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From mystery to modulation: the structural story of Rb2[Si2O5]

Authors:

Hejny, Clivia; Kahlenberg, Volker; Kruger, Hannes

Journal:

Acta Crystallographica Section B 82 471-480 (2026)

DOI:

https://doi.org/10.1107/S205252062600819X

B-IncStrDB ID: 8poePc7qaeg Entry date: 2026-09-30 Last revision: 2026-10-12

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Chemical data

Structural Formula Sum: O5 Rb2 Si2 [ Help ]

Formula weight: 307.1 Da [ Help ]

Absolute configuration: . [ 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,-x3+1/2,x4+1/2
3 -x1,-x2,-x3,-x4
4 x1,-x2,x3+1/2,-x4+1/2
5 x1+1/2,x2+1/2,x3,x4
6 -x1+1/2,x2+1/2,-x3+1/2,x4+1/2
7 -x1+1/2,-x2+1/2,-x3,-x4
8 x1+1/2,-x2+1/2,x3+1/2,-x4+1/2

a: 9.8662(6) Å [ Help ]

b: 8.3986(5) Å [ Help ]

c: 14.7641(9) Å [ Help ]

α: 90 ° [ Help ]

β: 90.114(5) ° [ Help ]

γ: 90 ° [ Help ]

Volume: 1223.38(13) Å3 [ Help ]

Z: 8 [ Help ]

Modulation dimension: 1 [ Help ]

Measured independent wave vectors: [ Help ]

Wave vector id q_x q_y q_z
1 0.000000 0.377000 0.000000

Cell determination reflection Nb.: 2736 [ Help ]

θ(min) for cell determination: 4.16 ° [ Help ]

θ(max) for cell determination: 29.4 ° [ Help ]

Cell measurement temperature: 193 K [ Help ]

μ: 16.335 mm-1 [ Help ]

Absorption correction type: analytical [ Help ]

Absorption correction remarks: CrysAlisPro 1.171.42.49 (Rigaku Oxford Diffraction, 2022) Analytical numeric absorption correction using a multifaceted crystal model based on expressions derived by R.C. Clark & J.S. Reid. (Clark, R. C. & Reid, J. S. (1995). Acta Cryst. A51, 887-897) Empirical absorption correction using spherical harmonics, implemented in SCALE3 ABSPACK scaling algorithm. [ Help ]

Minimum transmission factor: 0.228 [ Help ]

Maximum transmission factor: 0.481 [ Help ]

Refinement details

Total nb. of reflections: 4780 [ Help ]

Nb. of observed reflections: 2603 [ Help ]

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

Refinement based on: Fsqd [ Help ]

R(obs): 0.0419 [ Help ]

wR(obs): 0.0765 [ Help ]

R(all): 0.1061 [ Help ]

wR(all): 0.0984 [ Help ]

S(all): 1.1627 [ Help ]

S(obs): 1.2475 [ Help ]

Nb. of reflections: 4780 [ Help ]

Nb. of parameters: 226 [ Help ]

Number of restraints: 0 [ Help ]

Number of constraints: 7 [ Help ]

Weighting scheme: sigma [ Help ]

Weighting scheme remarks: calc w=1/[σ2(Fo2)+(0.02P)2+0.0000P] where P=(Fo2+2Fc2)/3 [ Help ]

Δ/σ(max): 0.0200 [ Help ]

Δ/σ(mean): 0.0022 [ Help ]

Δρ(max): 1.22 e_Å-3 [ Help ]

Δρ(min): -1.18 e_Å-3 [ Help ]

Extinction method: none [ Help ]

Structural Information

Average Structure: [ Help ]

