B-IncStrDB

(3+1)-incommensurately modulated crystal structure of Cs₃ScSi₆O₁₅

Authors:

Hejny, Clivia; Kahlenberg, Volker; Schmidmair, Daniela; Dabic, Predrag

Journal:

Acta Crystallographica, Section B 72 109-116 (2016)

DOI:

https://doi.org/10.1107/S2052520615022076

B-IncStrDB ID: 11472EwF4su Entry date: 2016-02-02 Last revision: 2022-01-19

I

Chemical data

Structural Formula Sum: Cs3 O15 Sc1 Si6 [ Help ]

Formula weight: 852.2 Da [ Help ]

Crystallographic data and experimental details

Crystal system: trigonal [ Help ]

Superspace group name: X-3m1(00γ)0s0 [ Help ]

Symmetry operations of the superspace group: (Show/hide table) [ Help ]

Operation code	Operation in algebraic form
1	x1,x2,x3,x4
2	-x2,x1-x2,x3,x4
3	-x2,-x1,x3,x4+1/2
4	-x1,-x2,-x3,-x4
5	-x1+x2,-x1,x3,x4
6	x1,x1-x2,x3,x4+1/2
7	x2,-x1+x2,-x3,-x4
8	-x1+x2,x2,x3,x4+1/2
9	x1-x2,x1,-x3,-x4
10	x2,x1,-x3,-x4+1/2
11	-x1,-x1+x2,-x3,-x4+1/2
12	x1-x2,-x2,-x3,-x4+1/2
13	x1+1/3,x2+2/3,x3+2/3,x4+1/3
14	-x2+1/3,x1-x2+2/3,x3+2/3,x4+1/3
15	-x2+1/3,-x1+2/3,x3+2/3,x4+5/6
16	-x1+1/3,-x2+2/3,-x3+2/3,-x4+1/3
17	-x1+x2+1/3,-x1+2/3,x3+2/3,x4+1/3
18	x1+1/3,x1-x2+2/3,x3+2/3,x4+5/6
19	x2+1/3,-x1+x2+2/3,-x3+2/3,-x4+1/3
20	-x1+x2+1/3,x2+2/3,x3+2/3,x4+5/6
21	x1-x2+1/3,x1+2/3,-x3+2/3,-x4+1/3
22	x2+1/3,x1+2/3,-x3+2/3,-x4+5/6
23	-x1+1/3,-x1+x2+2/3,-x3+2/3,-x4+5/6
24	x1-x2+1/3,-x2+2/3,-x3+2/3,-x4+5/6
25	x1+2/3,x2+1/3,x3+1/3,x4+2/3
26	-x2+2/3,x1-x2+1/3,x3+1/3,x4+2/3
27	-x2+2/3,-x1+1/3,x3+1/3,x4+1/6
28	-x1+2/3,-x2+1/3,-x3+1/3,-x4+2/3
29	-x1+x2+2/3,-x1+1/3,x3+1/3,x4+2/3
30	x1+2/3,x1-x2+1/3,x3+1/3,x4+1/6
31	x2+2/3,-x1+x2+1/3,-x3+1/3,-x4+2/3
32	-x1+x2+2/3,x2+1/3,x3+1/3,x4+1/6
33	x1-x2+2/3,x1+1/3,-x3+1/3,-x4+2/3
34	x2+2/3,x1+1/3,-x3+1/3,-x4+1/6
35	-x1+2/3,-x1+x2+1/3,-x3+1/3,-x4+1/6
36	x1-x2+2/3,-x2+1/3,-x3+1/3,-x4+1/6

a: 13.8611(13) Å [ Help ]

b: 13.8611(13) Å [ Help ]

c: 6.9924(10) Å [ Help ]

α: 90.0 ° [ Help ]

β: 90.0 ° [ Help ]

γ: 120.0 ° [ Help ]

Volume: 1163.4(2) Å³ [ Help ]

Modulation dimension: 1 [ Help ]

Measured independent wave vectors: (Show/hide table) [ Help ]

Wave vector id	q_x	q_y	q_z
1	0.000000	0.000000	0.141530

Z: 3 [ Help ]

Cell determination reflection Nb.: 7064 [ Help ]

θ(min) for cell determination: 3.3730 ° [ Help ]

θ(max) for cell determination: 28.4330 ° [ Help ]

Cell measurement temperature: 293 K [ Help ]

μ: 7.953 mm^-1 [ Help ]

Absorption correction type: analytical [ Help ]

Absorption correction remarks: CrysAlisPro, Agilent Technologies, Version 1.171.37.34 (release 22-05-2014 CrysAlis171 .NET) (compiled May 22 2014,16:03:01) 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: 0.558 [ Help ]

