research papers
The structural phases observed in LiKSO crystals due to thermotropic transitions have been studied for more than a century. Nowadays many different phases are referenced, but some of the results are still controversial. Structural studies by single-crystal X-ray diffraction from room temperature to 803 K are presented here. Phase II (708 T 943 K) is extensively discussed on the basis of ordered and disordered models, using harmonic and anharmonic atomic displacements, and considering a twinned crystal composed of three orthorhombic domains. Analyses of the same phase at different temperatures determine the best structure model.
Supporting information
Crystallographic Information File (CIF) https://doi.org/10.1107/S0108768100003219/ca0003sup1.cif | |
Structure factor file (CIF format) https://doi.org/10.1107/S0108768100003219/ca0003573Ksup2.hkl | |
Structure factor file (CIF format) https://doi.org/10.1107/S0108768100003219/ca0003723Ksup3.hkl | |
Structure factor file (CIF format) https://doi.org/10.1107/S0108768100003219/ca0003803Ksup4.hkl |
Computing details top
(573K) top
Crystal data top
LiO4SK | F(000) = 140 |
Mr = 142.1 | Dx = 2.328 Mg m−3 |
Hexagonal, P63 | Mo Kα radiation, λ = 0.71073 Å |
a = 5.202 (1) Å | µ = 1.69 mm−1 |
c = 8.647 (2) Å | T = 573 K |
V = 202.65 (9) Å3 | Hexagonal, colourless |
Z = 2 | 0.20 × 0.20 × 0.10 mm |
Data collection top
Image-Plate diffractometer | Rint = 0.029 |
Oscillating scans | θmax = 30.2°, θmin = 4.5° |
2231 measured reflections | h = −7→7 |
396 independent reflections | k = −7→7 |
363 reflections with I > 3σ(I) | l = −12→12 |
Refinement top
Refinement on F | Weighting scheme based on measured s.u.'s w = 1/[σ2(F) + 0.0001F2] |
R[F2 > 2σ(F2)] = 0.020 | (Δ/σ)max = 0.001 |
wR(F2) = 0.026 | Δρmax = 0.18 e Å−3 |
S = 2.24 | Δρmin = −0.19 e Å−3 |
394 reflections | Extinction correction: B-C type 1 Lorentzian isotropic |
41 parameters | Extinction coefficient: 1.4 (2) |
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
x | y | z | Uiso*/Ueq | Occ. (<1) | |
K | 0 | 0 | 0 | 3.71 (2) | 0.999999 |
Li | 0.333333 | 0.666667 | 0.311 (2) | 3.1 (1) | 0.999999 |
S | 0.333333 | 0.666667 | 0.70785 (9) | 2.04 (1) | 0.999999 |
O1 | 0.333333 | 0.666667 | 0.5411 (8) | 6.62 (8) | 0.999999 |
O2 | 0.3589 (7) | 0.4211 (6) | 0.7615 (6) | 5.07 (5) |
Atomic displacement parameters (Å2) top
U11 | U22 | U33 | U12 | U13 | U23 | |
K | 0.0484 (2) | 0.0484 (2) | 0.0443 (3) | 0.0242 (1) | 0 | 0 |
