The incommensurately modulated crystal structure of low SiO2 tridymite was refined based on single-crystal X-ray diffraction data in the superspace group Cc(α0γ)0. The data set consists of 885 main reflections, 1751 first-order, 924 second-order and 119 third-order satellite reflections with I > 3σ(I). The modulation is mainly made up from cooperative twistings of the rigid SiO4 tetrahedra. Two orders of displacement waves are used to describe the modulation of the Si atoms and three orders for the O atoms. The maximal amplitudes are ca 0.6 Å. O atoms bridging pairs of tetrahedra in cis and trans configurations show different positional modulation patterns. The anisotropic displacement parameters (ADPs) are also modulated. A correlation between ADP modulations and positional modulations was found.
Supporting information
Program(s) used to refine structure: Jana2006 (Petricek, Dusek & Palatinus, 2006); software used to prepare material for publication: Jana2006 (Petricek, Dusek & Palatinus, 2006).
Crystal data top
O2Si | V = 353.79 (18) Å3 |
Mr = 60.1 | Z = 8 |
Monoclinic, Cc(α0γ)0† | F(000) = 240 |
q = 0.65390a* + -0.49480c* | Dx = 2.255 Mg m−3 |
a = 5.007 (2) Å | Mo Kα radiation, λ = 0.71073 Å |
b = 8.599 (2) Å | µ = 0.85 mm−1 |
c = 8.2202 (16) Å | T = 294 K |
β = 91.57 (2)° | × × mm |
† Symmetry operations: (1) x1, x2, x3, x4; (2) x1, −x2, x3+1/2, x4; (3) x1+1/2, x2+1/2, x3, x4; (4) x1+1/2, −x2+1/2, x3+1/2, x4.
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Data collection top
Oxford Diffraction CCD diffractometer | 3679 reflections with I > 3σ(I) |
Radiation source: X-ray tube | Rint = 0.040 |
Graphite monochromator | θmax = 42.0°, θmin = 2.7° |
2phi and 4ω scans | h = −7→7 |
23130 measured reflections | k = −15→16 |
7927 independent reflections | l = −12→15 |
Refinement top
Refinement on F | 0 constraints |
R[F2 > 2σ(F2)] = 0.030 | Weighting scheme based on measured s.u.'s w = 1/(σ2(F) + 0.0001F2) |
wR(F2) = 0.036 | (Δ/σ)max = 0.008 |
S = 0.99 | Δρmax = 0.36 e Å−3 |
7927 reflections | Δρmin = −0.34 e Å−3 |
293 parameters | Extinction correction: B-C type 1 Gaussian isotropic (Becker & Coppens, 1974) |
20 restraints | Extinction coefficient: 4640 (90) |
Crystal data top
O2Si | β = 91.57 (2)° |
Mr = 60.1 | V = 353.79 (18) Å3 |
Monoclinic, Cc(α0γ)0† | Z = 8 |
q = 0.65390a* + -0.49480c* | Mo Kα radiation |
a = 5.007 (2) Å | µ = 0.85 mm−1 |
b = 8.599 (2) Å | T = 294 K |
c = 8.2202 (16) Å | × × mm |
† Symmetry operations: (1) x1, x2, x3, x4; (2) x1, −x2, x3+1/2, x4; (3) x1+1/2, x2+1/2, x3, x4; (4) x1+1/2, −x2+1/2, x3+1/2, x4.
