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Modulated structure of potassium sodium strontium barium niobates (KNSBN): harmonic solution

Authors:

Surmin, Audrey; Fertey, Pierre; Schaniel, Dominik; Woike, Theo

Journal:

Acta Crystallographica, Section B 62 228-235 (2006)

DOI:

https://doi.org/10.1107/S0108768106001510

B-IncStrDB ID: Q6md3S1F1yT Entry date: 2022-01-28 Last revision: 2022-01-28

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KNSBN60

Chemical data

Structural Formula Sum: Ba0.38 K0.085 Na0.07 Nb2 O6 Sr0.56 [ Help ]

Formula weight: 388 Da [ Help ]

Crystallographic data and experimental details

Crystal system: tetragonal [ Help ]

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

Superspace group name: X4bm(αα0)(α-α0) [ 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 1/2-x1,1/2+x2,x3,-x5,-x4
4 -x1,-x2,x3,-x4,-x5
5 1/2-x2,1/2-x1,x3,-x4,x5
6 x2,-x1,x3,-x5,x4
7 1/2+x1,1/2-x2,x3,x5,x4
8 1/2+x2,1/2+x1,x3,x4,-x5
9 x1,x2,1/2+x3,1/2+x4,1/2+x5
10 -x2,x1,1/2+x3,1/2+x5,1/2-x4
11 1/2-x1,1/2+x2,1/2+x3,1/2-x5,1/2-x4
12 -x1,-x2,1/2+x3,1/2-x4,1/2-x5
13 1/2-x2,1/2-x1,1/2+x3,1/2-x4,1/2+x5
14 x2,-x1,1/2+x3,1/2-x5,1/2+x4
15 1/2+x1,1/2-x2,1/2+x3,1/2+x5,1/2+x4
16 1/2+x2,1/2+x1,1/2+x3,1/2+x4,1/2-x5

a: 12.4375(5) Å [ Help ]

b: 12.4375(5) Å [ Help ]

c: 7.8807(2) Å [ Help ]

α: 90 ° [ Help ]

β: 90 ° [ Help ]

γ: 90 ° [ Help ]

Volume: 1219.08(8) Å3 [ Help ]

Z: 10 [ Help ]

Cell determination reflection Nb.: 4101 [ Help ]

Cell measurement temperature: 293 K [ Help ]

Modulation dimension: 2 [ Help ]

Measured independent wave vectors: [ Help ]

Wave vector id q_x q_y q_z
1 0.31100 0.31100 0.00000
2 0.31100 -0.31100 0.00000

μ: 13.79 mm-1 [ Help ]

Absorption correction type: sphere [ Help ]

Absorption correction remarks: (Jana2000; Petricek and Dusek, 2000) [ Help ]

Minimum transmission factor: 0.221 [ Help ]

Maximum transmission factor: 0.228 [ Help ]

Refinement details

Total nb. of reflections: 8612 [ Help ]

Nb. of observed reflections: 7718 [ Help ]

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

Refinement based on: F [ Help ]

R(all): 0.0593 [ Help ]

R(obs): 0.0506 [ Help ]

wR(obs): 0.0848 [ Help ]

wR(all): 0.0871 [ Help ]

S(all): 2.61 [ Help ]

Nb. of reflections: 8612 [ Help ]

Nb. of parameters: 150 [ Help ]

Weighting scheme: sigma [ Help ]

Weighting scheme remarks: w=1/(σ2(F)+0.0004F2) [ Help ]

Δ/σ(max): 0.0260 [ Help ]

Δ/σ(mean): 0.0019 [ Help ]

Δρ(max): 3.64 e_Å-3 [ Help ]

Δρ(min): -5.83 e_Å-3 [ Help ]

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

Extinction coefficient: 0.058(4) [ Help ]

Structural Information

Average Structure: [ Help ]