Li | 0.033 (1) | 0.033 (1) | 0.051 (4) | 0.0166 (6) | 0 | 0 |
S | 0.0254 (2) | 0.0254 (2) | 0.0265 (2) | 0.0127 (1) | 0 | 0 |
O1 | 0.111 (2) | 0.111 (2) | 0.0304 (8) | 0.0553 (8) | 0 | 0 |
O2 | 0.0590 (8) | 0.0447 (7) | 0.0982 (9) | 0.0328 (6) | −0.0014 (8) | 0.0190 (8) |
Bond lengths (Å) top
K—Lii | 3.419 (7) | Li—O1ii | 3.804 (9) |
K—Liii | 3.419 (7) | Li—O1iii | 3.804 (9) |
K—Liiii | 3.419 (7) | Li—O1xv | 3.804 (9) |
K—Siv | 3.9245 (5) | Li—O2ii | 1.920 (5) |
K—Sv | 3.9245 (5) | Li—O2xv | 3.423 (3) |
K—Svi | 3.9245 (5) | Li—O2xvi | 3.423 (4) |
K—Si | 3.5001 (4) | Li—O2x | 1.920 (5) |
K—Sii | 3.5001 (4) | Li—O2xiv | 3.423 (5) |
K—Siii | 3.5001 (4) | Li—O2xvii | 1.920 (6) |
K—O1i | 3.0243 (8) | S—O1 | 1.442 (7) |
K—O1ii | 3.0243 (8) | S—O2 | 1.426 (4) |
K—O1iii | 3.0243 (8) | S—O2xviii | 3.888 (4) |
K—O2iv | 3.795 (3) | S—O2xix | 3.888 (3) |
K—O2vi | 2.907 (4) | S—O2xx | 1.426 (3) |
K—O2i | 3.906 (4) | S—O2xxi | 1.426 (5) |
K—O2ii | 3.051 (5) | S—O2xxii | 3.888 (5) |
K—O2vii | 2.907 (4) | O1—O2 | 2.335 (7) |
K—O2viii | 3.795 (4) | O1—O2ii | 3.057 (7) |
K—O2ix | 3.051 (4) | O1—O2xx | 2.335 (7) |
K—O2x | 3.906 (4) | O1—O2x | 3.057 (7) |
K—O2xi | 2.907 (5) | O1—O2xxi | 2.335 (8) |
K—O2xii | 3.795 (4) | O1—O2xvii | 3.057 (7) |
K—O2xiii | 3.906 (4) | O2—O2xix | 3.547 (4) |
K—O2xiv | 3.051 (4) | O2—O2xxiii | 3.242 (6) |
Li—S | 3.43 (1) | O2—O2xx | 2.336 (5) |
Li—Sii | 3.133 (4) | O2—O2xxiv | 3.547 (4) |
Li—Siii | 3.133 (4) | O2—O2xxi | 2.336 (6) |
Li—Sxv | 3.133 (4) | O2—O2xxii | 3.242 (5) |
Li—O1 | 1.99 (2) |
Symmetry codes: (i) x−y, x−1, z−1/2; (ii) x−y, x, z−1/2; (iii) x−y+1, x, z−1/2; (iv) x−1, y−1, z−1; (v) x, y−1, z−1; (vi) x, y, z−1; (vii) −y, x−y, z−1; (viii) −y+1, x−y, z−1; (ix) −x, −y, z−1/2; (x) −x+1, −y+1, z−1/2; (xi) −x+y, −x, z−1; (xii) −x+y, −x+1, z−1; (xiii) y−1, −x+y, z−1/2; (xiv) y, −x+y, z−1/2; (xv) x−y+1, x+1, z−1/2; (xvi) −x, −y+1, z−1/2; (xvii) y, −x+y+1, z−1/2; (xviii) x, y+1, z; (xix) −y, x−y, z; (xx) −y+1, x−y+1, z; (xxi) −x+y, −x+1, z; (xxii) −x+y+1, −x+1, z; (xxiii) −y+1, x−y, z; (xxiv) −x+y, −x, z. |
(723K) top
Crystal data top
LiO4SK | F(000) = 280 |
Mr = 142.1 | Dx = 2.261 Mg m−3 |
Orthorhombic, Pmcn | Mo Kα radiation, λ = 0.71073 Å |
a = 5.264 (4) Å | µ = 1.64 mm−1 |
b = 9.148 (3) Å | T = 723 K |
c = 8.666 (4) Å | Hexagoal, colorless |
V = 417.3 (4) Å3 | 0.20 × 0.20 × 0.10 mm |
Z = 4 |
Data collection top
Image-Plate diffractometer | Rint = 0.063 |
Oscillating scans | θmax = 30.5°, θmin = 3.2° |
