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Modulated structure of nepheline

Authors:

Friese, Karen; Grzechnik, Andrzej; Petricek, Vaclav; Schonleber, Andreas; van Smaalen, Sander; Morgenroth, Wolfgang

Journal:

Acta Crystallographica, Section B 67 18-29 (2011)

DOI:

https://doi.org/10.1107/S0108768110050822

B-IncStrDB ID: buGbi7dahgj Entry date: 2022-01-19 Last revision: 2024-01-02

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Incommensurate

Chemical data

Structural Formula Sum: Al4 Ca0.03 K0.54 Na3.24 O16 Si4 [ Help ]

Formula weight: 573 Da [ Help ]

Crystallographic data and experimental details

Crystal system: trigonal [ Help ]

Superspace group name: X3(00γ)0 [ Help ]

Symmetry operations of the superspace group: [ Help ]

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

a: 17.2889(8) Å [ Help ]

b: 17.2889(8) Å [ Help ]

c: 8.3622(10) Å [ Help ]

α: 90 ° [ Help ]

β: 90 ° [ Help ]

γ: 120 ° [ Help ]

Volume: 2164.6(3) Å3 [ Help ]

Z: 6 [ Help ]

Cell determination reflection Nb.: 12279 [ Help ]

θ(min) for cell determination: 1.6 ° [ Help ]

θ(max) for cell determination: 27.6 ° [ Help ]

Cell measurement temperature: 293 K [ Help ]

Modulation dimension: 1 [ Help ]

Measured independent wave vectors: [ Help ]

Wave vector id q_x q_y q_z
1 0.00000 0.00000 0.2048(10)

μ: 0.208 mm-1 [ Help ]

Absorption correction type: numerical [ Help ]

Absorption correction remarks: Jana2006 (Petricek, Dusek & Palatinus, 2000) [ Help ]

Minimum transmission factor: 0.8719 [ Help ]

Maximum transmission factor: 0.9602 [ Help ]

Experimental remarks: Beamline D3, Synchrotron HASYLAB/DESY, MarCCD165 [ Help ]

Refinement details

Refinement remarks: Variuos restrictions used. Data only used up to (sinτ)/λ=0.85. Twin refinment; twin operation (1 0 0; 0 1 0; 0 0 -1) [ Help ]

Total nb. of reflections: 24784 [ Help ]

Nb. of observed reflections: 11997 [ Help ]

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

Refinement based on: F [ Help ]

R(all): 0.0762 [ Help ]

R(obs): 0.0380 [ Help ]

wR(obs): 0.0479 [ Help ]

wR(all): 0.0510 [ Help ]

S(all): 1.73 [ Help ]

Nb. of reflections: 24784 [ Help ]

Nb. of parameters: 282 [ Help ]

Number of restraints: 0 [ Help ]

Number of constraints: 9 [ Help ]

Weighting scheme: sigma [ Help ]

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

Δ/σ(max): 0.0381 [ Help ]

Δ/σ(mean): 0.0041 [ Help ]

Δρ(max): 1.50 e_Å-3 [ Help ]

Δρ(min): -0.74 e_Å-3 [ Help ]

Extinction method: B-C type 1 Lorentzian isotropic (Becker & Coppens, 1974) [ Help ]

Extinction coefficient: 30E2(3) [ Help ]

Absolute structure remarks: 7433 of Friedel pairs used in the refinement [ Help ]

