 0.0036 (3) | −0.0010 (3) | 0.0031 (3) |
O32 | 0.0097 (3) | 0.0072 (3) | 0.0084 (3) | −0.0011 (2) | 0.0035 (2) | −0.0031 (2) |
O33 | 0.0102 (3) | 0.0066 (3) | 0.0100 (3) | −0.0018 (2) | 0.0034 (2) | −0.0035 (2) |
O34 | 0.0107 (3) | 0.0068 (3) | 0.0087 (3) | 0.0014 (2) | 0.0031 (2) | 0.0031 (2) |
O35 | 0.0221 (4) | 0.0082 (3) | 0.0140 (3) | 0.0043 (3) | −0.0033 (3) | 0.0022 (3) |
O36 | 0.0086 (3) | 0.0075 (3) | 0.0088 (3) | −0.0010 (2) | 0.0032 (2) | −0.0040 (2) |
O21 | 0.0073 (4) | 0.0164 (5) | 0.0184 (5) | 0 | 0.0065 (4) | 0 |
O22 | 0.0089 (3) | 0.0228 (4) | 0.0179 (3) | 0.0017 (3) | 0.0071 (3) | −0.0019 (3) |
O11 | 0.0085 (3) | 0.0071 (3) | 0.0063 (3) | 0.0005 (2) | −0.0014 (2) | −0.0007 (2) |
O12 | 0.0109 (3) | 0.0073 (3) | 0.0052 (3) | 0.0012 (2) | −0.0007 (2) | 0.0000 (2) |
O13 | 0.0080 (3) | 0.0076 (3) | 0.0065 (3) | 0.0008 (2) | −0.0010 (2) | −0.0012 (2) |
Geometric parameters (Å, º) top
Zn1—O33i | 2.1123 (9) | Zn3—O11 | 2.0648 (9) |
Zn1—O34 | 2.0275 (9) | Zn3—O12iii | 2.0860 (9) |
Zn1—O35ii | 1.9419 (8) | P1—O31 | 1.4979 (8) |
Zn1—O11 | 2.0416 (8) | P1—O32 | 1.5245 (9) |
Zn1—O12iii | 2.0627 (10) | P1—O21 | 1.6002 (5) |
Zn2—O31 | 1.9688 (8) | P1—O11 | 1.5272 (11) |
Zn2—O32iv | 2.0268 (9) | P2—O33 | 1.5230 (8) |
Zn2—O36v | 2.0688 (9) | P2—O34 | 1.5191 (8) |
Zn2—O13vi | 2.0879 (10) | P2—O22 | 1.5773 (9) |
Zn2—O13vii | 2.0591 (8) | P2—O12 | 1.5213 (11) |
Zn3—O32viii | 2.1321 (9) | P3—O35 | 1.4904 (9) |
Zn3—O33ix | 2.1034 (8) | P3—O36 | 1.5235 (9) |
Zn3—O34i | 2.1923 (9) | P3—O22 | 1.5945 (9) |
Zn3—O36vii | 2.0436 (8) | P3—O13 | 1.5276 (10) |
| | | |
Zn3—Zn1—O33i | 88.38 (2) | O11—Zn3—O12iii | 80.62 (3) |
Zn3—Zn1—O34 | 130.20 (2) | O31—P1—O32 | 113.60 (5) |
Zn3—Zn1—O35ii | 130.88 (2) | O31—P1—O21 | 111.47 (5) |
Zn3—Zn1—O11 | 40.87 (2) | O31—P1—O11 | 112.64 (4) |
Zn3—Zn1—O12iii | 41.55 (2) | O32—P1—O21 | 103.13 (5) |
O33i—Zn1—O34 | 81.36 (3) | O32—P1—O11 | 110.14 (4) |
O33i—Zn1—O35ii | 116.22 (4) | O21—P1—O11 | 105.12 (4) |
O33i—Zn1—O11 | 92.55 (3) | O33—P2—O34 | 112.49 (5) |
O33i—Zn1—O12iii | 93.92 (3) | O33—P2—O22 | 108.68 (4) |
O34—Zn1—O35ii | 96.63 (3) | O33—P2—O12 | 111.27 (4) |
O34—Zn1—O11 | 169.80 (3) | O34—P2—O22 | 103.49 (4) |
O34—Zn1—O12iii | 90.49 (3) | O34—P2—O12 | 112.28 (4) |
O35ii—Zn1—O11 | 93.39 (3) | O22—P2—O12 | 108.20 (5) |
O35ii—Zn1—O12iii | 149.71 (4) | O35—P3—O36 | 112.22 (5) |
O11—Zn1—O12iii | 81.72 (3) | O35—P3—O22 | 111.60 (5) |
O31—Zn2—O32iv | 93.67 (3) | O35—P3—O13 | 113.88 (4) |
O31—Zn2—O36v | 114.37 (4) | O36—P3—O22 | 103.84 (4) |
O31—Zn2—O13vi | 149.23 (4) | O36—P3—O13 | 111.09 (4) |
O31—Zn2—O13vii | 98.55 (3) | O22—P3—O13 | 103.42 (5) |
O32iv—Zn2—O36v | 81.07 (3) | Zn2—O31—P1 | 150.91 (6) |
O32iv—Zn2—O13vi | 92.25 (3) | Zn2iv—O32—Zn3vii | 99.01 (4) |
O32iv—Zn2—O13vii | 167.42 (3) | Zn2iv—O32—P1 | 126.05 (5) |
O36v—Zn2—O13vi | 96.37 (3) | Zn3vii—O32—P1 | 130.94 (4) |
O36v—Zn2—O13vii | 91.14 (3) | Zn1x—O33—Zn3xi | 100.19 (3) |
O13vi—Zn2—O13vii | 78.74 (3) | Zn1x—O33—P2 | 115.75 (4) |
Zn1—Zn3—O32viii | 92.80 (2) | Zn3xi—O33—P2 | 141.04 (5) |
Zn1—Zn3—O33ix | 129.52 (2) | Zn1—O34—Zn3x | 99.98 (3) |
Zn1—Zn3—O34i | 75.972 (18) | Zn1—O34—P2 | 126.50 (5) |
Zn1—Zn3—O36vii | 134.51 (2) | Zn3x—O34—P2 | 127.86 (4) |
Zn1—Zn3—O11 | 40.315 (19) | Zn1xii—O35—P3 | 149.70 (6) |
Zn1—Zn3—O12iii | 40.99 (2) | Zn2v—O36—Zn3viii | 100.56 (3) |
O32viii—Zn3—O33ix | 110.33 (3) | Zn2v—O36—P3 | 125.72 (4) |
O32viii—Zn3—O34i | 168.77 (3) | Zn3viii—O36—P3 | 131.70 (5) |
O32viii—Zn3—O36vii | 79.18 (3) | P1—O21—P1xiii | 140.58 (7) |
O32viii—Zn3—O11 | 90.10 (3) | P2—O22—P3 | 148.95 (6) |
O32viii—Zn3—O12iii | 85.33 (3) | Zn1—O11—Zn3 | 98.82 (3) |
O33ix—Zn3—O34i | 77.83 (3) | Zn1—O11—P1 | 127.36 (4) |
O33ix—Zn3—O36vii | 94.59 (3) | Zn3—O11—P1 | 133.79 (4) |
O33ix—Zn3—O11 | 158.87 (3) | Zn1iii—O12—Zn3iii | 97.46 (3) |
O33ix—Zn3—O12iii | 95.27 (3) | Zn1iii—O12—P2 | 129.06 (4) |
O34i—Zn3—O36vii | 108.45 (3) | Zn3iii—O12—P2 | 132.54 (4) |
O34i—Zn3—O11 | 81.22 (3) | Zn2xiv—O13—Zn2viii | 101.26 (3) |
O34i—Zn3—O12iii | 86.23 (3) | Zn2xiv—O13—P3 | 130.61 (4) |
O36vii—Zn3—O11 | 94.54 (3) | Zn2viii—O13—P3 | 124.74 (4) |
O36vii—Zn3—O12iii | 163.79 (3) | | |
Symmetry codes: (i) −x+1/2, y−1/2, −z; (ii) x, −y+1, z+1/2; (iii) −x+1/2, −y+1/2, −z−1/2; (iv) −x+1, −y, −z+1; (v) −x+1, −y, −z; (vi) −x+1, y−1, −z+1/2; (vii) x, −y, z+1/2; (viii) x, −y, z−1/2; (ix) x, y−1, z; (x) −x+1/2, y+1/2, −z; (xi) x, y+1, z; (xii) x, −y+1, z−1/2; (xiii) −x+1, y, −z+1/2; (xiv) −x+1, y+1, −z+1/2. |
(alpha2_zn2p2o7_400) zinc(II) diphosphate(V)
top
Crystal data top
O7P2Zn2 | F(000) = 292 |
Mr = 304.7 | Dx = 4.239 Mg m−3 |
Monoclinic, C2/m(α0γ)0s† | Mo Kα radiation, λ = 0.71073 Å |
q = 0.332680a* + 0.407590c* | Cell parameters from 6552 reflections |
a = 6.6082 (2) Å | θ = 3.5–45.2° |
b = 8.2821 (3) Å | µ = 10.7 mm−1 |
c = 4.5238 (2) Å | T = 400 K |
β = 105.4390 (17)° | Rod, translucent colourless |
V = 238.65 (2) Å3 | 0.42 × 0.30 × 0.06 mm |
Z = 2 | |
† Symmetry operations: (1) x1, x2, x3, x4; (2) −x1, x2, −x3, −x4+1/2; (3) −x1, −x2, −x3, −x4; (4) x1, −x2, x3, x4+1/2; (5) x1+1/2, x2+1/2, x3, x4; (6) −x1+1/2, x2+1/2, −x3, −x4+1/2; (7) −x1+1/2, −x2+1/2, −x3, −x4; (8) x1+1/2, −x2+1/2, x3, x4+1/2.
