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Structural changes of relaxor ferroelectric Sr0.52Ba0.48Nb2O6 (SBN52) on quenching and reheating

Authors:

Graetsch, Heribert A.

Journal:

Acta Crystallographica Section B 73 820-826 (2017)

DOI:

https://doi.org/10.1107/S2052520617007880

B-IncStrDB ID: o3blFyoCoHA Entry date: 2022-01-18 Last revision: 2022-01-18

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sbn52untreated-tet

Chemical data

Formula (IUPAC): barium strontium niobium oxide [ Help ]

Structural Formula Sum: Ba0.476 Nb2 O6 Sr0.524 [ Help ]

Formula weight: 393.1 Da [ Help ]

Crystallographic data and experimental details

Crystal system: tetragonal [ Help ]

Space group name (H-M): X4bm [ Help ]

Superspace group name: P4bm(αα1/2)000(-αα1/2)000 [ Help ]

Symmetry operations of the superspace group: [ Help ]

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

a: 12.4693(3) Å [ Help ]

b: 12.4693(3) Å [ Help ]

c: 7.9006(3) Å [ Help ]

α: 90 ° [ Help ]

β: 90 ° [ Help ]

γ: 90 ° [ Help ]

Volume: 1228.41(6) Å3 [ Help ]

Modulation dimension: 2 [ Help ]

Measured independent wave vectors: [ Help ]

Wave vector id q_x q_y q_z
1 0.291(3) 0.291(3) 0.000000
2 -0.291(3) 0.291(3) 0.000000

Z: 10 [ Help ]

Cell determination reflection Nb.: 17512 [ Help ]

θ(min) for cell determination: 2.84 ° [ Help ]

θ(max) for cell determination: 31.03 ° [ Help ]

Cell measurement temperature: 293 K [ Help ]

μ: 13.961 mm-1 [ Help ]

Absorption correction type: analytical [ Help ]

Absorption correction remarks: CrysAlisPro 1.171.38.43 (Rigaku Oxford Diffraction, 2015) 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: 0.073 [ Help ]

Maximum transmission factor: 0.265 [ Help ]

Refinement details

Total nb. of reflections: 4873 [ Help ]

Nb. of observed reflections: 2033 [ Help ]

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

Refinement based on: F [ Help ]

R(obs): 0.0271 [ Help ]

wR(obs): 0.0357 [ Help ]

R(all): 0.0645 [ Help ]

wR(all): 0.0421 [ Help ]

S(all): 1.18 [ Help ]

S(obs): 1.59 [ Help ]

Nb. of reflections: 4873 [ Help ]

Nb. of parameters: 158 [ Help ]

Number of restraints: 0 [ Help ]

Number of constraints: 1 [ Help ]

Weighting scheme: sigma [ Help ]

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

Δ/σ(max): 0.0084 [ Help ]

Δ/σ(mean): 0.0016 [ Help ]

Δρ(max): 0.91 e_Å-3 [ Help ]

Δρ(min): -1.11 e_Å-3 [ Help ]

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

Extinction coefficient: 1000(30) [ Help ]

Absolute structure remarks: 2365 of Friedel pairs used in the refinement [ Help ]

Flack parameter: 0.587(10) [ 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
Ba2 Ba 0.171985(15) 0.671985(15) 0.25 Uani 0.02427(8) 8 0.5977 d . . .
Sr1 Sr 0 0 0.24659(8) Uani 0.00787(12) 4 0.7162 d . . .
Nb1 Nb 0 0.5 0.00997(6) Uani 0.00946(9) 4 1 d . . .
Nb2 Nb 0.074328(16) 0.211501(16) 0.00278(5) Uani 0.01081(6) 16 1 d . . .
O1 O 0.21748(15) 0.28252(15) -0.0141(5) Uani 0.0128(6) 8 1 d . . .
O2 O 0.13920(16) 0.06966(15) -0.0156(4) Uani 0.0221(7) 16 1 d . . .
O3 O -0.00652(16) 0.34319(15) -0.0167(4) Uani 0.0177(6) 16 1 d . . .
O4 O 0 0.5 0.2459(8) Uani 0.0324(11) 4 1 d . . .
O5 O 0.07605(20) 0.20431(18) 0.2342(3) Uani 0.0254(8) 16 1 d . . .
Sr2 Sr 0.171985(15) 0.671985(15) 0.25 Uani 0.02427(8) 8 0.296 d . . .

