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Melilite-like modulation and temperature-dependent evolution in the framework structure of K2Sc[Si2O6]F

Authors:

Hejny, Clivia; Kahlenberg, Volker; Eberhard, Tim; Kruger, Hannes

Journal:

Acta Crystallographica Section B 72 209-222 (2016)

DOI:

https://doi.org/10.1107/S2052520615024865

B-IncStrDB ID: 11562ExhL04 Entry date: 2016-04-04 Last revision: 2022-01-02

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I_rt

Chemical data

Structural Formula Sum: F1 K2 O6 Sc1 Si2 [ Help ]

Formula weight: 294.3 Da [ Help ]

Crystallographic data and experimental details

Crystal system: tetragonal [ Help ]

Space group name (H-M): P 42/m 21/n 2/m [ Help ]

Space group name (Hall): -P 4n;-2n [ Help ]

Space group nb.: 136 [ Help ]

Symmetry operations of the space group: [ Help ]

Operation code Operation in algebraic form
1 x,y,z
2 -x,-y,z
3 -y+1/2,x+1/2,z+1/2
4 y+1/2,-x+1/2,z+1/2
5 -x+1/2,y+1/2,-z+1/2
6 x+1/2,-y+1/2,-z+1/2
7 y,x,-z
8 -y,-x,-z
9 -x,-y,-z
10 x,y,-z
11 y+1/2,-x+1/2,-z+1/2
12 -y+1/2,x+1/2,-z+1/2
13 x+1/2,-y+1/2,z+1/2
14 -x+1/2,y+1/2,z+1/2
15 -y,-x,z
16 y,x,z

a: 8.978(2) Å [ Help ]

b: 8.978(2) Å [ Help ]

c: 8.2608(3) Å [ Help ]

α: 90 ° [ Help ]

β: 90 ° [ Help ]

γ: 90 ° [ Help ]

Volume: 665.86(3) Å3 [ Help ]

Z: 4 [ Help ]

Cell determination reflection Nb.: 3764 [ Help ]

θ(min) for cell determination: 3.2 ° [ Help ]

θ(max) for cell determination: 28.31 ° [ Help ]

Cell measurement temperature: 293 K [ Help ]

μ: 2.719 mm-1 [ Help ]

Absorption correction type: multi-scan [ Help ]

Absorption correction remarks: CrysAlisPro, Agilent Technologies, Version 1.171.35.19 (release 27-10-2011 CrysAlis171 .NET) (compiled Oct 27 2011,15:02:11) Empirical absorption correction using spherical harmonics, implemented in SCALE3 ABSPACK scaling algorithm. [ Help ]

Minimum transmission factor: 0.655 [ Help ]

Maximum transmission factor: 1 [ Help ]

Refinement details

Total nb. of reflections: 473 [ Help ]

Nb. of observed reflections: 457 [ Help ]

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

Refinement based on: F [ Help ]

R(obs): 0.0353 [ Help ]

wR(obs): 0.047 [ Help ]

R(all): 0.0362 [ Help ]

wR(all): 0.0472 [ Help ]

S(all): 3.77 [ Help ]

S(obs): 3.83 [ Help ]

Nb. of reflections: 473 [ Help ]

Nb. of parameters: 38 [ Help ]

Weighting scheme: sigma [ Help ]

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

Δ/σ(max): 0.0089 [ Help ]

Δ/σ(mean): 0.0009 [ Help ]

Δρ(max): 0.46 e_Å-3 [ Help ]

Δρ(min): -1.56 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
Sc Sc 0.5 0 0.25 Uani 0.0037(2) 4 1 d ? ? ?
K1 K 0.79325(8) 0.20675(8) 0 Uani 0.0201(3) 4 1 d ? ? ?
K2 K 0.34266(8) 0.34266(8) 0 Uani 0.0314(3) 4 1 d ? ? ?
Si Si 0.12239(6) 0.12239(6) 0.19665(9) Uani 0.0043(2) 8 1 d ? ? ?
O1 O 0 0 0.2594(3) Uani 0.0184(9) 4 1 d ? ? ?
O2 O 0.1163(2) 0.1163(2) 0 Uani 0.02(8) 4 1 d ? ? ?
F F 0.5 0 0 Uani 0.0197(9) 4 1 d ? ? ?
O3 O 0.0725(2) 0.28126(17) 0.2593(2) Uani 0.0234(6) 16 1 d ? ? ?

ADP components: [ Help ]

Atom site label Atom site symbol U11 U22 U33 U12 U13 U23
Sc Sc 0.0045(3) 0.0045(3) 0.002(5) 0 0 0
K1 K 0.025(4) 0.025(4) 0.0101(5) 0.0144(4) 0 0
K2 K 0.0408(5) 0.0408(5) 0.0124(6) -0.0332(6) 0 0
Si Si 0.005(3) 0.005(3) 0.003(5) 0.0013(3) -0.0003(18) -0.0003(18)
O1 O 0.0242(14) 0.0242(14) 0.0068(16) -0.0167(13) 0 0
O2 O 0.0276(12) 0.0276(12) 0.0048(15) -0.0142(14) 0 0
F F 0.0377(18) 0.0187(15) 0.0028(14) 0.0021(10) 0 0
O3 O 0.038(11) 0.0083(8) 0.024(10) 0.0094(8) -0.0065(8) -0.0056(6)

II_rt_incom

Chemical data

Structural Formula Sum: F1 K2 O6 Sc1 Si2 [ Help ]

Formula weight: 294.3 Da [ Help ]

Crystallographic data and experimental details

Crystal system: tetragonal [ Help ]

Space group name (H-M): P 42/m 21/n 2/m [ Help ]

Symmetry operations of the superspace group: [ Help ]

Operation code Operation in algebraic form
1 x1,x2,x3,x4,x5
2 -x1,-x2,x3,-x4,-x5
3 -x2+1/2,x1+1/2,x3+1/2,-x5+1/2,x4+1/2
4 x2+1/2,-x1+1/2,x3+1/2,x5+1/2,-x4+1/2
5 -x1+1/2,x2+1/2,-x3+1/2,x5,x4
6 x1+1/2,-x2+1/2,-x3+1/2,-x5,-x4
7 x2,x1,-x3,x4+1/2,-x5+1/2
8 -x2,-x1,-x3,-x4+1/2,x5+1/2
9 -x1,-x2,-x3,-x4,-x5
10 x1,x2,-x3,x4,x5
11 x2+1/2,-x1+1/2,-x3+1/2,x5+1/2,-x4+1/2
12 -x2+1/2,x1+1/2,-x3+1/2,-x5+1/2,x4+1/2
13 x1+1/2,-x2+1/2,x3+1/2,-x5,-x4
14 -x1+1/2,x2+1/2,x3+1/2,x5,x4
15 -x2,-x1,x3,-x4+1/2,x5+1/2
16 x2,x1,x3,x4+1/2,-x5+1/2

a: 8.9878(10) Å [ Help ]

b: 8.9878(10) Å [ Help ]

c: 8.2694(2) Å [ Help ]

α: 90 ° [ Help ]

β: 90 ° [ Help ]

γ: 90 ° [ Help ]

Volume: 668.007(19) Å3 [ Help ]

Modulation dimension: 2 [ Help ]

Measured independent wave vectors: [ Help ]

Wave vector id q_x q_y q_z
1 0.2982 0.2982 0
2 -0.2982 0.2982 0

Z: 4 [ Help ]

Cell determination reflection Nb.: 6650 [ Help ]

θ(min) for cell determination: 3 ° [ Help ]

θ(max) for cell determination: 23.22 ° [ Help ]

Cell measurement temperature: 293 K [ Help ]

μ: 2.71 mm-1 [ Help ]

Absorption correction type: multi-scan [ Help ]

Absorption correction remarks: CrysAlisPro, Agilent Technologies, Version 1.171.36.20 (release 27-06-2012 CrysAlis171 .NET) (compiled Jul 11 2012,15:38:31) Empirical absorption correction using spherical harmonics, implemented in SCALE3 ABSPACK scaling algorithm. [ Help ]

Minimum transmission factor: 0.649 [ Help ]

Maximum transmission factor: 1 [ Help ]

Refinement details

Total nb. of reflections: 3223 [ Help ]

Nb. of observed reflections: 3074 [ Help ]

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

Refinement based on: F [ Help ]

R(obs): 0.0515 [ Help ]

wR(obs): 0.0631 [ Help ]

R(all): 0.0545 [ Help ]

wR(all): 0.0639 [ Help ]

S(all): 4.21 [ Help ]

S(obs): 4.27 [ Help ]

Nb. of reflections: 3223 [ Help ]

Nb. of parameters: 268 [ Help ]

Weighting scheme: sigma [ Help ]

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

Δ/σ(max): 0.1401 [ Help ]

Δ/σ(mean): 0.0145 [ Help ]

Δρ(max): 0.79 e_Å-3 [ Help ]

Δρ(min): -0.75 e_Å-3 [ Help ]

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

Extinction coefficient: 76000(255) [ 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
Sc Sc 0.5 0 0.25 Uani 0.00838(13) 4 1 d ? ? ?
K1 K 0.79314(4) 0.20686(4) 0 Uani 0.02308(13) 4 1 d ? ? ?
K2 K 0.34293(4) 0.34293(4) 0 Uani 0.03292(14) 4 1 d ? ? ?
Si Si 0.12224(3) 0.12224(3) 0.19667(5) Uani 0.00955(12) 8 1 d ? ? ?
O1 O 0 0 0.25974(18) Uani 0.0182(3) 4 1 d ? ? ?
O2 O 0.11643(12) 0.11643(12) 0 Uani 0.0217(3) 4 1 d ? ? ?
F F 0.5 0 0 Uani 0.0235(4) 4 1 d ? ? ?
O3 O 0.07264(8) 0.28094(9) 0.25906(8) Uani 0.02148(19) 16 1 d ? ? ?