Flack parameter: 0.4984(8) [ 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
K K1a -0.00185(8) -0.00146(7) 0.25 0.0390(7) Uani d . 0.19 . .
Na Na1a -0.00185(8) -0.00146(7) 0.25 0.0390(7) Uani d . 0.08 . .
K K1b 0.00185(8) 0.00146(7) -0.2516(4) 0.0390(7) Uani d . 0.19 . .
Na Na1b 0.00185(8) 0.00146(7) -0.2516(4) 0.0390(7) Uani d . 0.08 . .
Na Na2a 0.36891(9) 0.18630(9) 0.2465(3) 0.02327(8) Uani d . 1 . .
Na Na2b -0.37180(9) -0.18686(9) -0.2570(2) 0.02327(8) Uani d . 1 . .
Si Si1 0.333334 0.333333 -0.0609(3) 0.0123(3) Uani d . 1 . .
Al Al1 -0.333334 -0.333333 0.0515(3) 0.0111(3) Uani d . 1 . .
Si Si2 -0.333334 -0.333333 -0.5608(3) 0.0115(3) Uani d . 1 . .
Al Al2 0.333334 0.333333 0.5505(3) 0.0115(3) Uani d . 1 . .
Si Si3 -0.19104(4) -0.14272(4) -0.0698(2) 0.0105(2) Uani d . 1 . .
Al Al3 0.19043(5) 0.14217(5) 0.0566(2) 0.0105(2) Uani d . 1 . .
Si Si4 0.19119(4) 0.14286(5) 0.4296(2) 0.0109(2) Uani d . 1 . .
Al Al4 -0.19011(5) -0.14187(5) -0.4436(2) 0.0104(2) Uani d . 1 . .
O O1a 0.3639(4) 0.3563(4) 0.7501(4) 0.0288(10) Uani d . 0.3333 . .
O O1b -0.3179(4) -0.3097(5) -0.7504(4) 0.0288(10) Uani d . 0.3333 . .
O O2a1 0.2045(3) 0.1142(4) 0.2505(5) 0.0226(4) Uani d . 0.6692 . .
O O2a2 0.1906(6) 0.1084(7) 0.2494(11) 0.0226(4) Uani d . 0.3308 . .
O O2b1 -0.2091(3) -0.1220(3) -0.2471(4) 0.0226(4) Uani d . 0.6692 . .
O O2b2 -0.1910(6) -0.1027(5) -0.2507(8) 0.0226(4) Uani d . 0.3308 . .
O O3a1 0.2690(2) 0.37747(18) 0.4732(5) 0.0190(4) Uani d . 0.6692 . .
O O3a2 0.2782(4) 0.3869(4) 0.5198(8) 0.0190(4) Uani d . 0.3308 . .
O O3b1 -0.29084(17) -0.2301(2) -0.5084(5) 0.0190(4) Uani d . 0.6692 . .
O O3b2 -0.2896(4) -0.2355(3) -0.4659(8) 0.0190(4) Uani d . 0.3308 . .
O O4a1 0.29077(18) 0.23168(18) -0.0186(4) 0.0177(3) Uani d . 0.6692 . .
O O4a2 0.2921(5) 0.2373(4) 0.0358(6) 0.0177(3) Uani d . 0.3308 . .
O O4b1 -0.28482(19) -0.2223(2) 0.0031(4) 0.0177(3) Uani d . 0.6692 . .
O O4b2 -0.2842(3) -0.2264(3) -0.0447(8) 0.0177(3) Uani d . 0.3308 . .
O O5a 0.10309(14) 0.16343(17) 0.0510(3) 0.0189(5) Uani d . 1 . .
O O5b -0.11498(14) -0.17059(16) -0.0709(3) 0.0189(5) Uani d . 1 . .
O O6a 0.11491(14) 0.17146(15) 0.4284(3) 0.0183(4) Uani d . 1 . .
O O6b -0.10366(13) -0.16413(15) -0.4475(3) 0.0183(4) Uani d . 1 . .

ADP components: [ Help ]

Atom site label U11 U22 U33 U12 U13 U23 Atom site symbol
K1a 0.0673(9) 0.0362(8) 0.0434(3) 0.0484(8) -0.0235(9) -0.0193(8) K
Na1a 0.0673(9) 0.0362(8) 0.0434(3) 0.0484(8) -0.0235(9) -0.0193(8) Na
K1b 0.0673(9) 0.0362(8) 0.0434(3) 0.0484(8) -0.0235(9) -0.0193(8) K
Na1b 0.0673(9) 0.0362(8) 0.0434(3) 0.0484(8) -0.0235(9) -0.0193(8) Na
Na2a 0.01941(11) 0.02504(11) 0.02000(10) 0.00708(9) -0.0003(3) 0.0010(4) Na
Na2b 0.01941(11) 0.02504(11) 0.02000(10) 0.00708(9) -0.0003(3) 0.0010(4) Na
Si1 0.0116(3) 0.0116(3) 0.0136(5) 0.00582(16) 0 0 Si
Al1 0.0106(3) 0.0106(3) 0.0120(6) 0.00532(17) 0 0 Al
Si2 0.0118(3) 0.0118(3) 0.0108(5) 0.00589(15) 0 0 Si
Al2 0.0114(4) 0.0114(4) 0.0116(5) 0.00570(18) 0 0 Al
Si3 0.0116(3) 0.0088(3) 0.0131(3) 0.0066(2) -0.00047(19) -0.00040(18) Si
Al3 0.0097(3) 0.0096(3) 0.0128(3) 0.0054(3) -0.0004(2) -0.0009(2) Al
Si4 0.0104(3) 0.0103(3) 0.0126(3) 0.0056(2) 0.00047(19) -0.00005(18) Si
Al4 0.0117(3) 0.0088(3) 0.0124(3) 0.0065(3) 0.0014(2) 0.0001(2) Al
O1a 0.0300(13) 0.0350(16) 0.0126(4) 0.0096(11) -0.0068(9) -0.0026(8) O
O1b 0.0300(13) 0.0350(16) 0.0126(4) 0.0096(11) -0.0068(9) -0.0026(8) O
O2a1 0.0346(6) 0.0394(5) 0.0115(2) 0.0318(5) 0.0018(4) 0.0015(5) O
O2a2 0.0346(6) 0.0394(5) 0.0115(2) 0.0318(5) 0.0018(4) 0.0015(5) O
O2b1 0.0346(6) 0.0394(5) 0.0115(2) 0.0318(5) 0.0018(4) 0.0015(5) O
O2b2 0.0346(6) 0.0394(5) 0.0115(2) 0.0318(5) 0.0018(4) 0.0015(5) O
O3a1 0.0100(5) 0.0085(5) 0.0383(7) 0.0044(3) -0.0057(6) -0.0005(5) O
O3a2 0.0100(5) 0.0085(5) 0.0383(7) 0.0044(3) -0.0057(6) -0.0005(5) O
O3b1 0.0100(5) 0.0085(5) 0.0383(7) 0.0044(3) -0.0057(6) -0.0005(5) O
O3b2 0.0100(5) 0.0085(5) 0.0383(7) 0.0044(3) -0.0057(6) -0.0005(5) O
O4a1 0.0131(5) 0.0094(4) 0.0293(5) 0.0047(3) 0.0032(4) -0.0003(4) O
O4a2 0.0131(5) 0.0094(4) 0.0293(5) 0.0047(3) 0.0032(4) -0.0003(4) O
O4b1 0.0131(5) 0.0094(4) 0.0293(5) 0.0047(3) 0.0032(4) -0.0003(4) O
O4b2 0.0131(5) 0.0094(4) 0.0293(5) 0.0047(3) 0.0032(4) -0.0003(4) O
O5a 0.0184(6) 0.0263(6) 0.0201(4) 0.0172(5) 0.0010(3) 0.0038(3) O
O5b 0.0184(6) 0.0263(6) 0.0201(4) 0.0172(5) 0.0010(3) 0.0038(3) O
O6a 0.0175(6) 0.0223(6) 0.0197(4) 0.0134(5) 0.0000(3) -0.0029(3) O
O6b 0.0175(6) 0.0223(6) 0.0197(4) 0.0134(5) 0.0000(3) -0.0029(3) O