ADP components: [ Help ]

Atom site label Atom site symbol U11 U22 U33 U12 U13 U23
Ba2 Ba 0.0290(1) 0.0290(1) 0.0149(1) -0.0168(1) -0.0005(2) -0.0005(2)
Sr1 Sr 0.00821(17) 0.00821(17) 0.0072(3) 0 0 0
Nb1 Nb 0.00966(13) 0.00966(13) 0.00908(19) -0.00140(13) 0 0
Nb2 Nb 0.01040(11) 0.01024(11) 0.01180(11) 0.00143(7) -0.00091(16) -0.00081(19)
O1 O 0.0116(7) 0.0116(7) 0.0150(15) -0.0042(9) -0.0065(10) 0.0065(10)
O2 O 0.0173(10) 0.0089(9) 0.0402(15) 0.0054(7) -0.0058(14) -0.0082(13)
O3 O 0.0193(10) 0.0071(8) 0.0267(13) 0.0029(6) -0.0009(12) -0.0040(11)
O4 O 0.0408(17) 0.0408(17) 0.016(2) 0.001(2) 0 0
O5 O 0.0532(16) 0.0226(11) 0.0003(13) -0.0137(10) 0.0023(12) 0.0001(10)
Sr2 Sr 0.0290(1) 0.0290(1) 0.0149(1) -0.0168(1) -0.0005(2) -0.0005(2)

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

Wave vector code q_x q_y q_z
1 0.291 0.291 0.000000
2 -0.291 0.291 0.000000

Definition of the occupation Fourier series: [ Help ]

Modulation code Atom site label Wave vector code
Ba2o1 Ba2 1
Ba2o2 Ba2 2
Sr1o1 Sr1 1
Sr1o2 Sr1 2
Sr2o1 Sr2 1
Sr2o2 Sr2 2

Occupation Fourier coefficients: [ Help ]

Modulation code Cosine coefficient Sine coefficient
Ba2o1 -0.002(3) 0.023(3)
Ba2o2 0.000(3) 0
Sr1o1 -0.0072(17) 0
Sr1o2 -0.0072(17) 0
Sr2o1 0.002(3) -0.023(3)
Sr2o2 0.000(3) 0

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

Modulation code Atom site label Displacement axis Wave vector code
Ba2x1 Ba2 x 1
Ba2y1 Ba2 y 1
Ba2z1 Ba2 z 1
Ba2x2 Ba2 x 2
Ba2y2 Ba2 y 2
Ba2z2 Ba2 z 2
Sr1x1 Sr1 x 1
Sr1y1 Sr1 y 1
Sr1z1 Sr1 z 1
Sr1x2 Sr1 x 2
Sr1y2 Sr1 y 2
Sr1z2 Sr1 z 2
Nb1x1 Nb1 x 1
Nb1y1 Nb1 y 1
Nb1z1 Nb1 z 1
Nb1x2 Nb1 x 2
Nb1y2 Nb1 y 2
Nb1z2 Nb1 z 2
Nb2x1 Nb2 x 1
Nb2y1 Nb2 y 1
Nb2z1 Nb2 z 1
Nb2x2 Nb2 x 2
Nb2y2 Nb2 y 2
Nb2z2 Nb2 z 2
O1x1 O1 x 1
O1y1 O1 y 1
O1z1 O1 z 1
O1x2 O1 x 2
O1y2 O1 y 2
O1z2 O1 z 2
O2x1 O2 x 1
O2y1 O2 y 1
O2z1 O2 z 1
O2x2 O2 x 2
O2y2 O2 y 2
O2z2 O2 z 2
O3x1 O3 x 1
O3y1 O3 y 1
O3z1 O3 z 1
O3x2 O3 x 2
O3y2 O3 y 2
O3z2 O3 z 2
O4x1 O4 x 1
O4y1 O4 y 1
O4z1 O4 z 1
O4x2 O4 x 2
O4y2 O4 y 2
O4z2 O4 z 2
O5x1 O5 x 1
O5y1 O5 y 1
O5z1 O5 z 1
O5x2 O5 x 2
O5y2 O5 y 2
O5z2 O5 z 2
Sr2x1 Sr2 x 1
Sr2y1 Sr2 y 1
Sr2z1 Sr2 z 1
Sr2x2 Sr2 x 2
Sr2y2 Sr2 y 2
Sr2z2 Sr2 z 2