Maximum transmission factor: 0.733 [ Help ]

Refinement details

Total nb. of reflections: 2193 [ Help ]

Nb. of observed reflections: 1838 [ Help ]

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

Refinement based on: F [ Help ]

R(obs): 0.0200 [ Help ]

wR(obs): 0.0235 [ Help ]

R(all): 0.0289 [ Help ]

wR(all): 0.0259 [ Help ]

S(all): 1.16 [ Help ]

S(obs): 1.16 [ Help ]

Nb. of reflections: 2193 [ Help ]

Nb. of parameters: 130 [ Help ]

Weighting scheme: sigma [ Help ]

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

Δ/σ(max): 0.0421 [ Help ]

Δ/σ(mean): 0.0031 [ Help ]

Δρ(max): 0.38 e_Å^-3 [ Help ]

Δρ(min): -0.35 e_Å^-3 [ Help ]

Extinction method: none [ Help ]

Structural Information

Average Structure: (Show/hide table) [ 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
Cs1	Cs	0.5	0	0.5	Uani	0.02358(8)	9	1	d	?	?	?
Sc1	Sc	0	0	0	Uani	0.00520(19)	3	1	d	?	?	?
Si1	Si	0.102025(18)	0.20405(4)	0.36553(6)	Uani	0.00563(15)	18	1	d	?	?	?
O1	O	0.18212(8)	0.18212(8)	0.5	Uani	0.0129(4)	18	1	d	?	?	?
O2	O	0.166666	0.333333	0.333333	Uani	0.0133(7)	9	1	d	?	?	?
O3	O	0.07041(5)	0.14082(10)	0.17032(17)	Uani	0.0139(4)	18	1	d	?	?	?

ADP components: (Show/hide table) [ Help ]

Atom site label	Atom site symbol	U11	U22	U33	U12	U13	U23
Cs1	Cs	0.03067(13)	0.02203(11)	0.01517(11)	0.01102(5)	-0.00410(3)	-0.00820(7)
Sc1	Sc	0.0060(2)	0.0060(2)	0.0036(3)	0.00300(11)	0	0
Si1	Si	0.00639(16)	0.0050(2)	0.0050(2)	0.00252(11)	0.00015(8)	0.00030(17)
O1	O	0.0143(4)	0.0143(4)	0.0124(6)	0.0089(5)	-0.0021(2)	0.0021(2)
O2	O	0.0130(10)	0.0061(8)	0.0183(10)	0.0031(4)	0.0007(3)	0.0015(7)
O3	O	0.0172(5)	0.0127(6)	0.0101(6)	0.0064(3)	-0.0022(2)	-0.0043(5)

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

Wave vector code	q_1
1	1
2	2
3	3

Definition of the displacive (translational) Fourier series: (Show/hide table) [ Help ]

Modulation code	Atom site label	Displacement axis	Wave vector code
Cs1x1	Cs1	x	1
Cs1y1	Cs1	y	1
Cs1z1	Cs1	z	1
Cs1x2	Cs1	x	2
Cs1y2	Cs1	y	2
Cs1z2	Cs1	z	2
Cs1x3	Cs1	x	3
Cs1y3	Cs1	y	3
Cs1z3	Cs1	z	3
Sc1x1	Sc1	x	1
Sc1y1	Sc1	y	1
Sc1z1	Sc1	z	1
Sc1x2	Sc1	x	2
Sc1y2	Sc1	y	2
Sc1z2	Sc1	z	2
Sc1x3	Sc1	x	3
Sc1y3	Sc1	y	3
Sc1z3	Sc1	z	3
Si1x1	Si1	x	1
Si1y1	Si1	y	1
Si1z1	Si1	z	1
Si1x2	Si1	x	2
Si1y2	Si1	y	2
Si1z2	Si1	z	2
Si1x3	Si1	x	3
Si1y3	Si1	y	3
Si1z3	Si1	z	3
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
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
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

Displacive (translational) Fourier coefficients: (Show/hide table) [ Help ]