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

Wave vector code q_x q_z
1 0.00000 0.20480

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

Modulation code Atom site label Displacement axis Wave vector code
K1ax1 K1a x 1
K1ay1 K1a y 1
K1az1 K1a z 1
Na1ax1 Na1a x 1
Na1ay1 Na1a y 1
Na1az1 Na1a z 1
K1bx1 K1b x 1
K1by1 K1b y 1
K1bz1 K1b z 1
Na1bx1 Na1b x 1
Na1by1 Na1b y 1
Na1bz1 Na1b z 1
Na2ax1 Na2a x 1
Na2ay1 Na2a y 1
Na2az1 Na2a z 1
Na2bx1 Na2b x 1
Na2by1 Na2b y 1
Na2bz1 Na2b z 1
Si1x1 Si1 x 1
Si1y1 Si1 y 1
Si1z1 Si1 z 1
Al1x1 Al1 x 1
Al1y1 Al1 y 1
Al1z1 Al1 z 1
Si2x1 Si2 x 1
Si2y1 Si2 y 1
Si2z1 Si2 z 1
Al2x1 Al2 x 1
Al2y1 Al2 y 1
Al2z1 Al2 z 1
Si3x1 Si3 x 1
Si3y1 Si3 y 1
Si3z1 Si3 z 1
Al3x1 Al3 x 1
Al3y1 Al3 y 1
Al3z1 Al3 z 1
Si4x1 Si4 x 1
Si4y1 Si4 y 1
Si4z1 Si4 z 1
Al4x1 Al4 x 1
Al4y1 Al4 y 1
Al4z1 Al4 z 1
O1ax1 O1a x 1
O1ay1 O1a y 1
O1az1 O1a z 1
O1bx1 O1b x 1
O1by1 O1b y 1
O1bz1 O1b z 1
O2a1x1 O2a1 x 1
O2a1y1 O2a1 y 1
O2a1z1 O2a1 z 1
O2a2x1 O2a2 x 1
O2a2y1 O2a2 y 1
O2a2z1 O2a2 z 1
O2b1x1 O2b1 x 1
O2b1y1 O2b1 y 1
O2b1z1 O2b1 z 1
O2b2x1 O2b2 x 1
O2b2y1 O2b2 y 1
O2b2z1 O2b2 z 1
O3a1x1 O3a1 x 1
O3a1y1 O3a1 y 1
O3a1z1 O3a1 z 1
O3a2x1 O3a2 x 1
O3a2y1 O3a2 y 1
O3a2z1 O3a2 z 1
O3b1x1 O3b1 x 1
O3b1y1 O3b1 y 1
O3b1z1 O3b1 z 1
O3b2x1 O3b2 x 1
O3b2y1 O3b2 y 1
O3b2z1 O3b2 z 1
O4a1x1 O4a1 x 1
O4a1y1 O4a1 y 1
O4a1z1 O4a1 z 1
O4a2x1 O4a2 x 1
O4a2y1 O4a2 y 1
O4a2z1 O4a2 z 1
O4b1x1 O4b1 x 1
O4b1y1 O4b1 y 1
O4b1z1 O4b1 z 1
O4b2x1 O4b2 x 1
O4b2y1 O4b2 y 1
O4b2z1 O4b2 z 1
O5ax1 O5a x 1
O5ay1 O5a y 1
O5az1 O5a z 1
O5bx1 O5b x 1
O5by1 O5b y 1
O5bz1 O5b z 1
O6ax1 O6a x 1
O6ay1 O6a y 1
O6az1 O6a z 1
O6bx1 O6b x 1
O6by1 O6b y 1
O6bz1 O6b z 1