|
Data collection top
Bruker KAPPA APEX II CCD diffractometer | 5020 independent reflections |
Radiation source: X-ray tube | 2280 reflections with I > 3σ(I) |
Graphite monochromator | Rint = 0.026 |
ω and φ scans | θmax = 50.3°, θmin = 2.7° |
Absorption correction: multi-scan SADABS | h = −13→13 |
Tmin = 0.025, Tmax = 0.60 | k = −16→16 |
13480 measured reflections | l = −9→5 |
Refinement top
Refinement on F | 1 constraint |
R[F > 3σ(F)] = 0.026 | Weighting scheme based on measured s.u.'s w = 1/(σ2(F) + 0.0001F2) |
wR(F) = 0.040 | (Δ/σ)max = 0.017 |
S = 1.24 | Δρmax = 0.90 e Å−3 |
5020 reflections | Δρmin = −0.83 e Å−3 |
146 parameters | Extinction correction: B-C type 1 Gaussian isotropic (Becker & Coppens, 1974) |
0 restraints | Extinction coefficient: 1840 (80) |
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top | x | y | z | Uiso*/Ueq | Occ. (<1) |
Zn | 0.5 | 0.18921 (3) | 1 | 0.01797 (6) | |
P | 0.78961 (3) | 0 | 0.59052 (4) | 0.00896 (4) | |
O1 | 0.62199 (8) | 0 | 0.28617 (12) | 0.01031 (11) | |
O2 | 1 | −0.0528 (10) | 0.5 | 0.0240 (10) | 0.234 (6) |
O2' | 1 | −0.011 (3) | 0.5 | 0.068 (6) | 0.266 (6) |
O3 | 0.78239 (9) | −0.15146 (6) | 0.77458 (11) | 0.01910 (12) | |
Atomic displacement parameters (Å2) top | U11 | U22 | U33 | U12 | U13 | U23 |
Zn | 0.02176 (12) | 0.00790 (5) | 0.01688 (11) | 0 | −0.00773 (6) | 0 |
P | 0.00772 (6) | 0.01115 (7) | 0.00709 (7) | 0 | 0.00037 (5) | 0 |
O1 | 0.01022 (17) | 0.01108 (17) | 0.00771 (17) | 0 | −0.00095 (13) | 0 |
O2 | 0.0090 (10) | 0.035 (2) | 0.0299 (13) | 0 | 0.0086 (9) | 0 |
O2' | 0.0090 (13) | 0.151 (17) | 0.047 (2) | 0 | 0.0122 (14) | 0 |
O3 | 0.0298 (2) | 0.01099 (15) | 0.01290 (16) | 0.00574 (14) | −0.00059 (15) | 0.00268 (12) |
Geometric parameters (Å, º) top | Average | Minimum | Maximum |
Zn—O1i | 2.0590 (11) | 2.0157 (12) | 2.0878 (14) |
Zn—O1ii | 2.0590 (11) | 2.0161 (12) | 2.0893 (14) |
Zn—O3iii | 2.0192 (16) | 1.9550 (17) | 2.0858 (18) |
Zn—O3iv | 2.0193 (16) | 1.9561 (17) | 2.0884 (18) |
Zn—O3v | 2.372 (2) | 2.178 (2) | 2.762 (2) |
Zn—O3vi | 2.375 (2) | 2.178 (2) | 2.765 (2) |
P—O1 | 1.5207 (11) | 1.5191 (11) | 1.5222 (11) |
P—O2 | 1.602 (5) | 1.558 (3) | 1.624 (3) |
P—O2vii | 1.601 (5) | 1.558 (3) | 1.624 (3) |
P—O2' | 1.5541 (17) | 1.5405 (10) | 1.569 (3) |
P—O2'vii | 1.5541 (16) | 1.5405 (10) | 1.569 (3) |
P—O3 | 1.5165 (14) | 1.5069 (14) | 1.5262 (14) |
P—O3vi | 1.5165 (14) | 1.5069 (14) | 1.5262 (14) |
O2—O2' | 0.35 (3) | 0.26 (3) | 0.40 (3) |
O2—O2'vii | 0.54 (3) | 0.44 (3) | 0.59 (3) |
O2'—O2'vii | 0.19 (4) | 0.19 (4) | 0.19 (4) |
| | | |
O1i—Zn—O1ii | 80.52 (4) | 79.71 (4) | 81.37 (4) |
O1i—Zn—O3iii | 157.50 (9) | 142.27 (11) | 169.17 (9) |
O1i—Zn—O3iv | 94.12 (6) | 91.25 (7) | 95.71 (5) |
O1i—Zn—O3v | 81.42 (6) | 74.25 (7) | 88.88 (8) |
O1i—Zn—O3vi | 87.04 (6) | 79.51 (7) | 92.10 (7) |
O1ii—Zn—O3iii | 94.10 (6) | 91.32 (7) | 95.71 (5) |
O1ii—Zn—O3iv | 157.39 (9) | 142.02 (11) | 168.96 (9) |
O1ii—Zn—O3v | 87.12 (6) | 79.60 (7) | 92.17 (7) |
O1ii—Zn—O3vi | 81.34 (6) | 74.14 (7) | 88.76 (8) |
O3iii—Zn—O3iv | 98.16 (5) | 97.18 (5) | 99.77 (5) |
O3iii—Zn—O3v | 76.61 (7) | 68.03 (7) | 82.44 (8) |
O3iii—Zn—O3vi | 113.84 (8) | 107.48 (9) | 124.79 (9) |
O3iv—Zn—O3v | 113.89 (8) | 107.68 (9) | 124.98 (9) |
O3iv—Zn—O3vi | 76.56 (7) | 67.89 (7) | 82.28 (8) |
O3v—Zn—O3vi | 164.83 (5) | 163.20 (5) | 166.39 (5) |
O1—P—O2 | 104.3 (3) | 100.8 (2) | 107.5 (3) |
O1—P—O2vii | 104.4 (3) | 100.8 (2) | 107.5 (3) |
O1—P—O2' | 104.35 (7) | 103.54 (7) | 105.22 (6) |
O1—P—O2'vii | 104.35 (7) | 103.54 (7) | 105.22 (6) |
O1—P—O3 | 112.02 (6) | 111.66 (6) | 112.66 (6) |
O1—P—O3vi | 112.03 (6) | 111.66 (6) | 112.66 (6) |
O2—P—O2' | 12.6 (10) | 8.9 (10) | 14.4 (10) |
O2—P—O2'vii | 19.5 (10) | 15.6 (10) | 21.4 (10) |
O2—P—O3 | 98.5 (4) | 96.3 (5) | 99.4 (3) |
O2—P—O3vi | 117.0 (3) | 115.9 (5) | 120.0 (4) |
O2vii—P—O2' | 19.4 (10) | 15.6 (10) | 21.4 (10) |
O2vii—P—O2'vii | 12.5 (10) | 8.9 (10) | 14.4 (10) |
O2vii—P—O3 | 116.9 (3) | 115.9 (5) | 120.0 (4) |
O2vii—P—O3vi | 98.5 (4) | 96.3 (5) | 99.4 (3) |
O2'—P—O2'vii | 7.0 (13) | 6.9 (13) | 7.0 (13) |
O2'—P—O3 | 104.8 (8) | 97.6 (8) | 112.2 (8) |
O2'—P—O3vi | 110.9 (8) | 103.7 (8) | 118.2 (8) |
O2'vii—P—O3 | 110.9 (8) | 103.7 (8) | 118.2 (8) |
O2'vii—P—O3vi | 104.9 (8) | 97.6 (8) | 112.2 (8) |
O3—P—O3vi | 112.10 (8) | 111.92 (8) | 112.27 (8) |
Znviii—O1—Znix | 99.40 (7) | 98.02 (7) | 100.38 (7) |
Znviii—O1—P | 129.67 (4) | 127.46 (4) | 131.73 (4) |
Znix—O1—P | 129.66 (4) | 127.46 (4) | 131.73 (4) |
P—O2—Px | 151.0 (8) | 148.9 (6) | 155.2 (10) |
P—O2—O2' | 75.5 (8) | 70.4 (6) | 84.7 (11) |
P—O2—O2'vii | 75.5 (6) | 73.0 (4) | 82.0 (7) |
Px—O2—O2' | 75.6 (8) | 70.5 (6) | 84.9 (11) |
Px—O2—O2'vii | 75.5 (6) | 73.0 (4) | 82.2 (7) |
O2'—O2—O2'vii | 3.6 (9) | 0.0 (5) | 10 (3) |
P—O2'—Px | 173.0 (19) | 168.3 (18) | 177.8 (19) |
P—O2'—O2 | 92.0 (15) | 85.8 (16) | 101 (2) |
P—O2'—O2vii | 85.0 (12) | 81.8 (12) | 91.4 (15) |
P—O2'—O2'vii | 86.5 (9) | 84.0 (9) | 89.0 (9) |
Px—O2'—O2 | 91.9 (15) | 85.6 (16) | 100 (2) |
Px—O2'—O2vii | 85.1 (12) | 81.8 (12) | 91.2 (15) |
Px—O2'—O2'vii | 86.5 (9) | 84.0 (9) | 89.0 (9) |
O2—O2'—O2'vii | 170.5 (12) | 156 (3) | 179.8 (11) |
O2vii—O2'—O2'vii | 6.1 (6) | 0.1 (7) | 13.7 (9) |
Znxi—O3—Znv | 103.31 (8) | 97.79 (9) | 112.35 (8) |
Znxi—O3—P | 134.34 (11) | 125.93 (11) | 141.43 (10) |
Znv—O3—P | 119.28 (8) | 113.93 (8) | 124.37 (9) |
Symmetry codes: (i) x1, x2, x3+1, x4; (ii) −x1+1, x2, −x3+1, −x4+1/2; (iii) x1−1/2, x2+1/2, x3, x4; (iv) −x1+3/2, x2+1/2, −x3+2, −x4+1/2; (v) −x1+1, −x2, −x3+2, −x4; (vi) x1, −x2, x3, x4+1/2; (vii) −x1+2, −x2, −x3+1, −x4; (viii) x1, x2, x3−1, x4; (ix) −x1+1, −x2, −x3+1, −x4; (x) −x1+2, x2, −x3+1, −x4+1/2; (xi) x1+1/2, x2−1/2, x3, x4. |
(alpha2_zn2p2o7_405) zinc(II) diphosphate(V)
top
Crystal data top
O7P2Zn2 | F(000) = 292 |
Mr = 304.7 | Dx = 4.240 Mg m−3 |
Monoclinic, C2/m(α0γ)0s† | Mo Kα radiation, λ = 0.71073 Å |
q = 0.33153(12)a* + 0.40487(8)c* | Cell parameters from 6325 reflections |
a = 6.6053 (2) Å | θ = 2.5–45.2° |
b = 8.2821 (2) Å | µ = 10.70 mm−1 |
c = 4.5243 (1) Å | T = 405 K |
β = 105.4163 (14)° | Rod, translucent colourless |
V = 238.60 (1) Å3 | 0.42 × 0.30 × 0.06 mm |
Z = 2 | |
† Symmetry operations: (1) x1, x2, x3, x4; (2) −x1, x2, −x3, −x4+1/2; (3) −x1, −x2, −x3, −x4; (4) x1, −x2, x3, x4+1/2; (5) x1+1/2, x2+1/2, x3, x4; (6) −x1+1/2, x2+1/2, −x3, −x4+1/2; (7) −x1+1/2, −x2+1/2, −x3, −x4; (8) x1+1/2, −x2+1/2, x3, x4+1/2.
