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The incommensurately modulated structure of K3In(PO4)2 has been solved and refined. The origin of the modulation relates to the ordering of K cations within the hexagonal close packing of the PO4 anions. The driving forces for the modulation of the other cations are In—P and K—P interactions. The modulation of O atoms of rigid PO4 units follows the cations in order to stabilize the InO6 octahedron. It is shown that the previously published three-dimensional structure refined from powder diffraction data obtained at room temperature is an average structure. Therefore the incommensurately modulated phase of K3In(PO4)2 is the only one that has been unequivocally identified at room temperature. The origin of the modulation is discussed in comparison with the structures of Na3InP2, α- and β-Na3In(PO4)2, Na3Fe(PO4)2 and Rb3In(PO4)2.
Supporting information
Data collection: Oxford Diffraction Ltd, 2001. CrysAlis Software System, Vertion 1.166.
Oxford. England.; cell refinement: CRYSALIS DATA REDUCTION (KM4 Software, Version 1.164
(release 08.06.00 CrysAlis164)); data reduction: CRYSALIS DATA REDUCTION (KM4 Software, Version 1.164
(release 08.06.00 CrysAlis164)); program(s) used to solve structure: Patterson function analysing
(Jana2000; Petricek and Dusek, 2000); program(s) used to refine structure: (Jana2000; Petricek and Dusek, 2000); software used to prepare material for publication: (Jana2000; Petricek and Dusek, 2000).
Crystal data top
InK3O8P2 | Reflections with I > 10σ(I)have been used for measurement of
the unit cell parameters. |
Mr = 422.1 | Dx = 3.284 (1) Mg m−3 |
Monoclinic, X2/b(αlphaβeta0)0s† | Melting point: higher than 1523 K K |
q = 0.18813a* + 0.21423b* | Mo Kα radiation, λ = 0.71073 Å |
a = 15.6537 (5) Å | Cell parameters from 12370 reflections |
b = 9.7357 (4) Å | θ = 3.0–51.8° |
c = 11.1975 (4) Å | µ = 4.62 mm−1 |
β = 90° | T = 293 K |
V = 1706.49 (11) Å3 | Plate, red |
Z = 8 | 0.2 × 0.19 × 0.18 mm |
F(000) = 1600 | |
† Symmetry operations: (1) x1, x2, x3, x4; (2) −x1, 1/2−x2, x3, 1/2−x4; (3) −x1, −x2, −x3, −x4; (4) x1, 1/2+x2, −x3, 1/2+x4; (5) 1/2+x1, x2, 1/2+x3, 1/2+x4; (6) 1/2−x1, 1/2−x2, 1/2+x3, −x4; (7) 1/2−x1, −x2, 1/2−x3, 1/2−x4; (8) 1/2+x1, 1/2+x2, 1/2−x3, x4.
|
Data collection top
KM4 diffractometer | Rint = 0.100 |
Graphite monochromator | θmax = 51.8°, θmin = 3.0° |
CCD detector KM4CCD/SAPPHIRE scans | h = −34→34 |
125808 measured reflections | k = 0→21 |
41649 independent reflections | l = 0→24 |
11828 reflections with I > 3σ(I) | |
Refinement top
Refinement on F | 364 parameters |
R[F2 > 2σ(F2)] = 0.059 | Weighting scheme based on measured s.u.'s w = 1/(σ2(F) + 0.0001F2) |
wR(F2) = 0.059 | (Δ/σ)max = 0.001 |
S = 2.03 | Δρmax = 4.16 e Å−3 |
11828 reflections | Δρmin = −3.31 e Å−3 |
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top | x | y | z | Uiso*/Ueq | |
In1 | 0.124307 (15) | 0.07525 (3) | 0.63801 (2) | 0.01340 (6) | |
K1 | 0.5 | 0.75 | 0.11385 (11) | 0.0220 (6) | |
K2 | 0 | 0.75 | 0.12291 (11) | 0.0174 (5) | |
K3 | 0.25206 (7) | 0.79319 (10) | 0.12190 (9) | 0.0217 (3) | |
K4a | 0.58340 (9) | 0.09850 (14) | 0.61346 (10) | 0.0318 (3) | |
K4b | 0.67419 (13) | 0.09868 (18) | 0.59005 (15) | 0.0318 (3) | |
P1a | 0.15201 (5) | −0.06926 (9) | 0.85523 (7) | 0.01219 (19) | |
O11a | 0.14011 (17) | 0.0875 (3) | 0.8373 (2) | 0.0184 (6) | |
O12a | 0.13384 (18) | −0.1288 (3) | 0.7297 (2) | 0.0198 (7) | |