Displacive (translational) Fourier coefficients: [ Help ]

Modulation code Cosine coefficient Sine coefficient
K1ax1 0 0.0036(4)
K1ay1 0 0.0026(4)
K1az1 -0.0092(3) 0
Na1ax1 0 0.0036(4)
Na1ay1 0 0.0026(4)
Na1az1 -0.0092(3) 0
K1bx1 0 0.0070(4)
K1by1 0 0.0045(4)
K1bz1 -0.0078(3) -0.00167(13)
Na1bx1 0 0.0070(4)
Na1by1 0 0.0045(4)
Na1bz1 -0.0078(3) -0.00167(13)
Na2ax1 0 -0.00244(7)
Na2ay1 0.00109(4) 0
Na2az1 0 -0.00305(13)
Na2bx1 -0.00149(4) 0.00299(8)
Na2by1 0 -0.00126(4)
Na2bz1 0.00187(6) 0.00324(13)
Si1x1 -0.00199(8) -0.00195(6)
Si1y1 0.00069(8) -0.00270(6)
Si1z1 0 0
Al1x1 -0.00199(9) 0.00229(7)
Al1y1 0.00099(9) 0.00287(7)
Al1z1 0 0
Si2x1 -0.00249(8) 0.00115(6)
Si2y1 -0.00025(8) 0.00273(6)
Si2z1 0 0
Al2x1 -0.00241(9) -0.00093(7)
Al2y1 -0.00040(9) -0.00255(7)
Al2z1 0 0
Si3x1 -0.00023(5) 0.00241(5)
Si3y1 -0.00043(5) 0.00146(5)
Si3z1 -0.00718(9) -0.00245(10)
Al3x1 -0.00036(6) -0.00204(5)
Al3y1 -0.00062(5) -0.00124(6)
Al3z1 -0.00687(10) 0.00345(10)
Si4x1 0 -0.00229(5)
Si4y1 0.00017(4) -0.00145(5)
Si4z1 -0.00734(8) -0.00237(10)
Al4x1 0.00032(3) 0.00229(5)
Al4y1 0.00042(5) 0.00150(5)
Al4z1 -0.00735(9) 0.00298(11)
O1ax1 0 0
O1ay1 0.0029(3) -0.0013(3)
O1az1 0 0
O1bx1 -0.0060(4) 0
O1by1 0.0020(3) 0.0030(6)
O1bz1 0 0
O2a1x1 0 -0.0051(3)
O2a1y1 0 -0.0061(4)
O2a1z1 -0.0080(4) 0.0029(4)
O2a2x1 0 0
O2a2y1 0 0
O2a2z1 -0.0084(8) -0.0049(12)
O2b1x1 -0.00396(13) 0.0044(2)
O2b1y1 -0.00439(15) 0.0071(2)
O2b1z1 -0.0104(3) 0.0026(4)
O2b2x1 0 0.0027(4)
O2b2y1 0 -0.0035(5)
O2b2z1 0 -0.0028(9)
O3a1x1 0.00110(15) -0.00259(19)
O3a1y1 0.00130(16) -0.00147(17)
O3a1z1 -0.0034(4) 0.0066(4)
O3a2x1 0 -0.0020(3)
O3a2y1 0.0020(3) -0.0036(3)
O3a2z1 0.0031(7) -0.0037(7)
O3b1x1 0 0
O3b1y1 0 0.00134(17)
O3b1z1 -0.0113(4) 0.0117(5)
O3b2x1 0 0.0029(3)
O3b2y1 0.0038(3) 0
O3b2z1 -0.0065(7) 0
O4a1x1 0 0
O4a1y1 0 0
O4a1z1 0 0.0042(4)
O4a2x1 -0.00061(19) -0.0024(4)
O4a2y1 0.0005(2) -0.0032(3)
O4a2z1 -0.0042(6) 0
O4b1x1 0 0.00085(15)
O4b1y1 0.00119(9) 0.00201(14)
O4b1z1 -0.00244(18) -0.0051(4)
O4b2x1 0 0
O4b2y1 0 0
O4b2z1 -0.0062(6) 0.0049(7)
O5ax1 -0.00132(9) -0.00149(8)
O5ay1 -0.00191(11) 0
O5az1 -0.00945(18) 0.00252(11)
O5bx1 -0.00071(9) 0.00190(8)
O5by1 -0.00125(11) 0.00131(7)
O5bz1 -0.00755(18) 0
O6ax1 -0.00034(6) -0.00148(8)
O6ay1 0 0
O6az1 -0.00741(18) 0
O6bx1 0 0.00179(8)
O6by1 0 0.00082(7)
O6bz1 -0.00794(18) 0.00284(10)