ADP components: [ Help ]

Atom site label Atom site symbol U11 U22 U33 U12 U13 U23
Sc Sc 0.009(2) 0.009(2) 0.0072(3) 0 0 0
K1 K 0.0263(2) 0.0263(2) 0.0167(3) 0.00903(16) 0 0
K2 K 0.0402(2) 0.0402(2) 0.0184(3) -0.0235(2) 0 0
Si Si 0.0104(19) 0.0104(19) 0.0078(2) 0.00047(11) -0.00024(7) -0.00024(7)
O1 O 0.0199(5) 0.0199(5) 0.0149(8) -0.0093(4) 0 0
O2 O 0.0281(5) 0.0281(5) 0.0089(6) -0.0091(5) 0 0
F F 0.0322(7) 0.0296(8) 0.0086(7) -0.003(5) 0 0
O3 O 0.0266(3) 0.0132(3) 0.0247(4) 0.0046(2) -0.0014(2) -0.0033(2)

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

Wave vector code q_1 q_2
1 1 0
2 0 1
3 1 1
4 -1 1

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

Modulation code Atom site label Displacement axis Wave vector code
Scx1 Sc x 1
Scy1 Sc y 1
Scz1 Sc z 1
Scx2 Sc x 2
Scy2 Sc y 2
Scz2 Sc z 2
Scx3 Sc x 3
Scy3 Sc y 3
Scz3 Sc z 3
Scx4 Sc x 4
Scy4 Sc y 4
Scz4 Sc z 4
K1x1 K1 x 1
K1y1 K1 y 1
K1z1 K1 z 1
K1x2 K1 x 2
K1y2 K1 y 2
K1z2 K1 z 2
K1x3 K1 x 3
K1y3 K1 y 3
K1z3 K1 z 3
K1x4 K1 x 4
K1y4 K1 y 4
K1z4 K1 z 4
K2x1 K2 x 1
K2y1 K2 y 1
K2z1 K2 z 1
K2x2 K2 x 2
K2y2 K2 y 2
K2z2 K2 z 2
K2x3 K2 x 3
K2y3 K2 y 3
K2z3 K2 z 3
K2x4 K2 x 4
K2y4 K2 y 4
K2z4 K2 z 4
Six1 Si x 1
Siy1 Si y 1
Siz1 Si z 1
Six2 Si x 2
Siy2 Si y 2
Siz2 Si z 2
Six3 Si x 3
Siy3 Si y 3
Siz3 Si z 3
Six4 Si x 4
Siy4 Si y 4
Siz4 Si z 4
O1x1 O1 x 1
O1y1 O1 y 1
O1z1 O1 z 1
O1x2 O1 x 2
O1y2 O1 y 2
O1z2 O1 z 2
O1x3 O1 x 3
O1y3 O1 y 3
O1z3 O1 z 3
O1x4 O1 x 4
O1y4 O1 y 4
O1z4 O1 z 4
O2x1 O2 x 1
O2y1 O2 y 1
O2z1 O2 z 1
O2x2 O2 x 2
O2y2 O2 y 2
O2z2 O2 z 2
O2x3 O2 x 3
O2y3 O2 y 3
O2z3 O2 z 3
O2x4 O2 x 4
O2y4 O2 y 4
O2z4 O2 z 4
Fx1 F x 1
Fy1 F y 1
Fz1 F z 1
Fx2 F x 2
Fy2 F y 2
Fz2 F z 2
Fx3 F x 3
Fy3 F y 3
Fz3 F z 3
Fx4 F x 4
Fy4 F y 4
Fz4 F z 4
O3x1 O3 x 1
O3y1 O3 y 1
O3z1 O3 z 1
O3x2 O3 x 2
O3y2 O3 y 2
O3z2 O3 z 2
O3x3 O3 x 3
O3y3 O3 y 3
O3z3 O3 z 3
O3x4 O3 x 4
O3y4 O3 y 4
O3z4 O3 z 4

Displacive (translational) Fourier coefficients: [ Help ]

Modulation code Cosine coefficient Sine coefficient
Scx1 0 -0.00314(2)
Scy1 0 -0.0054(3)
Scz1 -0.000148(15) 0
Scx2 0 -0.0054(3)
Scy2 0 0.00314(2)
Scz2 -0.000148(15) 0
Scx3 0 0.000253(16)
Scy3 0 0.0004(15)
Scz3 0.000201(19) 0
Scx4 0 -0.0004(15)
Scy4 0 0.000253(16)
Scz4 -0.000201(19) 0
K1x1 0.00982(5) 0.00409(3)
K1y1 0.00982(5) -0.00409(3)
K1z1 0 0
K1x2 -0.00429(3) 0.00054(2)
K1y2 -0.00429(3) 0.00054(2)
K1z2 0 0
K1x3 -0.00053(2) 0.00016(3)
K1y3 -0.00037(2) 0.0005(2)
K1z3 0 0
K1x4 0.00037(2) -0.0005(2)
K1y4 0.00053(2) -0.00016(3)
K1z4 0 0
K2x1 0.01136(6) -0.00316(4)
K2y1 -0.01136(6) 0.00316(4)
K2z1 0 0
K2x2 -0.0026(3) -0.00069(2)
K2y2 0.0026(3) -0.00069(2)
K2z2 0 0
K2x3 -0.00318(3) -0.00106(3)
K2y3 0.00255(3) 0.00093(3)
K2z3 0 0
K2x4 0.00255(3) -0.00093(3)
K2y4 -0.00318(3) 0.00106(3)
K2z4 0 0
Six1 0.000652(16) 0.001877(18)
Siy1 -0.000652(16) -0.001877(18)
Siz1 0 0
Six2 0.00346(2) -0.00553(3)
Siy2 -0.00346(2) -0.00553(3)
Siz2 0 0.00038(2)
Six3 -0.000265(17) -0.000178(18)
Siy3 0.000082(16) 0.00037(16)
Siz3 -0.000027(19) 0.000134(18)
Six4 0.000082(16) -0.00037(16)
Siy4 -0.000265(17) 0.000178(18)
Siz4 -0.000027(19) -0.000134(18)
O1x1 0 -0.01335(13)
O1y1 0 0.01335(13)
O1z1 0 0
O1x2 0 -0.0057(8)
O1y2 0 -0.0057(8)
O1z2 0 0
O1x3 0 0.00102(7)
O1y3 0 -0.0005(7)
O1z3 -0.00007(8) 0
O1x4 0 0.0005(7)
O1y4 0 -0.00102(7)
O1z4 -0.00007(8) 0
O2x1 0.00466(8) 0.01042(10)
O2y1 -0.00466(8) -0.01042(10)
O2z1 0 0
O2x2 0.00078(8) -0.00458(8)
O2y2 -0.00078(8) -0.00458(8)
O2z2 0 0
O2x3 0.00032(8) -0.00033(8)
O2y3 -0.00097(7) 0.00083(7)
O2z3 0 0
O2x4 -0.00097(7) -0.00083(7)
O2y4 0.00032(8) 0.00033(8)
O2z4 0 0
Fx1 0 -0.00976(12)
Fy1 0 -0.00129(9)
Fz1 0 0
Fx2 0 -0.01292(13)
Fy2 0 -0.00631(11)
Fz2 0 0
Fx3 0 -0.00102(10)
Fy3 0 0.00017(9)
Fz3 0 0
Fx4 0 -0.00132(9)
Fy4 0 -0.00041(9)
Fz4 0 0
O3x1 -0.01088(7) 0.01115(7)
O3y1 -0.00313(5) 0.00456(6)
O3z1 -0.00181(6) -0.01151(8)
O3x2 0.01258(7) -0.00242(5)
O3y2 0.0003(5) -0.0067(6)
O3z2 0.00236(6) 0.00203(6)
O3x3 0.00061(5) -0.00115(6)
O3y3 0.0006(5) 0.00011(5)
O3z3 -0.00109(6) -0.00017(6)
O3x4 0.00061(5) -0.00103(5)
O3y4 -0.00025(5) -0.00007(5)
O3z4 0.00084(6) 0.00007(6)

Definition of the ADP Fourier series: [ Help ]