Atom symbol Atom site label x y z Uiso/equiv ADP type Coords from (d)iffraction or (c)alculated Coords restraints or constraints Occupancy Disordered cluster Disordered group
Nb Nb1 0 0.5 0.00125(9) 0.00610(5) Uani d . 1 . .
Nb Nb2 0.074775(15) 0.211720(14) -0.00588(8) 0.00691(4) Uani d . 1 . .
Sr Sr1 0 0 0.23884(11) 0.00707(9) Uani d . 0.730(3) . .
O O1 0.34344(15) 0.00549(16) -0.0262(4) 0.0118(4) Uani d . 1 . .
O O2 0.13858(17) 0.06904(14) -0.0287(3) 0.0107(4) Uani d . 1 . .
O O3 0.28172(16) 0.78172(16) -0.0229(4) 0.0100(5) Uani d . 1 . .
O O4 0 0.5 0.2307(6) 0.0190(8) Uani d . 1 . .
O O5 0.29600(16) 0.42432(15) 0.2273(3) 0.0126(5) Uani d . 1 . .
Ba Ba 0.17168(2) 0.67168(2) 0.240438 0.02187(7) Uani d . 0.403(6) . .
Sr Sr2 0.17168(2) 0.67168(2) 0.240438 0.02187(7) Uani d . 0.411(7) . .
Na Na1 0 0 0.23884(11) 0.00707(9) Uani d . 0.175 . .
K K 0.17168(2) 0.67168(2) 0.240438 0.02187(7) Uani d . 0.1062 . .

ADP components: [ Help ]

Atom site label U11 U22 U33 U12 U13 U23 Atom site symbol
Nb1 0.00649(8) 0.00649(8) 0.00533(11) -0.00017(8) 0 0 Nb
Nb2 0.00727(7) 0.00625(6) 0.00720(7) 0.00083(4) 0.00020(8) -0.00146(8) Nb
Sr1 0.00684(12) 0.00684(12) 0.0075(2) 0 0 0 Sr
O1 0.0063(5) 0.0148(7) 0.0144(9) -0.0040(5) -0.0019(8) 0.0032(8) O
O2 0.0172(8) 0.0068(5) 0.0081(9) 0.0062(5) -0.0011(7) -0.0034(6) O
O3 0.0098(5) 0.0098(5) 0.0105(12) 0.0032(6) 0.0037(7) 0.0037(7) O
O4 0.0259(13) 0.0259(13) 0.0052(15) 0.0048(15) 0 0 O
O5 0.0148(8) 0.0195(10) 0.0034(8) -0.0030(7) 0.0007(6) -0.0014(8) O
Ba 0.02641(11) 0.02641(11) 0.01278(14) -0.01650(14) -0.00053(10) -0.00053(10) Ba
Sr2 0.02641(11) 0.02641(11) 0.01278(14) -0.01650(14) -0.00053(10) -0.00053(10) Sr
Na1 0.00684(12) 0.00684(12) 0.0075(2) 0 0 0 Na
K 0.02641(11) 0.02641(11) 0.01278(14) -0.01650(14) -0.00053(10) -0.00053(10) K

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 0.31100 0.31100 0.00000
2 0.31100 -0.31100 0.00000

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

Modulation code Atom site label Displacement axis Wave vector code
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
Sr1x1 Sr1 x 1
Sr1y1 Sr1 y 1
Sr1z1 Sr1 z 1
Sr1x2 Sr1 x 2
Sr1y2 Sr1 y 2
Sr1z2 Sr1 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
Bax1 Ba x 1
Bay1 Ba y 1
Baz1 Ba z 1
Bax2 Ba x 2
Bay2 Ba y 2
Baz2 Ba 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
Na1x1 Na1 x 1
Na1y1 Na1 y 1
Na1z1 Na1 z 1
Na1x2 Na1 x 2
Na1y2 Na1 y 2
Na1z2 Na1 z 2
Kx1 K x 1
Ky1 K y 1
Kz1 K z 1
Kx2 K x 2
Ky2 K y 2
Kz2 K z 2

Displacive (translational) Fourier coefficients: [ Help ]