Definition of the occupation Fourier series: [ Help ]

Modulation code Atom site label Wave vector code
K1ao1 K1a 1
Na1ao1 Na1a 1
K1bo1 K1b 1
Na1bo1 Na1b 1
O1ao1 O1a 1
O1bo1 O1b 1
O2a1o1 O2a1 1
O2a2o1 O2a2 1
O2b1o1 O2b1 1
O2b2o1 O2b2 1
O3a1o1 O3a1 1
O3a2o1 O3a2 1
O3b1o1 O3b1 1
O3b2o1 O3b2 1
O4a1o1 O4a1 1
O4a2o1 O4a2 1
O4b1o1 O4b1 1
O4b2o1 O4b2 1

Occupation Fourier coefficients: [ Help ]

Modulation code Cosine coefficient Sine coefficient
K1ao1 0 -0.033(3)
Na1ao1 0 -0.033(3)
K1bo1 0 -0.019(3)
Na1bo1 0 -0.019(3)
O1ao1 -0.150(4) -0.101(6)
O1bo1 -0.042(5) 0.176(4)
O2a1o1 0.056(3) -0.1980(16)
O2a2o1 -0.056(3) 0.1981(16)
O2b1o1 -0.073(3) -0.1925(17)
O2b2o1 0.074(3) 0.1922(17)
O3a1o1 0.110(3) -0.174(2)
O3a2o1 -0.120(3) 0.167(2)
O3b1o1 -0.132(3) -0.158(2)
O3b2o1 0.124(3) 0.165(2)
O4a1o1 -0.014(3) -0.2054(14)
O4a2o1 0.000(3) 0.2059(14)
O4b1o1 -0.008(3) -0.2057(14)
O4b2o1 0.021(3) 0.2048(15)

P63

Chemical data

Structural Formula Sum: Al4 Ca0.03 K0.54 Na3.24 O16 Si4 [ Help ]

Formula weight: 573 Da [ Help ]

Crystallographic data and experimental details

Crystal system: hexagonal [ Help ]

Space group name (H-M): P 63 [ Help ]

Space group name (Hall): P 6c [ Help ]

Symmetry operations of the space group: [ Help ]

Operation code Operation in algebraic form
1 x,y,z
2 -y,x-y,z
3 -x+y,-x,z
4 -x,-y,z+1/2
5 y,-x+y,z+1/2
6 x-y,x,z+1/2

a: 9.9818(4) Å [ Help ]

b: 9.9818(4) Å [ Help ]

c: 8.3622(10) Å [ Help ]

α: 90 ° [ Help ]

β: 90 ° [ Help ]

γ: 120 ° [ Help ]

Volume: 721.55(10) Å3 [ Help ]

Z: 2 [ Help ]

Cell determination reflection Nb.: 12279 [ Help ]

θ(min) for cell determination: 1.5 ° [ Help ]

θ(max) for cell determination: 27.6 ° [ Help ]

Cell measurement temperature: 293 K [ Help ]

μ: 0.208 mm-1 [ Help ]

Absorption correction type: numerical [ Help ]

Absorption correction remarks: Jana2006 [ Help ]

Minimum transmission factor: 0.8719 [ Help ]

Maximum transmission factor: 0.9602 [ Help ]

Experimental remarks: Beamline D3, Synchrotron HASYLAB/DESY, MarCCD165 [ Help ]

Refinement details

Total nb. of reflections: 5265 [ Help ]

Nb. of observed reflections: 4288 [ Help ]

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

Refinement based on: F [ Help ]

R(all): 0.0522 [ Help ]

R(obs): 0.0451 [ Help ]

wR(obs): 0.0609 [ Help ]

wR(all): 0.0613 [ Help ]

S(all): 3.45 [ Help ]

Nb. of reflections: 5265 [ Help ]

Nb. of parameters: 91 [ Help ]

Number of restraints: 0 [ Help ]

Number of constraints: 0 [ Help ]

Weighting scheme: sigma [ Help ]

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

Δ/σ(max): 0.0082 [ Help ]

Δ/σ(mean): 0.0024 [ Help ]

Δρ(max): 1.20 e_Å-3 [ Help ]