Modulation code Atom site label Tensor element Wave vector code
ScU111 Sc U11 1
ScU221 Sc U22 1
ScU331 Sc U33 1
ScU121 Sc U12 1
ScU131 Sc U13 1
ScU231 Sc U23 1
ScU112 Sc U11 2
ScU222 Sc U22 2
ScU332 Sc U33 2
ScU122 Sc U12 2
ScU132 Sc U13 2
ScU232 Sc U23 2
ScU113 Sc U11 3
ScU223 Sc U22 3
ScU333 Sc U33 3
ScU123 Sc U12 3
ScU133 Sc U13 3
ScU233 Sc U23 3
ScU114 Sc U11 4
ScU224 Sc U22 4
ScU334 Sc U33 4
ScU124 Sc U12 4
ScU134 Sc U13 4
ScU234 Sc U23 4
K1U111 K1 U11 1
K1U221 K1 U22 1
K1U331 K1 U33 1
K1U121 K1 U12 1
K1U131 K1 U13 1
K1U231 K1 U23 1
K1U112 K1 U11 2
K1U222 K1 U22 2
K1U332 K1 U33 2
K1U122 K1 U12 2
K1U132 K1 U13 2
K1U232 K1 U23 2
K1U113 K1 U11 3
K1U223 K1 U22 3
K1U333 K1 U33 3
K1U123 K1 U12 3
K1U133 K1 U13 3
K1U233 K1 U23 3
K1U114 K1 U11 4
K1U224 K1 U22 4
K1U334 K1 U33 4
K1U124 K1 U12 4
K1U134 K1 U13 4
K1U234 K1 U23 4
K2U111 K2 U11 1
K2U221 K2 U22 1
K2U331 K2 U33 1
K2U121 K2 U12 1
K2U131 K2 U13 1
K2U231 K2 U23 1
K2U112 K2 U11 2
K2U222 K2 U22 2
K2U332 K2 U33 2
K2U122 K2 U12 2
K2U132 K2 U13 2
K2U232 K2 U23 2
K2U113 K2 U11 3
K2U223 K2 U22 3
K2U333 K2 U33 3
K2U123 K2 U12 3
K2U133 K2 U13 3
K2U233 K2 U23 3
K2U114 K2 U11 4
K2U224 K2 U22 4
K2U334 K2 U33 4
K2U124 K2 U12 4
K2U134 K2 U13 4
K2U234 K2 U23 4
SiU111 Si U11 1
SiU221 Si U22 1
SiU331 Si U33 1
SiU121 Si U12 1
SiU131 Si U13 1
SiU231 Si U23 1
SiU112 Si U11 2
SiU222 Si U22 2
SiU332 Si U33 2
SiU122 Si U12 2
SiU132 Si U13 2
SiU232 Si U23 2
SiU113 Si U11 3
SiU223 Si U22 3
SiU333 Si U33 3
SiU123 Si U12 3
SiU133 Si U13 3
SiU233 Si U23 3
SiU114 Si U11 4
SiU224 Si U22 4
SiU334 Si U33 4
SiU124 Si U12 4
SiU134 Si U13 4
SiU234 Si U23 4
O1U111 O1 U11 1
O1U221 O1 U22 1
O1U331 O1 U33 1
O1U121 O1 U12 1
O1U131 O1 U13 1
O1U231 O1 U23 1
O1U112 O1 U11 2
O1U222 O1 U22 2
O1U332 O1 U33 2
O1U122 O1 U12 2
O1U132 O1 U13 2
O1U232 O1 U23 2
O1U113 O1 U11 3
O1U223 O1 U22 3
O1U333 O1 U33 3
O1U123 O1 U12 3
O1U133 O1 U13 3
O1U233 O1 U23 3
O1U114 O1 U11 4
O1U224 O1 U22 4
O1U334 O1 U33 4
O1U124 O1 U12 4
O1U134 O1 U13 4
O1U234 O1 U23 4
O2U111 O2 U11 1
O2U221 O2 U22 1
O2U331 O2 U33 1
O2U121 O2 U12 1
O2U131 O2 U13 1
O2U231 O2 U23 1
O2U112 O2 U11 2
O2U222 O2 U22 2
O2U332 O2 U33 2
O2U122 O2 U12 2
O2U132 O2 U13 2
O2U232 O2 U23 2
O2U113 O2 U11 3
O2U223 O2 U22 3
O2U333 O2 U33 3
O2U123 O2 U12 3
O2U133 O2 U13 3
O2U233 O2 U23 3
O2U114 O2 U11 4
O2U224 O2 U22 4
O2U334 O2 U33 4
O2U124 O2 U12 4
O2U134 O2 U13 4
O2U234 O2 U23 4
FU111 F U11 1
FU221 F U22 1
FU331 F U33 1
FU121 F U12 1
FU131 F U13 1
FU231 F U23 1
FU112 F U11 2
FU222 F U22 2
FU332 F U33 2
FU122 F U12 2
FU132 F U13 2
FU232 F U23 2
FU113 F U11 3
FU223 F U22 3
FU333 F U33 3
FU123 F U12 3
FU133 F U13 3
FU233 F U23 3
FU114 F U11 4
FU224 F U22 4
FU334 F U33 4
FU124 F U12 4
FU134 F U13 4
FU234 F U23 4
O3U111 O3 U11 1
O3U221 O3 U22 1
O3U331 O3 U33 1
O3U121 O3 U12 1
O3U131 O3 U13 1
O3U231 O3 U23 1
O3U112 O3 U11 2
O3U222 O3 U22 2
O3U332 O3 U33 2
O3U122 O3 U12 2
O3U132 O3 U13 2
O3U232 O3 U23 2
O3U113 O3 U11 3
O3U223 O3 U22 3
O3U333 O3 U33 3
O3U123 O3 U12 3
O3U133 O3 U13 3
O3U233 O3 U23 3
O3U114 O3 U11 4
O3U224 O3 U22 4
O3U334 O3 U33 4
O3U124 O3 U12 4
O3U134 O3 U13 4
O3U234 O3 U23 4

ADP Fourier coefficients: [ Help ]

Modulation code Cosine coefficient Sine coefficient
ScU111 -0.00025(7) 0
ScU221 0.00007(7) 0
ScU331 0.00007(6) 0
ScU121 -0.00014(5) 0
ScU131 0 0(5)
ScU231 0 0(5)
ScU112 -0.00007(7) 0
ScU222 0.00025(7) 0
ScU332 -0.00007(6) 0
ScU122 -0.00014(5) 0
ScU132 0 0(5)
ScU232 0 0(5)
ScU113 -0.00005(6) 0
ScU223 0.00019(6) 0
ScU333 -0.00001(7) 0
ScU123 -0.00007(5) 0
ScU133 0 0.00016(6)
ScU233 0 -0.00007(5)
ScU114 0.00019(6) 0
ScU224 -0.00005(6) 0
ScU334 -0.00001(7) 0
ScU124 0.00007(5) 0
ScU134 0 -0.00007(5)
ScU234 0 -0.00016(6)
K1U111 -0.00093(13) 0.00143(10)
K1U221 0.00093(13) 0.00143(10)
K1U331 0 -0.00063(11)
K1U121 0 0.00131(12)
K1U131 0 0
K1U231 0 0
K1U112 0.00238(12) -0.0007(11)
K1U222 -0.00238(12) 0.0007(11)
K1U332 0 0
K1U122 0 0
K1U132 0 0
K1U232 0 0
K1U113 0.001(11) -0.00039(11)
K1U223 0.00063(11) 0.00012(11)
K1U333 0.00005(10) 0.00007(10)
K1U123 0.00084(9) 0.00006(9)
K1U133 0 0
K1U233 0 0
K1U114 0.00063(11) 0.00012(11)
K1U224 0.001(11) -0.00039(11)
K1U334 0.00005(10) 0.00007(10)
K1U124 0.00084(9) 0.00006(9)
K1U134 0 0
K1U234 0 0
K2U111 0.00177(17) -0.00047(15)
K2U221 -0.00177(17) 0.00047(15)
K2U331 0 0
K2U121 0 0
K2U131 0 0
K2U231 0 0
K2U112 0.00064(14) -0.0177(13)
K2U222 -0.00064(14) -0.0177(13)
K2U332 0 0.00059(12)
K2U122 0 0.01936(16)
K2U132 0 0
K2U232 0 0
K2U113 0.00177(14) -0.00116(14)
K2U223 0.00249(14) 0.00068(13)
K2U333 -0.00021(11) 0.0001(11)
K2U123 -0.00197(11) 0.00013(11)
K2U133 0 0
K2U233 0 0
K2U114 0.00249(14) -0.00068(13)
K2U224 0.00177(14) 0.00116(14)
K2U334 -0.00021(11) -0.0001(11)
K2U124 -0.00197(11) -0.00013(11)
K2U134 0 0
K2U234 0 0
SiU111 -0.00008(8) 0.00017(8)
SiU221 0.00008(8) -0.00017(8)
SiU331 0 0
SiU121 0 0
SiU131 -0.00008(5) -0.00006(5)
SiU231 0.00008(5) 0.00006(5)
SiU112 -0.00017(8) -0.00015(6)
SiU222 0.00017(8) -0.00015(6)
SiU332 0 0.00008(8)
SiU122 0 -0.00023(8)
SiU132 0(5) -0.00005(5)
SiU232 0(5) -0.00005(5)
SiU113 0.0002(7) -0.00002(7)
SiU223 0.00001(7) 0.00021(7)
SiU333 0.00002(7) 0.00012(7)
SiU123 0(6) 0.00011(6)
SiU133 -0.00005(6) 0(6)
SiU233 0.00002(5) 0(6)
SiU114 0.00001(7) -0.00021(7)
SiU224 0.0002(7) 0.00002(7)
SiU334 0.00002(7) -0.00012(7)
SiU124 0(6) -0.00011(6)
SiU134 0.00002(5) 0(6)
SiU234 -0.00005(6) 0(6)
O1U111 -0.0006(4) 0
O1U221 0.0006(4) 0
O1U331 0 0
O1U121 0 0
O1U131 0 0.0035(3)
O1U231 0 -0.0035(3)
O1U112 -0.0008(3) 0
O1U222 0.0008(3) 0
O1U332 0 0
O1U122 0 0
O1U132 0 0.0001(2)
O1U232 0 0.0001(2)
O1U113 0.0003(3) 0
O1U223 0.0008(3) 0
O1U333 -0.0001(3) 0
O1U123 -0.001(3) 0
O1U133 0 -0.0005(3)
O1U233 0 0.0008(3)
O1U114 0.0008(3) 0
O1U224 0.0003(3) 0
O1U334 -0.0001(3) 0
O1U124 -0.001(3) 0
O1U134 0 -0.0008(3)
O1U234 0 0.0005(3)
O2U111 -0.0019(4) -0.0017(5)
O2U221 0.0019(4) 0.0017(5)
O2U331 0 0
O2U121 0 0
O2U131 0 0
O2U231 0 0
O2U112 0.0002(4) -0.0013(3)
O2U222 -0.0002(4) -0.0013(3)
O2U332 0 0.0005(3)
O2U122 0 0.0012(4)
O2U132 0 0
O2U232 0 0
O2U113 0.0013(4) 0.0001(4)
O2U223 0.0007(4) -0.0002(4)
O2U333 -0.0001(3) 0.0002(3)
O2U123 -0.0011(3) 0.0003(3)
O2U133 0 0
O2U233 0 0
O2U114 0.0007(4) 0.0002(4)
O2U224 0.0013(4) -0.0001(4)
O2U334 -0.0001(3) -0.0002(3)
O2U124 -0.0011(3) -0.0003(3)
O2U134 0 0
O2U234 0 0
FU111 -0.0008(4) 0
FU221 0.0008(4) 0
FU331 -0.0002(3) 0
FU121 0.0004(3) 0
FU131 0 0
FU231 0 0
FU112 -0.0005(4) 0
FU222 -0.0004(4) 0
FU332 0.0006(3) 0
FU122 -0.0002(3) 0
FU132 0 0
FU232 0 0
FU113 0.0017(5) 0
FU223 -0.0002(4) 0
FU333 -0.0008(4) 0
FU123 -0.001(4) 0
FU133 0 0
FU233 0 0
FU114 0.0023(5) 0
FU224 -0.0003(4) 0
FU334 0.0003(4) 0
FU124 0.0011(4) 0
FU134 0 0
FU234 0 0
O3U111 0.0008(3) 0.0007(3)
O3U221 0.0006(2) 0.0003(2)
O3U331 0.002(2) 0.0035(3)
O3U121 0.0009(2) -0.0004(2)
O3U131 0.0002(2) -0.0014(2)
O3U231 -0.00049(18) -0.00089(19)
O3U112 -0.0011(3) 0.0015(3)
O3U222 0.0004(2) -0.0006(2)
O3U332 -0.001(2) -0.0019(2)
O3U122 -0.0001(2) -0.00097(19)
O3U132 -0.0004(2) 0.00089(19)
O3U232 0.0001(17) 0.00071(18)
O3U113 0.0004(3) 0.0003(3)
O3U223 0.0003(2) 0.0003(2)
O3U333 0.0019(3) -0.0008(3)
O3U123 0.00022(18) 0.00022(18)
O3U133 -0.0006(2) 0(2)
O3U233 -0.0009(2) 0.0002(19)
O3U114 0.0005(3) 0.0004(3)
O3U224 0.0003(2) 0(2)
O3U334 0.0012(3) 0.0006(3)
O3U124 0.00008(18) 0.00009(18)
O3U134 0.0001(2) 0(2)
O3U234 -0.0006(2) -0.0004(2)