|
Data collection top
Bruker KAPPA APEX II CCD diffractometer | 5038 independent reflections |
Radiation source: X-ray tube | 2245 reflections with I > 3σ(I) |
Graphite monochromator | Rint = 0.025 |
ω and φ scans | θmax = 45.3°, θmin = 2.1° |
Absorption correction: multi-scan SADABS | h = −13→13 |
Tmin = 0.025, Tmax = 0.60 | k = −16→16 |
13503 measured reflections | l = −9→5 |
Refinement top
Refinement on F | 1 constraint |
R[F > 3σ(F)] = 0.024 | Weighting scheme based on measured s.u.'s w = 1/(σ2(F) + 0.0001F2) |
wR(F) = 0.038 | (Δ/σ)max = 0.037 |
S = 1.18 | Δρmax = 0.96 e Å−3 |
5038 reflections | Δρmin = −0.76 e Å−3 |
146 parameters | Extinction correction: B-C type 1 Gaussian isotropic (Becker & Coppens, 1974) |
0 restraints | Extinction coefficient: 2180 (80) |
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top | x | y | z | Uiso*/Ueq | Occ. (<1) |
Zn | 0.5 | 0.18950 (2) | 1 | 0.01805 (6) | |
P | 0.78950 (3) | 0 | 0.59053 (4) | 0.00889 (4) | |
O1 | 0.62167 (8) | 0 | 0.28594 (12) | 0.01034 (10) | |
O2 | 1 | −0.0566 (7) | 0.5 | 0.0181 (9) | 0.208 (3) |
O2' | 1 | −0.0202 (8) | 0.5 | 0.0332 (18) | 0.292 (3) |
O3 | 0.78233 (8) | −0.15128 (5) | 0.77488 (10) | 0.01919 (11) | |
Atomic displacement parameters (Å2) top | U11 | U22 | U33 | U12 | U13 | U23 |
Zn | 0.02193 (11) | 0.00802 (5) | 0.01689 (11) | 0 | −0.00762 (5) | 0 |
P | 0.00760 (6) | 0.01115 (7) | 0.00713 (7) | 0 | 0.00055 (5) | 0 |
O1 | 0.01032 (16) | 0.01113 (17) | 0.00783 (16) | 0 | −0.00064 (13) | 0 |
O2 | 0.0067 (8) | 0.022 (2) | 0.0268 (12) | 0 | 0.0063 (8) | 0 |
O2' | 0.0110 (7) | 0.043 (5) | 0.0494 (17) | 0 | 0.0150 (9) | 0 |
O3 | 0.0301 (2) | 0.01076 (14) | 0.01322 (16) | 0.00600 (14) | −0.00024 (15) | 0.00261 (12) |
Geometric parameters (Å, º) top | Average | Minimum | Maximum |
Zn—O1i | 2.0595 (11) | 2.0109 (12) | 2.0888 (14) |
Zn—O1ii | 2.0601 (11) | 2.0130 (12) | 2.0951 (14) |
Zn—O3iii | 2.0179 (16) | 1.9573 (17) | 2.0763 (18) |
Zn—O3iv | 2.0187 (16) | 1.9607 (17) | 2.0856 (18) |
P—O1 | 1.5223 (12) | 1.5194 (12) | 1.5252 (12) |
P—O2 | 1.611 (5) | 1.558 (3) | 1.646 (3) |
P—O2v | 1.610 (5) | 1.558 (3) | 1.646 (3) |
P—O2' | 1.5602 (9) | 1.5449 (8) | 1.5777 (11) |
P—O2'v | 1.5602 (9) | 1.5449 (8) | 1.5777 (11) |
P—O3 | 1.5157 (14) | 1.5038 (14) | 1.5254 (14) |
P—O3vi | 1.5157 (14) | 1.5038 (14) | 1.5254 (14) |
O2—O2' | 0.313 (10) | 0.248 (11) | 0.351 (9) |
O2—O2'v | 0.642 (11) | 0.558 (13) | 0.686 (9) |
O2'—O2'v | 0.335 (10) | 0.335 (10) | 0.335 (10) |
| | | |
O1i—Zn—O1ii | 80.38 (4) | 79.58 (4) | 81.15 (4) |
O1i—Zn—O3iii | 157.50 (9) | 142.77 (11) | 169.05 (9) |
O1i—Zn—O3iv | 94.19 (6) | 91.60 (7) | 95.66 (6) |
O1ii—Zn—O3iii | 94.18 (6) | 91.86 (7) | 95.66 (6) |
O1ii—Zn—O3iv | 157.22 (9) | 141.73 (11) | 168.24 (9) |
O3iii—Zn—O3iv | 98.19 (5) | 97.28 (5) | 99.73 (5) |
O1—P—O2 | 104.3 (3) | 99.7 (3) | 108.8 (3) |
O1—P—O2v | 104.4 (3) | 99.7 (3) | 108.8 (3) |
O1—P—O2' | 104.31 (6) | 103.53 (6) | 105.16 (6) |
O1—P—O2'v | 104.31 (6) | 103.53 (6) | 105.16 (6) |
O1—P—O3 | 112.09 (6) | 111.81 (6) | 112.67 (6) |
O1—P—O3vi | 112.10 (6) | 111.81 (6) | 112.67 (6) |
O2—P—O2' | 11.1 (4) | 8.4 (4) | 12.5 (3) |
O2—P—O2'v | 23.2 (4) | 19.9 (4) | 24.9 (3) |
O2—P—O3 | 97.3 (3) | 94.1 (4) | 98.3 (2) |
O2—P—O3vi | 118.1 (3) | 116.7 (3) | 121.7 (3) |
O2v—P—O2' | 23.2 (4) | 19.9 (4) | 24.9 (3) |
O2v—P—O2'v | 11.1 (4) | 8.4 (4) | 12.5 (3) |
O2v—P—O3 | 118.0 (3) | 116.7 (3) | 121.7 (3) |
O2v—P—O3vi | 97.3 (3) | 94.1 (4) | 98.3 (2) |
O2'—P—O2'v | 12.3 (4) | 12.2 (4) | 12.4 (4) |
O2'—P—O3 | 102.5 (2) | 95.7 (2) | 109.4 (2) |
O2'—P—O3vi | 113.2 (2) | 106.4 (2) | 120.1 (2) |
O2'v—P—O3 | 113.2 (2) | 106.4 (2) | 120.1 (2) |
O2'v—P—O3vi | 102.5 (2) | 95.7 (2) | 109.4 (2) |
O3—P—O3vi | 111.94 (8) | 111.59 (8) | 112.29 (8) |
Znvii—O1—Znviii | 99.54 (7) | 98.12 (8) | 100.72 (7) |
Znvii—O1—P | 129.60 (4) | 127.56 (3) | 131.64 (4) |
Znviii—O1—P | 129.59 (4) | 127.56 (3) | 131.64 (4) |
P—O2—Pix | 148.6 (6) | 147.1 (4) | 151.5 (7) |
P—O2—O2' | 74.4 (8) | 66.58 (17) | 85.8 (8) |
P—O2—O2'v | 74.3 (5) | 71.3 (3) | 80.4 (5) |
Pix—O2—O2' | 74.3 (8) | 66.51 (17) | 85.6 (8) |
Pix—O2—O2'v | 74.3 (5) | 71.3 (3) | 80.3 (5) |
O2'—O2—O2'v | 7.6 (7) | 0.2 (7) | 19.6 (15) |
P—O2'—Pix | 167.7 (5) | 163.2 (5) | 172.1 (5) |
P—O2'—O2 | 94.5 (15) | 85.1 (18) | 105.0 (18) |
P—O2'—O2v | 82.4 (8) | 79.0 (8) | 88.8 (9) |
P—O2'—O2'v | 83.8 (3) | 81.5 (2) | 86.2 (3) |
Pix—O2'—O2 | 94.5 (15) | 85.2 (18) | 105.1 (18) |
Pix—O2'—O2v | 82.6 (8) | 79.1 (8) | 88.9 (9) |
Pix—O2'—O2'v | 83.8 (3) | 81.5 (2) | 86.2 (3) |
O2—O2'—O2'v | 165.8 (11) | 146.0 (17) | 179.6 (13) |
O2v—O2'—O2'v | 6.7 (4) | 0.2 (7) | 14.4 (3) |
Znx—O3—P | 134.24 (10) | 125.54 (11) | 140.96 (10) |
Symmetry codes: (i) x1, x2, x3+1, x4; (ii) −x1+1, x2, −x3+1, −x4+1/2; (iii) x1−1/2, x2+1/2, x3, x4; (iv) −x1+3/2, x2+1/2, −x3+2, −x4+1/2; (v) −x1+2, −x2, −x3+1, −x4; (vi) x1, −x2, x3, x4+1/2; (vii) x1, x2, x3−1, x4; (viii) −x1+1, −x2, −x3+1, −x4; (ix) −x1+2, x2, −x3+1, −x4+1/2; (x) x1+1/2, x2−1/2, x3, x4. |
(alpha2_zn2p2o7_410) zinc(II) diphosphate(V)
top
Crystal data top
O7P2Zn2 | F(000) = 292 |
Mr = 304.7 | Dx = 4.240 Mg m−3 |
Monoclinic, C2/m(α0γ)0s† | Mo Kα radiation, λ = 0.71073 Å |
q = 0.33062(11)a* + 0.40287(8)c* | Cell parameters from 6378 reflections |
a = 6.6041 (2) Å | θ = 2.5–45.2° |
b = 8.2827 (2) Å | µ = 10.70 mm−1 |
c = 4.5249 (1) Å | T = 410 K |
β = 105.4064 (13)° | Rod, translucent colourless |
V = 238.62 (1) Å3 | 0.42 × 0.30 × 0.06 mm |
Z = 2 | |
† Symmetry operations: (1) x1, x2, x3, x4; (2) −x1, x2, −x3, −x4+1/2; (3) −x1, −x2, −x3, −x4; (4) x1, −x2, x3, x4+1/2; (5) x1+1/2, x2+1/2, x3, x4; (6) −x1+1/2, x2+1/2, −x3, −x4+1/2; (7) −x1+1/2, −x2+1/2, −x3, −x4; (8) x1+1/2, −x2+1/2, x3, x4+1/2.
