B-IncStrDB

Modulated crystal structure of Pr₂SbO₂

Authors:

Magdysyuk, Oxana V.; Nuss, Jurgen; Jansen, Martin

Journal:

Acta Crystallographica, Section B 69 547-555 (2013)

DOI:

https://doi.org/10.1107/S2052519213029436

B-IncStrDB ID: 8312EnSPI5 Entry date: 2021-10-26 Last revision: 2022-02-12

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Chemical data

Formula moiety: Pr2 Sb1 O2 [ Help ]

Structural Formula: Pr2 Sb1 O2 [ Help ]

Formula (IUPAC): Pr2 Sb1 O2 [ Help ]

Structural Formula Sum: O2 Pr2 Sb1 [ Help ]

Formula weight: 435.55 Da [ Help ]

Crystallographic data and experimental details

Crystal system: orthorhombic [ Help ]

Superspace group name: Immm(0β0)000 [ Help ]

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

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

a: 13.5724(10) Å [ Help ]

b: 3.9833(13) Å [ Help ]

c: 4.0066(12) Å [ Help ]

α: 90 ° [ Help ]

β: 90 ° [ Help ]

γ: 90 ° [ Help ]

Volume: 216.609(10) 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	0.750000	0.000000

Z: 2 [ Help ]

Cell measurement temperature: 100.0(2) K [ Help ]

μ: 28.15 mm^-1 [ Help ]

Refinement details

Total nb. of reflections: 3030 [ Help ]

Nb. of observed reflections: 2642 [ Help ]

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

Refinement based on: F [ Help ]

R(obs): 0.0526 [ Help ]

wR(obs): 0.1116 [ Help ]

R(all): 0.0578 [ Help ]

wR(all): 0.1136 [ Help ]

S(all): 2.41 [ Help ]

S(obs): 2.54 [ Help ]

Nb. of reflections: 3030 [ Help ]

Nb. of parameters: 96 [ 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): 0.0008 [ Help ]

Δ/σ(mean): 0.0001 [ 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
Pr1	Pr	0.16220(4)	0.5	0	Uani	0.00487(12)	4	1	d	.	.	.
Sb1	Sb	0.5	0.5	0.0303	Uani	0.0484(7)	4	0.5	d	.	.	.
O1	O	0.2512(3)	0	0	Uani	0.0070(9)	4	1	d	.	.	.

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

Atom site label	Atom site symbol	U11	U22	U33
Pr1	Pr	0.00779(15)	0.0045(3)	0.0024(2)
Sb1	Sb	0.0173(10)	0.0641(12)	0.0638(15)
O1	O	0.0118(13)	0.0060(17)	0.0033(15)

Anharmonic ADPs (C coefficients): (Show/hide table) [ Help ]

Atom site label	Atom symbol	C111	C112	C113	C122	C123	C133	C222	C223	C233	C333
Pr1	Pr	0.000009(16)	0	0	-0.00033(13)	0	-0.00021(8)	0	0	0	0
Sb1	Sb	0	0	-0.015(6)	0	0	0	0	-1.33(15)	0	-1.30(17)

Anharmonic ADPs (D coefficients): (Show/hide table) [ Help ]

Atom site label	Atom symbol	D1111	D1112	D1113	D1122	D1123	D1133	D1222	D1223	D1233	D1333	D2222	D2223	D2233	D2333	D3333
Sb1	Sb	0.00055(7)	0	0	0.0062(6)	0	0.0057(10)	0	0	0	0	0.71(5)	0	0.48(3)	0	0.77(7)

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

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

Modulation code	Atom site label	Displacement axis	Wave vector code
Pr1x1	Pr1	x	1
Pr1y1	Pr1	y	1
Pr1z1	Pr1	z	1
Pr1x2	Pr1	x	2
Pr1y2	Pr1	y	2
Pr1z2	Pr1	z	2
Sb1x1	Sb1	x	1
Sb1y1	Sb1	y	1
Sb1z1	Sb1	z	1
O1x1	O1	x	1
O1y1	O1	y	1
O1z1	O1	z	1

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

Modulation code	Cosine coefficient	Sine coefficient
Pr1x1	0.00912(7)	0
Pr1y1	0	0.00888(14)
Pr1z1	0	0
Pr1x2	0.00069(5)	0
Pr1y2	0	-0.0018(3)
Pr1z2	0	0
Sb1x1	0	0
Sb1y1	0	-0.0261
Sb1z1	0.0282	0
O1x1	-0.0091(3)	0
O1y1	0	0.0037(8)
O1z1	0	0

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

Atom site label	Ax	Ay	Az	Center (x0)	Width
Sb1	0.0004	-0.158	0.0023	0	1

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

Modulation code	Atom site label	Tensor element	Wave vector code
Pr1U111	Pr1	U11	1
Pr1U221	Pr1	U22	1
Pr1U331	Pr1	U33	1
Pr1U121	Pr1	U12	1
Pr1U131	Pr1	U13	1
Pr1U231	Pr1	U23	1
Pr1U112	Pr1	U11	2
Pr1U222	Pr1	U22	2
Pr1U332	Pr1	U33	2
Pr1U122	Pr1	U12	2
Pr1U132	Pr1	U13	2
Pr1U232	Pr1	U23	2
Sb1U111	Sb1	U11	1
Sb1U221	Sb1	U22	1
Sb1U331	Sb1	U33	1
Sb1U121	Sb1	U12	1
Sb1U131	Sb1	U13	1
Sb1U231	Sb1	U23	1
Sb1U112	Sb1	U11	2
Sb1U222	Sb1	U22	2
Sb1U332	Sb1	U33	2
Sb1U122	Sb1	U12	2
Sb1U132	Sb1	U13	2
Sb1U232	Sb1	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