Displacive (translational) Fourier coefficients: [ Help ]

Modulation code Cosine coefficient Sine coefficient
Ba2x1 0.00046(2) 0.00082(2)
Ba2y1 0.00046(2) 0.00082(2)
Ba2z1 0.00093(10) -0.00102(10)
Ba2x2 -0.00115(3) -0.00448(3)
Ba2y2 -0.00115(3) 0.00448(3)
Ba2z2 -0.00045(10) 0
Sr1x1 0 0.00007(5)
Sr1y1 0 0.00025(5)
Sr1z1 0.00011(14) 0
Sr1x2 0 -0.00025(5)
Sr1y2 0 0.00007(5)
Sr1z2 0.00011(14) 0
Nb1x1 0 -0.00075(6)
Nb1y1 0 -0.00075(6)
Nb1z1 0.00003(8) 0
Nb1x2 0 -0.00058(6)
Nb1y2 0 0.00058(6)
Nb1z2 -0.00040(8) 0
Nb2x1 -0.00071(5) -0.00026(5)
Nb2y1 0.00022(5) 0.00061(5)
Nb2z1 -0.00014(4) -0.00009(4)
Nb2x2 0.00082(5) 0.00054(5)
Nb2y2 -0.00044(5) -0.00032(5)
Nb2z2 0.00051(4) 0.00045(4)
O1x1 0.0002(4) 0.0002(4)
O1y1 -0.0002(4) 0.0002(4)
O1z1 0.0095(4) 0
O1x2 -0.0020(4) -0.0001(4)
O1y2 0.0020(4) 0.0001(4)
O1z2 -0.0073(4) -0.0056(4)
O2x1 -0.0018(4) -0.0007(4)
O2y1 -0.0009(4) -0.0007(4)
O2z1 0.0078(3) 0.0097(3)
O2x2 0.0019(4) 0.0005(4)
O2y2 -0.0004(4) -0.0005(4)
O2z2 -0.0129(3) -0.0068(3)
O3x1 0.0007(4) 0.0006(4)
O3y1 0.0006(4) -0.0001(4)
O3z1 -0.0045(3) -0.0130(3)
O3x2 0.0006(4) -0.0004(4)
O3y2 -0.0005(4) -0.0011(4)
O3z2 0.0039(3) 0.0153(3)
O4x1 0 -0.0084(3)
O4y1 0 -0.0084(3)
O4z1 0.0021(13) 0
O4x2 0 -0.0102(3)
O4y2 0 0.0102(3)
O4z2 0.0016(13) 0
O5x1 -0.0096(2) -0.0031(2)
O5y1 0.0006(2) 0.0069(2)
O5z1 0.0018(5) -0.0016(5)
O5x2 0.0087(3) 0.0095(2)
O5y2 -0.0034(2) -0.0045(2)
O5z2 0.0027(6) 0.0001(5)
Sr2x1 0.00046(2) 0.00082(2)
Sr2y1 0.00046(2) 0.00082(2)
Sr2z1 0.00093(10) -0.00102(10)
Sr2x2 -0.00115(3) -0.00448(3)
Sr2y2 -0.00115(3) 0.00448(3)
Sr2z2 -0.00045(10) 0

Definition of the ADP Fourier series: [ Help ]