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Data collection top
Oxford Diffraction CCD diffractometer | 3679 reflections with I > 3σ(I) |
23130 measured reflections | Rint = 0.040 |
7927 independent reflections | |
Refinement top
R[F2 > 2σ(F2)] = 0.030 | 293 parameters |
wR(F2) = 0.036 | 20 restraints |
S = 0.99 | Δρmax = 0.36 e Å−3 |
7927 reflections | Δρmin = −0.34 e Å−3 |
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top | x | y | z | Uiso*/Ueq | |
Si1 | 0.089528 | 0.30758 (3) | 0.21154 | 0.01252 (8) | |
Si2 | 0.09056 (9) | 0.64149 (3) | 0.33670 (5) | 0.01242 (8) | |
O1 | 0.30010 (19) | 0.75222 (11) | 0.25668 (13) | 0.0247 (3) | |
O2 | 0.16026 (19) | 0.46589 (9) | 0.30179 (12) | 0.0224 (3) | |
O3 | 0.30187 (19) | 0.18034 (9) | 0.26440 (14) | 0.0200 (3) | |
O4 | 0.0976 (3) | 0.33257 (12) | 0.02435 (14) | 0.0288 (3) | |
Atomic displacement parameters (Å2) top | U11 | U22 | U33 | U12 | U13 | U23 |
Si1 | 0.01151 (15) | 0.01154 (13) | 0.01448 (13) | 0.00027 (12) | −0.00007 (11) | 0.00135 (11) |
Si2 | 0.01143 (15) | 0.01149 (13) | 0.01434 (13) | 0.00041 (12) | 0.00025 (11) | −0.00112 (11) |
O1 | 0.0143 (5) | 0.0234 (5) | 0.0365 (5) | −0.0017 (4) | 0.0047 (4) | 0.0077 (4) |
O2 | 0.0215 (5) | 0.0136 (4) | 0.0318 (5) | 0.0032 (3) | −0.0065 (4) | −0.0056 (4) |
O3 | 0.0124 (4) | 0.0158 (4) | 0.0318 (6) | 0.0013 (3) | −0.0027 (4) | 0.0003 (4) |
O4 | 0.0364 (6) | 0.0348 (6) | 0.0152 (3) | −0.0017 (6) | 0.0010 (4) | 0.0053 (4) |
Geometric parameters (Å, º) top | Average | Minimum | Maximum |
Si1—Si2 | 3.0693 (15) | 3.0323 (15) | 3.0876 (15) |
Si1—Si2i | 3.112 (5) | 3.088 (4) | 3.138 (4) |
Si1—Si2ii | 3.047 (5) | 3.007 (5) | 3.074 (5) |
Si1—Si2iii | 3.1124 (14) | 3.1049 (14) | 3.1214 (14) |
Si1—O1i | 1.600 (6) | 1.579 (6) | 1.618 (6) |
Si1—O2 | 1.607 (5) | 1.592 (4) | 1.616 (5) |
Si1—O3 | 1.600 (5) | 1.588 (5) | 1.610 (5) |
Si1—O4 | 1.598 (4) | 1.585 (4) | 1.611 (4) |
Si2—O1 | 1.596 (5) | 1.588 (5) | 1.606 (5) |
Si2—O2 | 1.598 (4) | 1.584 (5) | 1.609 (4) |
Si2—O3iv | 1.605 (6) | 1.587 (6) | 1.617 (6) |
Si2—O4v | 1.601 (5) | 1.593 (4) | 1.608 (5) |
O1—O2 | 2.620 (7) | 2.599 (7) | 2.637 (7) |
O1—O2vi | 2.625 (7) | 2.606 (7) | 2.638 (7) |
O1—O3iv | 2.604 (8) | 2.582 (8) | 2.627 (8) |
O1—O3vi | 2.617 (8) | 2.588 (8) | 2.643 (8) |