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

Modulation code	Cosine coefficient	Sine coefficient
Pr1U111	0.00183(12)	0
Pr1U221	-0.00035(12)	0
Pr1U331	-0.00025(6)	0
Pr1U121	0	-0.00103(17)
Pr1U131	0	0
Pr1U231	0	0
Pr1U112	-0.00217(15)	0
Pr1U222	-0.0006(6)	0
Pr1U332	-0.00020(15)	0
Pr1U122	0	-0.0013(2)
Pr1U132	0	0
Pr1U232	0	0
Sb1U111	-0.0010(8)	0
Sb1U221	-0.0150(8)	0
Sb1U331	0.0139(16)	0
Sb1U121	0	0
Sb1U131	0	0
Sb1U231	0	0.0371(17)
Sb1U112	-0.0060(9)	0
Sb1U222	-0.0432(14)	0
Sb1U332	-0.0131(12)	0
Sb1U122	0	0
Sb1U132	0	0
Sb1U232	0	0.0212(9)
O1U111	0.0074(18)	0
O1U221	-0.0011(9)	0
O1U331	-0.0022(9)	0
O1U121	0	0.0024(10)
O1U131	0	0
O1U231	0	0
O1U112	0.0003(16)	0
O1U222	-0.0029(13)	0
O1U332	-0.0001(12)	0
O1U122	0	0.0056(11)
O1U132	0	0
O1U232	0	0

Modulated anharmonic ADPs (C coefficients): (Show/hide table) [ Help ]

Atom site label	Tensor element	Wave vector code	Cos coeff.	Sin coeff.
Pr1	C111	1	0.00004(2)	0
Pr1	C112	1	0	0.00014(5)
Pr1	C113	1	0	0
Pr1	C122	1	-0.0005(2)	0
Pr1	C123	1	0	0
Pr1	C133	1	-0.00003(15)	0
Pr1	C222	1	0	-0.0038(10)
Pr1	C223	1	0	0
Pr1	C233	1	0	0.0001(3)
Pr1	C333	1	0	0
Pr1	C111	2	-0.00009(2)	0
Pr1	C112	2	0	0.00007(5)
Pr1	C113	2	0	0
Pr1	C122	2	0.0001(2)	0
Pr1	C123	2	0	0
Pr1	C133	2	0.00023(12)	0
Pr1	C222	2	0	0.0003(18)
Pr1	C223	2	0	0
Pr1	C233	2	0	-0.0005(6)
Pr1	C333	2	0	0
Sb1	C111	1	0	0
Sb1	C112	1	0	-0.0030(5)
Sb1	C113	1	0.027(10)	0
Sb1	C122	1	0	0
Sb1	C123	1	0	0
Sb1	C133	1	0	0
Sb1	C222	1	0	-0.65(2)
Sb1	C223	1	2.0(3)	0
Sb1	C233	1	0	-0.257(17)
Sb1	C333	1	1.9(3)	0
Sb1	C111	2	0	0
Sb1	C112	2	0	0.0024(4)
Sb1	C113	2	-0.013(5)	0
Sb1	C122	2	0	0
Sb1	C123	2	0	0
Sb1	C133	2	0	0
Sb1	C222	2	0	0.541(14)
Sb1	C223	2	-0.68(13)	0
Sb1	C233	2	0	0.087(16)
Sb1	C333	2	-1.15(19)	0

Modulated anharmonic ADPs (D coefficients): (Show/hide table) [ Help ]

Atom site label	Tensor element	Wave vector code	Cos coeff.	Sin coeff.
Sb1	D1111	1	-0.00003(4)	0
Sb1	D1112	1	0	0
Sb1	D1113	1	0	0
Sb1	D1122	1	-0.0017(3)	0
Sb1	D1123	1	0	0.0022(19)
Sb1	D1133	1	-0.0031(12)	0
Sb1	D1222	1	0	0
Sb1	D1223	1	0	0
Sb1	D1233	1	0	0
Sb1	D1333	1	0	0
Sb1	D2222	1	-0.055(13)	0
Sb1	D2223	1	0	0.52(10)
Sb1	D2233	1	-0.18(4)	0
Sb1	D2333	1	0	0.02(9)
Sb1	D3333	1	-0.18(9)	0
Sb1	D1111	2	-0.00039(8)	0
Sb1	D1112	2	0	0
Sb1	D1113	2	0	0
Sb1	D1122	2	-0.0046(7)	0
Sb1	D1123	2	0	0.0036(16)
Sb1	D1133	2	-0.0024(11)	0
Sb1	D1222	2	0	0
Sb1	D1223	2	0	0
Sb1	D1233	2	0	0
Sb1	D1333	2	0	0
Sb1	D2222	2	-0.74(6)	0
Sb1	D2223	2	0	-0.05(6)
Sb1	D2233	2	-0.15(3)	0
Sb1	D2333	2	0	0.58(8)
Sb1	D3333	2	0.17(7)	0

Modulated crystal structure of Pr2SbO2