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Na2Si3O7: an incommensurate structure with crenel-type modulation functions, refined from a twinned crystal

Authors:

Kruger, Hannes; Kahlenberg, Volker; Friese, Karen

Journal:

Acta Crystallographica, Section B 62 440-446 (2006)

DOI:

https://doi.org/10.1107/S010876810600663X

B-IncStrDB ID: Cpbr6RjMnRX Entry date: 2022-01-28 Last revision: 2024-01-02

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Chemical data

Common Name: sodium trisilicate [ Help ]

Structural Formula Sum: Na2 O7 Si3 [ Help ]

Formula weight: 242.2 Da [ Help ]

Crystallographic data and experimental details

Crystal system: monoclinic [ Help ]

Superspace group name: C2/c(0β0)s0 [ Help ]

Symmetry operations of the superspace group: [ Help ]

Operation code Operation in algebraic form
1 x1,x2,x3,x4
2 -x1,x2,1/2-x3,1/2+x4
3 -x1,-x2,-x3,-x4
4 x1,-x2,1/2+x3,1/2-x4
5 1/2+x1,1/2+x2,x3,x4
6 1/2-x1,1/2+x2,1/2-x3,1/2+x4
7 1/2-x1,1/2-x2,-x3,-x4
8 1/2+x1,1/2-x2,1/2+x3,1/2-x4

a: 20.416(6) Å [ Help ]

b: 6.4987(15) Å [ Help ]

c: 4.9294(19) Å [ Help ]

α: 90 ° [ Help ]

β: 90.26(3) ° [ Help ]

γ: 90 ° [ Help ]

Volume: 654.0(4) Å3 [ Help ]

Z: 4 [ Help ]

Cell determination reflection Nb.: 2604 [ Help ]

θ(min) for cell determination: 2.00 ° [ Help ]

θ(max) for cell determination: 26.99 ° [ Help ]

Cell measurement temperature: 298 K [ Help ]

Modulation dimension: 1 [ Help ]

Measured independent wave vectors: [ Help ]

Wave vector id q_x q_y q_z
1 0.00000 0.562(2) 0.00000

μ: 0.85 mm-1 [ Help ]

Absorption correction type: none [ Help ]

Minimum transmission factor: 1.000 [ Help ]

Maximum transmission factor: 1.000 [ Help ]

Refinement details

Total nb. of reflections: 1914 [ Help ]

Nb. of observed reflections: 1327 [ Help ]

Intense reflections threshold: I>3σ(I) [ Help ]

Refinement based on: F [ Help ]

R(all): 0.1124 [ Help ]

R(obs): 0.0730 [ Help ]

wR(obs): 0.0610 [ Help ]

wR(all): 0.0651 [ Help ]

S(all): 2.30 [ Help ]

Nb. of reflections: 1914 [ Help ]

Nb. of parameters: 157 [ Help ]

Weighting scheme: sigma [ Help ]

Weighting scheme remarks: w=1/(σ2(F)+0.0001F2) [ Help ]

Δ/σ(max): 0.0004 [ Help ]

Δ/σ(mean): 0.0000 [ Help ]

Δρ(max): 1.07 e_Å-3 [ Help ]

Δρ(min): -0.80 e_Å-3 [ Help ]

Extinction method: none [ Help ]

Structural Information

Average Structure: [ Help ]

Atom symbol Atom site label x y z Uiso/equiv ADP type Coords from (d)iffraction or (c)alculated Coords restraints or constraints Occupancy Disordered cluster Disordered group
Si Si1 0.13414(6) 0.3581(2) 0.2013(3) 0.0218(4) Uani d . 1 . .
Si Si2 0 0.1359(3) 0.1855(4) 0.0177(5) Uani d . 1 . .
O O1 0.35972(18) 0.0666(5) 0.1199(7) 0.0283(11) Uani d . 1 . .
O O2 0.19026(14) 0.1984(4) 0.2567(7) 0.0216(10) Uani d . 1 . .
O O3 -0.0137(3) -0.0607(8) 0.3781(10) 0.0303(17) Uani d . 1 . .
O O4 0.06199(17) 0.2664(7) 0.2426(8) 0.0273(12) Uani d . 1 . .
Na Na1 0.29570(9) 0.3515(3) 0.2653(4) 0.0263(5) Uani d . 1 . .

ADP components: [ Help ]

Atom site label U11 U22 U33 U12 U13 U23 Atom site symbol
Si1 0.0243(6) 0.0201(6) 0.0208(6) -0.0023(6) 0.0034(6) -0.0010(6) Si
Si2 0.0217(9) 0.0184(8) 0.0130(11) 0.0008(8) 0.0016(10) 0.0005(9) Si
O1 0.040(2) 0.0226(17) 0.0225(18) 0.0010(15) 0.0030(15) -0.0010(15) O
O2 0.0310(17) 0.0210(14) 0.0129(19) 0.0032(12) -0.0023(16) -0.0020(13) O
O3 0.052(3) 0.027(3) 0.012(3) -0.009(2) 0.001(2) 0.005(2) O
O4 0.0260(16) 0.028(2) 0.028(2) -0.0037(16) 0.000(2) 0.004(2) O
Na1 0.0372(11) 0.0234(7) 0.0184(9) -0.0012(9) 0.0011(9) -0.0022(9) Na

