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: 8332EyvURZ Entry date: 2021-10-26 Last revision: 2021-12-12

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Chemical data

Full Name: ? [ Help ]

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: 13.5858(5) Å [ Help ]

b: 3.9882(6) Å [ Help ]

c: 4.0097(6) Å [ Help ]

α: 90 ° [ Help ]

β: 90 ° [ Help ]

γ: 90 ° [ Help ]

Volume: 217.26(5) 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: 250.0(2) K [ Help ]

Cell remarks: ? [ Help ]

μ: 28.06 mm^-1 [ Help ]

Refinement details

Refinement remarks: ? [ Help ]

Total nb. of reflections: 3051 [ Help ]

Nb. of observed reflections: 2531 [ Help ]

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

Refinement based on: F [ Help ]

R(obs): 0.0468 [ Help ]

wR(obs): 0.1051 [ Help ]

R(all): 0.0547 [ Help ]

wR(all): 0.1082 [ Help ]

S(all): 2.29 [ Help ]

S(obs): 2.45 [ Help ]

Nb. of reflections: 3051 [ 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): 0.0003 [ 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	0.16224(4)	0.5	0	Uani	0.00926(12)	4	1	d	.	.	.
Sb1	Sb	0.5	0.5	0.0234(5)	Uani	0.0511(8)	4	0.5	d	.	.	.
O1	O	0.2504(3)	0	0	Uani	0.0112(9)	4	1	d	.	.	.

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

Atom site label	Atom site symbol	U11	U22	U33
Pr1	Pr	0.01265(15)	0.0086(2)	0.0065(2)
Sb1	Sb	0.0223(9)	0.0752(12)	0.0560(18)
O1	O	0.0169(13)	0.0105(17)	0.0062(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	0.000016(16)	0	0	-0.00034(14)	0	-0.00041(9)	0	0	0	0
Sb1	Sb	0	0	-0.016(10)	0	0	0	0	4.8(4)	0	1.2(3)

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	0.00057(8)	0	0	0.0072(7)	0	0.008(2)	0	0	0	0	0.98(6)	0	-0.82(9)	0	0.24(12)

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	-0.00865(14)
Pr1z1	0	0
Pr1x2	0.00067(5)	0
Pr1y2	0	-0.0018(3)
Pr1z2	0	0
Sb1x1	0	0
Sb1y1	0	0.0231
Sb1z1	-0.0258	0
O1x1	0.0092(3)	0
O1y1	0	-0.0025(9)
O1z1	0	0

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

Atom site label	Ax	Ay	Az	Center (x0)	Width
Sb1	0.0004	-0.158	0.0007	0.5	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	-0.00196(12)	0
Pr1U221	0.00042(12)	0
Pr1U331	0.00043(7)	0
Pr1U121	0	0.00112(17)
Pr1U131	0	0
Pr1U231	0	0
Pr1U112	-0.00238(15)	0
Pr1U222	-0.0004(6)	0
Pr1U332	0.00005(18)	0
Pr1U122	0	-0.0013(2)
Pr1U132	0	0
Pr1U232	0	0
Sb1U111	-0.0008(8)	0
Sb1U221	0.0236(8)	0
Sb1U331	-0.0095(18)	0
Sb1U121	0	0
Sb1U131	0	0
Sb1U231	0	0
Sb1U112	-0.0092(10)	0
Sb1U222	-0.0537(13)	0
Sb1U332	-0.0078(16)	0
Sb1U122	0	0
Sb1U132	0	0
Sb1U232	0	0
O1U111	-0.0066(17)	0
O1U221	0.0014(9)	0
O1U331	0.0009(9)	0
O1U121	0	-0.0022(11)
O1U131	0	0
O1U231	0	0
O1U112	-0.0013(17)	0
O1U222	-0.0044(14)	0
O1U332	0.0003(14)	0
O1U122	0	0.0046(12)
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	-0.00004(6)
Pr1	C113	1	0	0
Pr1	C122	1	0.0004(2)	0
Pr1	C123	1	0	0
Pr1	C133	1	0.00002(16)	0
Pr1	C222	1	0	0.0035(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	0.00009(5)
Pr1	C113	2	0	0
Pr1	C122	2	0.0000(2)	0
Pr1	C123	2	0	0
Pr1	C133	2	0.00020(15)	0
Pr1	C222	2	0	0.0011(19)
Pr1	C223	2	0	0
Pr1	C233	2	0	0.0017(6)
Pr1	C333	2	0	0
Sb1	C111	1	0	0
Sb1	C112	1	0	0.0020(6)
Sb1	C113	1	-0.011(11)	0
Sb1	C122	1	0	0
Sb1	C123	1	0	0
Sb1	C133	1	0	0
Sb1	C222	1	0	0.80(3)
Sb1	C223	1	5.2(4)	0
Sb1	C233	1	0	0.123(19)
Sb1	C333	1	2.7(4)	0
Sb1	C111	2	0	0
Sb1	C112	2	0	0.0023(3)
Sb1	C113	2	0.008(7)	0
Sb1	C122	2	0	0
Sb1	C123	2	0	0
Sb1	C133	2	0	0
Sb1	C222	2	0	0.549(14)
Sb1	C223	2	-0.32(16)	0
Sb1	C233	2	0	0.134(12)
Sb1	C333	2	2.0(2)	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	-0.00004(4)	0
Sb1	D1112	1	0	0
Sb1	D1113	1	0	0
Sb1	D1122	1	0.0015(3)	0
Sb1	D1123	1	0	0.0052(19)
Sb1	D1133	1	-0.0011(7)	0
Sb1	D1222	1	0	0
Sb1	D1223	1	0	0
Sb1	D1233	1	0	0
Sb1	D1333	1	0	0
Sb1	D2222	1	0.146(14)	0
Sb1	D2223	1	0	1.88(12)
Sb1	D2233	1	0.03(6)	0
Sb1	D2333	1	0	0.59(7)
Sb1	D3333	1	0.03(8)	0
Sb1	D1111	2	-0.00059(10)	0
Sb1	D1112	2	0	0
Sb1	D1113	2	0	0
Sb1	D1122	2	-0.0073(10)	0
Sb1	D1123	2	0	0.0029(13)
Sb1	D1133	2	-0.009(4)	0
Sb1	D1222	2	0	0
Sb1	D1223	2	0	0
Sb1	D1233	2	0	0
Sb1	D1333	2	0	0
Sb1	D2222	2	-1.16(8)	0
Sb1	D2223	2	0	1.04(6)
Sb1	D2233	2	1.54(12)	0
Sb1	D2333	2	0	0.46(6)
Sb1	D3333	2	-0.2(2)	0

Modulated crystal structure of Pr2SbO2