Modulation code	Cosine coefficient	Sine coefficient
Cs1x1	0	0.05370(2)
Cs1y1	0	0
Cs1z1	0	0
Cs1x2	0	0.000308(9)
Cs1y2	0	0.000617(19)
Cs1z2	0	-0.00535(3)
Cs1x3	0	0.00070(3)
Cs1y3	0	0
Cs1z3	0	0
Sc1x1	0	0
Sc1y1	0	0
Sc1z1	0	0
Sc1x2	0	0
Sc1y2	0	0
Sc1z2	0	-0.00319(13)
Sc1x3	0	0
Sc1y3	0	0
Sc1z3	0	0
Si1x1	0.03790(4)	0.00370(5)
Si1y1	0	0
Si1z1	0	0
Si1x2	0.00036(2)	-0.00073(2)
Si1y2	0.00071(5)	-0.00146(5)
Si1z2	-0.00021(9)	-0.00331(8)
Si1x3	-0.00022(6)	-0.00002(6)
Si1y3	0	0
Si1z3	0	0
O1x1	0.01905(7)	0.03177(12)
O1y1	-0.01905(7)	0.03177(12)
O1z1	0.0161(2)	0
O1x2	0.00394(12)	0.00180(7)
O1y2	0.00394(12)	-0.00180(7)
O1z2	0	-0.0031(2)
O1x3	-0.00027(8)	-0.00173(13)
O1y3	0.00027(8)	-0.00173(13)
O1z3	0.0015(3)	0
O2x1	0.06076(16)	-0.03508(9)
O2y1	0	0
O2z1	0	0
O2x2	0.00148(8)	0.00086(4)
O2y2	0.00297(15)	0.00171(9)
O2z2	-0.0076(3)	-0.00436(17)
O2x3	0	0.0031(3)
O2y3	0	0
O2z3	0	0
O3x1	0.04169(12)	0.01087(12)
O3y1	0	0
O3z1	0	0
O3x2	-0.00224(6)	-0.00043(6)
O3y2	-0.00448(12)	-0.00087(12)
O3z2	0.0020(2)	-0.0033(2)
O3x3	-0.00008(14)	-0.00055(15)
O3y3	0	0
O3z3	0	0

Definition of the ADP Fourier series: (Show/hide table) [ Help ]

Modulation code	Atom site label	Tensor element	Wave vector code
Cs1U111	Cs1	U11	1
Cs1U221	Cs1	U22	1
Cs1U331	Cs1	U33	1
Cs1U121	Cs1	U12	1
Cs1U131	Cs1	U13	1
Cs1U231	Cs1	U23	1
Cs1U112	Cs1	U11	2
Cs1U222	Cs1	U22	2
Cs1U332	Cs1	U33	2
Cs1U122	Cs1	U12	2
Cs1U132	Cs1	U13	2
Cs1U232	Cs1	U23	2
Cs1U113	Cs1	U11	3
Cs1U223	Cs1	U22	3
Cs1U333	Cs1	U33	3
Cs1U123	Cs1	U12	3
Cs1U133	Cs1	U13	3
Cs1U233	Cs1	U23	3
Sc1U111	Sc1	U11	1
Sc1U221	Sc1	U22	1
Sc1U331	Sc1	U33	1
Sc1U121	Sc1	U12	1
Sc1U131	Sc1	U13	1
Sc1U231	Sc1	U23	1
Sc1U112	Sc1	U11	2
Sc1U222	Sc1	U22	2
Sc1U332	Sc1	U33	2
Sc1U122	Sc1	U12	2
Sc1U132	Sc1	U13	2
Sc1U232	Sc1	U23	2
Sc1U113	Sc1	U11	3
Sc1U223	Sc1	U22	3
Sc1U333	Sc1	U33	3
Sc1U123	Sc1	U12	3
Sc1U133	Sc1	U13	3
Sc1U233	Sc1	U23	3
Si1U111	Si1	U11	1
Si1U221	Si1	U22	1
Si1U331	Si1	U33	1
Si1U121	Si1	U12	1
Si1U131	Si1	U13	1
Si1U231	Si1	U23	1
Si1U112	Si1	U11	2
Si1U222	Si1	U22	2
Si1U332	Si1	U33	2
Si1U122	Si1	U12	2
Si1U132	Si1	U13	2
Si1U232	Si1	U23	2
Si1U113	Si1	U11	3
Si1U223	Si1	U22	3
Si1U333	Si1	U33	3
Si1U123	Si1	U12	3
Si1U133	Si1	U13	3
Si1U233	Si1	U23	3
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
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
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

ADP Fourier coefficients: (Show/hide table) [ Help ]