Modulation code Cosine coefficient Sine coefficient
Nb1x1 0 -0.00102(3)
Nb1y1 0 -0.00102(3)
Nb1z1 -0.00001(6) 0
Nb1x2 0 0.00077(3)
Nb1y2 0 -0.00077(3)
Nb1z2 -0.00037(6) 0
Nb2x1 -0.00124(2) -0.00067(2)
Nb2y1 0.00045(2) 0.00076(3)
Nb2z1 -0.00035(3) -0.00044(3)
Nb2x2 0.00118(3) -0.00074(3)
Nb2y2 -0.00058(2) 0.00035(3)
Nb2z2 0.00059(3) -0.00051(3)
Sr1x1 0 0.00018(3)
Sr1y1 0 0.00038(3)
Sr1z1 -0.00014(7) 0
Sr1x2 0 0.00038(3)
Sr1y2 0 -0.00018(3)
Sr1z2 -0.00014(7) 0
O1x1 -0.0004(2) -0.0010(2)
O1y1 0.0001(2) 0.0014(2)
O1z1 0.0059(3) 0.0202(3)
O1x2 0.0001(2) 0.0004(2)
O1y2 -0.0004(2) -0.0009(2)
O1z2 -0.0079(3) -0.0227(3)
O2x1 -0.0019(2) -0.0019(2)
O2y1 -0.00025(19) 0.00005(19)
O2z1 0.0133(3) 0.0155(3)
O2x2 0.0029(2) 0.0002(2)
O2y2 0.00105(19) -0.00009(19)
O2z2 -0.0185(3) 0.0076(2)
O3x1 0.0016(2) 0.0003(2)
O3y1 0.0016(2) 0.0003(2)
O3z1 -0.0130(3) -0.0076(3)
O3x2 -0.00038(19) 0.00022(19)
O3y2 -0.00038(19) -0.00022(19)
O3z2 0.0112(3) 0
O4x1 0 -0.0136(3)
O4y1 0 -0.0136(3)
O4z1 0.0059(7) 0
O4x2 0 0.0125(3)
O4y2 0 -0.0125(3)
O4z2 0.0035(8) 0
O5x1 -0.00194(15) 0.01050(16)
O5y1 0.01284(19) -0.00672(18)
O5z1 0.0002(3) -0.0008(4)
O5x2 0.00421(16) -0.00572(16)
O5y2 -0.01295(19) 0.01267(19)
O5z2 0.0026(3) 0.0030(3)
Bax1 0.000700(17) 0.000967(18)
Bay1 0.000700(17) 0.000967(18)
Baz1 0.00147(7) -0.00132(6)
Bax2 -0.001487(19) 0.00534(3)
Bay2 -0.001487(19) -0.00534(3)
Baz2 -0.00061(7) 0
Sr2x1 0.000700(17) 0.000967(18)
Sr2y1 0.000700(17) 0.000967(18)
Sr2z1 0.00147(7) -0.00132(6)
Sr2x2 -0.001487(19) 0.00534(3)
Sr2y2 -0.001487(19) -0.00534(3)
Sr2z2 -0.00061(7) 0
Na1x1 0 0.00018(3)
Na1y1 0 0.00038(3)
Na1z1 -0.00014(7) 0
Na1x2 0 0.00038(3)
Na1y2 0 -0.00018(3)
Na1z2 -0.00014(7) 0
Kx1 0.000700(17) 0.000967(18)
Ky1 0.000700(17) 0.000967(18)
Kz1 0.00147(7) -0.00132(6)
Kx2 -0.001487(19) 0.00534(3)
Ky2 -0.001487(19) -0.00534(3)
Kz2 -0.00061(7) 0

Definition of the ADP Fourier series: [ Help ]