O13a | 0.24329 (17) | −0.1026 (3) | 0.8923 (2) | 0.0235 (8) | |
O14a | 0.09284 (18) | −0.1272 (3) | 0.9487 (2) | 0.0249 (8) | |
P2a | 0.10058 (8) | −0.07634 (14) | 0.37002 (11) | 0.01139 (19) | |
O21a | 0.1155 (2) | −0.2119 (3) | 0.4383 (3) | 0.0212 (8) | |
O22a | 0.0143 (2) | −0.0827 (4) | 0.3041 (3) | 0.0222 (8) | |
O23a | 0.1705 (2) | −0.0500 (4) | 0.2800 (3) | 0.0245 (8) | |
O24a | 0.0974 (2) | 0.0401 (3) | 0.4626 (3) | 0.0205 (7) | |
P2b | 0.09589 (9) | −0.09306 (15) | 0.36682 (11) | 0.0114 (2) | |
O21b | 0.1104 (2) | −0.2335 (3) | 0.4274 (3) | 0.0212 (8) | |
O22b | −0.0006 (2) | −0.0624 (4) | 0.3607 (3) | 0.0222 (8) | |
O23b | 0.1319 (2) | −0.0908 (4) | 0.2418 (3) | 0.0245 (8) | |
O24b | 0.1394 (2) | 0.0168 (3) | 0.4446 (3) | 0.0205 (7) | |
P2c | 0.09799 (14) | −0.0761 (2) | 0.36988 (16) | 0.01139 (18) | |
O21c | 0.0991 (3) | −0.2306 (3) | 0.3388 (3) | 0.0212 (7) | |
O22c | 0.0121 (2) | −0.0130 (4) | 0.3316 (4) | 0.0222 (7) | |
O23c | 0.1694 (2) | 0.0000 (4) | 0.3078 (3) | 0.0245 (8) | |
O24c | 0.1069 (3) | −0.0634 (4) | 0.5061 (3) | 0.0205 (7) | |
Atomic displacement parameters (Å2) top | U11 | U22 | U33 | U12 | U13 | U23 |
In1 | 0.01291 (9) | 0.01279 (13) | 0.01451 (9) | 0.00144 (9) | −0.00224 (7) | −0.00025 (8) |
K1 | 0.0182 (11) | 0.0198 (11) | 0.0279 (9) | −0.0026 (9) | 0 | 0 |
K2 | 0.0176 (5) | 0.0189 (11) | 0.0158 (6) | −0.0010 (8) | 0 | 0 |
K3 | 0.0207 (5) | 0.0220 (7) | 0.0223 (6) | −0.0009 (4) | 0.0019 (4) | 0.0021 (5) |
K4a | 0.0434 (6) | 0.0237 (5) | 0.0282 (4) | 0.0010 (4) | −0.0030 (4) | 0.0030 (3) |
K4b | 0.0434 (6) | 0.0237 (5) | 0.0282 (4) | 0.0010 (4) | −0.0030 (4) | 0.0030 (3) |
P1a | 0.0104 (3) | 0.0122 (4) | 0.0140 (3) | 0.0005 (3) | −0.0006 (2) | 0.0007 (3) |
O11a | 0.0233 (11) | 0.0127 (11) | 0.0192 (9) | 0.0009 (10) | −0.0042 (8) | 0.0000 (8) |
O12a | 0.0271 (14) | 0.0152 (11) | 0.0171 (9) | 0.0011 (10) | −0.0045 (9) | −0.0019 (8) |
O13a | 0.0149 (11) | 0.0332 (17) | 0.0225 (12) | 0.0033 (12) | −0.0022 (9) | 0.0107 (11) |
O14a | 0.0219 (13) | 0.0271 (16) | 0.0256 (12) | −0.0060 (12) | 0.0074 (10) | 0.0055 (11) |
P2a | 0.0112 (3) | 0.0102 (4) | 0.0127 (3) | 0.0004 (3) | −0.0016 (3) | −0.0003 (2) |
O21a | 0.0292 (14) | 0.0140 (12) | 0.0204 (12) | 0.0024 (10) | −0.0016 (10) | 0.0038 (8) |
O22a | 0.0156 (11) | 0.0256 (14) | 0.0254 (14) | −0.0015 (10) | −0.0077 (10) | 0.0013 (9) |
O23a | 0.0202 (13) | 0.0292 (15) | 0.0240 (15) | −0.0033 (11) | 0.0068 (11) | 0.0005 (10) |
O24a | 0.0249 (13) | 0.0171 (13) | 0.0196 (12) | 0.0011 (10) | −0.0026 (10) | −0.0051 (8) |
P2b | 0.0103 (3) | 0.0101 (4) | 0.0138 (3) | 0.0001 (3) | −0.0004 (2) | 0.0000 (2) |
O21b | 0.0272 (14) | 0.0135 (12) | 0.0230 (13) | 0.0004 (10) | −0.0038 (10) | 0.0041 (9) |
O22b | 0.0118 (12) | 0.0255 (14) | 0.0293 (14) | 0.0026 (10) | −0.0003 (9) | 0.0023 (10) |
O23b | 0.0254 (14) | 0.0303 (15) | 0.0177 (15) | −0.0013 (11) | 0.0060 (10) | −0.0004 (10) |
O24b | 0.0208 (13) | 0.0174 (13) | 0.0234 (13) | −0.0026 (10) | −0.0046 (9) | −0.0036 (9) |
P2c | 0.0113 (3) | 0.0114 (4) | 0.0115 (3) | 0.0013 (3) | −0.0011 (2) | −0.0013 (3) |
O21c | 0.0295 (14) | 0.0128 (11) | 0.0213 (11) | 0.0005 (11) | −0.0009 (10) | −0.0031 (9) |
O22c | 0.0153 (11) | 0.0231 (14) | 0.0282 (13) | 0.0052 (10) | −0.0053 (10) | 0.0004 (10) |
O23c | 0.0194 (13) | 0.0279 (15) | 0.0261 (13) | −0.0058 (12) | 0.0039 (10) | 0.0030 (11) |
O24c | 0.0250 (13) | 0.0227 (13) | 0.0138 (10) | 0.0022 (11) | −0.0027 (9) | −0.0017 (9) |