Modulation code Atom site label Tensor element Wave vector code
Ba2U111 Ba2 U11 1
Ba2U221 Ba2 U22 1
Ba2U331 Ba2 U33 1
Ba2U121 Ba2 U12 1
Ba2U131 Ba2 U13 1
Ba2U231 Ba2 U23 1
Ba2U112 Ba2 U11 2
Ba2U222 Ba2 U22 2
Ba2U332 Ba2 U33 2
Ba2U122 Ba2 U12 2
Ba2U132 Ba2 U13 2
Ba2U232 Ba2 U23 2
Sr1U111 Sr1 U11 1
Sr1U221 Sr1 U22 1
Sr1U331 Sr1 U33 1
Sr1U121 Sr1 U12 1
Sr1U131 Sr1 U13 1
Sr1U231 Sr1 U23 1
Sr1U112 Sr1 U11 2
Sr1U222 Sr1 U22 2
Sr1U332 Sr1 U33 2
Sr1U122 Sr1 U12 2
Sr1U132 Sr1 U13 2
Sr1U232 Sr1 U23 2
Sr2U111 Sr2 U11 1
Sr2U221 Sr2 U22 1
Sr2U331 Sr2 U33 1
Sr2U121 Sr2 U12 1
Sr2U131 Sr2 U13 1
Sr2U231 Sr2 U23 1
Sr2U112 Sr2 U11 2
Sr2U222 Sr2 U22 2
Sr2U332 Sr2 U33 2
Sr2U122 Sr2 U12 2
Sr2U132 Sr2 U13 2
Sr2U232 Sr2 U23 2

ADP Fourier coefficients: [ Help ]

Modulation code Cosine coefficient Sine coefficient
Ba2U111 -0.0021(2) -0.0041(2)
Ba2U221 -0.0021(2) -0.0041(2)
Ba2U331 0.0001(2) 0.0001(2)
Ba2U121 0.0011(2) 0.0040(2)
Ba2U131 0.0003(2) 0.0001(2)
Ba2U231 0.0003(2) 0.0001(2)
Ba2U112 0.00611(19) 0.0060(2)
Ba2U222 0.00611(19) -0.0060(2)
Ba2U332 0.0006(2) 0
Ba2U122 -0.0054(2) 0
Ba2U132 0.0000(2) 0.0014(2)
Ba2U232 0.0000(2) -0.0014(2)
Sr1U111 -0.0007(3) 0
Sr1U221 0.0004(3) 0
Sr1U331 -0.0004(3) 0
Sr1U121 0.0001(2) 0
Sr1U131 0 0.0028(4)
Sr1U231 0 0.0000(4)
Sr1U112 0.0004(3) 0
Sr1U222 -0.0007(3) 0
Sr1U332 -0.0004(3) 0
Sr1U122 -0.0001(2) 0
Sr1U132 0 0.0000(4)
Sr1U232 0 0.0028(4)
Sr2U111 -0.0021(2) -0.0041(2)
Sr2U221 -0.0021(2) -0.0041(2)
Sr2U331 0.0001(2) 0.0001(2)
Sr2U121 0.0011(2) 0.0040(2)
Sr2U131 0.0003(2) 0.0001(2)
Sr2U231 0.0003(2) 0.0001(2)
Sr2U112 0.00611(19) 0.0060(2)
Sr2U222 0.00611(19) -0.0060(2)
Sr2U332 0.0006(2) 0
Sr2U122 -0.0054(2) 0
Sr2U132 0.0000(2) 0.0014(2)
Sr2U232 0.0000(2) -0.0014(2)

sbn52quenchedfrom1200-tet

Chemical data

Formula (IUPAC): barium strontium niobium oxide [ Help ]

Structural Formula Sum: Ba0.47 Nb2 O6 Sr0.53 [ Help ]

Formula weight: 392.8 Da [ Help ]

Crystallographic data and experimental details

Crystal system: tetragonal [ Help ]

Space group name (H-M): X4bm [ Help ]

Superspace group name: P4bm(αα1/2)000(-αα1/2)000 [ Help ]

Symmetry operations of the superspace group: [ Help ]

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

a: 12.4629(3) Å [ Help ]

b: 12.4629(3) Å [ Help ]

c: 7.9032(3) Å [ Help ]

α: 90 ° [ Help ]

β: 90 ° [ Help ]

γ: 90 ° [ Help ]

Volume: 1227.56(6) Å3 [ Help ]

Modulation dimension: 2 [ Help ]

Measured independent wave vectors: [ Help ]