Modulation code Atom site label Tensor element Wave vector code
BaU111 Ba U11 1
BaU221 Ba U22 1
BaU331 Ba U33 1
BaU121 Ba U12 1
BaU131 Ba U13 1
BaU231 Ba U23 1
BaU112 Ba U11 2
BaU222 Ba U22 2
BaU332 Ba U33 2
BaU122 Ba U12 2
BaU132 Ba U13 2
BaU232 Ba 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
KU111 K U11 1
KU221 K U22 1
KU331 K U33 1
KU121 K U12 1
KU131 K U13 1
KU231 K U23 1
KU112 K U11 2
KU222 K U22 2
KU332 K U33 2
KU122 K U12 2
KU132 K U13 2
KU232 K U23 2

ADP Fourier coefficients: [ Help ]

Modulation code Cosine coefficient Sine coefficient
BaU111 -0.00545(12) -0.00744(12)
BaU221 -0.00545(12) -0.00744(12)
BaU331 -0.00140(19) -0.00135(18)
BaU121 0.00309(15) 0.00708(15)
BaU131 0.00051(13) 0.00027(13)
BaU231 0.00051(13) 0.00027(13)
BaU112 0.00889(12) -0.00872(14)
BaU222 0.00889(12) 0.00872(14)
BaU332 0.00193(18) 0
BaU122 -0.00697(15) 0
BaU132 -0.00068(12) 0.00051(17)
BaU232 -0.00068(12) -0.00051(17)
Sr2U111 -0.00545(12) -0.00744(12)
Sr2U221 -0.00545(12) -0.00744(12)
Sr2U331 -0.00140(19) -0.00135(18)
Sr2U121 0.00309(15) 0.00708(15)
Sr2U131 0.00051(13) 0.00027(13)
Sr2U231 0.00051(13) 0.00027(13)
Sr2U112 0.00889(12) -0.00872(14)
Sr2U222 0.00889(12) 0.00872(14)
Sr2U332 0.00193(18) 0
Sr2U122 -0.00697(15) 0
Sr2U132 -0.00068(12) 0.00051(17)
Sr2U232 -0.00068(12) -0.00051(17)
KU111 -0.00545(12) -0.00744(12)
KU221 -0.00545(12) -0.00744(12)
KU331 -0.00140(19) -0.00135(18)
KU121 0.00309(15) 0.00708(15)
KU131 0.00051(13) 0.00027(13)
KU231 0.00051(13) 0.00027(13)
KU112 0.00889(12) -0.00872(14)
KU222 0.00889(12) 0.00872(14)
KU332 0.00193(18) 0
KU122 -0.00697(15) 0
KU132 -0.00068(12) 0.00051(17)
KU232 -0.00068(12) -0.00051(17)

KNSBN72

Chemical data

Structural Formula Sum: Ba0.26 K0.09 Na0.08 Nb2 O6 Sr0.67 [ Help ]

Formula weight: 381.6 Da [ Help ]

Crystallographic data and experimental details

Crystal system: tetragonal [ Help ]

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

Superspace group name: X4bm(αα0)(α-α0) [ 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 1/2-x1,1/2+x2,x3,-x5,-x4
4 -x1,-x2,x3,-x4,-x5
5 1/2-x2,1/2-x1,x3,-x4,x5
6 x2,-x1,x3,-x5,x4
7 1/2+x1,1/2-x2,x3,x5,x4
8 1/2+x2,1/2+x1,x3,x4,-x5
9 x1,x2,1/2+x3,1/2+x4,1/2+x5
10 -x2,x1,1/2+x3,1/2+x5,1/2-x4
11 1/2-x1,1/2+x2,1/2+x3,1/2-x5,1/2-x4
12 -x1,-x2,1/2+x3,1/2-x4,1/2-x5
13 1/2-x2,1/2-x1,1/2+x3,1/2-x4,1/2+x5
14 x2,-x1,1/2+x3,1/2-x5,1/2+x4
15 1/2+x1,1/2-x2,1/2+x3,1/2+x5,1/2+x4
16 1/2+x2,1/2+x1,1/2+x3,1/2+x4,1/2-x5

a: 12.4292(8) Å [ Help ]

b: 12.4292(8) Å [ Help ]

c: 7.8524(3) Å [ Help ]