Geometric parameters (Å, º) top | Average | Minimum | Maximum |
In1—O11a | 2.251 (12) | 2.174 (12) | 2.355 (12) |
In1—O12a | 2.247 (11) | 2.149 (12) | 2.388 (11) |
In1—O13ai | 2.128 (8) | 2.074 (8) | 2.212 (8) |
In1—O21aii | 2.11 (2) | 2.063 (19) | 2.19 (2) |
In1—O22aiii | 2.134 (18) | 2.002 (17) | 2.334 (18) |
In1—O24a | 2.08 (2) | 2.042 (19) | 2.100 (19) |
In1—O21bii | 2.114 (7) | 2.071 (6) | 2.173 (9) |
In1—O22biii | 2.090 (7) | 2.023 (9) | 2.132 (9) |
In1—O24b | 2.120 (7) | 2.104 (9) | 2.134 (6) |
In1—O21cii | 2.050 (4) | 1.987 (4) | 2.087 (4) |
In1—O22ciii | 2.185 (4) | 2.090 (4) | 2.305 (4) |
In1—O24c | 2.087 (4) | 1.966 (5) | 2.135 (4) |
P1a—O11a | 1.557 (8) | 1.551 (8) | 1.564 (8) |
P1a—O12a | 1.555 (9) | 1.547 (9) | 1.563 (9) |
P1a—O13a | 1.530 (9) | 1.524 (9) | 1.539 (10) |
P1a—O14a | 1.513 (11) | 1.507 (11) | 1.525 (11) |
P2a—O21a | 1.54 (2) | 1.54 (2) | 1.54 (2) |
P2a—O22a | 1.54 (2) | 1.54 (2) | 1.55 (2) |
P2a—O23a | 1.51 (3) | 1.51 (3) | 1.52 (2) |
P2a—O24a | 1.54 (2) | 1.54 (2) | 1.55 (2) |
P2b—O21b | 1.546 (7) | 1.544 (10) | 1.551 (10) |
P2b—O22b | 1.544 (7) | 1.541 (10) | 1.549 (10) |
P2b—O23b | 1.511 (8) | 1.509 (11) | 1.513 (12) |
P2b—O24b | 1.538 (8) | 1.537 (11) | 1.541 (11) |
P2c—O21c | 1.543 (4) | 1.543 (4) | 1.543 (4) |
P2c—O22c | 1.541 (4) | 1.541 (4) | 1.541 (4) |
P2c—O23c | 1.509 (4) | 1.509 (4) | 1.509 (4) |
P2c—O24c | 1.537 (4) | 1.537 (4) | 1.537 (4) |
In1—P1a | 2.845 (5) | 2.822 (5) | 2.891 (5) |
In1—P1ai | 3.507 (6) | 3.465 (6) | 3.543 (6) |
In1—P2a | 3.395 (12) | 3.355 (11) | 3.436 (12) |
In1—P2aiii | 3.420 (13) | 3.385 (13) | 3.610 (12) |
In1—P2aii | 3.332 (12) | 3.310 (11) | 3.396 (12) |
In1—P2b | 3.413 (4) | 3.392 (5) | 3.422 (3) |
In1—P2biii | 3.583 (4) | 3.541 (6) | 3.597 (5) |
In1—P2bii | 3.300 (4) | 3.160 (6) | 3.494 (6) |
In1—P2c | 3.472 (3) | 3.229 (3) | 3.519 (3) |
In1—P2ciii | 3.458 (3) | 3.359 (3) | 3.548 (3) |
In1—P2cii | 3.533 (3) | 3.467 (3) | 3.571 (4) |
K1—P1aiv | 4.014 (17) | 3.828 (17) | 4.209 (16) |
K1—P1av | 4.014 (17) | 3.828 (17) | 4.209 (16) |
K1—P2aiv | 3.684 (19) | 3.498 (19) | 3.812 (18) |
K1—P2avi | 3.630 (18) | 3.417 (15) | 3.80 (2) |
K1—P2av | 3.684 (19) | 3.499 (19) | 3.812 (18) |
K1—P2avii | 3.630 (18) | 3.418 (15) | 3.80 (2) |
K1—P2biv | 3.439 (16) | 3.336 (15) | 3.606 (17) |
K1—P2bvi | 3.470 (14) | 3.27 (2) | 3.674 (9) |
K1—P2bv | 3.440 (16) | 3.336 (15) | 3.608 (17) |
K1—P2bvii | 3.470 (14) | 3.27 (2) | 3.675 (9) |
K1—P2civ | 3.494 (17) | 3.443 (14) | 3.521 (14) |
K1—P2cvi | 3.749 (14) | 3.557 (2) | 3.833 (18) |
K1—P2cv | 3.495 (17) | 3.444 (14) | 3.522 (14) |
K1—P2cvii | 3.748 (14) | 3.554 (2) | 3.832 (18) |
K2—P1aviii | 4.218 (11) | 3.947 (10) | 4.402 (11) |
K2—P1aix | 3.958 (10) | 3.574 (14) | 4.306 (13) |
K2—P1ax | 4.220 (11) | 3.996 (11) | 4.452 (10) |
K2—P1aii | 3.951 (10) | 3.574 (14) | 4.305 (12) |
K2—P2axi | 3.848 (15) | 3.556 (18) | 4.079 (15) |
K2—P2axii | 3.853 (15) | 3.563 (18) | 4.078 (15) |
K2—P2bxi | 3.348 (10) | 3.285 (11) | 3.521 (14) |
K2—P2bxii | 3.349 (10) | 3.285 (11) | 3.526 (14) |
K2—P2cxi | 3.392 (10) | 3.305 (13) | 3.555 (9) |
K2—P2cxii | 3.402 (10) | 3.305 (12) | 3.611 (9) |
K3—P1aviii | 3.641 (16) | 3.394 (16) | 3.927 (15) |
K3—P1av | 3.725 (17) | 3.548 (18) | 3.893 (17) |
K3—P1aii | 3.876 (18) | 3.583 (18) | 4.036 (18) |
K3—P2axi | 3.822 (19) | 3.697 (19) | 4.01 (2) |
K3—P2avi | 3.50 (2) | 3.32 (2) | 3.65 (2) |