13569 measured reflections | h = −7→7 |
2380 independent reflections | k = −12→12 |
986 reflections with I > 3σ(I) | l = −12→12 |
Refinement top
Refinement on F | 60 parameters |
R[F2 > 2σ(F2)] = 0.055 | Weighting scheme based on measured s.u.'s w = 1/(σ2(F) + 0.0001F2) |
wR(F2) = 0.063 | (Δ/σ)max = 0.001 |
S = 3.55 | Δρmax = 0.18 e Å−3 |
1066 reflections | Δρmin = −0.14 e Å−3 |
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
x | y | z | Uiso*/Ueq | Occ. (<1) | |
K | 0.25 | 0.2050 (1) | 0.99706 (8) | 0.1039 (3) | |
Li | 0.75 | 0.0779 (4) | 0.6603 (5) | 0.072 (1) | |
S | 0.7500 (7) | 0.4048 (1) | 0.78394 (9) | 0.0766 (4) | |
O1 | 0.670 (2) | 0.400 (1) | 0.9370 (5) | 0.273 (5) | 0.5 |
O2 | 1.000 (1) | 0.442 (1) | 0.7481 (8) | 0.165 (3) | 0.5 |
O3 | 0.598 (2) | 0.498 (1) | 0.723 (2) | 0.281 (7) | 0.5 |
O4 | 0.842 (1) | 0.2692 (6) | 0.7347 (7) | 0.187 (5) | 0.5 |
Atomic displacement parameters (Å2) top
U11 | U22 | U33 | U12 | U13 | U23 | |
K | 0.1066 (7) | 0.1157 (6) | 0.0895 (5) | 0 | 0 | 0.0054 (4) |
Li | 0.059 (2) | 0.067 (3) | 0.090 (3) | 0 | 0 | 0.002 (2) |
S | 0.0751 (8) | 0.0800 (8) | 0.0747 (5) | 0.034 (2) | 0.019 (2) | 0.0025 (6) |
O1 | 0.27 (1) | 0.45 (1) | 0.092 (2) | −0.162 (8) | 0.098 (5) | −0.049 (4) |
O2 | 0.022 (3) | 0.235 (8) | 0.236 (7) | −0.031 (3) | 0.023 (2) | −0.080 (5) |
O3 | 0.120 (6) | 0.280 (9) | 0.44 (2) | −0.011 (6) | −0.019 (7) | 0.26 (1) |
O4 | 0.133 (6) | 0.103 (3) | 0.32 (1) | −0.006 (3) | 0.018 (3) | −0.084 (4) |
Bond lengths (Å) top
K—Lii | 3.939 (4) | Li—O3xiv | 3.93 (1) |
K—Liii | 3.588 (3) | Li—O3vi | 2.21 (1) |
K—Liiii | 3.588 (3) | Li—O3xv | 3.65 (1) |
K—Liiv | 3.674 (4) | Li—O3vii | 3.65 (1) |
K—Sv | 3.705 (3) | Li—O3xvi | 2.21 (1) |
K—S | 3.692 (3) | Li—O3xvii | 3.93 (1) |
K—Sii | 3.764 (3) | Li—O3xi | 3.97 (1) |
K—Siii | 3.751 (3) | Li—O4 | 1.927 (7) |
K—Svi | 3.670 (1) | Li—O4xiv | 3.973 (8) |
K—Svii | 3.670 (1) | Li—O4xv | 3.664 (7) |
K—Sviii | 3.751 (3) | Li—O4vii | 3.664 (7) |
K—Six | 3.764 (3) | Li—O4xvii | 3.973 (8) |
K—Sx | 3.692 (3) | Li—O4xi | 1.927 (7) |
K—Sxi | 3.705 (3) | S—Sxi | 0.018 (5) |
K—O1v | 3.572 (9) | S—O1 | 1.389 (5) |
K—O1 | 2.888 (9) | S—O1xii | 3.728 (8) |
K—O1xii | 3.685 (9) | S—O1xviii | 3.739 (8) |
K—O1xiii | 3.685 (9) | S—O1xi | 1.395 (5) |
K—O1x | 2.888 (9) | S—O2v | 3.964 (8) |
K—O1xi | 3.572 (9) | S—O2 | 1.405 (8) |
K—O2v | 3.331 (8) | S—O2xi | 1.388 (8) |
K—O2ii | 2.877 (8) | S—O2xix | 3.983 (8) |
K—O2vi | 3.468 (8) | S—O3 | 1.28 (1) |