Δρ(min): -1.66 e_Å-3 [ Help ]

Extinction method: B-C type 1 Lorentzian isotropic (Becker & Coppens, 1974) [ Help ]

Extinction coefficient: 66E2(8) [ Help ]

Absolute structure remarks: 1174 of Friedel pairs used in the refinement [ Help ]

Flack parameter: 0.1(3) [ 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
K K1a 0 0 0 0.0346(2) Uani d . 0.57 . .
Na Na1a 0 0 0 0.0346(2) Uani d . 0.24 . .
Na Na2a 0.55381(6) 0.99696(6) 0.5043(2) 0.02522(19) Uani d . 1 . .
Si Si1 0.666667 0.333333 0.3095(2) 0.01325(12) Uani d . 1 . .
Al Al1 0.666667 0.333333 0.6978(2) 0.01301(13) Uani d . 1 . .
Si Si2 0.90557(4) 0.66607(4) 0.8190(2) 0.01242(10) Uani d . 1 . .
Al Al2 0.90621(4) 0.66771(5) 0.1924(2) 0.01254(12) Uani d . 1 . .
O O1 0.6615(9) 0.2887(5) 0.4998(6) 0.0354(18) Uani d . 0.3333 . .
O O2 0.97226(12) 0.68311(17) -0.0018(3) 0.0333(4) Uani d . 1 . .
O O3 0.82611(14) 0.47710(14) 0.2482(3) 0.0374(5) Uani d . 1 . .
O O4 0.83682(14) 0.48963(14) 0.7601(3) 0.0335(4) Uani d . 1 . .
O O5 0.77296(12) 0.71372(13) 0.8207(3) 0.0191(3) Uani d . 1 . .
O O6 0.77594(13) 0.73328(13) 0.1973(3) 0.0213(3) Uani d . 1 . .

ADP components: [ Help ]

Atom site label U11 U22 U33 U12 U13 U23 Atom site symbol
K1a 0.02818(19) 0.02818(19) 0.0474(5) 0.01409(10) 0 0 K
Na1a 0.02818(19) 0.02818(19) 0.0474(5) 0.01409(10) 0 0 Na
Na2a 0.0274(2) 0.0325(2) 0.0218(2) 0.0196(2) -0.0004(3) -0.0008(4) Na
Si1 0.01361(14) 0.01361(14) 0.0125(2) 0.00681(7) 0 0 Si
Al1 0.01285(15) 0.01285(15) 0.0133(3) 0.00643(8) 0 0 Al
Si2 0.00902(11) 0.01232(12) 0.01565(14) 0.00514(9) -0.00047(13) 0.00061(13) Si
Al2 0.00892(13) 0.01207(14) 0.01644(18) 0.00511(11) -0.00014(14) -0.00106(15) Al
O1 0.0551(19) 0.043(2) 0.0152(8) 0.030(3) -0.005(3) -0.0068(18) O
O2 0.0291(4) 0.0706(7) 0.0158(3) 0.0367(5) -0.0005(5) -0.0004(6) O
O3 0.0118(4) 0.0114(4) 0.0866(11) 0.0041(3) 0.0054(5) 0.0064(5) O
O4 0.0125(4) 0.0111(3) 0.0755(9) 0.0049(3) -0.0005(5) -0.0042(5) O
O5 0.0174(3) 0.0238(4) 0.0220(4) 0.0147(3) -0.0022(3) -0.0014(4) O
O6 0.0211(4) 0.0265(5) 0.0238(4) 0.0175(4) 0.0053(4) 0.0027(4) O

P3

Chemical data

Structural Formula Sum: Al4 Ca0.03 K0.54 Na3.24 O16 Si4 [ Help ]

Formula weight: 573 Da [ Help ]

Crystallographic data and experimental details

Crystal system: trigonal [ Help ]

Space group name (H-M): P 3 [ Help ]

Space group name (Hall): P 3 [ Help ]

Symmetry operations of the space group: [ Help ]

Operation code Operation in algebraic form
1 x,y,z
2 -y,x-y,z
3 -x+y,-x,z

a: 9.9818(4) Å [ Help ]

b: 9.9818(4) Å [ Help ]

c: 8.3622(10) Å [ Help ]

α: 90 ° [ Help ]

β: 90 ° [ Help ]

γ: 120.0 ° [ Help ]

Volume: 721.54(10) Å3 [ Help ]

Z: 2 [ Help ]

Cell determination reflection Nb.: 12279 [ Help ]

θ(min) for cell determination: 1.5 ° [ Help ]

θ(max) for cell determination: 27.6 ° [ Help ]

Cell measurement temperature: 293 K [ Help ]

μ: 0.208 mm-1 [ Help ]

Absorption correction type: numerical [ Help ]

Absorption correction remarks: Jana2006 [ Help ]