K3—P2bxi | 4.054 (16) | 3.778 (17) | 4.185 (15) |
K3—P2bvi | 3.806 (17) | 3.740 (16) | 3.858 (17) |
K3—P2bv | 3.988 (16) | 3.697 (15) | 4.277 (17) |
K3—P2cxi | 3.603 (15) | 3.468 (16) | 3.854 (16) |
K3—P2cvi | 3.756 (17) | 3.655 (16) | 3.812 (16) |
K4a—P1axiii | 3.44 (2) | 3.33 (2) | 3.50 (2) |
K4a—P1ai | 3.63 (3) | 3.49 (3) | 3.87 (3) |
K4a—P1axiv | 3.49 (2) | 3.34 (2) | 3.73 (2) |
K4a—P2axv | 3.34 (3) | 3.28 (3) | 3.40 (2) |
K4a—P2bxv | 3.61 (2) | 3.61 (2) | 3.61 (2) |
K4a—P2cxv | 3.37 (2) | 3.32 (3) | 3.404 (19) |
K4b—P1axiii | 3.178 (10) | 3.126 (6) | 3.328 (14) |
K4b—P1axiv | 3.213 (11) | 3.167 (16) | 3.340 (12) |
K4b—P2axvi | 3.696 (15) | 3.486 (14) | 3.88 (2) |
K4b—P2bxv | 3.816 (10) | 3.653 (14) | 3.923 (13) |
K4b—P2cxvi | 3.465 (14) | 3.429 (18) | 3.542 (7) |
| | | |
O11a—In1—O12a | 65.7 (3) | 64.6 (3) | 66.3 (3) |
O11a—In1—O13ai | 92.5 (5) | 90.3 (5) | 96.4 (4) |
O11a—In1—O21aii | 106.0 (5) | 104.8 (6) | 108.8 (5) |
O11a—In1—O22aiii | 84.3 (7) | 75.3 (7) | 86.6 (7) |
O11a—In1—O24a | 173.9 (6) | 170.3 (6) | 177.8 (6) |
O11a—In1—O21bii | 112.2 (3) | 102.2 (3) | 120.7 (3) |
O11a—In1—O22biii | 89.2 (4) | 88.0 (4) | 92.0 (4) |
O11a—In1—O24b | 163.8 (3) | 160.2 (3) | 167.1 (3) |
O11a—In1—O21cii | 82.6 (2) | 79.7 (2) | 83.9 (2) |
O11a—In1—O22ciii | 89.3 (3) | 86.4 (3) | 91.4 (3) |
O11a—In1—O24c | 144.7 (2) | 132.3 (2) | 146.3 (2) |
O12a—In1—O13ai | 96.5 (5) | 90.8 (5) | 102.4 (5) |
O12a—In1—O21aii | 171.3 (6) | 165.9 (7) | 173.6 (6) |
O12a—In1—O22aiii | 85.9 (7) | 79.1 (7) | 93.6 (7) |
O12a—In1—O24a | 109.0 (6) | 104.3 (6) | 113.2 (6) |
O12a—In1—O21bii | 172.6 (4) | 167.4 (3) | 175.5 (3) |
O12a—In1—O22biii | 88.0 (4) | 84.7 (4) | 90.3 (4) |
O12a—In1—O24b | 98.5 (3) | 95.8 (3) | 103.5 (3) |
O12a—In1—O21cii | 148.0 (3) | 145.1 (3) | 149.0 (3) |
O12a—In1—O22ciii | 84.0 (4) | 79.7 (3) | 86.3 (4) |
O12a—In1—O24c | 80.3 (2) | 67.9 (3) | 82.1 (2) |
O13ai—In1—O21aii | 86.4 (8) | 79.3 (7) | 93.7 (8) |
O13ai—In1—O22aiii | 172.6 (7) | 167.5 (7) | 175.3 (7) |
O13ai—In1—O24a | 87.7 (8) | 85.4 (7) | 93.8 (8) |
O13ai—In1—O21bii | 87.1 (4) | 83.0 (4) | 89.5 (4) |
O13ai—In1—O22biii | 175.4 (4) | 173.1 (4) | 177.6 (4) |
O13ai—In1—O24b | 84.7 (4) | 79.9 (4) | 87.4 (4) |
O13ai—In1—O21cii | 89.2 (4) | 86.6 (4) | 94.6 (4) |
O13ai—In1—O22ciii | 174.1 (3) | 169.3 (4) | 177.8 (3) |
O13ai—In1—O24c | 91.1 (4) | 86.4 (4) | 101.1 (4) |
O21aii—In1—O22aiii | 89.2 (9) | 89.0 (9) | 89.4 (9) |
O21aii—In1—O24a | 75.2 (8) | 74.9 (8) | 75.5 (8) |
O21aii—In1—O22biii | 90.1 (8) | 87.5 (7) | 93.3 (8) |
O21aii—In1—O24b | 89.7 (6) | 87.2 (6) | 90.8 (6) |
O21aii—In1—O22ciii | 103.1 (7) | 103.1 (7) | 103.1 (7) |
O21aii—In1—O24c | 119.6 (6) | 119.6 (6) | 119.6 (6) |
O22aiii—In1—O24a | 97.1 (10) | 94.2 (10) | 98.4 (10) |
O22aiii—In1—O21bii | 90.0 (7) | 86.9 (7) | 93.4 (7) |
O22aiii—In1—O24b | 109.8 (6) | 109.8 (6) | 109.8 (6) |
O22aiii—In1—O21cii | 75.3 (7) | 75.3 (7) | 75.3 (7) |
O22aiii—In1—O24c | 96.0 (7) | 88.0 (6) | 99.7 (7) |
O24a—In1—O21bii | 81.2 (6) | 76.7 (6) | 83.3 (6) |
O24a—In1—O22biii | 83.3 (7) | 83.3 (7) | 83.3 (7) |
O24a—In1—O21cii | 99.4 (6) | 98.0 (6) | 102.2 (6) |
O24a—In1—O22ciii | 87.5 (7) | 86.2 (7) | 88.0 (7) |
O21bii—In1—O24c | 97.6 (2) | 94.5 (3) | 103.3 (3) |
O22biii—In1—O24b | 95.2 (3) | 92.7 (4) | 99.2 (4) |
O21cii—In1—O22ciii | 91.88 (19) | 89.98 (18) | 96.01 (19) |
O11a—P1a—O12a | 103.4 (7) | 103.1 (7) | 104.0 (6) |
O11a—P1a—O13a | 110.9 (7) | 110.5 (7) | 111.1 (7) |