K—O2vii | 3.468 (8) | S—O3xi | 1.29 (1) |
K—O2ix | 2.877 (8) | S—O4 | 1.401 (6) |
K—O2xi | 3.331 (8) | S—O4xx | 3.975 (6) |
K—O3xii | 3.73 (1) | S—O4xxi | 3.965 (6) |
K—O3iii | 3.26 (1) | S—O4xi | 1.395 (6) |
K—O3vi | 2.81 (1) | O1—O1xii | 2.79 (1) |
K—O3vii | 2.81 (1) | O1—O1xiii | 3.39 (1) |
K—O3viii | 3.26 (1) | O1—O1xviii | 3.39 (1) |
K—O3xiii | 3.73 (1) | O1—O1xi | 0.84 (1) |
K—O4v | 3.183 (7) | O1—O2v | 3.91 (1) |
K—O4 | 3.901 (7) | O1—O2 | 2.42 (1) |
K—O4ii | 2.986 (7) | O1—O2xxii | 3.54 (1) |
K—O4iii | 3.741 (7) | O1—O2xiii | 3.21 (1) |
K—O4viii | 3.741 (7) | O1—O2xi | 1.907 (9) |
K—O4ix | 2.986 (7) | O1—O3 | 2.09 (1) |
K—O4x | 3.901 (7) | O1—O3xii | 3.39 (1) |
K—O4xi | 3.183 (7) | O1—O3xviii | 3.82 (1) |
Li—S | 3.177 (4) | O1—O3xi | 2.39 (1) |
Li—Sxiv | 3.265 (4) | O1—O4 | 2.305 (9) |
Li—Svi | 3.102 (4) | O1—O4iii | 3.140 (9) |
Li—Sxv | 3.117 (4) | O1—O4ix | 3.008 (9) |
Li—Svii | 3.117 (4) | O1—O4xi | 2.122 (9) |
Li—Sxvi | 3.102 (4) | O2—O2xi | 2.64 (1) |
Li—Sxvii | 3.265 (4) | O2—O2xix | 2.63 (1) |
Li—Sxi | 3.177 (4) | O2—O3 | 2.19 (1) |
Li—O1 | 3.820 (9) | O2—O3xxiii | 3.19 (1) |
Li—O1xiv | 1.990 (6) | O2—O3xi | 0.76 (1) |
Li—O1vi | 2.874 (9) | O2—O4 | 1.79 (1) |
Li—O1xv | 3.561 (9) | O2—O4xx | 3.11 (1) |
Li—O1vii | 3.561 (9) | O2—O4xxiv | 3.49 (1) |
Li—O1xvi | 2.874 (9) | O2—O4xi | 2.40 (1) |
Li—O1xvii | 1.990 (6) | O2—O4xix | 3.81 (1) |
Li—O1xi | 3.820 (9) | O3—O3x | 3.66 (2) |
Li—O2 | 3.66 (1) | O3—O3xi | 1.60 (2) |
Li—O2xiv | 3.811 (8) | O3—O4 | 2.46 (1) |
Li—O2xv | 1.974 (9) | O3—O4iv | 3.41 (1) |
Li—O2vii | 1.974 (9) | O3—O4xx | 3.87 (1) |
Li—O2xvii | 3.811 (8) | O3—O4xxi | 2.84 (1) |
Li—O2xi | 3.66 (1) | O3—O4xi | 2.12 (1) |
Li—O3 | 3.97 (1) | O4—O4xi | 0.97 (1) |
Symmetry codes: (i) −x+1, −y, −z+2; (ii) x−1, −y+1/2, z+1/2; (iii) x, −y+1/2, z+1/2; (iv) −x+1, y+1/2, −z+3/2; (v) x−1, y, z; (vi) −x+1, y−1/2, −z+3/2; (vii) x−1/2, y−1/2, −z+3/2; (viii) −x+1/2, −y+1/2, z+1/2; (ix) −x+3/2, −y+1/2, z+1/2; (x) −x+1/2, y, z; (xi) −x+3/2, y, z; (xii) −x+1, −y+1, −z+2; (xiii) x−1/2, −y+1, −z+2; (xiv) x, −y+1/2, z−1/2; (xv) −x+2, y−1/2, −z+3/2; (xvi) x+1/2, y−1/2, −z+3/2; (xvii) −x+3/2, −y+1/2, z−1/2; (xviii) x+1/2, −y+1, −z+2; (xix) −x+5/2, y, z; (xx) −x+2, y+1/2, −z+3/2; (xxi) x−1/2, y+1/2, −z+3/2; (xxii) −x+2, −y+1, −z+2; (xxiii) x+1, y, z; (xxiv) x+1/2, y+1/2, −z+3/2. |
(803K) top
Crystal data top
LiO4SK | Z = 4 |
Mr = 142.1 | F(000) = 280 |
Orthorhombic, Pmcn | Mo Kα radiation, λ = 0.71073 Å |