II_473K

Chemical data

Structural Formula Sum: F1 K2 O6 Sc1 Si2 [ Help ]

Formula weight: 294.3 Da [ Help ]

Crystallographic data and experimental details

Crystal system: tetragonal [ Help ]

Space group name (H-M): P 42/m 21/n 2/m [ Help ]

Space group name (Hall): -P 4n;-2n [ Help ]

Space group nb.: 136 [ Help ]

Symmetry operations of the space group: [ Help ]

Operation code Operation in algebraic form
1 x,y,z
2 -x,-y,z
3 -y+1/2,x+1/2,z+1/2
4 y+1/2,-x+1/2,z+1/2
5 -x+1/2,y+1/2,-z+1/2
6 x+1/2,-y+1/2,-z+1/2
7 y,x,-z
8 -y,-x,-z
9 -x,-y,-z
10 x,y,-z
11 y+1/2,-x+1/2,-z+1/2
12 -y+1/2,x+1/2,-z+1/2
13 x+1/2,-y+1/2,z+1/2
14 -x+1/2,y+1/2,z+1/2
15 -y,-x,z
16 y,x,z

a: 8.9939(5) Å [ Help ]

b: 8.9939(5) Å [ Help ]

c: 8.2758(7) Å [ Help ]

α: 90 ° [ Help ]

β: 90 ° [ Help ]

γ: 90 ° [ Help ]

Volume: 669.43(8) Å3 [ Help ]

Z: 4 [ Help ]

Cell measurement temperature: 293 K [ Help ]

μ: 2.705 mm-1 [ Help ]

Refinement details

Total nb. of reflections: 406 [ Help ]

Nb. of observed reflections: 401 [ Help ]

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

Refinement based on: F [ Help ]

R(obs): 0.0262 [ Help ]

wR(obs): 0.038 [ Help ]

R(all): 0.0265 [ Help ]

wR(all): 0.0381 [ Help ]

S(all): 3.59 [ Help ]

S(obs): 3.61 [ Help ]

Nb. of reflections: 406 [ Help ]

Nb. of parameters: 38 [ Help ]

Weighting scheme: sigma [ Help ]

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

Δ/σ(max): 0.0184 [ Help ]

Δ/σ(mean): 0.0065 [ Help ]

Δρ(max): 0.4 e_Å-3 [ Help ]

Δρ(min): -0.89 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
Sc1 Sc 0.5 0 0.25 Uani 0.0098(2) 4 1 d ? ? ?
Si Si 0.1224(5) 0.1224(5) 0.19636(6) Uani 0.01029(19) 8 1 d ? ? ?
K1 K 0.79357(6) 0.20643(6) 0 Uani 0.03(2) 4 1 d ? ? ?
K2 K 0.34265(7) 0.34265(7) 0 Uani 0.0415(3) 4 1 d ? ? ?
O2bz O 0.1163(2) 0.1163(2) 0 Uani 0.0292(6) 4 1 d ? ? ?
Obxx O 0 0 0.2592(3) Uani 0.0241(7) 4 1 d ? ? ?
F F 0.5 0 0.5 Uani 0.0281(8) 4 1 d ? ? ?
Ot O 0.07257(17) 0.2814(13) 0.25854(15) Uani 0.0255(4) 16 1 d ? ? ?

ADP components: [ Help ]

Atom site label Atom site symbol U11 U22 U33 U12 U13 U23
Sc1 Sc 0.0112(3) 0.0112(3) 0.007(4) 0 0 0
Si Si 0.0113(3) 0.0113(3) 0.0083(4) 0.0002(2) -0.0003(13) -0.0003(13)
K1 K 0.0344(4) 0.0344(4) 0.0211(4) 0.0133(4) 0 0
K2 K 0.0501(5) 0.0501(5) 0.0243(5) -0.0311(5) 0 0
O2bz O 0.0398(10) 0.0398(10) 0.0079(11) -0.0147(12) 0 0
Obxx O 0.0287(11) 0.0287(11) 0.0148(13) -0.0147(10) 0 0
F F 0.0341(14) 0.0424(15) 0.0079(11) 0.0047(9) 0 0
Ot O 0.0348(7) 0.014(6) 0.0277(8) 0.0066(5) -0.0022(6) -0.0042(4)

II_rt

Chemical data

Structural Formula Sum: F1 K2 O6 Sc1 Si2 [ Help ]

Formula weight: 294.3 Da [ Help ]

Crystallographic data and experimental details

Crystal system: tetragonal [ Help ]

Space group name (H-M): P 42/m 21/n 2/m [ Help ]

Space group name (Hall): -P 4n;-2n [ Help ]

Space group nb.: 136 [ Help ]

Symmetry operations of the space group: [ Help ]

Operation code Operation in algebraic form
1 x,y,z
2 -x,-y,z
3 -y+1/2,x+1/2,z+1/2
4 y+1/2,-x+1/2,z+1/2
5 -x+1/2,y+1/2,-z+1/2
6 x+1/2,-y+1/2,-z+1/2
7 y,x,-z
8 -y,-x,-z
9 -x,-y,-z
10 x,y,-z
11 y+1/2,-x+1/2,-z+1/2
12 -y+1/2,x+1/2,-z+1/2
13 x+1/2,-y+1/2,z+1/2
14 -x+1/2,y+1/2,z+1/2
15 -y,-x,z
16 y,x,z

a: 8.9878(10) Å [ Help ]

b: 8.9878(10) Å [ Help ]

c: 8.2694(2) Å [ Help ]

α: 90 ° [ Help ]

β: 90 ° [ Help ]

γ: 90 ° [ Help ]

Volume: 668.007(19) Å3 [ Help ]

Z: 4 [ Help ]

Cell measurement temperature: 293 K [ Help ]

μ: 2.71 mm-1 [ Help ]

Refinement details

Total nb. of reflections: 264 [ Help ]

Nb. of observed reflections: 264 [ Help ]

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

Refinement based on: F [ Help ]

R(obs): 0.029 [ Help ]

wR(obs): 0.0528 [ Help ]

R(all): 0.029 [ Help ]

wR(all): 0.0528 [ Help ]

S(all): 3.95 [ Help ]

S(obs): 3.95 [ Help ]

Nb. of reflections: 264 [ Help ]

Nb. of parameters: 40 [ Help ]

Weighting scheme: sigma [ Help ]

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

Δ/σ(max): 0.0269 [ Help ]

Δ/σ(mean): 0.0131 [ Help ]

Δρ(max): 0.19 e_Å-3 [ Help ]

Δρ(min): -0.24 e_Å-3 [ Help ]

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

Extinction coefficient: 100000(255) [ 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
Sc Sc 0.5 0 0.25 Uani 0.0087(3) 4 1 d ? ? ?
K1 K 0.79325(5) 0.20675(5) 0 Uani 0.0256(4) 4 1 d ? ? ?
K2 K 0.34263(6) 0.34263(6) 0 Uani 0.0365(4) 4 1 d ? ? ?
Si Si 0.12233(4) 0.12233(4) 0.19652(6) Uani 0.0093(3) 8 1 d ? ? ?
O1 O 0 0 0.2604(3) Uani 0.0237(8) 4 1 d ? ? ?
O2 O 0.11596(17) 0.11596(17) 0 Uani 0.0239(6) 4 1 d ? ? ?
F F 0.5 0 0 Uani 0.0249(9) 4 1 d ? ? ?
O3 O 0.07211(18) 0.28113(15) 0.25936(14) Uani 0.0281(5) 16 1 d ? ? ?