Wave vector id q_x q_y q_z
1 0.292(3) 0.292(3) 0.000000
2 -0.292(3) 0.292(3) 0.000000

Z: 10 [ Help ]

Cell determination reflection Nb.: 13535 [ Help ]

θ(min) for cell determination: 2.98 ° [ Help ]

θ(max) for cell determination: 42.4 ° [ Help ]

Cell measurement temperature: 293 K [ Help ]

μ: 14 mm-1 [ Help ]

Absorption correction type: analytical [ Help ]

Absorption correction remarks: CrysAlisPro, Agilent Technologies, Version 1.171.37.35 (release 13-08-2014 CrysAlis171 .NET) (compiled Aug 13 2014,18:06:01) 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: 0.198 [ Help ]

Maximum transmission factor: 0.547 [ Help ]

Refinement details

Total nb. of reflections: 7638 [ Help ]

Nb. of observed reflections: 2775 [ Help ]

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

Refinement based on: F [ Help ]

R(obs): 0.0290 [ Help ]

wR(obs): 0.0365 [ Help ]

R(all): 0.0899 [ Help ]

wR(all): 0.0464 [ Help ]

S(all): 1.11 [ Help ]

S(obs): 1.47 [ Help ]

Nb. of reflections: 7638 [ Help ]

Nb. of parameters: 190 [ Help ]

Number of restraints: 0 [ Help ]

Number of constraints: 1 [ Help ]

Weighting scheme: sigma [ Help ]

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

Δ/σ(max): 0.0222 [ Help ]

Δ/σ(mean): 0.0028 [ Help ]

Δρ(max): 1.18 e_Å-3 [ Help ]

Δρ(min): -1.14 e_Å-3 [ Help ]

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

Extinction coefficient: 169(16) [ Help ]

Absolute structure remarks: 3726 of Friedel pairs used in the refinement [ Help ]

Flack parameter: 0.468(10) [ 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
Ba2 Ba 0.171927(13) 0.671927(13) 0.249999 Uani 0.02429(6) 8 0.598 d . . .
Sr1 Sr 0 0 0.24703(8) Uani 0.00778(9) 4 0.6808 d . . .
Nb1 Nb 0 0.5 0.00944(5) Uani 0.00829(6) 4 1 d . . .
Nb2 Nb 0.074330(13) 0.211081(13) 0.00306(5) Uani 0.00976(5) 16 1 d . . .
O1 O 0.21804(13) 0.28196(13) -0.0143(4) Uani 0.0111(5) 8 1 d . . .
O2 O 0.13972(14) 0.06969(13) -0.0180(4) Uani 0.0215(6) 16 1 d . . .
O3 O -0.00699(14) 0.34350(13) -0.0174(3) Uani 0.0172(5) 16 1 d . . .
O4 O 0 0.5 0.2451(7) Uani 0.0335(10) 4 1 d . . .
O5 O 0.07602(17) 0.20470(15) 0.2347(2) Uani 0.0250(6) 16 1 d . . .
Sr2 Sr 0.171927(13) 0.671927(13) 0.249999 Uani 0.02429(6) 8 0.3137 d . . .

ADP components: [ Help ]

Atom site label Atom site symbol U11 U22 U33 U12 U13 U23
Ba2 Ba 0.0292(1) 0.0292(1) 0.0144(1) -0.0174(1) -0.0001(1) -0.0001(1)
Sr1 Sr 0.00753(13) 0.00753(13) 0.0083(2) 0 0 0
Nb1 Nb 0.00829(9) 0.00829(9) 0.00830(13) -0.00075(10) 0 0
Nb2 Nb 0.00950(8) 0.00884(8) 0.01096(8) 0.00144(6) -0.00031(14) -0.00107(15)
O1 O 0.0105(5) 0.0105(5) 0.0124(12) -0.0035(7) -0.0061(8) 0.0061(8)
O2 O 0.0179(8) 0.0077(7) 0.0390(14) 0.0057(6) -0.0073(11) -0.0067(10)
O3 O 0.0171(8) 0.0071(7) 0.0275(11) 0.0030(5) 0.0001(10) -0.0071(9)
O4 O 0.0433(16) 0.0433(16) 0.0138(19) 0.0022(19) 0 0
O5 O 0.0535(14) 0.0206(9) 0.0010(10) -0.0141(9) 0.0030(9) -0.0008(7)
Sr2 Sr 0.0292(1) 0.0292(1) 0.0144(1) -0.0174(1) -0.0001(1) -0.0001(1)

