Download citation
Download citation
link to html
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

cif

Crystallographic Information File (CIF) https://doi.org/10.1107/S0108768109029127/ck5037sup1.cif
Contains datablocks global, I

hkl

Structure factor file (CIF format) https://doi.org/10.1107/S0108768109029127/ck5037Isup2.hkl
Contains datablock I

Computing details top

Program(s) used to refine structure: Jana2006 (Petricek, Dusek & Palatinus, 2006); software used to prepare material for publication: Jana2006 (Petricek, Dusek & Palatinus, 2006).

Figures top
[Figure 1]
[Figure 2]
[Figure 3]
[Figure 4]
[Figure 5]
[Figure 6]
[Figure 7]
(I) top
Crystal data top
O2SiV = 353.79 (18) Å3
Mr = 60.1Z = 8
Monoclinic, Cc(α0γ)0†F(000) = 240
q = 0.65390a* + -0.49480c*Dx = 2.255 Mg m3
a = 5.007 (2) ÅMo Kα radiation, λ = 0.71073 Å
b = 8.599 (2) ŵ = 0.85 mm1
c = 8.2202 (16) ÅT = 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.

Data collection top
Oxford Diffraction CCD
diffractometer
3679 reflections with I > 3σ(I)
Radiation source: X-ray tubeRint = 0.040
Graphite monochromatorθmax = 42.0°, θmin = 2.7°
2phi and 4ω scansh = 77
23130 measured reflectionsk = 1516
7927 independent reflectionsl = 1215
Refinement top
Refinement on F0 constraints
R[F2 > 2σ(F2)] = 0.030Weighting scheme based on measured s.u.'s w = 1/(σ2(F) + 0.0001F2)
wR(F2) = 0.036(Δ/σ)max = 0.008
S = 0.99Δρmax = 0.36 e Å3
7927 reflectionsΔρmin = 0.34 e Å3
293 parametersExtinction correction: B-C type 1 Gaussian isotropic (Becker & Coppens, 1974)
20 restraintsExtinction coefficient: 4640 (90)
Crystal data top
O2Siβ = 91.57 (2)°
Mr = 60.1V = 353.79 (18) Å3
Monoclinic, Cc(α0γ)0†Z = 8
q = 0.65390a* + -0.49480c*Mo Kα radiation
a = 5.007 (2) ŵ = 0.85 mm1
b = 8.599 (2) ÅT = 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.