O11a—P1a—O14a | 112.5 (7) | 112.1 (7) | 112.9 (7) |
O12a—P1a—O13a | 109.8 (7) | 109.4 (7) | 110.2 (7) |
O12a—P1a—O14a | 112.1 (7) | 111.8 (6) | 112.3 (7) |
O13a—P1a—O14a | 108.1 (6) | 107.7 (7) | 108.7 (6) |
O21a—P2a—O22a | 109.6 (15) | 109.5 (15) | 109.7 (15) |
O21a—P2a—O23a | 111.4 (15) | 111.2 (14) | 111.4 (15) |
O21a—P2a—O24a | 107.5 (12) | 107.5 (12) | 107.6 (12) |
O22a—P2a—O23a | 108.9 (14) | 108.8 (14) | 109.0 (13) |
O22a—P2a—O24a | 108.9 (15) | 108.9 (15) | 109.0 (15) |
O23a—P2a—O24a | 110.5 (14) | 110.5 (14) | 110.6 (14) |
O21b—P2b—O22b | 109.7 (5) | 109.7 (6) | 109.7 (6) |
O21b—P2b—O23b | 111.4 (4) | 111.3 (5) | 111.4 (5) |
O21b—P2b—O24b | 107.6 (4) | 107.5 (5) | 107.7 (5) |
O22b—P2b—O23b | 108.9 (4) | 108.8 (6) | 109.0 (5) |
O22b—P2b—O24b | 108.8 (5) | 108.7 (6) | 108.9 (6) |
O23b—P2b—O24b | 110.4 (4) | 110.2 (5) | 110.5 (6) |
O21c—P2c—O22c | 109.7 (3) | 109.7 (3) | 109.7 (3) |
O21c—P2c—O23c | 111.4 (2) | 111.4 (2) | 111.4 (2) |
O21c—P2c—O24c | 107.5 (2) | 107.5 (2) | 107.5 (2) |
O22c—P2c—O23c | 108.8 (2) | 108.8 (2) | 108.8 (2) |
O22c—P2c—O24c | 108.9 (2) | 108.9 (2) | 108.9 (2) |
O23c—P2c—O24c | 110.5 (2) | 110.5 (2) | 110.5 (2) |
P1a—In1—P1ai | 79.60 (14) | 78.19 (14) | 81.86 (15) |
P1a—In1—P2a | 124.6 (2) | 122.1 (2) | 126.7 (2) |
P1a—In1—P2aiii | 101.9 (2) | 93.8 (2) | 104.8 (2) |
P1a—In1—P2aii | 118.8 (2) | 117.6 (2) | 121.9 (2) |
P1a—In1—P2b | 120.30 (14) | 119.41 (14) | 122.37 (14) |
P1a—In1—P2biii | 97.67 (13) | 96.88 (13) | 98.47 (13) |
P1a—In1—P2bii | 124.53 (14) | 120.78 (13) | 128.05 (14) |
P1a—In1—P2c | 126.50 (13) | 120.24 (14) | 127.67 (13) |
P1a—In1—P2ciii | 103.14 (13) | 100.92 (12) | 104.17 (12) |
P1a—In1—P2cii | 123.26 (13) | 121.37 (12) | 124.38 (12) |
P1ai—In1—P1a | 79.60 (14) | 78.19 (14) | 81.86 (15) |
P1ai—In1—P2a | 94.8 (2) | 90.7 (2) | 100.2 (2) |
P1ai—In1—P2aiii | 176.5 (2) | 173.0 (2) | 178.7 (2) |
P1ai—In1—P2aii | 100.1 (2) | 95.5 (2) | 102.9 (2) |
P1ai—In1—P2b | 100.35 (11) | 99.51 (11) | 101.12 (11) |
P1ai—In1—P2biii | 176.70 (11) | 175.39 (12) | 178.03 (11) |
P1ai—In1—P2bii | 98.55 (12) | 96.44 (12) | 99.73 (13) |
P1ai—In1—P2c | 97.09 (10) | 95.01 (10) | 100.39 (11) |
P1ai—In1—P2ciii | 174.61 (12) | 172.66 (13) | 177.91 (12) |
P1ai—In1—P2cii | 93.44 (11) | 91.91 (11) | 95.90 (11) |
P2a—In1—P2aiii | 84.0 (3) | 83.6 (3) | 84.2 (3) |
P2a—In1—P2aii | 112.0 (3) | 111.8 (3) | 112.2 (3) |
P2a—In1—P2biii | 83.5 (2) | 83.5 (2) | 83.5 (2) |
P2a—In1—P2bii | 114.3 (2) | 111.8 (2) | 115.3 (2) |
P2a—In1—P2ciii | 82.6 (2) | 80.5 (2) | 84.2 (2) |
P2a—In1—P2cii | 110.5 (2) | 109.8 (2) | 112.2 (2) |
P2aiii—In1—P2a | 84.0 (3) | 83.6 (3) | 84.2 (3) |
P2aiii—In1—P2aii | 81.7 (3) | 81.6 (3) | 81.8 (3) |
P2aiii—In1—P2b | 81.90 (19) | 81.90 (19) | 81.90 (19) |
P2aiii—In1—P2bii | 83.1 (2) | 81.3 (2) | 85.0 (2) |
P2aiii—In1—P2c | 81.43 (19) | 80.75 (19) | 82.4 (2) |
P2aiii—In1—P2cii | 83.0 (2) | 83.0 (2) | 83.0 (2) |
P2aii—In1—P2a | 112.0 (3) | 111.8 (3) | 112.2 (3) |
P2aii—In1—P2aiii | 81.7 (3) | 81.6 (3) | 81.8 (3) |
P2aii—In1—P2b | 119.9 (2) | 118.3 (2) | 120.5 (2) |
P2aii—In1—P2biii | 80.1 (2) | 77.0 (2) | 83.2 (2) |
P2aii—In1—P2c | 120.4 (2) | 120.4 (2) | 120.4 (2) |
P2aii—In1—P2ciii | 82.4 (2) | 82.4 (2) | 82.4 (2) |
P2b—In1—P2biii | 82.22 (10) | 81.92 (9) | 83.10 (11) |
P2biii—In1—P2b | 82.22 (9) | 81.92 (9) | 83.10 (10) |
P2bii—In1—P2c | 107.02 (9) | 105.81 (10) | 110.05 (11) |
P2ciii—In1—P2cii | 81.54 (7) | 80.85 (8) | 83.46 (7) |