a = 5.270 (2) Å | µ = 1.62 mm−1 |
b = 9.193 (2) Å | T = 803 K |
c = 8.751 (2) Å | Hexagoal, colorless |
V = 424.0 (2) Å3 | 0.20 × 0.20 × 0.10 mm |
Data collection top
Image-Plate diffractometer | Rint = 0.077 |
Oscillating scans | θmax = 30.5°, θmin = 3.2° |
10251 measured reflections | h = −7→7 |
4752 independent reflections | k = −12→12 |
1433 reflections with I > 3σ(I) | l = −12→12 |
Refinement top
Refinement on F | 60 parameters |
R[F2 > 2σ(F2)] = 0.059 | Weighting scheme based on measured s.u.'s w = 1/(σ2(F) + 0.0001F2) |
wR(F2) = 0.065 | (Δ/σ)max = 0.0003 |
S = 2.95 | Δρmax = 0.93 e Å−3 |
1095 reflections | Δρmin = −1.03 e Å−3 |
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
x | y | z | Uiso*/Ueq | Occ. (<1) | |
K | 0.25 | 0.2070 (1) | 0.9972 (1) | 0.1209 (5) | |
Li | 0.75 | 0.0776 (5) | 0.6599 (5) | 0.069 (2) | |
S | 0.7500 (9) | 0.4059 (2) | 0.7809 (1) | 0.0845 (5) | |
O1 | 0.655 (2) | 0.401 (1) | 0.9316 (6) | 0.276 (6) | 0.5 |
O2 | 0.994 (2) | 0.443 (1) | 0.7488 (9) | 0.196 (5) | 0.5 |
O3 | 0.612 (3) | 0.489 (2) | 0.707 (2) | 0.40 (1) | 0.5 |
O4 | 0.847 (2) | 0.2717 (7) | 0.7350 (9) | 0.204 (6) | 0.5 |
Atomic displacement parameters (Å2) top
U11 | U22 | U33 | U12 | U13 | U23 | |
K | 0.1236 (9) | 0.1365 (9) | 0.1027 (6) | 0 | 0 | 0.0052 (6) |
Li | 0.067 (3) | 0.059 (3) | 0.083 (3) | 0 | 0 | 0.008 (3) |
S | 0.078 (1) | 0.089 (1) | 0.0864 (7) | 0.036 (2) | 0.019 (2) | 0.0049 (8) |
O1 | 0.25 (1) | 0.48 (1) | 0.106 (3) | −0.151 (9) | 0.088 (5) | −0.055 (6) |
O2 | 0.018 (3) | 0.28 (1) | 0.285 (9) | −0.054 (4) | 0.027 (3) | −0.077 (7) |
O3 | 0.16 (1) | 0.40 (2) | 0.63 (3) | −0.059 (8) | −0.06 (1) | 0.41 (2) |
O4 | 0.152 (7) | 0.090 (4) | 0.37 (2) | 0.007 (3) | 0.038 (5) | −0.074 (4) |
Bond lengths (Å) top
K—Lii | 3.981 (5) | Li—O2xi | 3.68 (1) |
K—Liii | 3.591 (3) | Li—O3 | 3.88 (2) |
K—Liiii | 3.591 (3) | Li—O3vi | 2.38 (2) |
K—Liiv | 3.674 (5) | Li—O3xv | 3.65 (1) |
K—Sv | 3.718 (4) | Li—O3vii | 3.65 (1) |
K—S | 3.731 (4) | Li—O3xvi | 2.38 (2) |
K—Sii | 3.760 (4) | Li—O3xi | 3.88 (2) |
K—Siii | 3.773 (4) | Li—O4 | 1.969 (8) |
K—Svi | 3.685 (2) | Li—O4xv | 3.642 (8) |
K—Svii | 3.685 (2) | Li—O4vii | 3.642 (8) |
K—Sviii | 3.773 (4) | Li—O4xi | 1.969 (8) |
K—Six | 3.760 (4) | S—Sxi | 0.018 (7) |
K—Sx | 3.731 (4) | S—O1 | 1.415 (7) |
K—Sxi | 3.718 (4) | S—O1xii | 3.753 (9) |
K—O1v | 3.65 (1) | S—O1xviii | 3.743 (9) |
K—O1 | 2.84 (1) | S—O1xi | 1.408 (7) |
K—O1xii | 3.69 (1) | S—O2 | 1.354 (9) |