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

Wave vector code q_x q_y q_z
1 0.292 0.292 0.000000
2 -0.292 0.292 0.000000

Definition of the occupation Fourier series: [ Help ]

Modulation code Atom site label Wave vector code
Ba2o1 Ba2 1
Ba2o2 Ba2 2
Sr1o1 Sr1 1
Sr1o2 Sr1 2
Sr2o1 Sr2 1
Sr2o2 Sr2 2

Occupation Fourier coefficients: [ Help ]

Modulation code Cosine coefficient Sine coefficient
Ba2o1 -0.009(3) 0.010(3)
Ba2o2 0.016(3) 0
Sr1o1 -0.0028(15) 0
Sr1o2 -0.0028(15) 0
Sr2o1 0.009(3) -0.010(3)
Sr2o2 -0.016(3) 0

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

Modulation code Atom site label Displacement axis Wave vector code
Ba2x1 Ba2 x 1
Ba2y1 Ba2 y 1
Ba2z1 Ba2 z 1
Ba2x2 Ba2 x 2
Ba2y2 Ba2 y 2
Ba2z2 Ba2 z 2
Sr1x1 Sr1 x 1
Sr1y1 Sr1 y 1
Sr1z1 Sr1 z 1
Sr1x2 Sr1 x 2
Sr1y2 Sr1 y 2
Sr1z2 Sr1 z 2
Nb1x1 Nb1 x 1
Nb1y1 Nb1 y 1
Nb1z1 Nb1 z 1
Nb1x2 Nb1 x 2
Nb1y2 Nb1 y 2
Nb1z2 Nb1 z 2
Nb2x1 Nb2 x 1
Nb2y1 Nb2 y 1
Nb2z1 Nb2 z 1
Nb2x2 Nb2 x 2
Nb2y2 Nb2 y 2
Nb2z2 Nb2 z 2
O1x1 O1 x 1
O1y1 O1 y 1
O1z1 O1 z 1
O1x2 O1 x 2
O1y2 O1 y 2
O1z2 O1 z 2
O2x1 O2 x 1
O2y1 O2 y 1
O2z1 O2 z 1
O2x2 O2 x 2
O2y2 O2 y 2
O2z2 O2 z 2
O3x1 O3 x 1
O3y1 O3 y 1
O3z1 O3 z 1
O3x2 O3 x 2
O3y2 O3 y 2
O3z2 O3 z 2
O4x1 O4 x 1
O4y1 O4 y 1
O4z1 O4 z 1
O4x2 O4 x 2
O4y2 O4 y 2
O4z2 O4 z 2
O5x1 O5 x 1
O5y1 O5 y 1
O5z1 O5 z 1
O5x2 O5 x 2
O5y2 O5 y 2
O5z2 O5 z 2
Sr2x1 Sr2 x 1
Sr2y1 Sr2 y 1
Sr2z1 Sr2 z 1
Sr2x2 Sr2 x 2
Sr2y2 Sr2 y 2
Sr2z2 Sr2 z 2

Displacive (translational) Fourier coefficients: [ Help ]

