Incommensurately modulated borate structures of a new type were studied in detail in the nonlinear optical (NLO) materials Cs2TB4O9 (T = Ge, Si) using single-crystal X-ray diffraction techniques. The structures were solved by the charge-flipping algorithm in the superspace group I2(αβ0)0. The refinement results strongly suggest that the main structure modulation feature of Cs2TB4O9 is the ordering of the O atoms. With these modulated structure models, the unreasonable B—O distances in the average structures were explained as the ordering of BO4 and BO3.
Supporting information
B-IncStrDB reference: 11442EEvkyY
CCDC references: 1432075; 1432076
For both compounds, data collection: CrysAlis PRO, Agilent Technologies, Version 1.171.37.35 (release 13-08-2014 CrysAlis171 .NET) (compiled Aug 13 2014,18:06:01); cell refinement: CrysAlis PRO, Agilent Technologies, Version 1.171.37.35 (release 13-08-2014 CrysAlis171 .NET) (compiled Aug 13 2014,18:06:01); data reduction: CrysAlis PRO, Agilent Technologies, Version 1.171.37.35 (release 13-08-2014 CrysAlis171 .NET) (compiled Aug 13 2014,18:06:01).
Crystal data top
B4Cs2GeO9 | Z = 2 |
Mr = 525.6 | F(000) = 468 |
Monoclinic, I2(αβ0)0† | Dx = 3.800 Mg m−3 |
q = -0.482300a* + 0.119200b* | Mo Kα radiation, λ = 0.71073 Å |
a = 6.7863 (10) Å | Cell parameters from 3052 reflections |
b = 6.7914 (10) Å | θ = 3.6–29.2° |
c = 9.9686 (15) Å | µ = 11.17 mm−1 |
β = 90° | T = 100 K |
V = 459.44 (12) Å3 | 0.05 × 0.03 × 0.02 mm |
† Symmetry operations: (1) x1, x2, x3, x4; (2) −x1, −x2, x3, −x4; (3) x1+1/2, x2+1/2, x3+1/2, x4; (4) −x1+1/2, −x2+1/2, x3+1/2, −x4.
|
Data collection top
SuperNova, Dual, Cu at zero, Atlas diffractometer | 4440 independent reflections |
Radiation source: X-ray tube | 3004 reflections with I > 3σ(I) |
Mirror monochromator | Rint = 0.030 |
Detector resolution: 10.3503 pixels mm-1 | θmax = 29.3°, θmin = 3.1° |
ω scans | h = −9→9 |
Absorption correction: multi-scan CrysAlisPro, Agilent Technologies,
Version 1.171.37.35 (release 13-08-2014 CrysAlis171 .NET)
(compiled Aug 13 2014,18:06:01)
Empirical absorption correction using spherical harmonics,
implemented in SCALE3 ABSPACK scaling algorithm.
Empirical absorption correction using spherical harmonics,
implemented in SCALE3 ABSPACK scaling algorithm. | k = −8→7 |
Tmin = 0.779, Tmax = 1 | l = −13→9 |
7489 measured reflections | |
Refinement top
Refinement on F | 6 constraints |
R[F2 > 2σ(F2)] = 0.050 | Weighting scheme based on measured s.u.'s w = 1/(σ2(F) + 0.0001F2) |
wR(F2) = 0.065 | (Δ/σ)max = 0.008 |
S = 1.69 | Δρmax = 3.39 e Å−3 |
4440 reflections | Δρmin = −5.58 e Å−3 |
