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: 8292Ebau5x Entry date: 2021-10-26 Last revision: 2022-02-12

40K

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: 435.6 Da [ Help ]

Crystallographic data and experimental details


Crystal system: orthorhombic [ Help ]

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

Symmetry operations of the superspace group: [ 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: 13.579 Å [ Help ]

b: 3.9818 Å [ Help ]

c: 4.0041 Å [ Help ]

α: 90 ° [ Help ]

β: 90 ° [ Help ]

γ: 90 ° [ Help ]

Volume: 216.4971 Å3 [ Help ]

Modulation dimension: 1 [ Help ]

Measured independent wave vectors: [ Help ]

Wave vector id q_x q_y q_z
1 0.000000 0.750000 0.000000

Z: 2 [ Help ]

Cell measurement temperature: 40.0(2) K [ Help ]

μ: 28.16 mm-1 [ Help ]

Refinement details


Total nb. of reflections: 2999 [ Help ]

Nb. of observed reflections: 2561 [ Help ]

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

Refinement based on: F [ Help ]

R(obs): 0.0598 [ Help ]

wR(obs): 0.1174 [ Help ]

R(all): 0.0720 [ Help ]

wR(all): 0.1290 [ Help ]

S(all): 2.31 [ Help ]

S(obs): 2.27 [ Help ]

Nb. of reflections: 2999 [ 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): 0.0015 [ Help ]

Δ/σ(mean): 0.0000 [ 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
Pr1 Pr 0.16224(5) 0.5 0 Uani 0.00470(16) 4 1 d . . .
Sb1 Sb 0.5 0.5 0.0326(13) Uani 0.0532(12) 4 0.5 d . . .
O1 O 0.2510(3) 0 0 Uani 0.0066(10) 4 1 d . . .

ADP components: [ Help ]

Atom site label Atom site symbol U11 U22 U33 U12 U13 U23
Pr1 Pr 0.00645(16) 0.0040(3) 0.0037(3) 0 0 0
Sb1 Sb 0.0098(10) 0.0701(14) 0.080(3) 0 0 0
O1 O 0.0114(14) 0.007(2) 0.0019(19) 0 0 0

Anharmonic ADPs (C coefficients): [ Help ]

Atom site label Atom symbol C111 C112 C113 C122 C123 C133 C222 C223 C233 C333
Pr1 Pr 0.000021(16) 0 0 -0.00002(14) 0 -0.00012(10) 0 0 0 0
Sb1 Sb 0 0 -0.0001(4) 0 0 0 0 -0.218(18) 0 -0.13(4)

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
Sb1 Sb 0.00019(4) 0 0 0.0051(6) 0 0.0040(7) 0 0 0 0 0.85(5) 0 0.75(4) 0 1.13(12)

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

Wave vector code q_1
1 1
2 2

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

Modulation code Cosine coefficient Sine coefficient
Pr1x1 -0.00946(7) 0
Pr1y1 0 -0.00882(16)
Pr1z1 0 0
Pr1x2 0.00079(5) 0
Pr1y2 0 -0.0017(3)
Pr1z2 0 0
Sb1x1 0 0
Sb1y1 0 0.0261
Sb1z1 -0.0327 0
O1x1 0.0096(3) 0
O1y1 0 -0.0051(10)
O1z1 0 0

Displacive sawtooth coefficients: [ Help ]

Atom site label Ax Ay Az Center (x0) Width
Sb1 0.0002 -0.158 0.0028 0.5 0.9999

Definition of the ADP Fourier series: [ 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: [ Help ]

Modulation code Cosine coefficient Sine coefficient
Pr1U111 -0.00134(12) 0
Pr1U221 0.00056(13) 0
Pr1U331 0.00029(9) 0
Pr1U121 0 0.00077(18)
Pr1U131 0 0
Pr1U231 0 0
Pr1U112 -0.00242(16) 0
Pr1U222 -0.0010(6) 0
Pr1U332 -0.00028(18) 0
Pr1U122 0 -0.0008(2)
Pr1U132 0 0
Pr1U232 0 0
Sb1U111 -0.0017(7) 0
Sb1U221 0.0159(9) 0
Sb1U331 -0.007(2) 0
Sb1U121 0 0
Sb1U131 0 0
Sb1U231 0 -0.078(2)
Sb1U112 -0.0050(9) 0
Sb1U222 -0.0475(15) 0
Sb1U332 -0.039(2) 0
Sb1U122 0 0
Sb1U132 0 0
Sb1U232 0 -0.0018(17)
O1U111 -0.0052(17) 0
O1U221 0.0012(11) 0
O1U331 0.0004(12) 0
O1U121 0 -0.0024(12)
O1U131 0 0
O1U231 0 0
O1U112 -0.0031(17) 0
O1U222 -0.0030(14) 0
O1U332 0.0010(15) 0
O1U122 0 0.0051(12)
O1U132 0 0
O1U232 0 0

Modulated anharmonic ADPs (C coefficients): [ Help ]