Atom site label Atom symbol x y z ADP type Uiso/equiv Symmetry multiplicity Occupancy Coords from (d)iffraction or (c)alculated Coords restraints or constraints Disordered cluster Disordered group
Rb1 Rb 0.33991(4) 0.11142(4) 0.08174(3) Uani 0.01599(13) 8 1 d . . .
Rb2 Rb 0.08717(4) 0.12676(5) 0.40881(3) Uani 0.01362(13) 8 1 d . . .
Si1a Si 0.3864(3) 0.3181(5) 0.3043(3) Uani 0.0067(8) 8 0.5 d . . .
Si1b Si 0.3602(3) 0.3031(4) 0.3147(3) Uani 0.0053(7) 8 0.5 d . . .
Si2a Si 0.1197(4) 0.4265(6) 0.2001(3) Uani 0.0066(8) 8 0.5 d . . .
Si2b Si 0.1439(4) 0.4389(5) 0.1891(3) Uani 0.0062(7) 8 0.5 d . . .
O1 O 0.3807(3) 0.3812(3) 0.4040(2) Uani 0.0224(11) 8 1 d . . .
O2 O 0.1345(3) 0.3545(3) 0.1019(2) Uani 0.0207(10) 8 1 d . . .
O3 O 0.3593(3) 0.1213(3) 0.3070(3) Uani 0.0084(10) 8 1 d . . .
O4a O 0.5428(4) 0.3454(5) 0.2716(3) Uani 0.0072(14) 8 0.5 d . . .
O4b O -0.0393(4) 0.3966(5) 0.2283(3) Uani 0.0077(14) 8 0.5 d . . .
O5a O 0.2939(5) 0.4151(6) 0.2305(4) Uani 0.0136(16) 8 0.5 d . . .
O5b O 0.2057(5) 0.3394(6) 0.2809(4) Uani 0.0110(15) 8 0.5 d . . .

ADP components: [ Help ]

Atom site label Atom site symbol U11 U22 U33 U12 U13 U23
Rb1 Rb 0.0152(2) 0.0204(2) 0.0124(2) 0.00013(16) -0.00062(16) 0.00270(18)
Rb2 Rb 0.0123(2) 0.0156(2) 0.0130(2) 0.00048(17) 0.00294(15) 0.00099(18)
Si1a Si 0.0048(13) 0.0057(13) 0.0097(12) 0.0018(9) 0.0019(9) -0.0007(8)
Si1b Si 0.0032(13) 0.0048(11) 0.0079(14) -0.0009(8) -0.0014(9) 0.0003(8)
Si2a Si 0.0033(13) 0.0081(13) 0.0085(14) 0.0010(9) 0.0010(8) -0.0013(9)
Si2b Si 0.0048(13) 0.0054(9) 0.0083(13) -0.0001(7) -0.0001(9) 0.0009(7)
O1 O 0.0395(19) 0.0148(17) 0.0128(18) -0.0025(15) 0.0021(15) -0.0017(15)
O2 O 0.0331(19) 0.0162(17) 0.0127(18) -0.0099(14) 0.0050(14) -0.0064(14)
O3 O 0.0096(14) 0.0048(14) 0.011(2) -0.0020(11) -0.0003(14) -0.0015(16)
O4a O 0.003(2) 0.009(2) 0.010(3) 0.0004(16) 0.0029(17) -0.0012(18)
O4b O 0.000(2) 0.013(2) 0.010(3) 0.0002(17) -0.0013(17) -0.0011(18)
O5a O 0.002(2) 0.017(3) 0.022(3) 0.0003(19) 0.0004(19) 0.012(2)
O5b O 0.002(2) 0.014(3) 0.017(3) 0.0032(18) -0.0004(18) 0.003(2)

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

Wave vector code q_1
1 1
2 2

Occupation crenel coefficients: [ Help ]

Atom site label Center (x0) Width
Si1a 0.4969 0.5
Si1b 0.9913(2) 0.5
Si2a 1.0378(4) 0.5
Si2b 0.5425(3) 0.5
O4a 0.5072(3) 0.5
O4b 1.0265(4) 0.5
O5a 1.5335(5) 0.5
O5b 1.0050(4) 0.5

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

Modulation code Atom site label Displacement axis Wave vector code
Rb1x1 Rb1 x 1
Rb1y1 Rb1 y 1
Rb1z1 Rb1 z 1
Rb2x1 Rb2 x 1
Rb2y1 Rb2 y 1
Rb2z1 Rb2 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
O3x1 O3 x 1
O3y1 O3 y 1
O3z1 O3 z 1
O3x2 O3 x 2
O3y2 O3 y 2
O3z2 O3 z 2

Displacive (translational) Fourier coefficients: [ Help ]