Minimum transmission factor: 0.8719 [ Help ]

Maximum transmission factor: 0.9602 [ Help ]

Experimental remarks: Beamline D3, Synchrotron HASYLAB/DESY, MarCCD165 [ Help ]

Refinement details

Refinement remarks: Restrictions correspond to the ones in incommensurate structure. Twin Matrix (1 0 0; 0 1 0; 0 0 -1) Volume fractions 0.500(4):0.500(4) [ Help ]

Total nb. of reflections: 10240 [ Help ]

Nb. of observed reflections: 7981 [ Help ]

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

Refinement based on: F [ Help ]

R(all): 0.0476 [ Help ]

R(obs): 0.0381 [ Help ]

wR(obs): 0.0459 [ Help ]

wR(all): 0.0465 [ Help ]

S(all): 2.38 [ Help ]

Nb. of reflections: 10240 [ Help ]

Nb. of parameters: 164 [ Help ]

Number of restraints: 0 [ Help ]

Number of constraints: 0 [ Help ]

Weighting scheme: sigma [ Help ]

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

Δ/σ(max): 0.0426 [ Help ]

Δ/σ(mean): 0.0072 [ Help ]

Δρ(max): 0.92 e_Å-3 [ Help ]

Δρ(min): -0.80 e_Å-3 [ Help ]

Extinction method: B-C type 1 Lorentzian isotropic (Becker & Coppens, 1974) [ Help ]

Extinction coefficient: 56E2(4) [ 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
K K1a 0.0011(7) 0.9991(9) 0.25 0.0415(7) Uani d . 0.19 . .
Na Na1a 0.0011(7) 0.9991(9) 0.25 0.0415(7) Uani d . 0.08 . .
K K1b 0.0029(7) 0.0044(9) 0.7500(10) 0.0415(7) Uani d . 0.19 . .
Na Na1b 0.0029(7) 0.0044(9) 0.7500(10) 0.0415 Uani d . 0.08 . .
Na Na2a 0.5545(3) 0.9970(3) 0.2453(6) 0.02523(11) Uani d . 1 . .
Na Na2b 0.4466(2) 0.0029(3) 0.7460(6) 0.02523(11) Uani d . 1 . .
Si Si1 0.333333 0.666667 0.9399(6) 0.0136(3) Uani d . 1 . .
Al Al1 0.666667 0.333333 0.0526(6) 0.0136(4) Uani d . 1 . .
Al Al2 0.333333 0.666667 0.5517(6) 0.0125(3) Uani d . 1 . .
Si Si2 0.666667 0.333333 0.4408(6) 0.0130(3) Uani d . 1 . .
Al Al3 0.09379(12) 0.33222(13) 0.0572(6) 0.0123(3) Uani d . 1 . .
Si Si3 0.90523(11) 0.66604(11) 0.9317(6) 0.0124(2) Uani d . 1 . .
Si Si4 0.09416(11) 0.33384(12) 0.4309(6) 0.0125(2) Uani d . 1 . .
Al Al4 0.90626(12) 0.66757(13) 0.5586(6) 0.0127(3) Uani d . 1 . .
O O1a 0.2840(10) 0.6404(13) 0.7523(10) 0.0280(12) Uani d . 0.3333 . .
O O1b 0.6752(8) 0.2927(12) 0.2534(12) 0.0280(12) Uani d . 0.3333 . .
O O2a1 0.0264(8) 0.3235(10) 0.2573(11) 0.0282(8) Uani d . 0.6686 . .
O O2a2 0.0291(17) 0.301(2) 0.2456(19) 0.0282(8) Uani d . 0.3314 . .
O O2b1 0.9726(9) 0.6758(11) 0.7488(10) 0.0282(8) Uani d . 0.6686 . .
O O2b2 0.971(2) 0.699(2) 0.7541(17) 0.0282(8) Uani d . 0.3314 . .
O O3a1 0.1613(5) 0.5130(5) 0.4718(7) 0.0211(8) Uani d . 0.6686 . .
O O3a2 0.1696(9) 0.5072(9) 0.5190(12) 0.0211(8) Uani d . 0.3314 . .
O O3b1 0.8319(5) 0.4775(5) 0.4942(7) 0.0211(8) Uani d . 0.6686 . .
O O3b2 0.8144(8) 0.4716(9) 0.5371(13) 0.0211(8) Uani d . 0.3314 . .
O O4a1 0.1744(4) 0.5203(4) 0.9779(6) 0.0178(6) Uani d . 0.6686 . .
O O4a2 0.1761(8) 0.5241(8) 0.0339(10) 0.0178(6) Uani d . 0.3314 . .
O O4b1 0.8418(5) 0.4926(4) 0.0043(6) 0.0178(6) Uani d . 0.6686 . .
O O4b2 0.8255(7) 0.4861(7) 0.9570(10) 0.0178(6) Uani d . 0.3314 . .
O O5a 0.2239(4) 0.2671(4) 0.0553(6) 0.0199(6) Uani d . 1 . .
O O5b -0.2279(4) -0.2862(4) 0.9298(7) 0.0199(6) Uani d . 1 . .
O O6a 0.2259(4) 0.2856(4) 0.4305(6) 0.0215(7) Uani d . 1 . .
O O6b 0.7748(4) 0.7322(4) 0.5512(7) 0.0215(7) Uani d . 1 . .