|
Data collection top
Bruker KAPPA APEX II CCD diffractometer | 5059 independent reflections |
Radiation source: X-ray tube | 2230 reflections with I > 3σ(I) |
Graphite monochromator | Rint = 0.026 |
ω and φ scans | θmax = 45.4°, θmin = 2.1° |
Absorption correction: multi-scan SADABS | h = −13→13 |
Tmin = 0.025, Tmax = 0.60 | k = −16→16 |
13567 measured reflections | l = −9→5 |
Refinement top
Refinement on F | 1 constraint |
R[F > 3σ(F)] = 0.024 | Weighting scheme based on measured s.u.'s w = 1/(σ2(F) + 0.0001F2) |
wR(F) = 0.038 | (Δ/σ)max = 0.025 |
S = 1.16 | Δρmax = 0.85 e Å−3 |
5059 reflections | Δρmin = −0.90 e Å−3 |
146 parameters | Extinction correction: B-C type 1 Gaussian isotropic (Becker & Coppens, 1974) |
0 restraints | Extinction coefficient: 2370 (80) |
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top | x | y | z | Uiso*/Ueq | Occ. (<1) |
Zn | 0.5 | 0.18943 (2) | 1 | 0.01840 (6) | |
P | 0.78941 (3) | 0 | 0.59057 (4) | 0.00902 (4) | |
O1 | 0.62166 (8) | 0 | 0.28602 (11) | 0.01067 (10) | |
O2 | 1 | −0.0572 (10) | 0.5 | 0.0193 (10) | 0.192 (4) |
O2' | 1 | −0.0215 (9) | 0.5 | 0.035 (2) | 0.308 (4) |
O3 | 0.78202 (8) | −0.15135 (5) | 0.77490 (10) | 0.01933 (11) | |
Atomic displacement parameters (Å2) top | U11 | U22 | U33 | U12 | U13 | U23 |
Zn | 0.02252 (11) | 0.00821 (5) | 0.01706 (11) | 0 | −0.00771 (5) | 0 |
P | 0.00772 (6) | 0.01148 (7) | 0.00710 (6) | 0 | 0.00067 (5) | 0 |
O1 | 0.01089 (16) | 0.01137 (17) | 0.00798 (15) | 0 | −0.00059 (12) | 0 |
O2 | 0.0073 (9) | 0.024 (3) | 0.0289 (14) | 0 | 0.0082 (9) | 0 |
O2' | 0.0111 (7) | 0.052 (6) | 0.0476 (15) | 0 | 0.0158 (8) | 0 |
O3 | 0.0300 (2) | 0.01112 (14) | 0.01342 (15) | 0.00610 (14) | −0.00017 (14) | 0.00258 (11) |
Geometric parameters (Å, º) top | Average | Minimum | Maximum |
Zn—O1i | 2.0598 (11) | 2.0107 (12) | 2.0975 (14) |
Zn—O1ii | 2.0591 (11) | 2.0091 (12) | 2.0928 (14) |
Zn—O3iii | 2.0198 (16) | 1.9664 (17) | 2.0793 (18) |
Zn—O3iv | 2.0188 (16) | 1.9642 (17) | 2.0729 (18) |
P—O1 | 1.5221 (11) | 1.5184 (11) | 1.5257 (11) |
P—O2 | 1.612 (6) | 1.565 (3) | 1.639 (3) |
P—O2v | 1.611 (5) | 1.565 (3) | 1.639 (3) |
P—O2' | 1.5617 (10) | 1.5487 (8) | 1.5771 (12) |
P—O2'v | 1.5616 (10) | 1.5487 (8) | 1.5771 (12) |
P—O3 | 1.5162 (13) | 1.5064 (14) | 1.5228 (13) |
P—O3vi | 1.5161 (13) | 1.5064 (14) | 1.5228 (13) |
O2—O2' | 0.303 (12) | 0.232 (13) | 0.341 (11) |
O2—O2'v | 0.655 (12) | 0.572 (15) | 0.697 (11) |
O2'—O2'v | 0.356 (10) | 0.356 (10) | 0.356 (10) |
| | | |
O1i—Zn—O1ii | 80.44 (4) | 79.63 (4) | 81.16 (4) |
O1i—Zn—O3iii | 157.26 (9) | 142.28 (11) | 168.00 (10) |
O1i—Zn—O3iv | 94.17 (6) | 92.17 (7) | 95.51 (7) |
O1ii—Zn—O3iii | 94.15 (6) | 92.00 (7) | 95.51 (7) |
O1ii—Zn—O3iv | 157.39 (9) | 143.03 (11) | 168.58 (9) |
O3iii—Zn—O3iv | 98.25 (5) | 97.39 (5) | 99.65 (5) |
O1—P—O2 | 104.3 (3) | 100.8 (3) | 107.6 (3) |
O1—P—O2v | 104.3 (3) | 100.8 (3) | 107.6 (3) |
O1—P—O2' | 104.28 (6) | 103.57 (6) | 105.04 (6) |
O1—P—O2'v | 104.28 (6) | 103.57 (6) | 105.04 (6) |
O1—P—O3 | 112.07 (6) | 111.79 (6) | 112.63 (6) |
O1—P—O3vi | 112.08 (6) | 111.79 (6) | 112.63 (6) |
O2—P—O2' | 10.8 (4) | 8.0 (5) | 12.1 (4) |
O2—P—O2'v | 23.7 (4) | 20.6 (5) | 25.2 (4) |
O2—P—O3 | 96.9 (3) | 94.3 (4) | 97.8 (3) |
O2—P—O3vi | 118.6 (3) | 117.6 (3) | 121.7 (4) |
O2v—P—O2' | 23.7 (4) | 20.6 (5) | 25.2 (4) |
O2v—P—O2'v | 10.7 (4) | 8.0 (5) | 12.1 (4) |
O2v—P—O3 | 118.5 (3) | 117.6 (3) | 121.7 (4) |
O2v—P—O3vi | 96.9 (3) | 94.3 (4) | 97.8 (3) |
O2'—P—O2'v | 13.1 (4) | 13.0 (4) | 13.2 (4) |
O2'—P—O3 | 102.2 (2) | 95.9 (2) | 108.6 (2) |
O2'—P—O3vi | 113.6 (2) | 107.3 (2) | 119.9 (2) |
O2'v—P—O3 | 113.6 (2) | 107.3 (2) | 119.9 (2) |
O2'v—P—O3vi | 102.2 (2) | 95.9 (2) | 108.6 (2) |
O3—P—O3vi | 111.93 (8) | 111.62 (8) | 112.23 (8) |
Znvii—O1—Znviii | 99.49 (7) | 98.05 (8) | 100.82 (7) |
Znvii—O1—P | 129.63 (4) | 127.78 (3) | 131.53 (4) |
Znviii—O1—P | 129.61 (4) | 127.78 (3) | 131.53 (4) |
P—O2—Pix | 148.2 (7) | 146.8 (5) | 151.3 (9) |
P—O2—O2' | 74.3 (9) | 67.53 (19) | 84.6 (9) |
P—O2—O2'v | 74.2 (5) | 71.8 (4) | 79.5 (5) |
Pix—O2—O2' | 74.1 (9) | 67.34 (19) | 84.1 (9) |
Pix—O2—O2'v | 74.1 (5) | 71.8 (4) | 79.3 (5) |
O2'—O2—O2'v | 6.2 (8) | 0.0 (5) | 16.5 (15) |
P—O2'—Pix | 166.9 (5) | 162.8 (5) | 171.1 (5) |
P—O2'—O2 | 95.0 (17) | 87 (2) | 104 (2) |
P—O2'—O2v | 82.1 (8) | 79.4 (9) | 87.5 (9) |
P—O2'—O2'v | 83.5 (3) | 81.3 (3) | 85.7 (3) |
Pix—O2'—O2 | 95.2 (17) | 87 (2) | 105 (2) |
Pix—O2'—O2v | 82.3 (8) | 79.5 (9) | 87.6 (9) |
Pix—O2'—O2'v | 83.5 (3) | 81.3 (3) | 85.7 (3) |
O2—O2'—O2'v | 168.9 (12) | 152.8 (17) | 179.9 (16) |
O2v—O2'—O2'v | 5.0 (4) | 0.0 (5) | 10.7 (3) |
Znx—O3—P | 134.18 (10) | 126.02 (10) | 140.35 (10) |
Symmetry codes: (i) x1, x2, x3+1, x4; (ii) −x1+1, x2, −x3+1, −x4+1/2; (iii) x1−1/2, x2+1/2, x3, x4; (iv) −x1+3/2, x2+1/2, −x3+2, −x4+1/2; (v) −x1+2, −x2, −x3+1, −x4; (vi) x1, −x2, x3, x4+1/2; (vii) x1, x2, x3−1, x4; (viii) −x1+1, −x2, −x3+1, −x4; (ix) −x1+2, x2, −x3+1, −x4+1/2; (x) x1+1/2, x2−1/2, x3, x4. |
(alpha2_zn2p2o7_415) zinc(II) diphosphate(V)
top
Crystal data top
O7P2Zn2 | F(000) = 292 |
Mr = 304.7 | Dx = 4.240 Mg m−3 |
Monoclinic, C2/m(α0γ)0s† | Mo Kα radiation, λ = 0.71073 Å |
q = 0.33004(12)a* + 0.40167(8)c* | Cell parameters from 6135 reflections |
a = 6.6036 (2) Å | θ = 2.4–45.3° |
b = 8.2830 (2) Å | µ = 10.70 mm−1 |
c = 4.5250 (1) Å | T = 415 K |
β = 105.4028 (13)° | Rod, translucent colourless |
V = 238.62 (1) Å3 | 0.42 × 0.30 × 0.06 mm |
Z = 2 | |
† Symmetry operations: (1) x1, x2, x3, x4; (2) −x1, x2, −x3, −x4+1/2; (3) −x1, −x2, −x3, −x4; (4) x1, −x2, x3, x4+1/2; (5) x1+1/2, x2+1/2, x3, x4; (6) −x1+1/2, x2+1/2, −x3, −x4+1/2; (7) −x1+1/2, −x2+1/2, −x3, −x4; (8) x1+1/2, −x2+1/2, x3, x4+1/2.
|
Data collection top
Bruker KAPPA APEX II CCD diffractometer | 5064 independent reflections |
Radiation source: X-ray tube | 2147 reflections with I > 3σ(I) |
Graphite monochromator | Rint = 0.026 |
ω and φ scans | θmax = 45.4°, θmin = 2.1° |
Absorption correction: multi-scan SADABS | h = −13→13 |
Tmin = 0.025, Tmax = 0.60 | k = −16→16 |
13588 measured reflections | l = −9→5 |
Refinement top
Refinement on F | 1 constraint |
R[F > 3σ(F)] = 0.024 | Weighting scheme based on measured s.u.'s w = 1/(σ2(F) + 0.0001F2) |
wR(F) = 0.039 | (Δ/σ)max = 0.028 |
S = 1.16 | Δρmax = 0.87 e Å−3 |
5064 reflections | Δρmin = −0.82 e Å−3 |
146 parameters | Extinction correction: B-C type 1 Gaussian isotropic (Becker & Coppens, 1974) |
0 restraints | Extinction coefficient: 2400 (80) |
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top | x | y | z | Uiso*/Ueq | Occ. (<1) |
Zn | 0.5 | 0.18966 (2) | 1 | 0.01864 (6) | |
P | 0.78938 (3) | 0 | 0.59065 (4) | 0.00910 (4) | |
O1 | 0.62157 (8) | 0 | 0.28621 (11) | 0.01072 (10) | |
O2 | 1 | −0.0561 (12) | 0.5 | 0.0183 (11) | 0.178 (4) |
O2' | 1 | −0.0210 (10) | 0.5 | 0.035 (2) | 0.322 (4) |
O3 | 0.78182 (8) | −0.15135 (5) | 0.77494 (10) | 0.01944 (11) | |
Atomic displacement parameters (Å2) top | U11 | U22 | U33 | U12 | U13 | U23 |
Zn | 0.02279 (12) | 0.00831 (5) | 0.01731 (12) | 0 | −0.00782 (6) | 0 |
P | 0.00774 (6) | 0.01165 (7) | 0.00720 (6) | 0 | 0.00072 (5) | 0 |