α: 90 ° [ Help ]

β: 90 ° [ Help ]

γ: 90 ° [ Help ]

Volume: 1213.08(12) Å3 [ Help ]

Z: 10 [ Help ]

Cell determination reflection Nb.: 2000 [ Help ]

Cell measurement temperature: 293 K [ Help ]

Modulation dimension: 2 [ Help ]

Measured independent wave vectors: [ Help ]

Wave vector id q_x q_y q_z
1 0.30720 0.30720 0.00000
2 0.30720 -0.30720 0.00000

μ: 14.106 mm-1 [ Help ]

Absorption correction type: sphere [ Help ]

Absorption correction remarks: (Jana2000; Petricek and Dusek, 2000) [ Help ]

Minimum transmission factor: 0.106 [ Help ]

Maximum transmission factor: 0.152 [ Help ]

Refinement details

Total nb. of reflections: 7577 [ Help ]

Nb. of observed reflections: 6196 [ Help ]

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

Refinement based on: F [ Help ]

R(all): 0.0548 [ Help ]

R(obs): 0.0548 [ Help ]

wR(obs): 0.0743 [ Help ]

wR(all): 0.0743 [ Help ]

S(all): 2.32 [ Help ]

Nb. of reflections: 6196 [ Help ]

Nb. of parameters: 129 [ Help ]

Weighting scheme: sigma [ Help ]

Weighting scheme remarks: w=1/(σ2(F)+0.0004F2) [ Help ]

Δ/σ(max): 0.0059 [ Help ]

Δ/σ(mean): 0.0010 [ Help ]

Δρ(max): 3.07 e_Å-3 [ Help ]

Δρ(min): -5.07 e_Å-3 [ Help ]

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

Extinction coefficient: 0.069(3) [ Help ]

Structural Information

Average Structure: [ Help ]

Atom symbol Atom site label x y z Uiso/equiv ADP type Coords from (d)iffraction or (c)alculated Coords restraints or constraints Occupancy Disordered cluster Disordered group
Nb Nb1 0 0.5 0.00128(12) 0.00738(8) Uani d . 1 . .
Nb Nb2 0.074907(18) 0.211795(17) -0.00681(10) 0.00831(6) Uani d . 1 . .
Sr Sr1 0 0 0.23820(13) 0.00745(13) Uani d . 0.712(4) . .
O O1 0.34394(15) 0.00525(14) -0.0263(3) 0.0090(3) Uiso d . 1 . .
O O2 0.13855(16) 0.06807(15) -0.0286(3) 0.0106(3) Uiso d . 1 . .
O O3 0.28142(15) 0.78142(15) -0.0207(4) 0.0093(4) Uiso d . 1 . .
O O4 0 0.5 0.2334(7) 0.0184(8) Uiso d . 1 . .
O O5 0.29630(13) 0.42457(15) 0.2277(3) 0.0091(4) Uiso d . 1 . .
Ba Ba 0.17129(3) 0.67129(3) 0.240438 0.02574(9) Uani d . 0.247(8) . .
Sr Sr2 0.17129(3) 0.67129(3) 0.240438 0.02574(9) Uani d . 0.560(8) . .
Na Na1 0 0 0.23820(13) 0.00745(13) Uani d . 0.1975 . .
Na K 0.17129(3) 0.67129(3) 0.240438 0.02574(9) Uani d . 0.12 . .