Atom site label Tensor element Wave vector code Cos coeff. Sin coeff.
Pr1 C111 1 -0.00011(2) 0
Pr1 C112 1 0 0.00001(6)
Pr1 C113 1 0 0
Pr1 C122 1 0.0002(3) 0
Pr1 C123 1 0 0
Pr1 C133 1 0.0006(2) 0
Pr1 C222 1 0 0.0057(13)
Pr1 C223 1 0 0
Pr1 C233 1 0 0.0009(4)
Pr1 C333 1 0 0
Pr1 C111 2 -0.00008(2) 0
Pr1 C112 2 0 0.00005(6)
Pr1 C113 2 0 0
Pr1 C122 2 -0.0005(3) 0
Pr1 C123 2 0 0
Pr1 C133 2 -0.00001(14) 0
Pr1 C222 2 0 -0.002(2)
Pr1 C223 2 0 0
Pr1 C233 2 0 0.0000(7)
Pr1 C333 2 0 0
Sb1 C111 1 0 0
Sb1 C112 1 0 0.0011(4)
Sb1 C113 1 -0.0014(4) 0
Sb1 C122 1 0 0
Sb1 C123 1 0 0
Sb1 C133 1 0 0
Sb1 C222 1 0 0.69(3)
Sb1 C223 1 -0.164(16) 0
Sb1 C233 1 0 0.27(3)
Sb1 C333 1 0.02(2) 0
Sb1 C111 2 0 0
Sb1 C112 2 0 0.0014(3)
Sb1 C113 2 -0.0014(6) 0
Sb1 C122 2 0 0
Sb1 C123 2 0 0
Sb1 C133 2 0 0
Sb1 C222 2 0 0.630(19)
Sb1 C223 2 0.22(2) 0
Sb1 C233 2 0 0.089(17)
Sb1 C333 2 0.16(4) 0

Modulated anharmonic ADPs (D coefficients): [ Help ]

Atom site label Tensor element Wave vector code Cos coeff. Sin coeff.
Sb1 D1111 1 -0.00006(3) 0
Sb1 D1112 1 0 0
Sb1 D1113 1 0 0
Sb1 D1122 1 0.0006(3) 0
Sb1 D1123 1 0 -0.0066(8)
Sb1 D1133 1 -0.0005(5) 0
Sb1 D1222 1 0 0
Sb1 D1223 1 0 0
Sb1 D1233 1 0 0
Sb1 D1333 1 0 0
Sb1 D2222 1 0.105(19) 0
Sb1 D2223 1 0 -1.02(6)
Sb1 D2233 1 0.18(3) 0
Sb1 D2333 1 0 -1.22(9)
Sb1 D3333 1 0.03(7) 0
Sb1 D1111 2 -0.00020(5) 0
Sb1 D1112 2 0 0
Sb1 D1113 2 0 0
Sb1 D1122 2 -0.0043(7) 0
Sb1 D1123 2 0 -0.0003(5)
Sb1 D1133 2 -0.0037(6) 0
Sb1 D1222 2 0 0
Sb1 D1223 2 0 0
Sb1 D1233 2 0 0
Sb1 D1333 2 0 0
Sb1 D2222 2 -0.75(7) 0
Sb1 D2223 2 0 -0.23(3)
Sb1 D2233 2 -0.43(3) 0
Sb1 D2333 2 0 -0.12(5)
Sb1 D3333 2 -0.93(9) 0

Pr2SbO2_40K_supercell

Chemical data


Full Name: Pr2 Sb1 O2 [ Help ]

Common Name: 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 ]

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

Space group name (Hall): -P 2c 2a [ Help ]

Space group nb.: 59 [ Help ]

Symmetry operations of the space group: [ Help ]

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

a: 13.5790(15) Å [ Help ]

b: 15.9272(18) Å [ Help ]

c: 4.0041(18) Å [ Help ]

α: 90.00 ° [ Help ]

β: 90.00 ° [ Help ]

γ: 90.00 ° [ Help ]

Volume: 866.0(4) Å3 [ Help ]

Z: 8 [ Help ]

Cell measurement temperature: 40.0(2) K [ Help ]

μ: 28.16 mm-1 [ Help ]

Absorption correction type: multi-scan [ Help ]

Minimum transmission factor: 0.201 [ Help ]

Maximum transmission factor: 0.430 [ Help ]

Absorption correction remarks: semi empirical absorption correction with SADABS, G.M. Sheldrick, SADABS, Version 2008/1, University of G\öttingen. Germany. [ Help ]

Refinement details


Total nb. of reflections: 6179 [ Help ]

Nb. of observed reflections: 3766 [ Help ]

Intense reflections threshold: >2sigma(I) [ Help ]

Refinement remarks: Refinement of F2 against ALL reflections. The weighted R-factor wR and goodness of fit S are based on F2, conventional R-factors R are based on F, with F set to zero for negative F2. The threshold expression of F2 > 2sigma(F2) is used only for calculating R-factors(gt) etc. and is not relevant to the choice of reflections for refinement. R-factors based on F2 are statistically about twice as large as those based on F, and R- factors based on ALL data will be even larger. [ Help ]