ADP components: [ Help ]

Atom site label Atom site symbol U11 U22 U33 U12 U13 U23
Sc Sc 0.0106(6) 0.0106(6) 0.005(7) 0 0 0
K1 K 0.0313(6) 0.0313(6) 0.0142(7) 0.0137(3) 0 0
K2 K 0.0467(6) 0.0467(6) 0.0159(7) -0.0328(4) 0 0
Si Si 0.0109(6) 0.0109(6) 0.0062(6) 0.00103(16) -0.00025(10) -0.00025(10)
O1 O 0.0286(13) 0.0286(13) 0.014(16) -0.0173(9) 0 0
O2 O 0.0343(10) 0.0343(10) 0.0031(10) -0.0152(11) 0 0
F F 0.0402(17) 0.0261(14) 0.0084(17) 0.0008(8) 0 0
O3 O 0.042(9) 0.0159(8) 0.0265(9) 0.0083(5) -0.0053(6) -0.0061(4)

III_223K

Chemical data

Structural Formula Sum: F1 K2 O6 Sc1 Si2 [ Help ]

Formula weight: 294.3 Da [ Help ]

Crystallographic data and experimental details

Crystal system: tetragonal [ Help ]

Space group name (H-M): P 42/m 21/n 2/m [ Help ]

Symmetry operations of the superspace group: [ Help ]

Operation code Operation in algebraic form
1 x1,x2,x3,x4,x5
2 -x1,-x2,x3,-x4,-x5
3 -x2+1/2,x1+1/2,x3+1/2,-x5+1/2,x4+1/2
4 x2+1/2,-x1+1/2,x3+1/2,x5+1/2,-x4+1/2
5 -x1+1/2,x2+1/2,-x3+1/2,x5,x4
6 x1+1/2,-x2+1/2,-x3+1/2,-x5,-x4
7 x2,x1,-x3,x4+1/2,-x5+1/2
8 -x2,-x1,-x3,-x4+1/2,x5+1/2
9 -x1,-x2,-x3,-x4,-x5
10 x1,x2,-x3,x4,x5
11 x2+1/2,-x1+1/2,-x3+1/2,x5+1/2,-x4+1/2
12 -x2+1/2,x1+1/2,-x3+1/2,-x5+1/2,x4+1/2
13 x1+1/2,-x2+1/2,x3+1/2,-x5,-x4
14 -x1+1/2,x2+1/2,x3+1/2,x5,x4
15 -x2,-x1,x3,-x4+1/2,x5+1/2
16 x2,x1,x3,x4+1/2,-x5+1/2

a: 8.9705(4) Å [ Help ]

b: 8.9705(4) Å [ Help ]

c: 8.2615(4) Å [ Help ]

α: 90 ° [ Help ]

β: 90 ° [ Help ]

γ: 90 ° [ Help ]

Volume: 664.8(5) Å3 [ Help ]

Modulation dimension: 2 [ Help ]

Measured independent wave vectors: [ Help ]

Wave vector id q_x q_y q_z
1 0.2986 0.2986 0
2 -0.2986 0.2986 0

Z: 4 [ Help ]

Cell determination reflection Nb.: 4774 [ Help ]

θ(min) for cell determination: 3.02 ° [ Help ]

θ(max) for cell determination: 29.33 ° [ Help ]

Cell measurement temperature: 293 K [ Help ]

μ: 2.728 mm-1 [ Help ]

Absorption correction type: analytical [ Help ]

Absorption correction remarks: CrysAlisPro, Agilent Technologies, Version 1.171.36.20 (release 27-06-2012 CrysAlis171 .NET) (compiled Jul 11 2012,15:38:31) 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) [ Help ]

Minimum transmission factor: 0.406 [ Help ]

Maximum transmission factor: 0.552 [ Help ]

Refinement details

Total nb. of reflections: 4131 [ Help ]

Nb. of observed reflections: 1684 [ Help ]

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

Refinement based on: F [ Help ]

R(obs): 0.0404 [ Help ]

wR(obs): 0.054 [ Help ]

R(all): 0.1086 [ Help ]

wR(all): 0.0628 [ Help ]

S(all): 1.32 [ Help ]

S(obs): 1.83 [ Help ]

Nb. of reflections: 4131 [ Help ]

Nb. of parameters: 187 [ Help ]

Weighting scheme: sigma [ Help ]

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

Δ/σ(max): 0.0366 [ Help ]

Δ/σ(mean): 0.0060 [ Help ]

Δρ(max): 1.69 e_Å-3 [ Help ]

Δρ(min): -1.73 e_Å-3 [ Help ]

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

Extinction coefficient: 8000(200) [ 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
Sc Sc 0.5 0 0.25 Uani 0.00436(14) 4 1 d ? ? ?
K1 K 0.79288(5) 0.20712(5) 0 Uani 0.01446(17) 4 1 d ? ? ?
K2 K 0.34291(5) 0.34291(5) 0 Uani 0.0234(2) 4 1 d ? ? ?
Si Si 0.12243(4) 0.12243(4) 0.19662(7) Uani 0.0051(15) 8 1 d ? ? ?
O1 O 0 0 0.2591(3) Uani 0.0103(5) 4 1 d ? ? ?
O2 O 0.11661(15) 0.11661(15) 0 Uani 0.0127(5) 4 1 d ? ? ?
F F 0.5 0 0 Uani 0.0134(5) 4 1 d ? ? ?
O3 O 0.07265(12) 0.28124(11) 0.25894(14) Uani 0.0121(3) 16 1 d ? ? ?

ADP components: [ Help ]

Atom site label Atom site symbol U11 U22 U33 U12 U13 U23
Sc Sc 0.00438(19) 0.00438(19) 0.0043(3) 0 0 0
K1 K 0.0162(2) 0.0162(2) 0.0109(4) 0.0061(3) 0 0
K2 K 0.0288(3) 0.0288(3) 0.0125(4) -0.0191(3) 0 0
Si Si 0.0052(2) 0.0052(2) 0.0049(3) 0.00006(19) -0.00002(15) -0.00002(15)
O1 O 0.011(7) 0.011(7) 0.0087(12) -0.0048(8) 0 0
O2 O 0.017(7) 0.017(7) 0.0039(12) -0.0055(8) 0 0
F F 0.0199(9) 0.0154(9) 0.0048(10) -0.0019(7) 0 0
O3 O 0.0144(6) 0.007(5) 0.0148(7) 0.0026(4) -0.0008(5) -0.0022(4)

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

Wave vector code q_1 q_2
1 1 0
2 0 1
3 1 1
4 -1 1

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

Modulation code Atom site label Displacement axis Wave vector code
Scx1 Sc x 1
Scy1 Sc y 1
Scz1 Sc z 1
Scx2 Sc x 2
Scy2 Sc y 2
Scz2 Sc z 2
Scx3 Sc x 3
Scy3 Sc y 3
Scz3 Sc z 3
Scx4 Sc x 4
Scy4 Sc y 4
Scz4 Sc z 4
K1x1 K1 x 1
K1y1 K1 y 1
K1z1 K1 z 1
K1x2 K1 x 2
K1y2 K1 y 2
K1z2 K1 z 2
K1x3 K1 x 3
K1y3 K1 y 3
K1z3 K1 z 3
K1x4 K1 x 4
K1y4 K1 y 4
K1z4 K1 z 4
K2x1 K2 x 1
K2y1 K2 y 1
K2z1 K2 z 1
K2x2 K2 x 2
K2y2 K2 y 2
K2z2 K2 z 2
K2x3 K2 x 3
K2y3 K2 y 3
K2z3 K2 z 3
K2x4 K2 x 4
K2y4 K2 y 4
K2z4 K2 z 4
Six1 Si x 1
Siy1 Si y 1
Siz1 Si z 1
Six2 Si x 2
Siy2 Si y 2
Siz2 Si z 2
Six3 Si x 3
Siy3 Si y 3
Siz3 Si z 3
Six4 Si x 4
Siy4 Si y 4
Siz4 Si z 4
O1x1 O1 x 1
O1y1 O1 y 1
O1z1 O1 z 1
O1x2 O1 x 2
O1y2 O1 y 2
O1z2 O1 z 2
O1x3 O1 x 3
O1y3 O1 y 3
O1z3 O1 z 3
O1x4 O1 x 4
O1y4 O1 y 4
O1z4 O1 z 4
O2x1 O2 x 1
O2y1 O2 y 1
O2z1 O2 z 1
O2x2 O2 x 2
O2y2 O2 y 2
O2z2 O2 z 2
O2x3 O2 x 3
O2y3 O2 y 3
O2z3 O2 z 3
O2x4 O2 x 4
O2y4 O2 y 4
O2z4 O2 z 4
Fx1 F x 1
Fy1 F y 1
Fz1 F z 1
Fx2 F x 2
Fy2 F y 2
Fz2 F z 2
Fx3 F x 3
Fy3 F y 3
Fz3 F z 3
Fx4 F x 4
Fy4 F y 4
Fz4 F z 4
O3x1 O3 x 1
O3y1 O3 y 1
O3z1 O3 z 1
O3x2 O3 x 2
O3y2 O3 y 2
O3z2 O3 z 2
O3x3 O3 x 3
O3y3 O3 y 3
O3z3 O3 z 3
O3x4 O3 x 4
O3y4 O3 y 4
O3z4 O3 z 4

Displacive (translational) Fourier coefficients: [ Help ]