ADP components: [ Help ]

Atom site label U11 U22 U33 U12 U13 U23 Atom site symbol
Nb1 0.00770(11) 0.00770(11) 0.00672(17) -0.00021(11) 0 0 Nb
Nb2 0.00844(10) 0.00717(10) 0.00933(12) 0.00080(5) 0.00013(11) -0.00158(11) Nb
Sr1 0.00702(18) 0.00702(18) 0.0083(3) 0 0 0 Sr
Ba 0.03204(13) 0.03204(13) 0.0131(2) -0.0214(2) 0.00100(15) 0.00100(15) Ba
Sr2 0.03204(13) 0.03204(13) 0.0131(2) -0.0214(2) 0.00100(15) 0.00100(15) Sr
Na1 0.00702(18) 0.00702(18) 0.0083(3) 0 0 0 Na
K 0.03204(13) 0.03204(13) 0.0131(2) -0.0214(2) 0.00100(15) 0.00100(15) Na

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 0.30720 -0.30720 0.00000
2 0.30720 -0.30720 0.00000

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

Modulation code Atom site label Displacement axis Wave vector code
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
Sr1x1 Sr1 x 1
Sr1y1 Sr1 y 1
Sr1z1 Sr1 z 1
Sr1x2 Sr1 x 2
Sr1y2 Sr1 y 2
Sr1z2 Sr1 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
Bax1 Ba x 1
Bay1 Ba y 1
Baz1 Ba z 1
Bax2 Ba x 2
Bay2 Ba y 2
Baz2 Ba 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
Na1x1 Na1 x 1
Na1y1 Na1 y 1
Na1z1 Na1 z 1
Na1x2 Na1 x 2
Na1y2 Na1 y 2
Na1z2 Na1 z 2
Kx1 K x 1
Ky1 K y 1
Kz1 K z 1
Kx2 K x 2
Ky2 K y 2
Kz2 K z 2

Displacive (translational) Fourier coefficients: [ Help ]

Modulation code Cosine coefficient Sine coefficient
Nb1x1 0 -0.00164(3)
Nb1y1 0 -0.00164(3)
Nb1z1 -0.00030(6) 0
Nb1x2 0 0.00116(3)
Nb1y2 0 -0.00116(3)
Nb1z2 -0.00026(6) 0
Nb2x1 -0.00154(2) -0.00082(2)
Nb2y1 0.00056(2) 0.00106(2)
Nb2z1 -0.00036(3) -0.00061(3)
Nb2x2 0.00136(2) -0.00106(2)
Nb2y2 -0.00041(2) 0.00051(2)
Nb2z2 0.00055(3) -0.00070(3)
Sr1x1 0 0.00026(3)
Sr1y1 0 0.00047(3)
Sr1z1 -0.00022(7) 0
Sr1x2 0 0.00047(3)
Sr1y2 0 -0.00026(3)
Sr1z2 -0.00022(7) 0
O1x1 -0.00196(19) -0.00126(19)
O1y1 -0.00055(19) 0.00210(19)
O1z1 0.0077(3) 0.0249(3)
O1x2 0.00045(18) -0.00015(19)
O1y2 0.00145(18) -0.00329(18)
O1z2 -0.0085(3) -0.0314(3)
O2x1 -0.00120(18) -0.00078(18)
O2y1 0.00011(18) -0.00053(18)
O2z1 0.0139(3) 0.0212(3)
O2x2 0.00272(18) 0.00174(18)
O2y2 0.00121(18) -0.00084(18)
O2z2 -0.0218(3) 0.0090(3)
O3x1 0.00057(17) 0.00102(18)
O3y1 0.00057(17) 0.00102(18)
O3z1 -0.0168(4) -0.0108(3)
O3x2 -0.00017(17) 0.00180(18)
O3y2 -0.00017(17) -0.00180(18)
O3z2 0.0172(4) 0
O4x1 0 -0.0178(3)
O4y1 0 -0.0178(3)
O4z1 0.0048(8) 0
O4x2 0 0.0124(3)
O4y2 0 -0.0124(3)
O4z2 0.0060(8) 0
O5x1 -0.00283(16) 0.01273(16)
O5y1 0.01675(19) -0.0082(2)
O5z1 -0.0010(3) 0.0020(4)
O5x2 0.00482(16) -0.00632(17)
O5y2 -0.01620(19) 0.01583(19)
O5z2 -0.0003(3) 0.0025(4)
Bax1 0.00108(2) 0.00140(2)
Bay1 0.00108(2) 0.00140(2)
Baz1 0.00343(7) -0.00242(7)
Bax2 -0.00195(2) 0.00694(4)
Bay2 -0.00195(2) -0.00694(4)
Baz2 -0.00037(7) 0
Sr2x1 0.00108(2) 0.00140(2)
Sr2y1 0.00108(2) 0.00140(2)
Sr2z1 0.00343(7) -0.00242(7)
Sr2x2 -0.00195(2) 0.00694(4)
Sr2y2 -0.00195(2) -0.00694(4)
Sr2z2 -0.00037(7) 0
Na1x1 0 0.00026(3)
Na1y1 0 0.00047(3)
Na1z1 -0.00022(7) 0
Na1x2 0 0.00047(3)
Na1y2 0 -0.00026(3)
Na1z2 -0.00022(7) 0
Kx1 0.00108(2) 0.00140(2)
Ky1 0.00108(2) 0.00140(2)
Kz1 0.00343(7) -0.00242(7)
Kx2 -0.00195(2) 0.00694(4)
Ky2 -0.00195(2) -0.00694(4)
Kz2 -0.00037(7) 0