Refinement based on: Fsqd [ Help ]

Matrix type used for the least-squares: full [ Help ]

Weighting scheme: calc [ Help ]

Weighting scheme remarks: calc w=1/[σ2(Fo2)+(0.1684P)2+3.5110P] where P=(Fo2+2Fc2)/3 [ Help ]

Extinction method: SHELXL [ Help ]

Extinction coefficient: 0.0016(3) [ Help ]

Extinction expression: Fc*=kFc[1+0.001xFc2λ3/sin(2θ)]-1/4 [ Help ]

Nb. of reflections: 5994 [ Help ]

Nb. of parameters: 76 [ Help ]

Number of restraints: 0 [ Help ]

R(all): 0.1008 [ Help ]

R(obs): 0.0644 [ Help ]

wR(all): 0.3022 [ Help ]

wR(obs): 0.2628 [ Help ]

S(all): 1.132 [ Help ]

Restrained S(all): 1.132 [ Help ]

Δ/σ(max): 0.0090 [ Help ]

Δ/σ(mean): 0.0015 [ Help ]

Structural Information


Average Structure: [ Help ]

Atom site label Atom symbol x y z Uiso/equiv ADP type Occupancy Symmetry multiplicity Coords from (d)iffraction or (c)alculated Coords restraints or constraints Occ constraints or restraints Disordered cluster Disordered group
Pr1 Pr 0.57908(3) 0.31215(2) 0.7500 0.00758(9) Uani 1 2 d S . . .
Pr2 Pr 0.58454(2) 0.06427(2) 0.7500 0.00928(9) Uani 1 2 d S . . .
Pr3 Pr 0.40472(3) 0.18642(2) 0.2500 0.00760(9) Uani 1 2 d S . . .
Pr4 Pr 0.40824(2) 0.43980(2) 0.2500 0.00752(9) Uani 1 2 d S . . .
Sb1A Sb 0.7500 0.21779(5) 0.2500 0.0116(2) Uani 0.716(2) 4 d S P . .
Sb1B Sb 0.7500 0.1552(2) 0.2500 0.0116(2) Uani 0.285(2) 4 d S P . .
Sb2A Sb 0.7500 0.40685(7) 0.2500 0.0099(2) Uani 0.700(4) 4 d S P . .
Sb2B Sb 0.7500 0.4239(2) 0.329(1) 0.0099(2) Uani 0.150(2) 2 d S P . .
Sb3A Sb 0.7500 0.9684(2) 0.2500 0.0127(2) Uani 0.263(4) 4 d S P . .
Sb3B Sb 0.7500 0.94904(8) 0.3112(3) 0.0127(2) Uani 0.369(2) 2 d S P . .
Sb4 Sb 0.2500 0.31981(6) 0.6850(3) 0.0219(2) Uani 0.50 2 d S P . .
O1 O 0.4923(4) 0.3124(2) 0.2500 0.0108(7) Uani 1 2 d S . . .
O2 O 0.4920(4) 0.1868(2) 0.7500 0.0094(6) Uani 1 2 d S . . .
O3 O 0.4950(3) 0.4389(2) 0.7500 0.0088(6) Uani 1 2 d S . . .
O4 O 0.4982(4) 0.0636(2) 0.2500 0.0124(7) Uani 1 2 d S . . .

ADP components: [ Help ]

Atom site label U11 U22 U33 U23 U13 U12
Pr1 0.00962(13) 0.00646(14) 0.00666(14) 0.000 0.000 -0.00026(5)
Pr2 0.01268(13) 0.00803(14) 0.00714(15) 0.000 0.000 0.00187(7)
Pr3 0.00781(12) 0.00782(14) 0.00717(14) 0.000 0.000 -0.00039(5)
Pr4 0.00960(12) 0.00601(13) 0.00696(14) 0.000 0.000 -0.00069(6)
Sb1A 0.0060(2) 0.0100(2) 0.0188(3) 0.000 0.000 0.000
Sb1B 0.0060(2) 0.0100(2) 0.0188(3) 0.000 0.000 0.000
Sb2A 0.00524(18) 0.0096(3) 0.0150(4) 0.000 0.000 0.000
Sb2B 0.00524(18) 0.0096(3) 0.0150(4) 0.000 0.000 0.000
Sb3A 0.0054(2) 0.0039(3) 0.0289(7) 0.000 0.000 0.000
Sb3B 0.0054(2) 0.0039(3) 0.0289(7) 0.000 0.000 0.000
Sb4 0.0069(3) 0.0291(4) 0.0296(6) -0.0010(3) 0.000 0.000
O1 0.0163(18) 0.0103(17) 0.0060(15) 0.000 0.000 0.0006(9)
O2 0.0102(14) 0.0097(16) 0.0081(15) 0.000 0.000 -0.0007(8)
O3 0.0117(13) 0.0100(15) 0.0046(14) 0.000 0.000 0.0001(9)
O4 0.0176(17) 0.0115(17) 0.0082(17) 0.000 0.000 0.0010(12)