O1 | 0.01077 (15) | 0.01164 (17) | 0.00801 (15) | 0 | −0.00056 (12) | 0 |
O2 | 0.0060 (9) | 0.024 (3) | 0.0266 (14) | 0 | 0.0070 (9) | 0 |
O2' | 0.0123 (7) | 0.048 (6) | 0.0495 (17) | 0 | 0.0160 (9) | 0 |
O3 | 0.0302 (2) | 0.01116 (15) | 0.01367 (15) | 0.00617 (14) | 0.00000 (14) | 0.00265 (12) |
Geometric parameters (Å, º) top | Average | Minimum | Maximum |
Zn—O1i | 2.0612 (13) | 2.0128 (14) | 2.0977 (16) |
Zn—O1ii | 2.0608 (13) | 2.0119 (14) | 2.0952 (15) |
Zn—O3iii | 2.0190 (17) | 1.9664 (19) | 2.075 (2) |
Zn—O3iv | 2.0184 (17) | 1.9653 (19) | 2.072 (2) |
P—O1 | 1.5219 (13) | 1.5162 (13) | 1.5275 (13) |
P—O2 | 1.611 (7) | 1.569 (4) | 1.631 (4) |
P—O2v | 1.610 (6) | 1.569 (4) | 1.631 (4) |
P—O2' | 1.5613 (11) | 1.5501 (9) | 1.5749 (13) |
P—O2'v | 1.5613 (11) | 1.5501 (9) | 1.5749 (13) |
P—O3 | 1.5159 (15) | 1.5063 (15) | 1.5237 (15) |
P—O3vi | 1.5159 (15) | 1.5063 (15) | 1.5237 (15) |
O2—O2' | 0.298 (14) | 0.228 (15) | 0.335 (12) |
O2—O2'v | 0.642 (14) | 0.560 (17) | 0.684 (12) |
O2'—O2'v | 0.348 (11) | 0.348 (11) | 0.348 (11) |
| | | |
O1i—Zn—O1ii | 80.40 (4) | 79.57 (4) | 81.07 (4) |
O1i—Zn—O3iii | 157.23 (10) | 142.79 (12) | 167.84 (11) |
O1i—Zn—O3iv | 94.16 (7) | 92.23 (8) | 95.42 (8) |
O1ii—Zn—O3iii | 94.14 (7) | 92.14 (8) | 95.42 (8) |
O1ii—Zn—O3iv | 157.27 (10) | 143.18 (12) | 168.14 (10) |
O3iii—Zn—O3iv | 98.37 (6) | 97.53 (6) | 99.75 (6) |
O1—P—O2 | 104.3 (3) | 100.8 (3) | 107.7 (4) |
O1—P—O2v | 104.3 (3) | 100.8 (3) | 107.7 (4) |
O1—P—O2' | 104.31 (7) | 103.63 (7) | 105.03 (7) |
O1—P—O2'v | 104.31 (7) | 103.63 (7) | 105.03 (7) |
O1—P—O3 | 112.04 (6) | 111.78 (6) | 112.55 (6) |
O1—P—O3vi | 112.05 (6) | 111.78 (6) | 112.55 (6) |
O2—P—O2' | 10.6 (5) | 8.0 (5) | 11.9 (5) |
O2—P—O2'v | 23.2 (5) | 20.3 (6) | 24.7 (4) |
O2—P—O3 | 96.9 (4) | 94.6 (5) | 97.7 (4) |
O2—P—O3vi | 118.6 (4) | 117.5 (5) | 121.5 (4) |
O2v—P—O2' | 23.2 (5) | 20.3 (6) | 24.7 (4) |
O2v—P—O2'v | 10.6 (5) | 8.0 (5) | 11.9 (5) |
O2v—P—O3 | 118.6 (4) | 117.5 (5) | 121.5 (4) |
O2v—P—O3vi | 96.9 (4) | 94.6 (5) | 97.7 (4) |
O2'—P—O2'v | 12.8 (4) | 12.7 (4) | 12.9 (4) |
O2'—P—O3 | 102.4 (3) | 96.6 (3) | 108.3 (3) |
O2'—P—O3vi | 113.5 (3) | 107.7 (3) | 119.3 (3) |
O2'v—P—O3 | 113.5 (3) | 107.7 (3) | 119.3 (3) |
O2'v—P—O3vi | 102.4 (3) | 96.6 (3) | 108.3 (3) |
O3—P—O3vi | 111.90 (9) | 111.52 (9) | 112.28 (9) |
Znvii—O1—Znviii | 99.53 (8) | 98.19 (9) | 100.92 (8) |
Znvii—O1—P | 129.60 (5) | 127.90 (4) | 131.41 (4) |
Znviii—O1—P | 129.59 (5) | 127.90 (4) | 131.41 (4) |
P—O2—Pix | 148.7 (8) | 147.1 (7) | 151.9 (10) |
P—O2—O2' | 74.5 (11) | 69.1 (2) | 83.6 (10) |
P—O2—O2'v | 74.4 (6) | 72.4 (5) | 79.3 (6) |
Pix—O2—O2' | 74.3 (11) | 68.9 (2) | 83.0 (10) |
Pix—O2—O2'v | 74.3 (6) | 72.4 (5) | 79.0 (6) |
O2'—O2—O2'v | 6.4 (9) | 0.0 (5) | 17.1 (18) |
P—O2'—Pix | 167.2 (6) | 163.4 (6) | 171.0 (6) |
P—O2'—O2 | 95 (2) | 88 (3) | 103 (3) |
P—O2'—O2v | 82.3 (10) | 80.2 (11) | 87.0 (11) |
P—O2'—O2'v | 83.6 (3) | 81.6 (3) | 85.7 (3) |
Pix—O2'—O2 | 95 (2) | 88 (3) | 103 (3) |
Pix—O2'—O2v | 82.5 (10) | 80.2 (11) | 87.2 (11) |
Pix—O2'—O2'v | 83.6 (3) | 81.6 (3) | 85.7 (3) |
O2—O2'—O2'v | 168.6 (14) | 152 (2) | 180.0 (5) |
O2v—O2'—O2'v | 5.1 (5) | 0.0 (5) | 11.1 (3) |
Znx—O3—P | 134.11 (11) | 126.37 (11) | 139.82 (11) |
Symmetry codes: (i) x1, x2, x3+1, x4; (ii) −x1+1, x2, −x3+1, −x4+1/2; (iii) x1−1/2, x2+1/2, x3, x4; (iv) −x1+3/2, x2+1/2, −x3+2, −x4+1/2; (v) −x1+2, −x2, −x3+1, −x4; (vi) x1, −x2, x3, x4+1/2; (vii) x1, x2, x3−1, x4; (viii) −x1+1, −x2, −x3+1, −x4; (ix) −x1+2, x2, −x3+1, −x4+1/2; (x) x1+1/2, x2−1/2, x3, x4. |
(alpha2_zn2p2o7_420) zinc(II) diphosphate(V)
top
Crystal data top
O7P2Zn2 | F(000) = 292 |
Mr = 304.7 | Dx = 4.240 Mg m−3 |
Monoclinic, C2/m(α0γ)0s† | Mo Kα radiation, λ = 0.71073 Å |
q = 0.32940(14)a* + 0.40083(9)c* | Cell parameters from 5902 reflections |
a = 6.6025 (2) Å | θ = 3.4–45.3° |
b = 8.2826 (2) Å | µ = 10.70 mm−1 |
c = 4.5251 (1) Å | T = 420 K |
β = 105.3996 (14)° | Rod, translucent colourless |
V = 238.58 (1) Å3 | 0.42 × 0.30 × 0.06 mm |
Z = 2 | |
† Symmetry operations: (1) x1, x2, x3, x4; (2) −x1, x2, −x3, −x4+1/2; (3) −x1, −x2, −x3, −x4; (4) x1, −x2, x3, x4+1/2; (5) x1+1/2, x2+1/2, x3, x4; (6) −x1+1/2, x2+1/2, −x3, −x4+1/2; (7) −x1+1/2, −x2+1/2, −x3, −x4; (8) x1+1/2, −x2+1/2, x3, x4+1/2.
|
Data collection top
Bruker KAPPA APEX II CCD diffractometer | 5064 independent reflections |
Radiation source: X-ray tube | 2089 reflections with I > 3σ(I) |
Graphite monochromator | Rint = 0.026 |
ω and φ scans | θmax = 45.4°, θmin = 2.1° |
Absorption correction: multi-scan SADABS | h = −13→13 |
Tmin = 0.025, Tmax = 0.60 | k = −16→16 |
13592 measured reflections | l = −9→5 |
Refinement top
Refinement on F | 1 constraint |
R[F > 3σ(F)] = 0.025 | Weighting scheme based on measured s.u.'s w = 1/(σ2(F) + 0.0001F2) |
wR(F) = 0.041 | (Δ/σ)max = 0.039 |
S = 1.19 | Δρmax = 0.94 e Å−3 |
5064 reflections | Δρmin = −0.83 e Å−3 |
146 parameters | Extinction correction: B-C type 1 Gaussian isotropic (Becker & Coppens, 1974) |
0 restraints | Extinction coefficient: 2380 (80) |
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top | x | y | z | Uiso*/Ueq | Occ. (<1) |
Zn | 0.5 | 0.18963 (2) | 1 | 0.01887 (7) | |
P | 0.78928 (3) | 0 | 0.59062 (4) | 0.00919 (4) | |
O1 | 0.62148 (8) | 0 | 0.28611 (12) | 0.01086 (10) | |
O2 | 1 | −0.0563 (14) | 0.5 | 0.0183 (13) | 0.153 (5) |
O2' | 1 | −0.0219 (13) | 0.5 | 0.041 (3) | 0.347 (5) |
O3 | 0.78161 (8) | −0.15143 (5) | 0.77487 (10) | 0.01948 (11) | |
Atomic displacement parameters (Å2) top | U11 | U22 | U33 | U12 | U13 | U23 |
Zn | 0.02312 (13) | 0.00841 (5) | 0.01745 (13) | 0 | −0.00798 (7) | 0 |
P | 0.00769 (6) | 0.01192 (8) | 0.00725 (7) | 0 | 0.00074 (5) | 0 |
O1 | 0.01088 (16) | 0.01193 (18) | 0.00802 (16) | 0 | −0.00057 (13) | 0 |
O2 | 0.0053 (13) | 0.025 (3) | 0.0263 (18) | 0 | 0.0071 (12) | 0 |
O2' | 0.0116 (7) | 0.066 (7) | 0.0486 (16) | 0 | 0.0155 (9) | 0 |
O3 | 0.0303 (2) | 0.01123 (15) | 0.01359 (16) | 0.00608 (14) | 0.00000 (15) | 0.00262 (12) |
Geometric parameters (Å, º) top | Average | Minimum | Maximum |
Zn—O1i | 2.0602 (14) | 2.0129 (15) | 2.1023 (17) |
Zn—O1ii | 2.0600 (14) | 2.0126 (15) | 2.1015 (17) |
Zn—O3iii | 2.0193 (19) | 1.969 (2) | 2.066 (2) |
Zn—O3iv | 2.0189 (19) | 1.969 (2) | 2.065 (2) |
P—O1 | 1.5219 (14) | 1.5197 (14) | 1.5241 (14) |
P—O2 | 1.613 (8) | 1.595 (5) | 1.622 (12) |
P—O2v | 1.613 (8) | 1.595 (5) | 1.622 (12) |
P—O2' | 1.5624 (14) | 1.5500 (12) | 1.5772 (17) |
P—O2'v | 1.5624 (14) | 1.5500 (12) | 1.5772 (17) |
P—O3 | 1.5161 (16) | 1.5058 (16) | 1.5241 (16) |
P—O3vi | 1.5161 (16) | 1.5058 (16) | 1.5241 (16) |
O2—O2' | 0.295 (18) | 0.225 (19) | 0.333 (16) |
O2—O2'v | 0.651 (18) | 0.56 (2) | 0.696 (16) |
O2'—O2'v | 0.362 (15) | 0.362 (15) | 0.362 (15) |
| | | |
O1i—Zn—O1ii | 80.40 (4) | 79.83 (4) | 81.07 (4) |
O1i—Zn—O3iii | 157.23 (12) | 143.42 (14) | 167.70 (12) |
O1i—Zn—O3iv | 94.15 (8) | 92.60 (9) | 95.31 (10) |
O1ii—Zn—O3iii | 94.13 (8) | 92.57 (9) | 95.31 (10) |
O1ii—Zn—O3iv | 157.22 (12) | 143.54 (14) | 167.80 (12) |
O3iii—Zn—O3iv | 98.44 (6) | 97.53 (6) | 99.53 (6) |
O1—P—O2 | 104.1 (5) | 99.8 (4) | 108.1 (5) |