Definition of the ADP Fourier series: [ Help ]

Modulation code Atom site label Tensor element Wave vector code
BaU111 Ba U11 1
BaU221 Ba U22 1
BaU331 Ba U33 1
BaU121 Ba U12 1
BaU131 Ba U13 1
BaU231 Ba U23 1
BaU112 Ba U11 2
BaU222 Ba U22 2
BaU332 Ba U33 2
BaU122 Ba U12 2
BaU132 Ba U13 2
BaU232 Ba 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
KU111 K U11 1
KU221 K U22 1
KU331 K U33 1
KU121 K U12 1
KU131 K U13 1
KU231 K U23 1
KU112 K U11 2
KU222 K U22 2
KU332 K U33 2
KU122 K U12 2
KU132 K U13 2
KU232 K U23 2

ADP Fourier coefficients: [ Help ]

Modulation code Cosine coefficient Sine coefficient
BaU111 -0.00890(14) -0.01454(16)
BaU221 -0.00890(14) -0.01454(16)
BaU331 -0.0019(2) -0.0014(2)
BaU121 0.00600(17) 0.01362(19)
BaU131 0.00063(12) -0.00077(12)
BaU231 0.00063(12) -0.00077(12)
BaU112 0.01438(15) -0.01199(16)
BaU222 0.01438(15) 0.01199(16)
BaU332 0.0034(2) 0
BaU122 -0.01290(19) 0
BaU132 0.00021(13) 0.00068(18)
BaU232 0.00021(13) -0.00068(18)
Sr2U111 -0.00890(14) -0.01454(16)
Sr2U221 -0.00890(14) -0.01454(16)
Sr2U331 -0.0019(2) -0.0014(2)
Sr2U121 0.00600(17) 0.01362(19)
Sr2U131 0.00063(12) -0.00077(12)
Sr2U231 0.00063(12) -0.00077(12)
Sr2U112 0.01438(15) -0.01199(16)
Sr2U222 0.01438(15) 0.01199(16)
Sr2U332 0.0034(2) 0
Sr2U122 -0.01290(19) 0
Sr2U132 0.00021(13) 0.00068(18)
Sr2U232 0.00021(13) -0.00068(18)
KU111 -0.00890(14) -0.01454(16)
KU221 -0.00890(14) -0.01454(16)
KU331 -0.0019(2) -0.0014(2)
KU121 0.00600(17) 0.01362(19)
KU131 0.00063(12) -0.00077(12)
KU231 0.00063(12) -0.00077(12)
KU112 0.01438(15) -0.01199(16)
KU222 0.01438(15) 0.01199(16)
KU332 0.0034(2) 0
KU122 -0.01290(19) 0
KU132 0.00021(13) 0.00068(18)
KU232 0.00021(13) -0.00068(18)