K—O1xiii | 3.69 (1) | S—O2xi | 1.371 (9) |
K—O1x | 2.84 (1) | S—O2xix | 3.997 (9) |
K—O1xi | 3.65 (1) | S—O3 | 1.24 (2) |
K—O2v | 3.355 (9) | S—O3xi | 1.23 (2) |
K—O2ii | 2.928 (9) | S—O4 | 1.391 (7) |
K—O2vi | 3.49 (1) | S—O4xx | 3.976 (7) |
K—O2vii | 3.49 (1) | S—O4xxi | 3.985 (7) |
K—O2ix | 2.928 (9) | S—O4xi | 1.397 (7) |
K—O2xi | 3.355 (9) | O1—O1xii | 2.73 (1) |
K—O3xii | 3.88 (2) | O1—O1xiii | 3.42 (1) |
K—O3iii | 3.20 (2) | O1—O1xviii | 3.42 (1) |
K—O3vi | 2.78 (2) | O1—O1xi | 1.00 (1) |
K—O3vii | 2.78 (2) | O1—O2v | 3.85 (1) |
K—O3viii | 3.20 (2) | O1—O2 | 2.43 (1) |
K—O3xiii | 3.88 (2) | O1—O2xxii | 3.64 (1) |
K—O4v | 3.183 (8) | O1—O2xiii | 3.25 (1) |
K—O4 | 3.938 (9) | O1—O2xi | 1.83 (1) |
K—O4ii | 2.981 (8) | O1—O3 | 2.14 (2) |
K—O4iii | 3.777 (9) | O1—O3xii | 3.60 (2) |
K—O4viii | 3.777 (9) | O1—O3xi | 2.45 (2) |
K—O4ix | 2.981 (8) | O1—O4 | 2.32 (1) |
K—O4x | 3.938 (9) | O1—O4iii | 3.25 (1) |
K—O4xi | 3.183 (8) | O1—O4ix | 3.09 (1) |
Li—S | 3.199 (5) | O1—O4xi | 2.09 (1) |
Li—Sxiv | 3.321 (5) | O2—O2xi | 2.58 (1) |
Li—Svi | 3.122 (5) | O2—O2xix | 2.69 (1) |
Li—Sxv | 3.107 (5) | O2—O3 | 2.09 (2) |
Li—Svii | 3.107 (5) | O2—O3xxiii | 3.30 (2) |
Li—Sxvi | 3.122 (5) | O2—O3xi | 0.79 (2) |
Li—Sxvii | 3.321 (5) | O2—O4 | 1.76 (1) |
Li—Sxi | 3.199 (5) | O2—O4xx | 3.14 (1) |
Li—O1 | 3.84 (1) | O2—O4xxiv | 3.55 (1) |
Li—O1xiv | 2.069 (7) | O2—O4xi | 2.39 (1) |
Li—O1vi | 2.80 (1) | O2—O4xix | 3.81 (1) |
Li—O1xv | 3.62 (1) | O3—O3xxv | 3.82 (3) |
Li—O1vii | 3.62 (1) | O3—O3x | 3.81 (2) |
Li—O1xvi | 2.80 (1) | O3—O3xi | 1.46 (2) |
Li—O1xvii | 2.069 (7) | O3—O4 | 2.36 (2) |
Li—O1xi | 3.84 (1) | O3—O4iv | 3.58 (2) |
Li—O2 | 3.68 (1) | O3—O4xx | 3.89 (2) |
Li—O2xiv | 3.826 (9) | O3—O4xxi | 2.99 (2) |
Li—O2xv | 1.99 (1) | O3—O4xi | 2.03 (2) |
Li—O2vii | 1.99 (1) | O4—O4xi | 1.02 (1) |
Li—O2xvii | 3.826 (9) |
Symmetry codes: (i) −x+1, −y, −z+2; (ii) x−1, −y+1/2, z+1/2; (iii) x, −y+1/2, z+1/2; (iv) −x+1, y+1/2, −z+3/2; (v) x−1, y, z; (vi) −x+1, y−1/2, −z+3/2; (vii) x−1/2, y−1/2, −z+3/2; (viii) −x+1/2, −y+1/2, z+1/2; (ix) −x+3/2, −y+1/2, z+1/2; (x) −x+1/2, y, z; (xi) −x+3/2, y, z; (xii) −x+1, −y+1, −z+2; (xiii) x−1/2, −y+1, −z+2; (xiv) x, −y+1/2, z−1/2; (xv) −x+2, y−1/2, −z+3/2; (xvi) x+1/2, y−1/2, −z+3/2; (xvii) −x+3/2, −y+1/2, z−1/2; (xviii) x+1/2, −y+1, −z+2; (xix) −x+5/2, y, z; (xx) −x+2, y+1/2, −z+3/2; (xxi) x−1/2, y+1/2, −z+3/2; (xxii) −x+2, −y+1, −z+2; (xxiii) x+1, y, z; (xxiv) x+1/2, y+1/2, −z+3/2; (xxv) −x+1, −y+1, −z+1. |