P2cii—In1—P2ciii | 81.54 (7) | 80.85 (8) | 83.46 (7) |
P1aiv—K1—P1av | 95.1 (3) | 85.8 (5) | 101.4 (4) |
P1aiv—K1—P2aiv | 91.5 (4) | 88.4 (4) | 94.1 (4) |
P1aiv—K1—P2avi | 78.0 (3) | 74.5 (3) | 80.2 (3) |
P1aiv—K1—P2av | 165.2 (5) | 159.4 (5) | 169.5 (4) |
P1aiv—K1—P2avii | 94.3 (4) | 93.3 (4) | 95.6 (4) |
P1aiv—K1—P2biv | 94.1 (4) | 91.8 (2) | 97.4 (5) |
P1aiv—K1—P2bvi | 81.3 (3) | 79.3 (3) | 82.1 (3) |
P1aiv—K1—P2bv | 168.2 (5) | 165.9 (5) | 171.5 (4) |
P1aiv—K1—P2bvii | 97.9 (4) | 94.5 (4) | 99.9 (3) |
P1aiv—K1—P2civ | 96.4 (4) | 90.5 (3) | 97.6 (4) |
P1aiv—K1—P2cvi | 80.4 (3) | 78.7 (3) | 81.3 (3) |
P1aiv—K1—P2cv | 172.3 (5) | 171.2 (6) | 173.6 (5) |
P1aiv—K1—P2cvii | 95.5 (4) | 95.1 (5) | 96.6 (3) |
P1av—K1—P1aiv | 95.1 (3) | 85.8 (5) | 101.4 (4) |
P1av—K1—P2aiv | 165.2 (5) | 159.4 (5) | 169.5 (4) |
P1av—K1—P2avi | 94.3 (4) | 93.3 (4) | 95.6 (4) |
P1av—K1—P2av | 91.5 (4) | 88.4 (4) | 94.0 (4) |
P1av—K1—P2avii | 78.0 (3) | 74.5 (3) | 80.2 (3) |
P1av—K1—P2biv | 168.2 (5) | 165.9 (5) | 171.5 (4) |
P1av—K1—P2bvi | 97.9 (4) | 94.5 (4) | 99.9 (3) |
P1av—K1—P2bv | 94.1 (4) | 91.8 (2) | 97.4 (5) |
P1av—K1—P2bvii | 81.3 (3) | 79.3 (3) | 82.1 (3) |
P1av—K1—P2civ | 172.3 (5) | 171.2 (6) | 173.6 (5) |
P1av—K1—P2cvi | 95.5 (4) | 95.1 (5) | 96.6 (3) |
P1av—K1—P2cv | 96.4 (4) | 90.5 (3) | 97.6 (4) |
P1av—K1—P2cvii | 80.4 (3) | 78.7 (3) | 81.4 (3) |
P2aiv—K1—P2avi | 76.6 (4) | 75.5 (4) | 79.2 (4) |
P2aiv—K1—P2av | 76.9 (6) | 76.9 (6) | 76.9 (6) |
P2aiv—K1—P2avii | 107.9 (5) | 107.8 (5) | 107.9 (5) |
P2aiv—K1—P2bvi | 80.6 (3) | 80.6 (3) | 80.6 (3) |
P2aiv—K1—P2bv | 77.2 (4) | 73.3 (3) | 81.0 (3) |
P2aiv—K1—P2bvii | 109.0 (5) | 107.4 (4) | 110.8 (6) |
P2aiv—K1—P2cvi | 73.9 (3) | 72.2 (3) | 76.7 (3) |
P2aiv—K1—P2cv | 82.5 (4) | 82.5 (4) | 82.5 (4) |
P2aiv—K1—P2cvii | 104.5 (5) | 104.5 (5) | 104.5 (5) |
P2avi—K1—P2aiv | 76.6 (4) | 75.5 (4) | 79.2 (4) |
P2avi—K1—P2av | 107.9 (5) | 107.8 (5) | 107.9 (4) |
P2avi—K1—P2avii | 170.7 (6) | 170.5 (6) | 170.8 (3) |
P2avi—K1—P2biv | 81.9 (3) | 81.9 (3) | 81.9 (3) |
P2avi—K1—P2bv | 105.0 (4) | 101.2 (4) | 106.3 (4) |
P2avi—K1—P2bvii | 172.2 (5) | 170.8 (4) | 174.9 (4) |
P2avi—K1—P2civ | 79.8 (4) | 78.6 (4) | 81.2 (3) |
P2avi—K1—P2cv | 107.4 (5) | 106.2 (5) | 108.9 (5) |
P2av—K1—P2aiv | 76.9 (6) | 76.9 (6) | 76.9 (6) |
P2av—K1—P2avi | 107.9 (5) | 107.8 (5) | 107.9 (5) |
P2av—K1—P2avii | 76.5 (4) | 75.5 (4) | 79.2 (4) |
P2av—K1—P2biv | 77.2 (4) | 73.3 (3) | 81.0 (3) |
P2av—K1—P2bvi | 109.0 (5) | 107.4 (4) | 110.8 (6) |
P2av—K1—P2bvii | 80.6 (3) | 80.6 (3) | 80.6 (3) |
P2av—K1—P2civ | 82.5 (4) | 82.5 (4) | 82.5 (4) |
P2av—K1—P2cvi | 104.5 (5) | 104.5 (5) | 104.5 (5) |
P2av—K1—P2cvii | 73.9 (3) | 72.2 (3) | 76.7 (3) |
P2avii—K1—P2aiv | 107.9 (5) | 107.8 (5) | 107.9 (4) |
P2avii—K1—P2avi | 170.7 (6) | 170.5 (6) | 170.8 (3) |
P2avii—K1—P2av | 76.5 (4) | 75.5 (4) | 79.2 (4) |
P2avii—K1—P2biv | 105.0 (4) | 101.2 (4) | 106.3 (4) |
P2avii—K1—P2bvi | 172.2 (5) | 170.8 (4) | 175.0 (4) |
P2avii—K1—P2bv | 81.9 (3) | 81.9 (3) | 81.9 (3) |
P2avii—K1—P2civ | 107.4 (5) | 106.2 (5) | 108.9 (5) |
P2avii—K1—P2cv | 79.8 (4) | 78.6 (4) | 81.1 (3) |
P2biv—K1—P2bvi | 83.6 (3) | 78.9 (3) | 86.8 (4) |
P2biv—K1—P2cvii | 97.2 (4) | 94.8 (3) | 101.4 (4) |
P2bvi—K1—P2biv | 83.6 (3) | 78.9 (3) | 86.8 (4) |
P2bvi—K1—P2cvii | 175.9 (5) | 173.7 (9) | 177.2 (5) |
P2bv—K1—P2bvii | 83.6 (3) | 78.9 (3) | 86.8 (4) |
P2bv—K1—P2cvi | 97.2 (4) | 94.8 (3) | 101.5 (4) |
P2bvii—K1—P2bv | 83.6 (3) | 78.9 (3) | 86.8 (4) |