177 parameters | Absolute structure: 1517 of Friedel pairs used in the refinement |
13 restraints | |
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top | x | y | z | Uiso*/Ueq | Occ. (<1) |
Cs1 | 0 | 0 | 0.00120 (10) | 0.00767 (17) | |
Cs2 | −0.5 | 0 | 0.24904 (7) | 0.0083 (2) | |
Ge1 | 0 | −0.5 | 0.25095 (17) | 0.0041 (4) | |
O5b | 0 | 0 | 0.6619 (13) | 0.0029 (14)* | 0.5 |
O5a | 0 | 0 | 0.3372 (12) | 0.0029 (14)* | 0.5 |
O1 | −0.8417 (8) | −0.6483 (7) | 0.1559 (5) | 0.0068 (11)* | |
O4 | −0.7269 (6) | −0.3979 (5) | 0.0047 (8) | 0.0058 (9)* | |
O2 | −0.3523 (8) | −0.8399 (7) | 0.8419 (5) | 0.0070 (11)* | |
O3 | −0.6055 (6) | −0.7311 (5) | 0.9930 (8) | 0.0062 (9)* | |
B2a | −0.1661 (17) | −0.0615 (16) | 0.5797 (12) | 0.003 (2)* | 0.5 |
B1a | 0.0579 (18) | −0.1663 (16) | 0.4192 (13) | 0.004 (2)* | 0.5 |
B2b | −0.227 (2) | −0.0876 (17) | 0.5555 (14) | 0.006 (3)* | 0.5 |
B1b | 0.0886 (19) | −0.2241 (19) | 0.4423 (14) | 0.007 (3)* | 0.5 |
Atomic displacement parameters (Å2) top | U11 | U22 | U33 | U12 | U13 | U23 |
Cs1 | 0.0053 (3) | 0.0056 (3) | 0.0121 (3) | 0.00035 (19) | 0 | 0 |
Cs2 | 0.0106 (4) | 0.0092 (4) | 0.0050 (3) | 0.0006 (3) | 0 | 0 |
Ge1 | 0.0062 (7) | 0.0042 (6) | 0.0020 (6) | 0.0002 (5) | 0 | 0 |
Bond lengths (Å) top | Average | Minimum | Maximum |
B2a—O5b | 1.45 (9) | 1.44 (12) | 1.48 (12) |
B2a—O1i | 1.47 (7) | 1.46 (8) | 1.50 (8) |
B2a—O4i | 1.47 (6) | 1.43 (7) | 1.51 (7) |
B2a—O3ii | 1.53 (6) | 1.52 (7) | 1.54 (7) |
B1a—O5a | 1.45 (10) | 1.42 (14) | 1.47 (14) |
B1a—O4iii | 1.53 (8) | 1.44 (9) | 1.55 (9) |
B1a—O2ii | 1.47 (7) | 1.46 (9) | 1.51 (9) |
B1a—O3ii | 1.46 (8) | 1.40 (9) | 1.48 (9) |
B2b—O5b | 1.96 (14) | 1.96 (14) | 1.96 (14) |
B2b—O1i | 1.38 (16) | 1.4 (2) | 1.4 (2) |
B2b—O4i | 1.35 (9) | 1.30 (12) | 1.36 (12) |
B2b—O3ii | 1.39 (13) | 1.38 (18) | 1.44 (18) |
B1b—O5a | 1.86 (18) | 1.86 (18) | 1.86 (18) |
B1b—O4iii | 1.38 (16) | 1.4 (2) | 1.4 (2) |
B1b—O2ii | 1.39 (19) | 1.4 (3) | 1.4 (3) |
B1b—O3ii | 1.37 (12) | 1.35 (16) | 1.39 (16) |
Symmetry codes: (i) x1+1/2, x2+1/2, x3+1/2, x4; (ii) x1+1/2, x2+1/2, x3−1/2, x4; (iii) −x1−1/2, −x2−1/2, x3+1/2, −x4. |
Crystal data top
B4Cs2O9Si | Z = 2 |
Mr = 481.1 | F(000) = 432 |
Monoclinic, I2(αβ0)0† | Dx = 3.548 Mg m−3 |
q = -0.478500a* + 0.175300b* | Mo Kα radiation, λ = 0.71073 Å |
a = 6.7489 (10) Å | Cell parameters from 2986 reflections |
b = 6.7479 (13) Å | θ = 3.5–28.8° |
c = 9.8894 (13) Å | µ = 8.26 mm−1 |
β = 90° | T = 180 K |
V = 450.37 (12) Å3 | 0.05 × 0.02 × 0.02 mm |
† Symmetry operations: (1) x1, x2, x3, x4; (2) −x1, −x2, x3, −x4; (3) x1+1/2, x2+1/2, x3+1/2, x4; (4) −x1+1/2, −x2+1/2, x3+1/2, −x4.