Modulation code	Cosine coefficient	Sine coefficient
Cs1U111	0.01314(10)	0
Cs1U221	0	0
Cs1U331	0	0
Cs1U121	0.01314(10)	0
Cs1U131	-0.00413(10)	0
Cs1U231	0	0
Cs1U112	0.01145(15)	0
Cs1U222	0.00158(12)	0
Cs1U332	-0.00027(11)	0
Cs1U122	0.00079(6)	0
Cs1U132	-0.00019(5)	0
Cs1U232	-0.00038(9)	0
Cs1U113	0.00339(11)	0
Cs1U223	0	0
Cs1U333	0	0
Cs1U123	0.00339(11)	0
Cs1U133	0.00005(12)	0
Cs1U233	0	0
Sc1U111	0	0
Sc1U221	0	0
Sc1U331	0	0
Sc1U121	0	0
Sc1U131	0	0
Sc1U231	0	0
Sc1U112	-0.0010(3)	0
Sc1U222	-0.0010(3)	0
Sc1U332	0.0013(4)	0
Sc1U122	-0.00051(14)	0
Sc1U132	0	0
Sc1U232	0	0
Sc1U113	0	0
Sc1U223	0	0
Sc1U333	0	0
Sc1U123	0	0
Sc1U133	0	0
Sc1U233	0	0
Si1U111	0.0002(2)	-0.00012(19)
Si1U221	0	0
Si1U331	0	0
Si1U121	0.0002(2)	-0.00012(19)
Si1U131	0.0001(2)	-0.0004(2)
Si1U231	0	0
Si1U112	-0.0006(3)	-0.0006(2)
Si1U222	0.0002(3)	0.0001(3)
Si1U332	0.0003(3)	0.0003(3)
Si1U122	0.00010(14)	0.00004(14)
Si1U132	-0.00006(11)	-0.00012(11)
Si1U232	-0.0001(2)	-0.0002(2)
Si1U113	-0.0006(2)	0.0006(2)
Si1U223	0	0
Si1U333	0	0
Si1U123	-0.0006(2)	0.0006(2)
Si1U133	0.0000(3)	-0.0005(3)
Si1U233	0	0
O1U111	0.0020(6)	-0.0059(7)
O1U221	-0.0020(6)	-0.0059(6)
O1U331	0	0.0004(9)
O1U121	0	-0.0052(7)
O1U131	0.0010(6)	-0.0003(3)
O1U231	0.0010(6)	0.0003(3)
O1U112	0.0002(7)	-0.0022(6)
O1U222	0.0002(7)	0.0022(6)
O1U332	0.0011(8)	0
O1U122	-0.0001(8)	0
O1U132	0.0000(4)	-0.0023(6)
O1U232	0.0000(4)	-0.0023(6)
O1U113	-0.0020(8)	0.0002(8)
O1U223	0.0020(8)	0.0002(8)
O1U333	0	-0.0011(11)
O1U123	0	0.0012(9)
O1U133	-0.0014(7)	-0.0005(4)
O1U233	-0.0014(7)	0.0005(4)
O2U111	0.0016(5)	0.0028(9)
O2U221	0	0
O2U331	0	0
O2U121	0.0016(5)	0.0028(9)
O2U131	-0.0027(6)	-0.0046(10)
O2U231	0	0
O2U112	-0.0018(8)	0.0030(14)
O2U222	-0.0008(6)	0.0013(10)
O2U332	0.0000(7)	-0.0001(12)
O2U122	-0.0004(3)	0.0007(5)
O2U132	0.0006(2)	-0.0011(4)
O2U232	0.0013(5)	-0.0022(8)
O2U113	-0.0033(11)	0
O2U223	0	0
O2U333	0	0
O2U123	-0.0033(11)	0
O2U133	0.0032(13)	0
O2U233	0	0
O3U111	-0.0035(6)	0.0005(6)
O3U221	0	0
O3U331	0	0
O3U121	-0.0035(6)	0.0005(6)
O3U131	0.0013(6)	0.0009(6)
O3U231	0	0
O3U112	-0.0009(8)	-0.0033(7)
O3U222	0.0004(8)	-0.0011(8)
O3U332	0.0002(8)	-0.0017(8)
O3U122	0.0002(4)	-0.0005(4)
O3U132	-0.0002(3)	0.0008(3)
O3U232	-0.0004(7)	0.0015(7)
O3U113	0.0012(7)	0.0006(7)
O3U223	0	0
O3U333	0	0
O3U123	0.0012(7)	0.0006(7)
O3U133	0.0000(8)	-0.0008(8)
O3U233	0	0

(3+1)-incommensurately modulated crystal structure of Cs₃ScSi₆O₁₅

Hejny, Clivia; Kahlenberg, Volker; Schmidmair, Daniela; Dabic, Predrag

Acta Crystallographica, Section B 72 109-116 (2016)

https://doi.org/10.1107/S2052520615022076

Download CIF

Open in JSmol

I

Chemical data

Crystallographic data and experimental details

Refinement details

Structural Information

(3+1)-incommensurately modulated crystal structure of Cs3ScSi6O15

Hejny, Clivia; Kahlenberg, Volker; Schmidmair, Daniela; Dabic, Predrag

Acta Crystallographica, Section B 72 109-116 (2016)

https://doi.org/10.1107/S2052520615022076

Download CIF

Open in JSmol

I

Chemical data

Crystallographic data and experimental details

Refinement details

Structural Information

(3+1)-incommensurately modulated crystal structure of Cs₃ScSi₆O₁₅