Modulation code Cosine coefficient Sine coefficient
Scx1 0 -0.00441(5)
Scy1 0 -0.00736(5)
Scz1 -0.00033(7) 0
Scx2 0 -0.00736(5)
Scy2 0 0.00441(5)
Scz2 -0.00033(7) 0
Scx3 0 0.00046(6)
Scy3 0 0.00067(6)
Scz3 0.00053(10) 0
Scx4 0 -0.00067(6)
Scy4 0 0.00046(6)
Scz4 -0.00053(10) 0
K1x1 0.01404(7) 0.00554(6)
K1y1 0.01404(7) -0.00554(6)
K1z1 0 0
K1x2 -0.00583(7) 0.00135(7)
K1y2 -0.00583(7) 0.00135(7)
K1z2 0 0
K1x3 -0.0012(9) 0.00033(9)
K1y3 -0.00053(8) 0.00112(8)
K1z3 0 0
K1x4 0.00053(8) -0.00112(8)
K1y4 0.0012(9) -0.00033(9)
K1z4 0 0
K2x1 0.01659(9) -0.00719(9)
K2y1 -0.01659(9) 0.00719(9)
K2z1 0 0
K2x2 -0.00451(8) -0.00103(7)
K2y2 0.00451(8) -0.00103(7)
K2z2 0 0
K2x3 -0.00662(9) -0.00228(10)
K2y3 0.00534(9) 0.00205(10)
K2z3 0 0
K2x4 0.00534(9) -0.00205(10)
K2y4 -0.00662(9) 0.00228(10)
K2z4 0 0
Six1 0.00106(5) 0.003(5)
Siy1 -0.00106(5) -0.003(5)
Siz1 0 0
Six2 0.00471(5) -0.00744(5)
Siy2 -0.00471(5) -0.00744(5)
Siz2 0 0.00055(10)
Six3 -0.00039(7) -0.00013(7)
Siy3 0.00006(6) 0.00118(7)
Siz3 -0.00002(10) 0.00014(10)
Six4 0.00006(6) -0.00118(7)
Siy4 -0.00039(7) 0.00013(7)
Siz4 -0.00002(10) -0.00014(10)
O1x1 0 -0.0181(2)
O1y1 0 0.0181(2)
O1z1 0 0
O1x2 0 -0.00798(18)
O1y2 0 -0.00798(18)
O1z2 0 0
O1x3 0 0.0023(2)
O1y3 0 -0.0005(2)
O1z3 0.0001(4) 0
O1x4 0 0.0005(2)
O1y4 0 -0.0023(2)
O1z4 0.0001(4) 0
O2x1 0.0073(2) 0.0159(2)
O2y1 -0.0073(2) -0.0159(2)
O2z1 0 0
O2x2 0.0008(2) -0.00645(19)
O2y2 -0.0008(2) -0.00645(19)
O2z2 0 0
O2x3 0.0005(3) -0.0006(3)
O2y3 -0.0016(2) 0.0025(2)
O2z3 0 0
O2x4 -0.0016(2) -0.0025(2)
O2y4 0.0005(3) 0.0006(3)
O2z4 0 0
Fx1 0 -0.0144(2)
Fy1 0 -0.0012(2)
Fz1 0 0
Fx2 0 -0.019(2)
Fy2 0 -0.0095(2)
Fz2 0 0
Fx3 0 -0.0022(3)
Fy3 0 0.0004(3)
Fz3 0 0
Fx4 0 -0.0025(3)
Fy4 0 -0.0004(3)
Fz4 0 0
O3x1 -0.01443(15) 0.0152(14)
O3y1 -0.00418(14) 0.00607(13)
O3z1 -0.00319(19) -0.01713(19)
O3x2 0.01674(14) -0.00338(14)
O3y2 0.0003(13) -0.009(13)
O3z2 0.00341(19) 0.0033(19)
O3x3 0.00095(16) -0.00191(17)
O3y3 0.0014(16) 0.00131(15)
O3z3 -0.0022(3) -0.0004(3)
O3x4 0.00126(16) -0.00151(16)
O3y4 -0.00006(15) -0.00039(16)
O3z4 0.0018(3) 0(3)

Definition of the ADP Fourier series: [ Help ]

Modulation code Atom site label Tensor element Wave vector code
ScU111 Sc U11 1
ScU221 Sc U22 1
ScU331 Sc U33 1
ScU121 Sc U12 1
ScU131 Sc U13 1
ScU231 Sc U23 1
ScU112 Sc U11 2
ScU222 Sc U22 2
ScU332 Sc U33 2
ScU122 Sc U12 2
ScU132 Sc U13 2
ScU232 Sc U23 2
K1U111 K1 U11 1
K1U221 K1 U22 1
K1U331 K1 U33 1
K1U121 K1 U12 1
K1U131 K1 U13 1
K1U231 K1 U23 1
K1U112 K1 U11 2
K1U222 K1 U22 2
K1U332 K1 U33 2
K1U122 K1 U12 2
K1U132 K1 U13 2
K1U232 K1 U23 2
K2U111 K2 U11 1
K2U221 K2 U22 1
K2U331 K2 U33 1
K2U121 K2 U12 1
K2U131 K2 U13 1
K2U231 K2 U23 1
K2U112 K2 U11 2
K2U222 K2 U22 2
K2U332 K2 U33 2
K2U122 K2 U12 2
K2U132 K2 U13 2
K2U232 K2 U23 2
SiU111 Si U11 1
SiU221 Si U22 1
SiU331 Si U33 1
SiU121 Si U12 1
SiU131 Si U13 1
SiU231 Si U23 1
SiU112 Si U11 2
SiU222 Si U22 2
SiU332 Si U33 2
SiU122 Si U12 2
SiU132 Si U13 2
SiU232 Si U23 2
O1U111 O1 U11 1
O1U221 O1 U22 1
O1U331 O1 U33 1
O1U121 O1 U12 1
O1U131 O1 U13 1
O1U231 O1 U23 1
O1U112 O1 U11 2
O1U222 O1 U22 2
O1U332 O1 U33 2
O1U122 O1 U12 2
O1U132 O1 U13 2
O1U232 O1 U23 2
O2U111 O2 U11 1
O2U221 O2 U22 1
O2U331 O2 U33 1
O2U121 O2 U12 1
O2U131 O2 U13 1
O2U231 O2 U23 1
O2U112 O2 U11 2
O2U222 O2 U22 2
O2U332 O2 U33 2
O2U122 O2 U12 2
O2U132 O2 U13 2
O2U232 O2 U23 2
FU111 F U11 1
FU221 F U22 1
FU331 F U33 1
FU121 F U12 1
FU131 F U13 1
FU231 F U23 1
FU112 F U11 2
FU222 F U22 2
FU332 F U33 2
FU122 F U12 2
FU132 F U13 2
FU232 F U23 2
O3U111 O3 U11 1
O3U221 O3 U22 1
O3U331 O3 U33 1
O3U121 O3 U12 1
O3U131 O3 U13 1
O3U231 O3 U23 1
O3U112 O3 U11 2
O3U222 O3 U22 2
O3U332 O3 U33 2
O3U122 O3 U12 2
O3U132 O3 U13 2
O3U232 O3 U23 2

ADP Fourier coefficients: [ Help ]

Modulation code Cosine coefficient Sine coefficient
ScU111 -0.0005(2) 0
ScU221 0.0001(2) 0
ScU331 -0.0001(3) 0
ScU121 -0.00024(18) 0
ScU131 0 -0.0002(2)
ScU231 0 0.0001(2)
ScU112 -0.0001(2) 0
ScU222 0.0005(2) 0
ScU332 0.0001(3) 0
ScU122 -0.00024(18) 0
ScU132 0 -0.0001(2)
ScU232 0 -0.0002(2)
K1U111 -0.0011(4) 0.0015(3)
K1U221 0.0011(4) 0.0015(3)
K1U331 0 -0.0004(6)
K1U121 0 0.0007(4)
K1U131 0 0
K1U231 0 0
K1U112 0.0027(4) -0.0007(4)
K1U222 -0.0027(4) 0.0007(4)
K1U332 0 0
K1U122 0 0
K1U132 0 0
K1U232 0 0
K2U111 0.0016(4) -0.0008(4)
K2U221 -0.0016(4) 0.0008(4)
K2U331 0 0
K2U121 0 0
K2U131 0 0
K2U231 0 0
K2U112 0.0007(4) -0.0186(4)
K2U222 -0.0007(4) -0.0186(4)
K2U332 0 0.0005(6)
K2U122 0 0.0203(5)
K2U132 0 0
K2U232 0 0
SiU111 -0.0003(3) -0.0001(3)
SiU221 0.0003(3) 0.0001(3)
SiU331 0 0
SiU121 0 0
SiU131 -0.0002(2) 0.0001(2)
SiU231 0.0002(2) -0.0001(2)
SiU112 -0.0005(3) 0.0001(2)
SiU222 0.0005(3) 0.0001(2)
SiU332 0 -0.0002(5)
SiU122 0 -0.0004(3)
SiU132 -0.0001(2) -0.0001(2)
SiU232 0.0001(2) -0.0001(2)
O1U111 -0.0006(11) 0
O1U221 0.0006(11) 0
O1U331 0 0
O1U121 0 0
O1U131 0 0.0038(9)
O1U231 0 -0.0038(9)
O1U112 0.0027(11) 0
O1U222 -0.0027(11) 0
O1U332 0 0
O1U122 0 0
O1U132 0 0(8)
O1U232 0 0(8)
O2U111 -0.0048(12) -0.0009(12)
O2U221 0.0048(12) 0.0009(12)
O2U331 0 0
O2U121 0 0
O2U131 0 0
O2U231 0 0
O2U112 -0.0024(12) -0.0013(10)
O2U222 0.0024(12) -0.0013(10)
O2U332 0 -0.0002(18)
O2U122 0 0.0026(12)
O2U132 0 0
O2U232 0 0
FU111 -0.0027(14) 0
FU221 -0.0001(12) 0
FU331 0.0005(15) 0
FU121 0.0014(10) 0
FU131 0 0
FU231 0 0
FU112 0.001(14) 0
FU222 0.0008(12) 0
FU332 -0.0016(15) 0
FU122 -0.0001(10) 0
FU132 0 0
FU232 0 0
O3U111 0.002(8) 0.0029(8)
O3U221 0.0012(7) -0.0008(7)
O3U331 0.0025(11) 0.0041(10)
O3U121 0.0008(6) -0.0011(6)
O3U131 -0.0015(7) -0.0018(7)
O3U231 -0.001(7) -0.0007(6)
O3U112 -0.0012(8) 0.0015(8)
O3U222 -0.0006(7) 0.0007(7)
O3U332 0.0008(11) -0.0015(11)
O3U122 -0.0015(6) -0.0009(6)
O3U132 0.0003(7) 0.002(7)
O3U232 0.0008(6) 0.0004(6)