O1—P—O2v | 104.1 (5) | 99.8 (4) | 108.1 (5) |
O1—P—O2' | 104.29 (7) | 103.66 (7) | 104.99 (7) |
O1—P—O2'v | 104.29 (7) | 103.66 (7) | 104.99 (7) |
O1—P—O3 | 112.04 (7) | 111.58 (7) | 112.43 (7) |
O1—P—O3vi | 112.04 (7) | 111.58 (7) | 112.43 (7) |
O2—P—O2' | 10.5 (6) | 8.0 (7) | 11.8 (6) |
O2—P—O2'v | 23.6 (7) | 20.5 (8) | 25.2 (6) |
O2—P—O3 | 96.6 (5) | 94.6 (6) | 97.8 (6) |
O2—P—O3vi | 119.1 (5) | 116.9 (6) | 122.0 (6) |
O2v—P—O2' | 23.5 (7) | 20.5 (8) | 25.2 (6) |
O2v—P—O2'v | 10.5 (6) | 8.0 (7) | 11.8 (6) |
O2v—P—O3 | 119.0 (5) | 116.9 (6) | 122.0 (6) |
O2v—P—O3vi | 96.6 (5) | 94.6 (6) | 97.8 (6) |
O2'—P—O2'v | 13.3 (6) | 13.2 (5) | 13.4 (6) |
O2'—P—O3 | 102.1 (4) | 96.8 (3) | 107.6 (4) |
O2'—P—O3vi | 113.8 (3) | 108.5 (3) | 119.1 (3) |
O2'v—P—O3 | 113.7 (3) | 108.5 (3) | 119.1 (3) |
O2'v—P—O3vi | 102.2 (4) | 96.8 (3) | 107.6 (4) |
O3—P—O3vi | 111.91 (10) | 111.51 (10) | 112.31 (9) |
Znvii—O1—Znviii | 99.54 (9) | 97.95 (10) | 100.83 (10) |
Znvii—O1—P | 129.61 (5) | 127.99 (4) | 131.16 (5) |
Znviii—O1—P | 129.59 (5) | 127.99 (4) | 131.16 (5) |
P—O2—Pix | 148.2 (10) | 146.5 (8) | 151.8 (13) |
P—O2—O2' | 74.2 (14) | 73.0 (18) | 77.5 (8) |
P—O2—O2'v | 74.1 (8) | 73.0 (9) | 76.7 (7) |
Pix—O2—O2' | 74.2 (14) | 73.0 (18) | 77.8 (8) |
Pix—O2—O2'v | 74.2 (8) | 73.0 (9) | 76.9 (7) |
O2'—O2—O2'v | 7.6 (13) | 0.0 (5) | 21 (3) |
P—O2'—Pix | 166.7 (8) | 163.2 (8) | 170.1 (8) |
P—O2'—O2 | 95 (3) | 94 (3) | 97 (3) |
P—O2'—O2v | 82.3 (13) | 81.5 (12) | 84.5 (14) |
P—O2'—O2'v | 83.3 (4) | 81.5 (4) | 85.2 (4) |
Pix—O2'—O2 | 95 (3) | 94 (4) | 97 (3) |
Pix—O2'—O2v | 82.3 (13) | 81.5 (12) | 84.4 (14) |
Pix—O2'—O2'v | 83.3 (4) | 81.5 (4) | 85.2 (4) |
O2—O2'—O2'v | 166.7 (18) | 147 (3) | 180.0 (5) |
O2v—O2'—O2'v | 5.8 (6) | 0.0 (5) | 12.6 (5) |
Znx—O3—P | 134.07 (12) | 127.00 (12) | 139.13 (12) |
Symmetry codes: (i) x1, x2, x3+1, x4; (ii) −x1+1, x2, −x3+1, −x4+1/2; (iii) x1−1/2, x2+1/2, x3, x4; (iv) −x1+3/2, x2+1/2, −x3+2, −x4+1/2; (v) −x1+2, −x2, −x3+1, −x4; (vi) x1, −x2, x3, x4+1/2; (vii) x1, x2, x3−1, x4; (viii) −x1+1, −x2, −x3+1, −x4; (ix) −x1+2, x2, −x3+1, −x4+1/2; (x) x1+1/2, x2−1/2, x3, x4. |
(alpha2_zn2p2o7_430) zinc(II) diphosphate(V)
top
Crystal data top
O7P2Zn2 | F(000) = 292 |
Mr = 304.7 | Dx = 4.239 Mg m−3 |
Monoclinic, C2/m(α0γ)0s† | Mo Kα radiation, λ = 0.71073 Å |
q = 0.32790(8)a* + 0.40041(5)c* | Cell parameters from 5548 reflections |
a = 6.6018 (2) Å | θ = 3.4–45.3° |
b = 8.2835 (2) Å | µ = 10.70 mm−1 |
c = 4.5260 (1) Å | T = 430 K |
β = 105.3906 (15)° | Rod, translucent colourless |
V = 238.63 (1) Å3 | 0.42 × 0.30 × 0.06 mm |
Z = 2 | |
† Symmetry operations: (1) x1, x2, x3, x4; (2) −x1, x2, −x3, −x4+1/2; (3) −x1, −x2, −x3, −x4; (4) x1, −x2, x3, x4+1/2; (5) x1+1/2, x2+1/2, x3, x4; (6) −x1+1/2, x2+1/2, −x3, −x4+1/2; (7) −x1+1/2, −x2+1/2, −x3, −x4; (8) x1+1/2, −x2+1/2, x3, x4+1/2.
|
Data collection top
Bruker KAPPA APEX II CCD diffractometer | 5061 independent reflections |
Radiation source: X-ray tube | 1949 reflections with I > 3σ(I) |
Graphite monochromator | Rint = 0.027 |
ω and φ scans | θmax = 45.3°, θmin = 2.1° |
Absorption correction: multi-scan SADABS | h = −13→13 |
Tmin = 0.025, Tmax = 0.60 | k = −16→16 |
13656 measured reflections | l = −9→5 |
Refinement top
Refinement on F | 1 constraint |
R[F > 3σ(F)] = 0.027 | Weighting scheme based on measured s.u.'s w = 1/(σ2(F) + 0.0001F2) |
wR(F) = 0.044 | (Δ/σ)max = 0.043 |
S = 1.22 | Δρmax = 0.79 e Å−3 |
5061 reflections | Δρmin = −0.78 e Å−3 |
146 parameters | Extinction correction: B-C type 1 Gaussian isotropic (Becker & Coppens, 1974) |
0 restraints | Extinction coefficient: 2260 (90) |
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top | x | y | z | Uiso*/Ueq | Occ. (<1) |
Zn | 0.5 | 0.18972 (2) | 1 | 0.01846 (8) | |
P | 0.78924 (3) | 0 | 0.59062 (4) | 0.00869 (4) | |
O1 | 0.62139 (8) | 0 | 0.28648 (12) | 0.01024 (11) | |
O2 | 1 | −0.0579 (18) | 0.5 | 0.0140 (16) | 0.105 (4) |
O2' | 1 | −0.0244 (9) | 0.5 | 0.038 (2) | 0.395 (4) |
O3 | 0.78147 (9) | −0.15150 (6) | 0.77500 (11) | 0.01886 (12) | |
Atomic displacement parameters (Å2) top | U11 | U22 | U33 | U12 | U13 | U23 |
Zn | 0.02256 (16) | 0.00800 (5) | 0.01712 (16) | 0 | −0.00821 (8) | 0 |
P | 0.00694 (7) | 0.01182 (8) | 0.00663 (7) | 0 | 0.00062 (5) | 0 |
O1 | 0.00970 (17) | 0.01160 (18) | 0.00768 (16) | 0 | −0.00075 (13) | 0 |
O2 | 0.0037 (17) | 0.018 (4) | 0.022 (2) | 0 | 0.0051 (16) | 0 |
O2' | 0.0104 (6) | 0.060 (6) | 0.0482 (14) | 0 | 0.0147 (8) | 0 |
O3 | 0.0290 (2) | 0.01106 (16) | 0.01344 (16) | 0.00644 (15) | 0.00022 (15) | 0.00268 (12) |
Geometric parameters (Å, º) top | Average | Minimum | Maximum |
Zn—O1i | 2.0613 (16) | 2.0108 (18) | 2.104 (2) |
Zn—O1ii | 2.0615 (16) | 2.0114 (18) | 2.106 (2) |
Zn—O3iii | 2.019 (2) | 1.974 (2) | 2.063 (3) |
Zn—O3iv | 2.019 (2) | 1.975 (2) | 2.066 (3) |
P—O1 | 1.5210 (16) | 1.5103 (16) | 1.5319 (16) |
P—O2 | 1.619 (13) | 1.568 (7) | 1.633 (19) |
P—O2v | 1.619 (13) | 1.568 (7) | 1.633 (19) |
P—O2' | 1.5649 (12) | 1.5553 (11) | 1.5773 (13) |
P—O2'v | 1.5648 (12) | 1.5553 (11) | 1.5773 (13) |
P—O3 | 1.5166 (19) | 1.5068 (19) | 1.5248 (19) |
P—O3vi | 1.5166 (19) | 1.5068 (19) | 1.5248 (19) |
O2—O2' | 0.29 (2) | 0.20 (2) | 0.336 (16) |
O2—O2'v | 0.69 (2) | 0.58 (3) | 0.741 (16) |
O2'—O2'v | 0.405 (11) | 0.405 (11) | 0.405 (11) |
| | | |
O1i—Zn—O1ii | 80.45 (5) | 79.75 (5) | 80.96 (5) |
O1i—Zn—O3iii | 157.21 (14) | 143.74 (17) | 167.56 (14) |
O1i—Zn—O3iv | 94.12 (9) | 92.89 (11) | 94.92 (10) |
O1ii—Zn—O3iii | 94.11 (9) | 92.85 (11) | 94.92 (10) |
O1ii—Zn—O3iv | 157.11 (14) | 143.40 (17) | 167.30 (14) |
O3iii—Zn—O3iv | 98.51 (7) | 97.73 (7) | 99.41 (7) |
O1—P—O2 | 104.1 (7) | 99.9 (7) | 108.0 (7) |
O1—P—O2v | 104.1 (7) | 99.9 (7) | 108.0 (7) |
O1—P—O2' | 104.33 (8) | 104.11 (8) | 104.69 (8) |
O1—P—O2'v | 104.33 (8) | 104.11 (8) | 104.69 (8) |
O1—P—O3 | 112.02 (8) | 111.62 (8) | 112.45 (8) |
O1—P—O3vi | 112.03 (8) | 111.62 (8) | 112.45 (8) |
O2—P—O2' | 10.2 (7) | 7.0 (8) | 11.8 (6) |
O2—P—O2'v | 24.8 (8) | 20.9 (10) | 26.7 (6) |
O2—P—O3 | 95.5 (7) | 94.3 (9) | 98.1 (9) |
O2—P—O3vi | 120.2 (7) | 117.0 (9) | 121.6 (8) |
O2v—P—O2' | 24.7 (8) | 20.9 (10) | 26.7 (6) |
O2v—P—O2'v | 10.1 (7) | 7.0 (8) | 11.8 (6) |
O2v—P—O3 | 120.1 (7) | 117.0 (9) | 121.6 (8) |
O2v—P—O3vi | 95.5 (7) | 94.3 (9) | 98.1 (9) |
O2'—P—O2'v | 14.9 (4) | 14.8 (4) | 14.9 (4) |
O2'—P—O3 | 101.5 (3) | 97.5 (3) | 105.8 (3) |
O2'—P—O3vi | 114.4 (2) | 110.5 (3) | 118.7 (2) |
O2'v—P—O3 | 114.4 (2) | 110.5 (3) | 118.7 (2) |
O2'v—P—O3vi | 101.5 (3) | 97.5 (3) | 105.8 (3) |
O3—P—O3vi | 111.85 (11) | 111.67 (11) | 112.03 (11) |
Znvii—O1—Znviii | 99.50 (11) | 98.10 (11) | 101.17 (11) |
Znvii—O1—P | 129.61 (6) | 128.44 (6) | 131.03 (5) |
Znviii—O1—P | 129.60 (6) | 128.44 (6) | 131.03 (5) |
P—O2—Pix | 146.9 (14) | 144.2 (10) | 152 (2) |
P—O2—O2' | 73 (2) | 68.3 (3) | 85 (2) |
P—O2—O2'v | 73.4 (12) | 71.6 (12) | 79.0 (11) |
Pix—O2—O2' | 74 (2) | 68.4 (3) | 85 (2) |
Pix—O2—O2'v | 73.5 (12) | 71.6 (12) | 79.3 (12) |
O2'—O2—O2'v | 9(2) | 0.1 (19) | 25 (5) |
P—O2'—Pix | 165.1 (5) | 162.5 (5) | 167.9 (5) |
P—O2'—O2 | 96 (5) | 88 (6) | 105 (6) |