ADP components: [ Help ]

Atom site label U11 U22 U33 U12 U13 U23 Atom site symbol
K1a 0.0059(4) 0.0613(10) 0.0487(5) 0.0103(9) -0.0020(19) -0.0249(14) K
Na1a 0.0059(4) 0.0613(10) 0.0487(5) 0.0103(9) -0.0020(19) -0.0249(14) Na
K1b 0.0059(4) 0.0613(10) 0.0487(5) 0.0103(9) -0.0020(19) -0.0249(14) K
Na1b 0.005941 0.061322 0.048719 0.010349 -0.002015 -0.024949 Na
Na2a 0.02759(14) 0.03248(15) 0.02173(12) 0.01961(12) -0.0013(6) -0.0004(7) Na
Na2b 0.02759(14) 0.03248(15) 0.02173(12) 0.01961(12) -0.0013(6) -0.0004(7) Na
Si1 0.0126(4) 0.0126(4) 0.0157(6) 0.00629(18) 0 0 Si
Al1 0.0146(5) 0.0146(5) 0.0118(6) 0.0073(2) 0 0 Al
Al2 0.0116(4) 0.0116(4) 0.0143(6) 0.0058(2) 0 0 Al
Si2 0.0141(4) 0.0141(4) 0.0108(5) 0.00706(18) 0 0 Si
Al3 0.0090(3) 0.0124(4) 0.0152(4) 0.0051(3) 0.0002(3) -0.0010(3) Al
Si3 0.0093(3) 0.0114(3) 0.0167(4) 0.0053(3) 0.0005(3) -0.0001(3) Si
Si4 0.0086(3) 0.0133(3) 0.0151(3) 0.0051(3) 0.0002(2) 0.0011(3) Si
Al4 0.0092(3) 0.0117(4) 0.0171(4) 0.0053(3) -0.0001(3) 0.0011(3) Al
O1a 0.0349(16) 0.0417(16) 0.0142(6) 0.0243(15) -0.0016(14) 0.0028(10) O
O1b 0.0349(16) 0.0417(16) 0.0142(6) 0.0243(15) -0.0016(14) 0.0028(10) O
O2a1 0.0287(3) 0.0613(14) 0.0143(7) 0.0372(7) -0.0004(11) -0.0011(15) O
O2a2 0.0287(3) 0.0613(14) 0.0143(7) 0.0372(7) -0.0004(11) -0.0011(15) O
O2b1 0.0287(3) 0.0613(14) 0.0143(7) 0.0372(7) -0.0004(11) -0.0011(15) O
O2b2 0.0287(3) 0.0613(14) 0.0143(7) 0.0372(7) -0.0004(11) -0.0011(15) O
O3a1 0.0093(7) 0.0122(7) 0.0413(17) 0.0049(6) 0.0004(8) 0.0007(9) O
O3a2 0.0093(7) 0.0122(7) 0.0413(17) 0.0049(6) 0.0004(8) 0.0007(9) O
O3b1 0.0093(7) 0.0122(7) 0.0413(17) 0.0049(6) 0.0004(8) 0.0007(9) O
O3b2 0.0093(7) 0.0122(7) 0.0413(17) 0.0049(6) 0.0004(8) 0.0007(9) O
O4a1 0.0108(7) 0.0098(6) 0.0298(8) 0.0029(6) -0.0030(6) 0.0026(6) O
O4a2 0.0108(7) 0.0098(6) 0.0298(8) 0.0029(6) -0.0030(6) 0.0026(6) O
O4b1 0.0108(7) 0.0098(6) 0.0298(8) 0.0029(6) -0.0030(6) 0.0026(6) O
O4b2 0.0108(7) 0.0098(6) 0.0298(8) 0.0029(6) -0.0030(6) 0.0026(6) O
O5a 0.0175(7) 0.0251(9) 0.0237(8) 0.0157(7) 0.0031(6) 0.0010(7) O
O5b 0.0175(7) 0.0251(9) 0.0237(8) 0.0157(7) 0.0031(6) 0.0010(7) O
O6a 0.0206(8) 0.0266(9) 0.0233(8) 0.0163(7) -0.0050(7) -0.0045(7) O
O6b 0.0206(8) 0.0266(9) 0.0233(8) 0.0163(7) -0.0050(7) -0.0045(7) O