III_173K

Chemical data

Structural Formula Sum: F1 K2 O6 Sc1 Si2 [ Help ]

Formula weight: 294.3 Da [ Help ]

Crystallographic data and experimental details

Crystal system: tetragonal [ Help ]

Space group name (H-M): P 42/m 21/n 2/m [ Help ]

Symmetry operations of the superspace group: [ Help ]

Operation code Operation in algebraic form
1 x1,x2,x3,x4,x5
2 -x1,-x2,x3,-x4,-x5
3 -x2+1/2,x1+1/2,x3+1/2,-x5+1/2,x4+1/2
4 x2+1/2,-x1+1/2,x3+1/2,x5+1/2,-x4+1/2
5 -x1+1/2,x2+1/2,-x3+1/2,x5,x4
6 x1+1/2,-x2+1/2,-x3+1/2,-x5,-x4
7 x2,x1,-x3,x4+1/2,-x5+1/2
8 -x2,-x1,-x3,-x4+1/2,x5+1/2
9 -x1,-x2,-x3,-x4,-x5
10 x1,x2,-x3,x4,x5
11 x2+1/2,-x1+1/2,-x3+1/2,x5+1/2,-x4+1/2
12 -x2+1/2,x1+1/2,-x3+1/2,-x5+1/2,x4+1/2
13 x1+1/2,-x2+1/2,x3+1/2,-x5,-x4
14 -x1+1/2,x2+1/2,x3+1/2,x5,x4
15 -x2,-x1,x3,-x4+1/2,x5+1/2
16 x2,x1,x3,x4+1/2,-x5+1/2

a: 8.9622(4) Å [ Help ]

b: 8.9622(4) Å [ Help ]

c: 8.2705(4) Å [ Help ]

α: 90 ° [ Help ]

β: 90 ° [ Help ]

γ: 90 ° [ Help ]

Volume: 664.3(5) Å3 [ Help ]

Modulation dimension: 2 [ Help ]

Measured independent wave vectors: [ Help ]

Wave vector id q_x q_y q_z
1 0.2987 0.2987 0
2 -0.2987 0.2987 0

Z: 4 [ Help ]

Cell determination reflection Nb.: 5195 [ Help ]

θ(min) for cell determination: 3 ° [ Help ]

θ(max) for cell determination: 29.29 ° [ Help ]

Cell measurement temperature: 293 K [ Help ]

μ: 2.721 mm-1 [ Help ]

Absorption correction type: analytical [ Help ]

Absorption correction remarks: CrysAlisPro, Agilent Technologies, Version 1.171.36.20 (release 27-06-2012 CrysAlis171 .NET) (compiled Jul 11 2012,15:38:31) 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) [ Help ]

Minimum transmission factor: 0.443 [ Help ]

Maximum transmission factor: 0.676 [ Help ]

Refinement details

Total nb. of reflections: 3986 [ Help ]

Nb. of observed reflections: 2178 [ Help ]

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

Refinement based on: F [ Help ]

R(obs): 0.0498 [ Help ]

wR(obs): 0.0619 [ Help ]

R(all): 0.099 [ Help ]

wR(all): 0.0674 [ Help ]

S(all): 1.82 [ Help ]

S(obs): 2.31 [ Help ]

Nb. of reflections: 3986 [ Help ]

Nb. of parameters: 187 [ Help ]

Weighting scheme: sigma [ Help ]

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

Δ/σ(max): 0.0336 [ Help ]

Δ/σ(mean): 0.0037 [ Help ]

Δρ(max): 2.77 e_Å-3 [ Help ]

Δρ(min): -3.32 e_Å-3 [ Help ]

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

Extinction coefficient: 9100(255) [ 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
Sc Sc 0.5 0 0.25 Uani 0.00357(15) 4 1 d ? ? ?
K1 K 0.79283(5) 0.20717(5) 0 Uani 0.01151(17) 4 1 d ? ? ?
K2 K 0.34303(5) 0.34303(5) 0 Uani 0.0179(2) 4 1 d ? ? ?
Si Si 0.12251(4) 0.12251(4) 0.19664(7) Uani 0.0044(15) 8 1 d ? ? ?
O1 O 0 0 0.2586(3) Uani 0.0082(5) 4 1 d ? ? ?
O2 O 0.11637(16) 0.11637(16) 0 Uani 0.0111(5) 4 1 d ? ? ?
F F 0.5 0 0 Uani 0.0107(5) 4 1 d ? ? ?
O3 O 0.0726(12) 0.28133(11) 0.25896(14) Uani 0.0099(3) 16 1 d ? ? ?

ADP components: [ Help ]

Atom site label Atom site symbol U11 U22 U33 U12 U13 U23
Sc Sc 0.003(2) 0.003(2) 0.0047(3) 0 0 0
K1 K 0.0123(3) 0.0123(3) 0.01(4) 0.0045(3) 0 0
K2 K 0.0214(3) 0.0214(3) 0.011(4) -0.0137(3) 0 0
Si Si 0.004(2) 0.004(2) 0.0051(3) -0.0001(2) -0.00002(15) -0.00002(15)
O1 O 0.0081(7) 0.0081(7) 0.0085(12) -0.0034(8) 0 0
O2 O 0.014(7) 0.014(7) 0.0052(12) -0.0033(9) 0 0
F F 0.0143(9) 0.0114(9) 0.0063(10) -0.0021(7) 0 0
O3 O 0.0103(5) 0.0054(5) 0.0139(7) 0.0018(4) -0.0006(5) -0.0017(4)

Anharmonic ADPs (C coefficients): [ Help ]

Atom site label Atom symbol C111 C112 C113 C122 C123 C133 C222 C223 C233 C333
? ? ? ? ? ? ? ? ? ? ? ?

Anharmonic ADPs (D coefficients): [ Help ]

Atom site label Atom symbol D1111 D1112 D1113 D1122 D1123 D1133 D1222 D1223 D1233 D1333 D2222 D2223 D2233 D2333 D3333
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?

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

Wave vector code q_1 q_2
1 1 0
2 0 1
3 1 1
4 -1 1

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

Modulation code Atom site label Displacement axis Wave vector code
Scx1 Sc x 1
Scy1 Sc y 1
Scz1 Sc z 1
Scx2 Sc x 2
Scy2 Sc y 2
Scz2 Sc z 2
Scx3 Sc x 3
Scy3 Sc y 3
Scz3 Sc z 3
Scx4 Sc x 4
Scy4 Sc y 4
Scz4 Sc z 4
K1x1 K1 x 1
K1y1 K1 y 1
K1z1 K1 z 1
K1x2 K1 x 2
K1y2 K1 y 2
K1z2 K1 z 2
K1x3 K1 x 3
K1y3 K1 y 3
K1z3 K1 z 3
K1x4 K1 x 4
K1y4 K1 y 4
K1z4 K1 z 4
K2x1 K2 x 1
K2y1 K2 y 1
K2z1 K2 z 1
K2x2 K2 x 2
K2y2 K2 y 2
K2z2 K2 z 2
K2x3 K2 x 3
K2y3 K2 y 3
K2z3 K2 z 3
K2x4 K2 x 4
K2y4 K2 y 4
K2z4 K2 z 4
Six1 Si x 1
Siy1 Si y 1
Siz1 Si z 1
Six2 Si x 2
Siy2 Si y 2
Siz2 Si z 2
Six3 Si x 3
Siy3 Si y 3
Siz3 Si z 3
Six4 Si x 4
Siy4 Si y 4
Siz4 Si z 4
O1x1 O1 x 1
O1y1 O1 y 1
O1z1 O1 z 1
O1x2 O1 x 2
O1y2 O1 y 2
O1z2 O1 z 2
O1x3 O1 x 3
O1y3 O1 y 3
O1z3 O1 z 3
O1x4 O1 x 4
O1y4 O1 y 4
O1z4 O1 z 4
O2x1 O2 x 1
O2y1 O2 y 1
O2z1 O2 z 1
O2x2 O2 x 2
O2y2 O2 y 2
O2z2 O2 z 2
O2x3 O2 x 3
O2y3 O2 y 3
O2z3 O2 z 3
O2x4 O2 x 4
O2y4 O2 y 4
O2z4 O2 z 4
Fx1 F x 1
Fy1 F y 1
Fz1 F z 1
Fx2 F x 2
Fy2 F y 2
Fz2 F z 2
Fx3 F x 3
Fy3 F y 3
Fz3 F z 3
Fx4 F x 4
Fy4 F y 4
Fz4 F z 4
O3x1 O3 x 1
O3y1 O3 y 1
O3z1 O3 z 1
O3x2 O3 x 2
O3y2 O3 y 2
O3z2 O3 z 2
O3x3 O3 x 3
O3y3 O3 y 3
O3z3 O3 z 3
O3x4 O3 x 4
O3y4 O3 y 4
O3z4 O3 z 4

Displacive (translational) Fourier coefficients: [ Help ]