P—O2'—O2v | 81.8 (19) | 79 (2) | 86 (2) |
P—O2'—O2'v | 82.6 (3) | 81.2 (3) | 84.0 (3) |
Pix—O2'—O2 | 96 (5) | 87 (6) | 104 (6) |
Pix—O2'—O2v | 81.8 (19) | 79 (2) | 86 (2) |
Pix—O2'—O2'v | 82.6 (3) | 81.2 (3) | 84.0 (3) |
O2—O2'—O2'v | 166 (3) | 143 (5) | 180 (4) |
O2v—O2'—O2'v | 5.5 (9) | 0.0 (5) | 12.1 (6) |
Znx—O3—P | 133.91 (14) | 126.64 (15) | 138.26 (14) |
Symmetry codes: (i) x1, x2, x3+1, x4; (ii) −x1+1, x2, −x3+1, −x4+1/2; (iii) x1−1/2, x2+1/2, x3, x4; (iv) −x1+3/2, x2+1/2, −x3+2, −x4+1/2; (v) −x1+2, −x2, −x3+1, −x4; (vi) x1, −x2, x3, x4+1/2; (vii) x1, x2, x3−1, x4; (viii) −x1+1, −x2, −x3+1, −x4; (ix) −x1+2, x2, −x3+1, −x4+1/2; (x) x1+1/2, x2−1/2, x3, x4. |
(alpha2_zn2p2o7_450) zinc(II) diphosphate(V)
top
Crystal data top
O7P2Zn2 | F(000) = 292 |
Mr = 304.7 | Dx = 4.239 Mg m−3 |
Monoclinic, C2/m(α0γ)0s† | Mo Kα radiation, λ = 0.71073 Å |
q = 0.3268(3)a* + 0.3989(2)c* | Cell parameters from 4377 reflections |
a = 6.6011 (2) Å | θ = 4.0–45.3° |
b = 8.2839 (3) Å | µ = 10.7 mm−1 |
c = 4.5266 (2) Å | T = 450 K |
β = 105.3869 (17)° | Rod, translucent colourless |
V = 238.66 (2) Å3 | 0.42 × 0.30 × 0.06 mm |
Z = 2 | |
† Symmetry operations: (1) x1, x2, x3, x4; (2) −x1, x2, −x3, −x4+1/2; (3) −x1, −x2, −x3, −x4; (4) x1, −x2, x3, x4+1/2; (5) x1+1/2, x2+1/2, x3, x4; (6) −x1+1/2, x2+1/2, −x3, −x4+1/2; (7) −x1+1/2, −x2+1/2, −x3, −x4; (8) x1+1/2, −x2+1/2, x3, x4+1/2.
|
Data collection top
Bruker KAPPA APEX II CCD diffractometer | 5061 independent reflections |
Radiation source: X-ray tube | 1643 reflections with I > 3σ(I) |
Graphite monochromator | Rint = 0.026 |
ω and φ scans | θmax = 45.4°, θmin = 2.1° |
Absorption correction: multi-scan SADABS | h = −13→13 |
Tmin = 0.025, Tmax = 0.60 | k = −16→16 |
13609 measured reflections | l = −9→5 |
Refinement top
Refinement on F | 1 constraint |
R[F > 3σ(F)] = 0.029 | Weighting scheme based on measured s.u.'s w = 1/(σ2(F) + 0.0001F2) |
wR(F) = 0.048 | (Δ/σ)max = 0.041 |
S = 1.22 | Δρmax = 0.81 e Å−3 |
5061 reflections | Δρmin = −0.82 e Å−3 |
143 parameters | Extinction correction: B-C type 1 Gaussian isotropic (Becker & Coppens, 1974) |
0 restraints | Extinction coefficient: 2610 (90) |
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top | x | y | z | Uiso*/Ueq | Occ. (<1) |
Zn | 0.5 | 0.18982 (3) | 1 | 0.02042 (11) | |
P | 0.78911 (3) | 0 | 0.59073 (4) | 0.00965 (5) | |
O1 | 0.62120 (8) | 0 | 0.28642 (13) | 0.01136 (11) | |
O2 | 1 | −0.068 (3) | 0.5 | 0.009 (2) | 0.050 (3) |
O2' | 1 | −0.0281 (6) | 0.5 | 0.0337 (17) | 0.450 (3) |
O3 | 0.78150 (10) | −0.15154 (6) | 0.77508 (12) | 0.02031 (14) | |
Atomic displacement parameters (Å2) top | U11 | U22 | U33 | U12 | U13 | U23 |
Zn | 0.02518 (18) | 0.00904 (5) | 0.0185 (3) | 0 | −0.00906 (10) | 0 |
P | 0.00785 (7) | 0.01289 (8) | 0.00750 (7) | 0 | 0.00081 (5) | 0 |
O1 | 0.01101 (17) | 0.01278 (19) | 0.00846 (17) | 0 | −0.00059 (13) | 0 |
O2 | 0.001 (2) | 0.004 (5) | 0.023 (4) | 0 | 0.004 (2) | 0 |
O2' | 0.0116 (5) | 0.046 (5) | 0.0470 (12) | 0 | 0.0141 (6) | 0 |
O3 | 0.0309 (3) | 0.01222 (17) | 0.01455 (18) | 0.00677 (16) | 0.00043 (18) | 0.00303 (13) |
Geometric parameters (Å, º) top | Average | Minimum | Maximum |
Zn—O1i | 2.061 (2) | 2.007 (3) | 2.110 (3) |
Zn—O1ii | 2.061 (2) | 2.009 (3) | 2.114 (3) |
Zn—O3iii | 2.017 (3) | 1.993 (3) | 2.040 (2) |
Zn—O3iv | 2.017 (3) | 1.993 (3) | 2.040 (2) |
P—O1 | 1.522 (2) | 1.519 (2) | 1.524 (2) |
P—O2 | 1.646 (7) | 1.641 (7) | 1.653 (7) |
P—O2v | 1.646 (7) | 1.641 (7) | 1.653 (7) |
P—O2' | 1.5699 (12) | 1.5626 (11) | 1.5791 (12) |
P—O2'v | 1.5699 (12) | 1.5626 (11) | 1.5791 (12) |
P—O3 | 1.516 (3) | 1.508 (3) | 1.527 (3) |
P—O3vi | 1.516 (3) | 1.508 (3) | 1.527 (3) |
O2—O2' | 0.33 (2) | 0.33 (2) | 0.33 (2) |
O2—O2'v | 0.79 (2) | 0.79 (2) | 0.79 (2) |
O2'—O2'v | 0.465 (7) | 0.465 (7) | 0.465 (7) |
| | | |
O1i—Zn—O1ii | 80.43 (7) | 80.20 (7) | 80.79 (7) |
O1i—Zn—O3iii | 157.2 (2) | 148.3 (3) | 165.8 (2) |
O1i—Zn—O3iv | 94.18 (14) | 92.18 (16) | 94.82 (14) |
O1ii—Zn—O3iii | 94.15 (14) | 92.07 (16) | 94.82 (14) |
O1ii—Zn—O3iv | 157.1 (2) | 147.7 (3) | 165.4 (2) |
O3iii—Zn—O3iv | 98.59 (10) | 97.48 (10) | 99.24 (10) |
O1—P—O2 | 103.79 (12) | 103.54 (12) | 104.09 (12) |
O1—P—O2v | 103.79 (12) | 103.54 (12) | 104.09 (12) |
O1—P—O2' | 104.27 (11) | 103.83 (12) | 104.68 (12) |
O1—P—O2'v | 104.27 (11) | 103.83 (12) | 104.68 (12) |
O1—P—O3 | 112.07 (11) | 111.64 (11) | 112.61 (11) |
O1—P—O3vi | 112.07 (11) | 111.64 (11) | 112.61 (11) |
O2—P—O2' | 11.4 (7) | 11.4 (7) | 11.5 (7) |
O2—P—O2'v | 28.5 (7) | 28.4 (7) | 28.6 (7) |
O2—P—O3 | 92.0 (6) | 89.2 (6) | 94.0 (6) |
O2—P—O3vi | 123.4 (6) | 122.5 (6) | 124.0 (6) |
O2v—P—O2' | 28.5 (7) | 28.4 (7) | 28.6 (7) |
O2v—P—O2'v | 11.4 (7) | 11.4 (7) | 11.5 (7) |
O2v—P—O3 | 123.4 (6) | 122.5 (6) | 124.0 (6) |
O2v—P—O3vi | 92.0 (6) | 89.2 (6) | 94.0 (6) |
O2'—P—O2'v | 17.0 (2) | 17.0 (2) | 17.1 (2) |
O2'—P—O3 | 100.50 (19) | 97.93 (19) | 104.15 (19) |
O2'—P—O3vi | 115.33 (19) | 112.78 (19) | 118.94 (18) |
O2'v—P—O3 | 115.32 (19) | 112.78 (19) | 118.94 (18) |
O2'v—P—O3vi | 100.51 (19) | 97.93 (19) | 104.15 (19) |
O3—P—O3vi | 111.86 (16) | 110.54 (16) | 113.14 (16) |
Znvii—O1—Znviii | 99.54 (17) | 97.78 (17) | 101.16 (17) |
Znvii—O1—P | 129.60 (8) | 128.56 (10) | 130.43 (10) |
Znviii—O1—P | 129.59 (8) | 128.56 (10) | 130.43 (10) |
P—O2—Pix | 141.2 (14) | 140.2 (14) | 141.8 (14) |
P—O2—O2' | 70.6 (7) | 69.8 (7) | 71.0 (7) |
P—O2—O2'v | 70.6 (7) | 69.8 (7) | 71.0 (7) |
Pix—O2—O2' | 70.6 (7) | 69.8 (7) | 71.0 (7) |
Pix—O2—O2'v | 70.6 (7) | 69.8 (7) | 71.0 (7) |
O2'—O2—O2'v | 0.0 (5) | 0.0 (5) | 0.0 (5) |
P—O2'—Pix | 163.0 (3) | 161.2 (3) | 164.7 (3) |
P—O2'—O2 | 97.96 (17) | 97.55 (17) | 98.85 (17) |
P—O2'—O2v | 80.92 (17) | 80.55 (17) | 81.79 (17) |
P—O2'—O2'v | 81.47 (17) | 80.55 (17) | 82.45 (17) |
Pix—O2'—O2 | 97.95 (17) | 97.55 (17) | 98.83 (17) |
Pix—O2'—O2v | 80.93 (17) | 80.55 (17) | 81.78 (17) |
Pix—O2'—O2'v | 81.48 (17) | 80.55 (17) | 82.45 (17) |
O2—O2'—O2'v | 180.0 (5) | 180.0 (5) | 180.0 (5) |
O2v—O2'—O2'v | 0.0 (5) | 0.0 (5) | 0.0 (5) |
Znx—O3—P | 133.98 (19) | 129.14 (17) | 138.8 (2) |
Symmetry codes: (i) x1, x2, x3+1, x4; (ii) −x1+1, x2, −x3+1, −x4+1/2; (iii) x1−1/2, x2+1/2, x3, x4; (iv) −x1+3/2, x2+1/2, −x3+2, −x4+1/2; (v) −x1+2, −x2, −x3+1, −x4; (vi) x1, −x2, x3, x4+1/2; (vii) x1, x2, x3−1, x4; (viii) −x1+1, −x2, −x3+1, −x4; (ix) −x1+2, x2, −x3+1, −x4+1/2; (x) x1+1/2, x2−1/2, x3, x4. |
(alpha2_zn2p2o7_500) zinc(II) diphosphate(V)
top
Crystal data top
O7P2Zn2 | F(000) = 292 |
Mr = 304.7 | Dx = 4.235 Mg m−3 |
Monoclinic, C2/m(α0γ)0s† | Mo Kα radiation, λ = 0.71073 Å |
q = 0.3239(14)a* + 0.3966(9)c* | Cell parameters from 3836 reflections |
a = 6.5998 (4) Å | θ = 4.0–45.3° |
b = 8.2845 (5) Å | µ = 10.69 mm−1 |
c = 4.5300 (3) Å | T = 500 K |
β = 105.335 (3)° | Rod, translucent colourless |
V = 238.86 (3) Å3 | 0.42 × 0.30 × 0.06 mm |
Z = 2 | |
† Symmetry operations: (1) x1, x2, x3, x4; (2) −x1, x2, −x3, −x4+1/2; (3) −x1, −x2, −x3, −x4; (4) x1, −x2, x3, x4+1/2; (5) x1+1/2, x2+1/2, x3, x4; (6) −x1+1/2, x2+1/2, −x3, −x4+1/2; (7) −x1+1/2, −x2+1/2, −x3, −x4; (8) x1+1/2, −x2+1/2, x3, x4+1/2.