P2bvii—K1—P2cvi | 175.9 (5) | 173.7 (9) | 177.3 (5) |
P2civ—K1—P2cv | 81.5 (3) | 81.42 (14) | 81.6 (2) |
P2cv—K1—P2civ | 81.5 (3) | 81.42 (14) | 81.6 (2) |
P1aviii—K2—P1aix | 93.3 (2) | 83.0 (2) | 107.3 (2) |
P1aviii—K2—P1ax | 89.1 (2) | 84.1 (4) | 92.3 (4) |
P1aviii—K2—P1aii | 91.5 (2) | 88.2 (2) | 94.8 (2) |
P1aviii—K2—P2axi | 90.7 (2) | 87.6 (3) | 96.92 (19) |
P1aviii—K2—P2axii | 167.5 (3) | 163.3 (4) | 171.6 (3) |
P1aviii—K2—P2bxi | 103.9 (2) | 98.1 (2) | 107.2 (3) |
P1aviii—K2—P2bxii | 165.7 (3) | 162.3 (3) | 173.0 (3) |
P1aviii—K2—P2cxi | 95.5 (2) | 94.01 (19) | 98.0 (2) |
P1aviii—K2—P2cxii | 172.2 (3) | 170.9 (3) | 173.7 (3) |
P1aix—K2—P1aviii | 93.3 (2) | 83.0 (2) | 107.3 (2) |
P1aix—K2—P1ax | 91.4 (2) | 88.2 (2) | 94.8 (2) |
P1aix—K2—P1aii | 166.4 (3) | 157.3 (3) | 178.8 (3) |
P1aix—K2—P2axi | 75.3 (2) | 71.4 (2) | 80.0 (3) |
P1aix—K2—P2axii | 89.3 (3) | 86.5 (3) | 96.5 (3) |
P1aix—K2—P2bxi | 86.9 (2) | 84.1 (2) | 89.1 (2) |
P1aix—K2—P2bxii | 92.4 (2) | 89.9 (3) | 96.2 (2) |
P1aix—K2—P2cxi | 83.0 (2) | 79.9 (2) | 84.19 (16) |
P1aix—K2—P2cxii | 97.6 (2) | 93.8 (2) | 99.5 (2) |
P1ax—K2—P1aviii | 89.1 (2) | 84.1 (4) | 92.3 (4) |
P1ax—K2—P1aix | 91.4 (2) | 88.2 (2) | 94.8 (2) |
P1ax—K2—P1aii | 93.6 (2) | 83.0 (2) | 107.3 (2) |
P1ax—K2—P2axi | 167.5 (3) | 163.3 (4) | 172.3 (3) |
P1ax—K2—P2axii | 90.6 (2) | 87.6 (3) | 96.75 (19) |
P1ax—K2—P2bxi | 165.8 (3) | 162.3 (3) | 173.1 (3) |
P1ax—K2—P2bxii | 104.0 (2) | 98.3 (2) | 107.3 (3) |
P1ax—K2—P2cxi | 172.3 (3) | 171.0 (2) | 173.7 (3) |
P1ax—K2—P2cxii | 95.6 (2) | 94.02 (15) | 99.6 (2) |
P1aii—K2—P1aviii | 91.5 (2) | 88.2 (2) | 94.8 (2) |
P1aii—K2—P1aix | 166.4 (3) | 157.3 (3) | 178.8 (3) |
P1aii—K2—P1ax | 93.6 (2) | 83.0 (2) | 107.3 (2) |
P1aii—K2—P2axi | 89.4 (3) | 86.5 (3) | 96.5 (3) |
P1aii—K2—P2axii | 75.3 (2) | 71.4 (2) | 79.4 (3) |
P1aii—K2—P2bxi | 92.5 (2) | 89.9 (3) | 96.3 (2) |
P1aii—K2—P2bxii | 87.0 (2) | 84.2 (2) | 89.1 (2) |
P1aii—K2—P2cxi | 97.7 (2) | 94.5 (3) | 99.5 (2) |
P1aii—K2—P2cxii | 82.9 (2) | 78.78 (19) | 84.2 (2) |
P2axi—K2—P2axii | 77.9 (4) | 77.9 (4) | 78.0 (5) |
P2axi—K2—P2bxii | 75.7 (3) | 73.1 (2) | 81.5 (3) |
P2axi—K2—P2cxii | 79.7 (3) | 79.7 (3) | 79.7 (3) |
P2axii—K2—P2axi | 77.9 (4) | 77.9 (4) | 78.0 (5) |
P2axii—K2—P2bxi | 75.8 (3) | 73.1 (2) | 81.7 (3) |
P2cxi—K2—P2cxii | 84.5 (2) | 80.37 (18) | 87.1 (5) |
P2cxii—K2—P2cxi | 84.5 (2) | 80.37 (18) | 87.1 (5) |
P1aviii—K3—P1av | 165.3 (5) | 155.7 (5) | 172.9 (5) |
P1aviii—K3—P1aii | 102.4 (4) | 93.7 (4) | 109.7 (4) |
P1aviii—K3—P2axi | 99.3 (4) | 98.2 (4) | 103.1 (4) |
P1aviii—K3—P2avi | 90.0 (4) | 87.5 (4) | 93.2 (4) |
P1aviii—K3—P2av | 82.1 (3) | 79.0 (3) | 86.9 (4) |
P1aviii—K3—P2bxi | 102.5 (4) | 98.8 (4) | 105.6 (4) |
P1aviii—K3—P2bvi | 92.2 (4) | 88.7 (4) | 95.5 (4) |
P1aviii—K3—P2bv | 85.5 (3) | 82.7 (3) | 88.2 (3) |
P1aviii—K3—P2cxi | 104.7 (4) | 101.0 (4) | 106.7 (5) |
P1aviii—K3—P2cvi | 89.2 (4) | 88.6 (4) | 92.6 (4) |
P1aviii—K3—P2cv | 76.8 (3) | 73.8 (3) | 83.2 (3) |
P1av—K3—P1aviii | 165.3 (5) | 155.7 (5) | 172.9 (5) |
P1av—K3—P1aii | 65.2 (3) | 63.4 (3) | 67.8 (3) |
P1av—K3—P2axi | 88.6 (4) | 85.4 (3) | 91.9 (4) |
P1av—K3—P2avi | 102.3 (4) | 97.4 (4) | 107.8 (4) |
P1av—K3—P2av | 86.3 (4) | 82.5 (3) | 89.3 (4) |
P1av—K3—P2bxi | 82.5 (3) | 79.7 (3) | 87.0 (3) |
P1av—K3—P2bvi | 97.8 (4) | 94.1 (4) | 102.4 (4) |
P1av—K3—P2bv | 88.5 (3) | 85.8 (3) | 91.8 (4) |
P1av—K3—P2cxi | 88.7 (3) | 85.2 (3) | 90.6 (3) |