Modulation code Cosine coefficient Sine coefficient
Scx1 0 -0.00473(5)
Scy1 0 -0.00788(5)
Scz1 -0.00037(6) 0
Scx2 0 -0.00788(5)
Scy2 0 0.00473(5)
Scz2 -0.00037(6) 0
Scx3 0 0.00073(6)
Scy3 0 0.00069(5)
Scz3 0.00055(9) 0
Scx4 0 -0.00069(5)
Scy4 0 0.00073(6)
Scz4 -0.00055(9) 0
K1x1 0.01551(7) 0.00598(6)
K1y1 0.01551(7) -0.00598(6)
K1z1 0 0
K1x2 -0.00623(7) 0.0019(7)
K1y2 -0.00623(7) 0.0019(7)
K1z2 0 0
K1x3 -0.00152(8) 0.00057(8)
K1y3 -0.00062(7) 0.00145(8)
K1z3 0 0
K1x4 0.00062(7) -0.00145(8)
K1y4 0.00152(8) -0.00057(8)
K1z4 0 0
K2x1 0.01831(9) -0.00988(9)
K2y1 -0.01831(9) 0.00988(9)
K2z1 0 0
K2x2 -0.00528(8) -0.00108(7)
K2y2 0.00528(8) -0.00108(7)
K2z2 0 0
K2x3 -0.0088(8) -0.00302(9)
K2y3 0.00748(8) 0.00269(9)
K2z3 0 0
K2x4 0.00748(8) -0.00269(9)
K2y4 -0.0088(8) 0.00302(9)
K2z4 0 0
Six1 0.00128(5) 0.00349(5)
Siy1 -0.00128(5) -0.00349(5)
Siz1 0 0
Six2 0.00508(5) -0.00806(5)
Siy2 -0.00508(5) -0.00806(5)
Siz2 0 0.00059(10)
Six3 -0.0004(6) -0.00037(7)
Siy3 -0.00005(6) 0.00095(6)
Siz3 0.00002(8) 0.00026(8)
Six4 -0.00005(6) -0.00095(6)
Siy4 -0.0004(6) 0.00037(7)
Siz4 0.00002(8) -0.00026(8)
O1x1 0 -0.0196(2)
O1y1 0 0.0196(2)
O1z1 0 0
O1x2 0 -0.00865(19)
O1y2 0 -0.00865(19)
O1z2 0 0
O1x3 0 0.0023(2)
O1y3 0 -0.0011(2)
O1z3 0(3) 0
O1x4 0 0.0011(2)
O1y4 0 -0.0023(2)
O1z4 0(3) 0
O2x1 0.0088(2) 0.0182(2)
O2y1 -0.0088(2) -0.0182(2)
O2z1 0 0
O2x2 0.0006(2) -0.00685(19)
O2y2 -0.0006(2) -0.00685(19)
O2z2 0 0
O2x3 0.0009(2) -0.0005(3)
O2y3 -0.0023(2) 0.0025(2)
O2z3 0 0
O2x4 -0.0023(2) -0.0025(2)
O2y4 0.0009(2) 0.0005(3)
O2z4 0 0
Fx1 0 -0.0158(2)
Fy1 0 -0.0011(2)
Fz1 0 0
Fx2 0 -0.0213(2)
Fy2 0 -0.0112(2)
Fz2 0 0
Fx3 0 -0.0033(3)
Fy3 0 0.0002(3)
Fz3 0 0
Fx4 0 -0.003(3)
Fy4 0 -0.0008(3)
Fz4 0 0
O3x1 -0.01546(15) 0.01659(15)
O3y1 -0.00458(14) 0.00648(13)
O3z1 -0.00379(18) -0.01955(19)
O3x2 0.01806(15) -0.00397(14)
O3y2 0.00033(13) -0.01004(13)
O3z2 0.00389(18) 0.00372(19)
O3x3 0.00126(15) -0.00247(17)
O3y3 0.00154(15) 0.00062(14)
O3z3 -0.0029(2) 0(2)
O3x4 0.00134(16) -0.0021(16)
O3y4 -0.00038(14) -0.00021(15)
O3z4 0.0018(2) 0.0003(2)

Definition of the ADP Fourier series: [ Help ]

Modulation code Atom site label Tensor element Wave vector code
ScU111 Sc U11 1
ScU221 Sc U22 1
ScU331 Sc U33 1
ScU121 Sc U12 1
ScU131 Sc U13 1
ScU231 Sc U23 1
ScU112 Sc U11 2
ScU222 Sc U22 2
ScU332 Sc U33 2
ScU122 Sc U12 2
ScU132 Sc U13 2
ScU232 Sc U23 2
K1U111 K1 U11 1
K1U221 K1 U22 1
K1U331 K1 U33 1
K1U121 K1 U12 1
K1U131 K1 U13 1
K1U231 K1 U23 1
K1U112 K1 U11 2
K1U222 K1 U22 2
K1U332 K1 U33 2
K1U122 K1 U12 2
K1U132 K1 U13 2
K1U232 K1 U23 2
K2U111 K2 U11 1
K2U221 K2 U22 1
K2U331 K2 U33 1
K2U121 K2 U12 1
K2U131 K2 U13 1
K2U231 K2 U23 1
K2U112 K2 U11 2
K2U222 K2 U22 2
K2U332 K2 U33 2
K2U122 K2 U12 2
K2U132 K2 U13 2
K2U232 K2 U23 2
SiU111 Si U11 1
SiU221 Si U22 1
SiU331 Si U33 1
SiU121 Si U12 1
SiU131 Si U13 1
SiU231 Si U23 1
SiU112 Si U11 2
SiU222 Si U22 2
SiU332 Si U33 2
SiU122 Si U12 2
SiU132 Si U13 2
SiU232 Si U23 2
O1U111 O1 U11 1
O1U221 O1 U22 1
O1U331 O1 U33 1
O1U121 O1 U12 1
O1U131 O1 U13 1
O1U231 O1 U23 1
O1U112 O1 U11 2
O1U222 O1 U22 2
O1U332 O1 U33 2
O1U122 O1 U12 2
O1U132 O1 U13 2
O1U232 O1 U23 2
O2U111 O2 U11 1
O2U221 O2 U22 1
O2U331 O2 U33 1
O2U121 O2 U12 1
O2U131 O2 U13 1
O2U231 O2 U23 1
O2U112 O2 U11 2
O2U222 O2 U22 2
O2U332 O2 U33 2
O2U122 O2 U12 2
O2U132 O2 U13 2
O2U232 O2 U23 2
FU111 F U11 1
FU221 F U22 1
FU331 F U33 1
FU121 F U12 1
FU131 F U13 1
FU231 F U23 1
FU112 F U11 2
FU222 F U22 2
FU332 F U33 2
FU122 F U12 2
FU132 F U13 2
FU232 F U23 2
O3U111 O3 U11 1
O3U221 O3 U22 1
O3U331 O3 U33 1
O3U121 O3 U12 1
O3U131 O3 U13 1
O3U231 O3 U23 1
O3U112 O3 U11 2
O3U222 O3 U22 2
O3U332 O3 U33 2
O3U122 O3 U12 2
O3U132 O3 U13 2
O3U232 O3 U23 2

ADP Fourier coefficients: [ Help ]

Modulation code Cosine coefficient Sine coefficient
ScU111 -0.0006(2) 0
ScU221 -0.0001(2) 0
ScU331 0.0004(3) 0
ScU121 -0.00013(19) 0
ScU131 0 0.00009(19)
ScU231 0 -0.0001(19)
ScU112 0.0001(2) 0
ScU222 0.0006(2) 0
ScU332 -0.0004(3) 0
ScU122 -0.00013(19) 0
ScU132 0 0.0001(19)
ScU232 0 0.00009(19)
K1U111 -0.0015(3) 0.0012(3)
K1U221 0.0015(3) 0.0012(3)
K1U331 0 -0.0002(5)
K1U121 0 0.0006(4)
K1U131 0 0
K1U231 0 0
K1U112 0.0022(3) -0.0006(3)
K1U222 -0.0022(3) 0.0006(3)
K1U332 0 0
K1U122 0 0
K1U132 0 0
K1U232 0 0
K2U111 0.0019(4) -0.0007(4)
K2U221 -0.0019(4) 0.0007(4)
K2U331 0 0
K2U121 0 0
K2U131 0 0
K2U231 0 0
K2U112 0.0003(4) -0.015(4)
K2U222 -0.0003(4) -0.015(4)
K2U332 0 0.0005(6)
K2U122 0 0.0163(5)
K2U132 0 0
K2U232 0 0
SiU111 0(2) -0.0001(3)
SiU221 0(2) 0.0001(3)
SiU331 0 0
SiU121 0 0
SiU131 -0.0002(2) 0(2)
SiU231 0.0002(2) 0(2)
SiU112 -0.0003(2) 0.0001(2)
SiU222 0.0003(2) 0.0001(2)
SiU332 0 -0.0001(4)
SiU122 0 -0.0007(3)
SiU132 -0.0001(2) -0.0001(2)
SiU232 0.0001(2) -0.0001(2)
O1U111 -0.0013(11) 0
O1U221 0.0013(11) 0
O1U331 0 0
O1U121 0 0
O1U131 0 0.0039(9)
O1U231 0 -0.0039(9)
O1U112 0.0004(10) 0
O1U222 -0.0004(10) 0
O1U332 0 0
O1U122 0 0
O1U132 0 0.0003(8)
O1U232 0 0.0003(8)
O2U111 -0.0042(11) -0.0039(12)
O2U221 0.0042(11) 0.0039(12)
O2U331 0 0
O2U121 0 0
O2U131 0 0
O2U231 0 0
O2U112 0(11) -0.0007(9)
O2U222 0(11) -0.0007(9)
O2U332 0 -0.0007(17)
O2U122 0 0.001(12)
O2U132 0 0
O2U232 0 0
FU111 -0.0025(13) 0
FU221 -0.0006(11) 0
FU331 0(14) 0
FU121 -0.0001(10) 0
FU131 0 0
FU231 0 0
FU112 -0.0011(13) 0
FU222 0.0023(11) 0
FU332 0.0002(14) 0
FU122 0(10) 0
FU132 0 0
FU232 0 0
O3U111 0.0016(8) 0.0021(8)
O3U221 0.0017(6) -0.0007(6)
O3U331 0.0035(10) 0.0038(10)
O3U121 0.0005(6) -0.0005(6)
O3U131 -0.002(7) -0.0021(7)
O3U231 -0.0019(6) -0.0006(6)
O3U112 -0.0022(7) 0.0022(8)
O3U222 0.0003(6) 0(6)
O3U332 -0.0007(10) -0.0012(10)
O3U122 -0.0005(6) -0.0012(6)
O3U132 0(7) 0.0016(7)
O3U232 0.0003(6) 0.0003(6)