|
Data collection top
Bruker KAPPA APEX II CCD diffractometer | 2969 independent reflections |
Radiation source: X-ray tube | 1331 reflections with I > 3σ(I) |
Graphite monochromator | Rint = 0.025 |
ω and φ scans | θmax = 45.4°, θmin = 3.5° |
Absorption correction: multi-scan SADABS | h = −13→12 |
Tmin = 0.025, Tmax = 0.60 | k = −16→16 |
8052 measured reflections | l = −5→9 |
Refinement top
Refinement on F | 1 constraint |
R[F > 3σ(F)] = 0.030 | Weighting scheme based on measured s.u.'s w = 1/(σ2(F) + 0.0001F2) |
wR(F) = 0.047 | (Δ/σ)max = 0.020 |
S = 1.50 | Δρmax = 1.04 e Å−3 |
2969 reflections | Δρmin = −1.13 e Å−3 |
98 parameters | Extinction correction: B-C type 1 Gaussian isotropic (Becker & Coppens, 1974) |
0 restraints | Extinction coefficient: 2750 (110) |
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top | x | y | z | Uiso*/Ueq | Occ. (<1) |
Zn | 0.5 | 0.18988 (3) | 1 | 0.02339 (5) | |
P | 0.78921 (3) | 0 | 0.59064 (5) | 0.01022 (6) | |
O1 | 0.62136 (11) | 0 | 0.28655 (16) | 0.01244 (14) | |
O2 | 1 | −0.072 (5) | 0.5 | 0.013 (6) | 0.027 (4) |
O2' | 1 | −0.0304 (7) | 0.5 | 0.037 (2) | 0.473 (4) |
O3 | 0.78098 (12) | −0.15170 (8) | 0.77509 (15) | 0.02105 (15) | |
Atomic displacement parameters (Å2) top | U11 | U22 | U33 | U12 | U13 | U23 |
Zn | 0.02790 (9) | 0.00998 (6) | 0.02228 (9) | 0 | −0.01094 (6) | 0 |
P | 0.00840 (8) | 0.01341 (10) | 0.00826 (9) | 0 | 0.00114 (6) | 0 |
O1 | 0.0124 (2) | 0.0138 (2) | 0.0092 (2) | 0 | −0.00059 (17) | 0 |
O2 | 0.007 (7) | 0.002 (8) | 0.024 (11) | 0 | −0.008 (7) | 0 |
O2' | 0.0111 (6) | 0.056 (6) | 0.0486 (14) | 0 | 0.0155 (8) | 0 |
O3 | 0.0313 (3) | 0.0131 (2) | 0.0157 (2) | 0.00649 (19) | 0.0007 (2) | 0.00333 (17) |
Geometric parameters (Å, º) top | Average | Minimum | Maximum |
Zn—O1i | 2.0619 (11) | 2.0542 (11) | 2.0692 (11) |
Zn—O1ii | 2.0618 (11) | 2.0542 (11) | 2.0692 (11) |
Zn—O3iii | 2.0178 (12) | 2.0087 (12) | 2.0265 (12) |
Zn—O3iv | 2.0176 (12) | 2.0080 (12) | 2.0265 (12) |
P—O1 | 1.5224 (7) | 1.5223 (7) | 1.5224 (7) |
P—O2 | 1.659 (15) | 1.657 (15) | 1.663 (15) |
P—O2v | 1.659 (15) | 1.657 (15) | 1.663 (15) |
P—O2' | 1.5716 (10) | 1.5692 (10) | 1.5740 (11) |
P—O2'v | 1.5715 (10) | 1.5692 (10) | 1.5740 (11) |
P—O3 | 1.5182 (13) | 1.5158 (13) | 1.5204 (13) |
P—O3vi | 1.5182 (13) | 1.5158 (13) | 1.5204 (13) |
O2—O2' | 0.34 (4) | 0.34 (4) | 0.34 (4) |
O2—O2'v | 0.85 (4) | 0.85 (4) | 0.85 (4) |
O2'—O2'v | 0.504 (8) | 0.504 (8) | 0.504 (8) |
| | | |
O1i—Zn—O1ii | 80.55 (4) | 80.30 (4) | 80.80 (4) |
O1i—Zn—O3iii | 157.11 (5) | 156.01 (6) | 157.89 (6) |
O1i—Zn—O3iv | 94.09 (4) | 93.67 (4) | 94.45 (4) |
O1ii—Zn—O3iii | 94.08 (4) | 93.64 (4) | 94.45 (4) |
O1ii—Zn—O3iv | 157.13 (5) | 156.06 (6) | 157.93 (6) |
O3iii—Zn—O3iv | 98.84 (5) | 98.58 (5) | 99.11 (5) |
O1—P—O2 | 103.61 (12) | 103.42 (13) | 103.70 (12) |
O1—P—O2v | 103.61 (12) | 103.42 (13) | 103.70 (12) |
O1—P—O2' | 104.25 (4) | 104.13 (4) | 104.36 (3) |
O1—P—O2'v | 104.25 (4) | 104.13 (4) | 104.36 (3) |
O1—P—O3 | 112.00 (6) | 111.95 (6) | 112.05 (6) |
O1—P—O3vi | 112.00 (6) | 111.95 (6) | 112.05 (6) |
O2—P—O2' | 11.8 (14) | 11.8 (14) | 11.9 (14) |
O2—P—O2'v | 30.3 (14) | 30.2 (14) | 30.3 (14) |
O2—P—O3 | 90.5 (12) | 89.6 (12) | 91.0 (12) |
O2—P—O3vi | 125.1 (11) | 124.6 (11) | 126.0 (11) |
O2v—P—O2' | 30.3 (14) | 30.2 (14) | 30.3 (14) |
O2v—P—O2'v | 11.8 (14) | 11.8 (14) | 11.9 (14) |
O2v—P—O3 | 125.1 (11) | 124.6 (11) | 126.0 (11) |
O2v—P—O3vi | 90.5 (12) | 89.6 (12) | 91.0 (12) |
O2'—P—O2'v | 18.4 (3) | 18.4 (3) | 18.4 (3) |
O2'—P—O3 | 100.02 (19) | 98.56 (19) | 101.49 (19) |
O2'—P—O3vi | 116.07 (19) | 114.62 (19) | 117.53 (19) |
O2'v—P—O3 | 116.07 (19) | 114.62 (19) | 117.53 (19) |
O2'v—P—O3vi | 100.03 (19) | 98.56 (19) | 101.49 (19) |
O3—P—O3vi | 111.77 (7) | 111.76 (7) | 111.77 (7) |
Znvii—O1—Znviii | 99.45 (3) | 99.43 (3) | 99.46 (3) |
Znvii—O1—P | 129.66 (7) | 129.08 (7) | 130.25 (7) |
Znviii—O1—P | 129.66 (7) | 129.08 (7) | 130.25 (7) |
P—O2—Pix | 139 (3) | 138 (3) | 139 (3) |
P—O2—O2' | 69.3 (14) | 68.8 (14) | 69.5 (14) |
P—O2—O2'v | 69.3 (14) | 68.8 (14) | 69.5 (14) |
Pix—O2—O2' | 69.3 (14) | 68.8 (14) | 69.5 (14) |
Pix—O2—O2'v | 69.3 (14) | 68.8 (14) | 69.5 (14) |
O2'—O2—O2'v | 0.0 (5) | 0.0 (5) | 0.0 (5) |
P—O2'—Pix | 161.6 (4) | 160.5 (4) | 162.6 (4) |
P—O2'—O2 | 98.9 (2) | 98.7 (2) | 99.4 (2) |
P—O2'—O2v | 80.5 (2) | 80.2 (2) | 80.9 (2) |
P—O2'—O2'v | 80.8 (2) | 80.2 (2) | 81.3 (2) |
Pix—O2'—O2 | 98.9 (2) | 98.7 (2) | 99.4 (2) |
Pix—O2'—O2v | 80.5 (2) | 80.2 (2) | 81.0 (2) |
Pix—O2'—O2'v | 80.8 (2) | 80.2 (2) | 81.3 (2) |
O2—O2'—O2'v | 180.0 (5) | 180.0 (5) | 180.0 (5) |
O2v—O2'—O2'v | 0.0 (5) | 0.0 (5) | 0.0 (5) |
Znx—O3—P | 133.74 (8) | 132.27 (8) | 135.25 (8) |
Symmetry codes: (i) x1, x2, x3+1, x4; (ii) −x1+1, x2, −x3+1, −x4+1/2; (iii) x1−1/2, x2+1/2, x3, x4; (iv) −x1+3/2, x2+1/2, −x3+2, −x4+1/2; (v) −x1+2, −x2, −x3+1, −x4; (vi) x1, −x2, x3, x4+1/2; (vii) x1, x2, x3−1, x4; (viii) −x1+1, −x2, −x3+1, −x4; (ix) −x1+2, x2, −x3+1, −x4+1/2; (x) x1+1/2, x2−1/2, x3, x4. |