O1—O4vi | 2.603 (7) | 2.571 (7) | 2.659 (8) |
O1—O4v | 2.611 (7) | 2.589 (7) | 2.632 (7) |
O2—O3 | 2.608 (6) | 2.590 (6) | 2.625 (7) |
O2—O3iv | 2.614 (7) | 2.599 (7) | 2.628 (7) |
O2—O4 | 2.619 (7) | 2.586 (7) | 2.634 (7) |
O2—O4v | 2.601 (7) | 2.563 (7) | 2.640 (7) |
O3—O4 | 2.613 (7) | 2.583 (7) | 2.635 (7) |
O3—O4vii | 2.624 (7) | 2.594 (7) | 2.644 (8) |
| | | |
O1—Si2—Si1—O3 | 0.79 (5) |
O2—Si2—Si1—O2 | −0.28 (6) |
O3—Si2—Si1—O1 | 0.15 (5) |
O3—Si1—Si2—O1 | 77.92 (7) |
O3—Si1—Si2—O4 | −53.39 (8) |
O3—Si1—Si2—O3 | −168.52 (6) |
O1—Si1—Si2—O3 | −44.42 (6) |
O1—Si1—Si2—O4 | 70.71 (7) |
O1—Si1—Si2—O1 | −157.98 (6) |
O4—Si1—Si2—O1 | −45.74 (7) |
O4—Si1—Si2—O3 | 67.82 (7) |
O4—Si1—Si2—O4 | −177.05 (8) |
O4—Si1—Si2—O2 | −69.90 (7) |
O4—Si1—Si2—O1 | 51.41 (6) |
O4—Si1—Si2—O4 | 163.74 (6) |
O2—Si1—Si2—O1 | −61.23 (5) |
O2—Si1—Si2—O4 | 51.10 (6) |
O2—Si1—Si2—O2 | 177.46 (6) |
O1—Si1—Si2—O4 | −65.85 (6) |
O1—Si1—Si2—O2 | 60.51 (7) |
O1—Si1—Si2—O3 | 110.66 (5) |
O2—Si1—Si2—O4 | −37.46 (6) |
O2—Si1—Si2—O3 | 87.78 (6) |
O2—Si1—Si2—O2 | −150.58 (5) |
O4—Si1—Si2—O3 | −41.18 (7) |
O4—Si1—Si2—O2 | 80.46 (6) |
O4—Si1—Si2—O4 | −166.42 (7) |
O3—Si1—Si2—O3 | −157.21 (6) |
O3—Si1—Si2—O2 | −35.57 (6) |
O3—Si1—Si2—O4 | 77.56 (6) |
Symmetry codes: (i) x1−1/2, x2−1/2, x3, x4; (ii) x1+1/2, x2−1/2, x3, x4; (iii) x1, −x2+1, x3−1/2, x4; (iv) x1−1/2, x2+1/2, x3, x4; (v) x1, −x2+1, x3+1/2, x4; (vi) x1+1/2, x2+1/2, x3, x4; (vii) x1+1/2, −x2+1/2, x3+1/2, x4. |
Experimental details
Crystal data |
Chemical formula | O2Si |
Mr | 60.1 |
Crystal system, space group | Monoclinic, Cc(α0γ)0† |
Temperature (K) | 294 |
Wave vectors | q = 0.65390a* + -0.49480c* |
a, b, c (Å) | 5.007 (2), 8.599 (2), 8.2202 (16) |
β (°) | 91.57 (2) |
V (Å3) | 353.79 (18) |
Z | 8 |
Radiation type | Mo Kα |
µ (mm−1) | 0.85 |
Crystal size (mm) | × × |
|
Data collection |
Diffractometer | Oxford Diffraction CCD diffractometer |
Absorption correction | – |
No. of measured, independent and observed [I > 3σ(I)] reflections | 23130, 7927, 3679 |
Rint | 0.040 |
(sin θ/λ)max (Å−1) | 0.941 |
|
Refinement |
R[F2 > 2σ(F2)], wR(F2), S | 0.030, 0.036, 0.99 |
No. of reflections | 7927 |
No. of parameters | 293 |
No. of restraints | 20 |
Δρmax, Δρmin (e Å−3) | 0.36, −0.34 |