Modulation code Cosine coefficient Sine coefficient
Ba2x1 0.000507(19) 0.00098(2)
Ba2y1 0.000507(19) 0.00098(2)
Ba2z1 0.00152(8) -0.00087(8)
Ba2x2 -0.00123(2) -0.00475(3)
Ba2y2 -0.00123(2) 0.00475(3)
Ba2z2 -0.00047(8) 0
Sr1x1 0 0.00002(4)
Sr1y1 0 0.00020(4)
Sr1z1 0.00035(12) 0
Sr1x2 0 -0.00020(4)
Sr1y2 0 0.00002(4)
Sr1z2 0.00035(12) 0
Nb1x1 0 -0.00082(5)
Nb1y1 0 -0.00082(5)
Nb1z1 0.00008(7) 0
Nb1x2 0 -0.00101(5)
Nb1y2 0 0.00101(5)
Nb1z2 -0.00046(7) 0
Nb2x1 -0.00084(4) -0.00032(4)
Nb2y1 0.00013(4) 0.00061(4)
Nb2z1 -0.00032(4) -0.00021(4)
Nb2x2 0.00093(4) 0.00062(4)
Nb2y2 -0.00046(4) -0.00028(4)
Nb2z2 0.00052(4) 0.00040(4)
O1x1 0.0003(3) 0.0002(3)
O1y1 -0.0003(3) 0.0002(3)
O1z1 0.0104(3) 0
O1x2 -0.0015(3) -0.0001(3)
O1y2 0.0015(3) 0.0001(3)
O1z2 -0.0075(3) -0.0064(3)
O2x1 -0.0010(3) -0.0011(3)
O2y1 -0.0005(3) -0.0006(3)
O2z1 0.0090(3) 0.0119(3)
O2x2 0.0021(3) 0.0003(3)
O2y2 0.0000(3) 0.0003(3)
O2z2 -0.0141(3) -0.0071(3)
O3x1 0.0009(3) 0.0007(3)
O3y1 0.0003(3) -0.0006(3)
O3z1 -0.0049(3) -0.0146(3)
O3x2 0.0004(3) -0.0008(3)
O3y2 -0.0003(3) 0.0000(3)
O3z2 0.0045(3) 0.0172(3)
O4x1 0 -0.0103(3)
O4y1 0 -0.0103(3)
O4z1 0.0029(10) 0
O4x2 0 -0.0113(3)
O4y2 0 0.0113(3)
O4z2 -0.0017(11) 0
O5x1 -0.0112(2) -0.0037(2)
O5y1 0.00089(18) 0.00793(19)
O5z1 0.0006(4) -0.0007(4)
O5x2 0.0096(2) 0.0112(2)
O5y2 -0.00383(19) -0.00508(19)
O5z2 0.0013(5) 0.0013(4)
Sr2x1 0.000507(19) 0.00098(2)
Sr2y1 0.000507(19) 0.00098(2)
Sr2z1 0.00152(8) -0.00087(8)
Sr2x2 -0.00123(2) -0.00475(3)
Sr2y2 -0.00123(2) 0.00475(3)
Sr2z2 -0.00047(8) 0

Definition of the ADP Fourier series: [ Help ]

Modulation code Atom site label Tensor element Wave vector code
Ba2U111 Ba2 U11 1
Ba2U221 Ba2 U22 1
Ba2U331 Ba2 U33 1
Ba2U121 Ba2 U12 1
Ba2U131 Ba2 U13 1
Ba2U231 Ba2 U23 1
Ba2U112 Ba2 U11 2
Ba2U222 Ba2 U22 2
Ba2U332 Ba2 U33 2
Ba2U122 Ba2 U12 2
Ba2U132 Ba2 U13 2
Ba2U232 Ba2 U23 2
Sr1U111 Sr1 U11 1
Sr1U221 Sr1 U22 1
Sr1U331 Sr1 U33 1
Sr1U121 Sr1 U12 1
Sr1U131 Sr1 U13 1
Sr1U231 Sr1 U23 1
Sr1U112 Sr1 U11 2
Sr1U222 Sr1 U22 2
Sr1U332 Sr1 U33 2
Sr1U122 Sr1 U12 2
Sr1U132 Sr1 U13 2
Sr1U232 Sr1 U23 2
Nb1U111 Nb1 U11 1
Nb1U221 Nb1 U22 1
Nb1U331 Nb1 U33 1
Nb1U121 Nb1 U12 1
Nb1U131 Nb1 U13 1
Nb1U231 Nb1 U23 1
Nb1U112 Nb1 U11 2
Nb1U222 Nb1 U22 2
Nb1U332 Nb1 U33 2
Nb1U122 Nb1 U12 2
Nb1U132 Nb1 U13 2
Nb1U232 Nb1 U23 2
Nb2U111 Nb2 U11 1
Nb2U221 Nb2 U22 1
Nb2U331 Nb2 U33 1
Nb2U121 Nb2 U12 1
Nb2U131 Nb2 U13 1
Nb2U231 Nb2 U23 1
Nb2U112 Nb2 U11 2
Nb2U222 Nb2 U22 2
Nb2U332 Nb2 U33 2
Nb2U122 Nb2 U12 2
Nb2U132 Nb2 U13 2
Nb2U232 Nb2 U23 2
Sr2U111 Sr2 U11 1
Sr2U221 Sr2 U22 1
Sr2U331 Sr2 U33 1
Sr2U121 Sr2 U12 1
Sr2U131 Sr2 U13 1
Sr2U231 Sr2 U23 1
Sr2U112 Sr2 U11 2
Sr2U222 Sr2 U22 2
Sr2U332 Sr2 U33 2
Sr2U122 Sr2 U12 2
Sr2U132 Sr2 U13 2
Sr2U232 Sr2 U23 2