P1av—K3—P2cvi | 99.0 (4) | 97.2 (4) | 101.5 (4) |
P1av—K3—P2cv | 89.3 (3) | 86.4 (4) | 90.6 (4) |
P1aii—K3—P1aviii | 102.4 (4) | 93.7 (4) | 109.7 (4) |
P1aii—K3—P1av | 65.2 (3) | 63.4 (3) | 67.8 (3) |
P1aii—K3—P2axi | 88.6 (4) | 85.9 (4) | 92.1 (4) |
P1aii—K3—P2avi | 164.8 (5) | 161.2 (5) | 169.1 (6) |
P1aii—K3—P2av | 76.7 (3) | 72.5 (3) | 80.1 (4) |
P1aii—K3—P2bxi | 86.4 (3) | 84.5 (3) | 92.2 (4) |
P1aii—K3—P2bvi | 160.0 (5) | 151.8 (5) | 167.9 (5) |
P1aii—K3—P2bv | 84.7 (3) | 80.0 (3) | 90.8 (4) |
P1aii—K3—P2cxi | 95.9 (4) | 92.5 (3) | 98.0 (4) |
P1aii—K3—P2cvi | 162.5 (5) | 158.8 (5) | 165.4 (5) |
P1aii—K3—P2cv | 78.0 (3) | 76.3 (3) | 81.7 (4) |
P2axi—K3—P2avi | 102.3 (5) | 96.5 (5) | 105.8 (5) |
P2axi—K3—P2av | 168.8 (5) | 167.8 (5) | 169.6 (5) |
P2axi—K3—P2bvi | 97.0 (4) | 96.5 (4) | 98.1 (4) |
P2axi—K3—P2cv | 163.9 (5) | 161.1 (5) | 168.0 (5) |
P2avi—K3—P2axi | 102.3 (5) | 96.5 (5) | 105.8 (5) |
P2avi—K3—P2av | 93.1 (4) | 93.1 (4) | 93.2 (4) |
P2avi—K3—P2bxi | 96.5 (4) | 94.7 (4) | 98.7 (5) |
P2avi—K3—P2bv | 94.2 (4) | 91.6 (4) | 96.0 (4) |
P2avi—K3—P2cv | 92.9 (4) | 91.9 (4) | 95.4 (4) |
P2bxi—K3—P2bv | 169.1 (5) | 163.9 (5) | 174.1 (5) |
P2bxi—K3—P2cvi | 92.8 (4) | 89.7 (3) | 97.8 (4) |
P2bvi—K3—P2cxi | 99.6 (4) | 95.2 (4) | 101.5 (4) |
P2bv—K3—P2bxi | 169.1 (5) | 163.9 (5) | 174.1 (5) |
P2bv—K3—P2cvi | 90.8 (3) | 87.0 (3) | 91.9 (3) |
P2cxi—K3—P2cvi | 96.2 (4) | 96.2 (4) | 96.2 (4) |
P2cvi—K3—P2cxi | 96.2 (4) | 96.2 (4) | 96.2 (4) |
P1axiii—K4a—P1ai | 108.9 (7) | 105.2 (6) | 118.2 (7) |
P1axiii—K4a—P1axiv | 117.9 (7) | 113.0 (7) | 120.3 (8) |
P1axiii—K4a—P2axv | 117.4 (7) | 112.6 (8) | 122.2 (7) |
P1axiii—K4a—P2bxv | 120.2 (6) | 120.2 (6) | 120.2 (6) |
P1axiii—K4a—P2cxv | 109.1 (6) | 107.6 (6) | 112.3 (8) |
P1ai—K4a—P1axiii | 108.9 (7) | 105.2 (6) | 118.2 (7) |
P1ai—K4a—P1axiv | 110.7 (7) | 106.2 (6) | 117.3 (6) |
P1ai—K4a—P2axv | 89.9 (7) | 81.8 (5) | 91.4 (7) |
P1ai—K4a—P2bxv | 81.9 (5) | 81.9 (5) | 81.9 (5) |
P1ai—K4a—P2cxv | 88.0 (6) | 87.4 (5) | 88.7 (7) |
P1axiv—K4a—P1axiii | 117.9 (7) | 113.0 (7) | 120.3 (8) |
P1axiv—K4a—P1ai | 110.7 (7) | 106.2 (6) | 117.3 (6) |
P1axiv—K4a—P2axv | 109.7 (7) | 105.4 (6) | 112.5 (6) |
P1axiv—K4a—P2bxv | 113.1 (6) | 113.1 (6) | 113.1 (6) |
P1axiv—K4a—P2cxv | 115.0 (6) | 112.2 (8) | 116.0 (6) |
P1axiii—K4b—P1axiv | 127.1 (3) | 120.3 (4) | 130.7 (5) |
P1axiii—K4b—P2axvi | 92.5 (2) | 87.6 (4) | 99.2 (2) |
P1axiii—K4b—P2bxv | 117.2 (3) | 114.8 (5) | 120.03 (19) |
P1axiii—K4b—P2cxvi | 104.2 (4) | 100.50 (19) | 105.8 (4) |
P1axiv—K4b—P1axiii | 127.1 (3) | 120.3 (4) | 130.7 (5) |
P1axiv—K4b—P2axvi | 97.7 (3) | 95.8 (4) | 99.2 (2) |
P1axiv—K4b—P2bxv | 106.8 (3) | 100.6 (4) | 118.8 (4) |
P1axiv—K4b—P2cxvi | 99.6 (4) | 97.9 (3) | 100.3 (4) |
P2axvi—K4b—P2bxv | 101.1 (2) | 100.3 (4) | 101.7 (2) |
P2bxv—K4b—P2cxvi | 100.5 (3) | 100.4 (4) | 100.7 (3) |
Symmetry codes: (i) −x1+1/2, −x2, −x3+3/2, −x1/2; (ii) x1, x2+1/2, −x3+1, x1/2; (iii) −x1, −x2, −x3+1, −x4; (iv) x1+1/2, x2+1, x3−1/2, x1/2; (v) −x1+1/2, −x2+1/2, x3−1/2, −x4; (vi) −x1+1/2, −x2+1, −x3+1/2, −x1/2; (vii) x1+1/2, x2+1/2, −x3+1/2, x4; (viii) x1, x2+1, x3−1, x4; (ix) −x1, −x2+1, −x3+1, −x4; (x) −x1, −x2+1/2, x3−1, −x1/2; (xi) x1, x2+1, x3, x4; (xii) −x1, −x2+1/2, x3, −x1/2; (xiii) x1+1/2, x2, x3−1/2, x1/2; (xiv) x1+1/2, x2+1/2, −x3+3/2, x4; (xv) x1+1/2, x2, x3+1/2, x1/2; (xvi) −x1+1, −x2, −x3+1, −x4. |
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