Data collection top
Oxford Diffraction CCD
diffractometer
3679 reflections with I > 3σ(I)
23130 measured reflectionsRint = 0.040
7927 independent reflections
Refinement top
R[F2 > 2σ(F2)] = 0.030293 parameters
wR(F2) = 0.03620 restraints
S = 0.99Δρmax = 0.36 e Å3
7927 reflectionsΔρmin = 0.34 e Å3
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzUiso*/Ueq
Si10.0895280.30758 (3)0.211540.01252 (8)
Si20.09056 (9)0.64149 (3)0.33670 (5)0.01242 (8)
O10.30010 (19)0.75222 (11)0.25668 (13)0.0247 (3)
O20.16026 (19)0.46589 (9)0.30179 (12)0.0224 (3)
O30.30187 (19)0.18034 (9)0.26440 (14)0.0200 (3)
O40.0976 (3)0.33257 (12)0.02435 (14)0.0288 (3)
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
Si10.01151 (15)0.01154 (13)0.01448 (13)0.00027 (12)0.00007 (11)0.00135 (11)
Si20.01143 (15)0.01149 (13)0.01434 (13)0.00041 (12)0.00025 (11)0.00112 (11)
O10.0143 (5)0.0234 (5)0.0365 (5)0.0017 (4)0.0047 (4)0.0077 (4)
O20.0215 (5)0.0136 (4)0.0318 (5)0.0032 (3)0.0065 (4)0.0056 (4)
O30.0124 (4)0.0158 (4)0.0318 (6)0.0013 (3)0.0027 (4)0.0003 (4)
O40.0364 (6)0.0348 (6)0.0152 (3)0.0017 (6)0.0010 (4)0.0053 (4)
Geometric parameters (Å, º) top
AverageMinimumMaximum
Si1—Si23.0693 (15)3.0323 (15)3.0876 (15)
Si1—Si2i3.112 (5)3.088 (4)3.138 (4)
Si1—Si2ii3.047 (5)3.007 (5)3.074 (5)
Si1—Si2iii3.1124 (14)3.1049 (14)3.1214 (14)
Si1—O1i1.600 (6)1.579 (6)1.618 (6)
Si1—O21.607 (5)1.592 (4)1.616 (5)
Si1—O31.600 (5)1.588 (5)1.610 (5)
Si1—O41.598 (4)1.585 (4)1.611 (4)
Si2—O11.596 (5)1.588 (5)1.606 (5)
Si2—O21.598 (4)1.584 (5)1.609 (4)
Si2—O3iv1.605 (6)1.587 (6)1.617 (6)
Si2—O4v1.601 (5)1.593 (4)1.608 (5)
O1—O22.620 (7)2.599 (7)2.637 (7)
O1—O2vi2.625 (7)2.606 (7)2.638 (7)
O1—O3iv2.604 (8)2.582 (8)2.627 (8)
O1—O3vi2.617 (8)2.588 (8)2.643 (8)
O1—O4vi2.603 (7)2.571 (7)2.659 (8)
O1—O4v2.611 (7)2.589 (7)2.632 (7)
O2—O32.608 (6)2.590 (6)2.625 (7)
O2—O3iv2.614 (7)2.599 (7)2.628 (7)
O2—O42.619 (7)2.586 (7)2.634 (7)
O2—O4v2.601 (7)2.563 (7)2.640 (7)
O3—O42.613 (7)2.583 (7)2.635 (7)
O3—O4vii2.624 (7)2.594 (7)2.644 (8)
O1—Si2—Si1—O30.79 (5)
O2—Si2—Si1—O20.28 (6)
O3—Si2—Si1—O10.15 (5)
O3—Si1—Si2—O177.92 (7)
O3—Si1—Si2—O453.39 (8)
O3—Si1—Si2—O3168.52 (6)
O1—Si1—Si2—O344.42 (6)
O1—Si1—Si2—O470.71 (7)
O1—Si1—Si2—O1157.98 (6)
O4—Si1—Si2—O145.74 (7)
O4—Si1—Si2—O367.82 (7)
O4—Si1—Si2—O4177.05 (8)
O4—Si1—Si2—O269.90 (7)
O4—Si1—Si2—O151.41 (6)
O4—Si1—Si2—O4163.74 (6)
O2—Si1—Si2—O161.23 (5)
O2—Si1—Si2—O451.10 (6)
O2—Si1—Si2—O2177.46 (6)
O1—Si1—Si2—O465.85 (6)
O1—Si1—Si2—O260.51 (7)
O1—Si1—Si2—O3110.66 (5)
O2—Si1—Si2—O437.46 (6)
O2—Si1—Si2—O387.78 (6)
O2—Si1—Si2—O2150.58 (5)
O4—Si1—Si2—O341.18 (7)
O4—Si1—Si2—O280.46 (6)
O4—Si1—Si2—O4166.42 (7)
O3—Si1—Si2—O3157.21 (6)
O3—Si1—Si2—O235.57 (6)
O3—Si1—Si2—O477.56 (6)
Symmetry codes: (i) x11/2, x21/2, x3, x4; (ii) x1+1/2, x21/2, x3, x4; (iii) x1, x2+1, x31/2, x4; (iv) x11/2, 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 formulaO2Si
Mr60.1
Crystal system, space groupMonoclinic, Cc(α0γ)0†
Temperature (K)294
Wave vectorsq = 0.65390a* + -0.49480c*
a, b, c (Å)5.007 (2), 8.599 (2), 8.2202 (16)
β (°) 91.57 (2)
V3)353.79 (18)
Z8
Radiation typeMo Kα
µ (mm1)0.85
Crystal size (mm) × ×
Data collection
DiffractometerOxford Diffraction CCD
diffractometer
Absorption correction
No. of measured, independent and
observed [I > 3σ(I)] reflections
23130, 7927, 3679
Rint0.040
(sin θ/λ)max1)0.941
Refinement
R[F2 > 2σ(F2)], wR(F2), S 0.030, 0.036, 0.99
No. of reflections7927
No. of parameters293
No. of restraints20
Δρmax, Δρmin (e Å3)0.36, 0.34

† 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.