ADP Fourier coefficients: [ Help ]

Modulation code Cosine coefficient Sine coefficient
Ba2U111 -0.00175(17) -0.00605(17)
Ba2U221 -0.00175(17) -0.00605(17)
Ba2U331 -0.0006(2) 0.0003(2)
Ba2U121 0.00127(18) 0.00573(18)
Ba2U131 -0.00032(15) -0.00005(15)
Ba2U231 -0.00032(15) -0.00005(15)
Ba2U112 0.00655(17) 0.00723(16)
Ba2U222 0.00655(17) -0.00723(16)
Ba2U332 0.0011(2) 0
Ba2U122 -0.00613(18) 0
Ba2U132 0.00047(16) 0.0021(2)
Ba2U232 0.00047(16) -0.0021(2)
Sr1U111 0.0003(3) 0
Sr1U221 0.0009(3) 0
Sr1U331 0.0007(3) 0
Sr1U121 -0.0002(2) 0
Sr1U131 0 -0.0001(3)
Sr1U231 0 -0.0027(3)
Sr1U112 0.0009(3) 0
Sr1U222 0.0003(3) 0
Sr1U332 0.0007(3) 0
Sr1U122 0.0002(2) 0
Sr1U132 0 0.0027(3)
Sr1U232 0 -0.0001(3)
Nb1U111 -0.0005(2) 0
Nb1U221 -0.0005(2) 0
Nb1U331 -0.0004(3) 0
Nb1U121 0.0008(3) 0
Nb1U131 0 0.00021(15)
Nb1U231 0 0.00021(15)
Nb1U112 0.0006(2) 0
Nb1U222 0.0006(2) 0
Nb1U332 -0.0002(3) 0
Nb1U122 0.0002(3) 0
Nb1U132 0 0.00118(15)
Nb1U232 0 -0.00118(15)
Nb2U111 0.0003(2) -0.0015(2)
Nb2U221 -0.0003(2) -0.0008(2)
Nb2U331 0.00024(16) -0.00013(15)
Nb2U121 0.00046(17) 0.00083(16)
Nb2U131 0.00060(10) -0.00017(10)
Nb2U231 0.00044(10) -0.00016(10)
Nb2U112 0.0003(2) 0.0008(2)
Nb2U222 -0.0006(2) 0.0001(2)
Nb2U332 -0.00032(15) -0.00158(16)
Nb2U122 -0.00047(15) 0.00021(16)
Nb2U132 -0.00050(10) -0.00026(10)
Nb2U232 -0.00008(10) -0.00030(10)
Sr2U111 -0.00175(17) -0.00605(17)
Sr2U221 -0.00175(17) -0.00605(17)
Sr2U331 -0.0006(2) 0.0003(2)
Sr2U121 0.00127(18) 0.00573(18)
Sr2U131 -0.00032(15) -0.00005(15)
Sr2U231 -0.00032(15) -0.00005(15)
Sr2U112 0.00655(17) 0.00723(16)
Sr2U222 0.00655(17) -0.00723(16)
Sr2U332 0.0011(2) 0
Sr2U122 -0.00613(18) 0
Sr2U132 0.00047(16) 0.0021(2)
Sr2U232 0.00047(16) -0.0021(2)