Fourier Wave Vectors (explicit: q_x,q_y,q_z or coefficients: q_1,q_2,...): [ Help ]

Wave vector code q_x q_y q_z
1 0.00000 0.56200 0.00000

Definition of the displacive (translational) Fourier series: [ Help ]

Modulation code Atom site label Displacement axis Wave vector code
Si1x1 Si1 x 1
Si1y1 Si1 y 1
Si1z1 Si1 z 1
Si2x1 Si2 x 1
Si2y1 Si2 y 1
Si2z1 Si2 z 1
O1x1 O1 x 1
O1y1 O1 y 1
O1z1 O1 z 1
O2x1 O2 x 1
O2y1 O2 y 1
O2z1 O2 z 1
O4x1 O4 x 1
O4y1 O4 y 1
O4z1 O4 z 1
Na1x1 Na1 x 1
Na1y1 Na1 y 1
Na1z1 Na1 z 1

Displacive (translational) Fourier coefficients: [ Help ]

Modulation code Cosine coefficient Sine coefficient
Si1x1 -0.00202(11) 0.00759(9)
Si1y1 0.0204(3) -0.0107(3)
Si1z1 0.0049(7) 0.0053(6)
Si2x1 0.00632(15) -0.00209(13)
Si2y1 0 0
Si2z1 0 0
O1x1 0.0040(3) 0.0054(3)
O1y1 -0.0216(8) -0.0054(8)
O1z1 0.0019(13) -0.0061(13)
O2x1 0.0012(3) 0.0134(2)
O2y1 0.0047(8) 0.0010(7)
O2z1 -0.0044(13) 0.0040(12)
O4x1 -0.0024(3) 0.0126(2)
O4y1 0.0401(11) -0.0497(9)
O4z1 0.0105(14) -0.0046(16)
Na1x1 -0.00296(17) 0.01285(14)
Na1y1 -0.0001(5) -0.0007(5)
Na1z1 -0.0020(9) 0.0007(7)

Definition of the ADP Fourier series: [ Help ]

Modulation code Atom site label Tensor element Wave vector code
Si1U111 Si1 U11 1
Si1U221 Si1 U22 1
Si1U331 Si1 U33 1
Si1U121 Si1 U12 1
Si1U131 Si1 U13 1
Si1U231 Si1 U23 1
O1U111 O1 U11 1
O1U221 O1 U22 1
O1U331 O1 U33 1
O1U121 O1 U12 1
O1U131 O1 U13 1
O1U231 O1 U23 1
O2U111 O2 U11 1
O2U221 O2 U22 1
O2U331 O2 U33 1
O2U121 O2 U12 1
O2U131 O2 U13 1
O2U231 O2 U23 1
O4U111 O4 U11 1
O4U221 O4 U22 1
O4U331 O4 U33 1
O4U121 O4 U12 1
O4U131 O4 U13 1
O4U231 O4 U23 1
Na1U111 Na1 U11 1
Na1U221 Na1 U22 1
Na1U331 Na1 U33 1
Na1U121 Na1 U12 1
Na1U131 Na1 U13 1
Na1U231 Na1 U23 1

ADP Fourier coefficients: [ Help ]

Modulation code Cosine coefficient Sine coefficient
Si1U111 0.0086(11) 0.0023(9)
Si1U221 -0.0009(11) 0.0000(10)
Si1U331 0.0049(16) 0.0158(14)
Si1U121 -0.0017(8) 0.0025(9)
Si1U131 0.0104(13) 0.0055(10)
Si1U231 -0.0044(10) 0.0011(11)
O1U111 0.003(3) -0.015(3)
O1U221 0.001(3) -0.007(3)
O1U331 -0.005(5) -0.019(4)
O1U121 -0.006(2) -0.002(2)
O1U131 0.002(3) -0.003(3)
O1U231 0.003(3) 0.001(3)
O2U111 0.007(3) -0.006(2)
O2U221 -0.003(3) -0.004(3)
O2U331 0.013(5) -0.004(4)
O2U121 -0.001(2) -0.005(2)
O2U131 0.012(3) 0.001(3)
O2U231 0.000(2) -0.002(2)
O4U111 0.006(3) -0.004(3)
O4U221 -0.008(4) 0.006(4)
O4U331 -0.014(5) 0.008(5)
O4U121 0.003(3) 0.002(3)
O4U131 0.003(4) -0.007(3)
O4U231 0.002(4) 0.016(3)
Na1U111 0.015(2) 0.0038(15)
Na1U221 0.0002(17) 0.0016(15)
Na1U331 0.000(3) -0.004(2)
Na1U121 -0.0027(14) -0.0008(13)
Na1U131 0.006(2) 0.0039(14)
Na1U231 -0.0004(14) -0.0012(15)

Occupation crenel coefficients: [ Help ]

Atom site label Center (x0) Width
Si2 0.3276(17) 0.5
O3 0.2172(17) 0.5