Modulation code Cosine coefficient Sine coefficient
Rb1x1 -0.00111(6) -0.00115(7)
Rb1y1 0.00253(8) -0.01514(7)
Rb1z1 0.00295(4) 0.00053(6)
Rb2x1 -0.01729(6) -0.00074(8)
Rb2y1 -0.00353(8) 0.02797(7)
Rb2z1 -0.00042(5) -0.00107(6)
O1x1 0.0132(4) 0.0013(6)
O1y1 0.0140(7) 0.0381(5)
O1z1 0.0003(3) -0.0028(4)
O2x1 0.0129(4) -0.0046(6)
O2y1 0.0226(6) -0.0325(5)
O2z1 -0.0005(3) 0.0002(4)
O3x1 0.0145(4) 0.0035(5)
O3y1 -0.0029(5) 0.0176(5)
O3z1 0.0384(4) 0.0043(5)
O3x2 0.0010(7) 0.0003(9)
O3y2 0.0007(9) -0.0063(8)
O3z2 0.0119(5) 0.0028(6)

Displacive (translational) XHarm coefficients: [ Help ]

Atom site label Displacement axis XHarm order XHarm coefficient
Si1a x 1 -0.0022(5)
Si1a y 1 -0.0187(8)
Si1a z 1 -0.0018(5)
Si1a x 2 0.0041(14)
Si1a y 2 0.0004(13)
Si1a z 2 -0.0024(11)
Si1b x 1 0.0037(5)
Si1b y 1 0.0096(9)
Si1b z 1 0.0050(5)
Si1b x 2 -0.0048(17)
Si1b y 2 0.003(2)
Si1b z 2 0.0040(11)
Si2a x 1 -0.0019(5)
Si2a y 1 -0.0175(9)
Si2a z 1 -0.0026(5)
Si2a x 2 -0.0037(16)
Si2a y 2 -0.0041(15)
Si2a z 2 -0.0006(12)
Si2b x 1 0.0016(5)
Si2b y 1 0.0108(10)
Si2b z 1 0.0049(5)
Si2b x 2 0.0048(19)
Si2b y 2 0.002(2)
Si2b z 2 -0.0017(14)
O4a x 1 -0.0024(10)
O4a y 1 -0.0200(10)
O4a z 1 0.0020(7)
O4a x 2 0.0080(19)
O4a y 2 -0.0005(16)
O4a z 2 -0.0026(14)
O4b x 1 -0.0003(10)
O4b y 1 -0.0189(9)
O4b z 1 0.0015(8)
O4b x 2 -0.0081(18)
O4b y 2 0.0010(19)
O4b z 2 0.0020(14)
O5a x 1 0.0010(9)
O5a y 1 -0.0099(9)
O5a z 1 0.0007(8)
O5a x 2 0.006(2)
O5a y 2 0.014(2)
O5a z 2 0.0014(17)
O5b x 1 0.0032(9)
O5b y 1 -0.0085(9)
O5b z 1 -0.0026(7)
O5b x 2 -0.006(2)
O5b y 2 -0.010(2)
O5b z 2 -0.0022(17)

Definition of the ADP Fourier series: [ Help ]

Modulation code Atom site label Tensor element Wave vector code
Rb1U111 Rb1 U11 1
Rb1U221 Rb1 U22 1
Rb1U331 Rb1 U33 1
Rb1U121 Rb1 U12 1
Rb1U131 Rb1 U13 1
Rb1U231 Rb1 U23 1
Rb2U111 Rb2 U11 1
Rb2U221 Rb2 U22 1
Rb2U331 Rb2 U33 1
Rb2U121 Rb2 U12 1
Rb2U131 Rb2 U13 1
Rb2U231 Rb2 U23 1

ADP Fourier coefficients: [ Help ]

Modulation code Cosine coefficient Sine coefficient
Rb1U111 -0.0015(3) 0.0004(4)
Rb1U221 -0.0092(3) -0.0010(3)
Rb1U331 -0.0027(4) 0.0004(5)
Rb1U121 0.0025(3) 0.0012(2)
Rb1U131 -0.0006(2) 0.0006(3)
Rb1U231 -0.0028(3) 0.0006(3)
Rb2U111 0.0039(3) 0.0015(4)
Rb2U221 0.0090(3) 0.0013(3)
Rb2U331 0.0018(4) 0.0004(5)
Rb2U121 0.0002(3) 0.0018(2)
Rb2U131 0.0012(3) 0.0012(3)
Rb2U231 -0.0019(3) 0.0009(3)