|
Data collection top
SuperNova, Dual, Cu at zero, Atlas diffractometer | 4933 independent reflections |
Radiation source: X-ray tube | 3155 reflections with I > 3σ(I) |
Mirror monochromator | Rint = 0.019 |
Detector resolution: 10.3914 pixels mm-1 | θmax = 29.1°, θmin = 2.9° |
ω scans | h = −9→9 |
Absorption correction: multi-scan CrysAlisPro, Agilent Technologies,
Version 1.171.37.35 (release 13-08-2014 CrysAlis171 .NET)
(compiled Aug 13 2014,18:06:01)
Empirical absorption correction using spherical harmonics,
implemented in SCALE3 ABSPACK scaling algorithm. | k = −7→9 |
Tmin = 0.93, Tmax = 1 | l = −13→13 |
7483 measured reflections | |
Refinement top
Refinement on F | 6 constraints |
R[F2 > 2σ(F2)] = 0.036 | Weighting scheme based on measured s.u.'s w = 1/(σ2(F) + 0.0001F2) |
wR(F2) = 0.047 | (Δ/σ)max = 0.037 |
S = 1.25 | Δρmax = 2.57 e Å−3 |
4933 reflections | Δρmin = −2.47 e Å−3 |
178 parameters | Absolute structure: 2223 of Friedel pairs used in the refinement |
14 restraints | |
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top | x | y | z | Uiso*/Ueq | Occ. (<1) |
Cs1 | 0 | 0 | 0.00139 (7) | 0.01290 (14) | |
Cs2 | −0.5 | 0 | 0.24894 (8) | 0.0196 (3) | |
Si1 | 0 | −0.5 | 0.2467 (5) | 0.0043 (8) | |
O5b | 0 | 0 | 0.6640 (10) | 0.0065 (8)* | 0.5 |
O5a | 0 | 0 | 0.3347 (10) | 0.0065 (8)* | 0.5 |
O1 | −0.8470 (8) | −0.6289 (8) | 0.1598 (6) | 0.0091 (12)* | |
O4 | −0.7229 (7) | −0.3871 (7) | 0.0051 (6) | 0.0099 (10)* | |
O2 | −0.3705 (8) | −0.8463 (7) | 0.8405 (6) | 0.0063 (11)* | |
O3 | −0.6143 (8) | −0.7262 (7) | 0.9957 (6) | 0.0106 (10)* | |
B2a | −0.1696 (15) | −0.0558 (14) | 0.5840 (10) | 0.009 (2)* | 0.5 |
B1a | 0.0527 (14) | −0.1691 (14) | 0.4188 (10) | 0.0075 (19)* | 0.5 |
B2b | −0.2264 (14) | −0.0773 (13) | 0.5584 (9) | 0.0066 (18)* | 0.5 |
B1b | 0.0789 (15) | −0.2286 (16) | 0.4439 (10) | 0.010 (2)* | 0.5 |
Atomic displacement parameters (Å2) top | U11 | U22 | U33 | U12 | U13 | U23 |
Cs1 | 0.0093 (3) | 0.0109 (2) | 0.0185 (2) | −0.0001 (2) | 0 | 0 |
Cs2 | 0.0237 (6) | 0.0227 (5) | 0.01224 (17) | 0.0017 (5) | 0 | 0 |
Si1 | 0.0031 (15) | 0.0081 (16) | 0.0018 (6) | −0.0049 (15) | 0 | 0 |
Bond lengths (Å) top | Average | Minimum | Maximum |
B2a—O5b | 1.44 (9) | 1.43 (12) | 1.45 (12) |
B2a—O1i | 1.44 (7) | 1.42 (8) | 1.47 (8) |
B2a—O4i | 1.49 (6) | 1.45 (7) | 1.52 (7) |
B2a—O3ii | 1.52 (6) | 1.50 (7) | 1.54 (7) |
B1a—O5a | 1.46 (10) | 1.45 (14) | 1.50 (14) |
B1a—O4iii | 1.51 (7) | 1.44 (9) | 1.54 (9) |
B1a—O2ii | 1.47 (7) | 1.45 (8) | 1.56 (8) |
B1a—O3ii | 1.47 (7) | 1.42 (9) | 1.48 (9) |
B2b—O5b | 1.94 (11) | 1.94 (11) | 1.94 (11) |
B2b—O1i | 1.38 (11) | 1.37 (15) | 1.38 (15) |
B2b—O4i | 1.36 (5) | 1.34 (7) | 1.37 (7) |
B2b—O3ii | 1.37 (8) | 1.37 (11) | 1.41 (11) |
B1b—O5a | 1.89 (14) | 1.89 (14) | 1.89 (14) |
B1b—O4iii | 1.37 (11) | 1.34 (16) | 1.40 (16) |
B1b—O2ii | 1.38 (14) | 1.4 (2) | 1.4 (2) |
B1b—O3ii | 1.36 (8) | 1.35 (11) | 1.38 (11) |
Symmetry codes: (i) x1+1/2, x2+1/2, x3+1/2, x4; (ii) x1+1/2, x2+1/2, x3−1/2, x4; (iii) −x1−1/2, −x2−1/2, x3+1/2, −x4. |