Computer programs: Jana2006 (Petricek, Dusek & Palatinus, 2006).

Selected geometric parameters (Å, º) top
AverageMinimumMaximum
Si1—Si23.0693 (15)3.0323 (15)3.0876 (15)
Si1—Si2i3.112 (5)3.088 (4)3.138 (4)
Si1—Si2ii3.047 (5)3.007 (5)3.074 (5)
Si1—Si2iii3.1124 (14)3.1049 (14)3.1214 (14)
Si1—O1i1.600 (6)1.579 (6)1.618 (6)
Si1—O21.607 (5)1.592 (4)1.616 (5)
Si1—O31.600 (5)1.588 (5)1.610 (5)
Si1—O41.598 (4)1.585 (4)1.611 (4)
Si2—O11.596 (5)1.588 (5)1.606 (5)
Si2—O21.598 (4)1.584 (5)1.609 (4)
Si2—O3iv1.605 (6)1.587 (6)1.617 (6)
Si2—O4v1.601 (5)1.593 (4)1.608 (5)
O1—O22.620 (7)2.599 (7)2.637 (7)
O1—O2vi2.625 (7)2.606 (7)2.638 (7)
O1—O3iv2.604 (8)2.582 (8)2.627 (8)
O1—O3vi2.617 (8)2.588 (8)2.643 (8)
O1—O4vi2.603 (7)2.571 (7)2.659 (8)
O1—O4v2.611 (7)2.589 (7)2.632 (7)
O2—O32.608 (6)2.590 (6)2.625 (7)
O2—O3iv2.614 (7)2.599 (7)2.628 (7)
O2—O42.619 (7)2.586 (7)2.634 (7)
O2—O4v2.601 (7)2.563 (7)2.640 (7)
O3—O42.613 (7)2.583 (7)2.635 (7)
O3—O4vii2.624 (7)2.594 (7)2.644 (8)
O1—Si2—Si1—O30.79 (5)
O2—Si2—Si1—O20.28 (6)
O3—Si2—Si1—O10.15 (5)
O3—Si1—Si2—O177.92 (7)
O3—Si1—Si2—O453.39 (8)
O3—Si1—Si2—O3168.52 (6)
O1—Si1—Si2—O344.42 (6)
O1—Si1—Si2—O470.71 (7)
O1—Si1—Si2—O1157.98 (6)
O4—Si1—Si2—O145.74 (7)
O4—Si1—Si2—O367.82 (7)
O4—Si1—Si2—O4177.05 (8)
O4—Si1—Si2—O269.90 (7)
O4—Si1—Si2—O151.41 (6)
O4—Si1—Si2—O4163.74 (6)
O2—Si1—Si2—O161.23 (5)
O2—Si1—Si2—O451.10 (6)
O2—Si1—Si2—O2177.46 (6)
O1—Si1—Si2—O465.85 (6)
O1—Si1—Si2—O260.51 (7)
O1—Si1—Si2—O3110.66 (5)
O2—Si1—Si2—O437.46 (6)
O2—Si1—Si2—O387.78 (6)
O2—Si1—Si2—O2150.58 (5)
O4—Si1—Si2—O341.18 (7)
O4—Si1—Si2—O280.46 (6)
O4—Si1—Si2—O4166.42 (7)
O3—Si1—Si2—O3157.21 (6)
O3—Si1—Si2—O235.57 (6)
O3—Si1—Si2—O477.56 (6)
Symmetry codes: (i) x11/2, x21/2, x3, x4; (ii) x1+1/2, x21/2, x3, x4; (iii) x1, x2+1, x31/2, x4; (iv) x11/2, 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.
 

Follow Acta Cryst. B
Sign up for e-alerts
Follow Acta Cryst. on Twitter
Follow us on facebook
Sign up for RSS feeds