Selected geometric parameters (Å, º) top | Average | Minimum | Maximum |
Si1—Si2 | 3.0693 (15) | 3.0323 (15) | 3.0876 (15) |
Si1—Si2i | 3.112 (5) | 3.088 (4) | 3.138 (4) |
Si1—Si2ii | 3.047 (5) | 3.007 (5) | 3.074 (5) |
Si1—Si2iii | 3.1124 (14) | 3.1049 (14) | 3.1214 (14) |
Si1—O1i | 1.600 (6) | 1.579 (6) | 1.618 (6) |
Si1—O2 | 1.607 (5) | 1.592 (4) | 1.616 (5) |
Si1—O3 | 1.600 (5) | 1.588 (5) | 1.610 (5) |
Si1—O4 | 1.598 (4) | 1.585 (4) | 1.611 (4) |
Si2—O1 | 1.596 (5) | 1.588 (5) | 1.606 (5) |
Si2—O2 | 1.598 (4) | 1.584 (5) | 1.609 (4) |
Si2—O3iv | 1.605 (6) | 1.587 (6) | 1.617 (6) |
Si2—O4v | 1.601 (5) | 1.593 (4) | 1.608 (5) |
O1—O2 | 2.620 (7) | 2.599 (7) | 2.637 (7) |
O1—O2vi | 2.625 (7) | 2.606 (7) | 2.638 (7) |
O1—O3iv | 2.604 (8) | 2.582 (8) | 2.627 (8) |
O1—O3vi | 2.617 (8) | 2.588 (8) | 2.643 (8) |
O1—O4vi | 2.603 (7) | 2.571 (7) | 2.659 (8) |
O1—O4v | 2.611 (7) | 2.589 (7) | 2.632 (7) |
O2—O3 | 2.608 (6) | 2.590 (6) | 2.625 (7) |
O2—O3iv | 2.614 (7) | 2.599 (7) | 2.628 (7) |
O2—O4 | 2.619 (7) | 2.586 (7) | 2.634 (7) |
O2—O4v | 2.601 (7) | 2.563 (7) | 2.640 (7) |
O3—O4 | 2.613 (7) | 2.583 (7) | 2.635 (7) |
O3—O4vii | 2.624 (7) | 2.594 (7) | 2.644 (8) |
| | | |
O1—Si2—Si1—O3 | 0.79 (5) |
O2—Si2—Si1—O2 | −0.28 (6) |
O3—Si2—Si1—O1 | 0.15 (5) |
O3—Si1—Si2—O1 | 77.92 (7) |
O3—Si1—Si2—O4 | −53.39 (8) |
O3—Si1—Si2—O3 | −168.52 (6) |
O1—Si1—Si2—O3 | −44.42 (6) |
O1—Si1—Si2—O4 | 70.71 (7) |
O1—Si1—Si2—O1 | −157.98 (6) |
O4—Si1—Si2—O1 | −45.74 (7) |
O4—Si1—Si2—O3 | 67.82 (7) |
O4—Si1—Si2—O4 | −177.05 (8) |
O4—Si1—Si2—O2 | −69.90 (7) |
O4—Si1—Si2—O1 | 51.41 (6) |
O4—Si1—Si2—O4 | 163.74 (6) |
O2—Si1—Si2—O1 | −61.23 (5) |
O2—Si1—Si2—O4 | 51.10 (6) |
O2—Si1—Si2—O2 | 177.46 (6) |
O1—Si1—Si2—O4 | −65.85 (6) |
O1—Si1—Si2—O2 | 60.51 (7) |
O1—Si1—Si2—O3 | 110.66 (5) |
O2—Si1—Si2—O4 | −37.46 (6) |
O2—Si1—Si2—O3 | 87.78 (6) |
O2—Si1—Si2—O2 | −150.58 (5) |
O4—Si1—Si2—O3 | −41.18 (7) |
O4—Si1—Si2—O2 | 80.46 (6) |
O4—Si1—Si2—O4 | −166.42 (7) |
O3—Si1—Si2—O3 | −157.21 (6) |
O3—Si1—Si2—O2 | −35.57 (6) |
O3—Si1—Si2—O4 | 77.56 (6) |
Symmetry codes: (i) x1−1/2, x2−1/2, x3, x4; (ii) x1+1/2, x2−1/2, x3, x4; (iii) x1, −x2+1, x3−1/2, x4; (iv) x1−1/2, x2+1/2, x3, x4; (v) x1, −x2+1, x3+1/2, x4; (vi) x1+1/2, x2+1/2, x3, x4; (vii) x1+1/2, −x2+1/2, x3+1/2, x4. |