B-IncStrDB

Unusual Strong Incommensurate Modulation in a Tungsten-Bronze-Type Relaxor PbBiNb₅O₁₅

Authors:

Lin, Kun; Zhou, Zhengyang; Liu, Laijun; Ma, Hongqiang; Chen, Jun; Deng, Jinxia; Sun, Junliang; You, Li; Kasai, Hidetaka; Kato, Kenichi; Takata, Masaki; Xing, Xianran

Journal:

Journal of the American Chemical Society 137 13468-13471 (2015)

DOI:

https://dx.doi.org/10.1021/jacs.5b08230

B-IncStrDB ID: K8a2NnIcvUG Entry date: 2021-12-21 Last revision: 2022-02-12

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Chemical data

Structural Formula Sum: Bi1 Nb5 O15 Pb1 [ Help ]

Formula weight: 1120.7 Da [ Help ]

Crystallographic data and experimental details

Crystal system: orthorhombic [ Help ]

Superspace group name: Xm2m(α00)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+1/2,x2+1/2,x3,x4
6	x1+1/2,x2+1/2,-x3,x4
7	-x1+1/2,x2+1/2,x3,-x4
8	-x1+1/2,x2+1/2,-x3,-x4
9	x1,x2,x3+1/2,x4+1/2
10	x1,x2,-x3+1/2,x4+1/2
11	-x1,x2,x3+1/2,-x4+1/2
12	-x1,x2,-x3+1/2,-x4+1/2
13	x1+1/2,x2+1/2,x3+1/2,x4+1/2
14	x1+1/2,x2+1/2,-x3+1/2,x4+1/2
15	-x1+1/2,x2+1/2,x3+1/2,-x4+1/2
16	-x1+1/2,x2+1/2,-x3+1/2,-x4+1/2

a: 17.65852(10) Å [ Help ]

b: 17.67709(10) Å [ Help ]

c: 7.75289(3) Å [ Help ]

α: 90 ° [ Help ]

β: 90 ° [ Help ]

γ: 90 ° [ Help ]

Volume: 2420.07(2) Å³ [ Help ]

Modulation dimension: 1 [ Help ]

Measured independent wave vectors: (Show/hide table) [ Help ]

Wave vector id	q_x	q_y	q_z
1	0.612154	0.000000	0.000000

Z: 8 [ Help ]

Cell measurement temperature: 300 K [ Help ]

μ: 36.619 mm^-1 [ Help ]

Refinement details

R(obs): 0.0386 [ Help ]

wR(obs): 0.0496 [ Help ]

R(all): 0.0402 [ Help ]

wR(all): 0.0502 [ Help ]

S(all): 3.47 [ Help ]

Nb. of parameters: 252 [ Help ]

Number of restraints: 29 [ Help ]

Number of constraints: 39 [ Help ]

Weighting scheme: sigma [ Help ]

Δ/σ(max): 0.0498 [ Help ]

Δ/σ(mean): 0.0053 [ Help ]

Δρ(max): 1.99 e_Å^-3 [ Help ]

Δρ(min): -2.07 e_Å^-3 [ 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
Nb1	Nb	-0.5	0.4858(8)	0.25	Uani	0.0277(9)	4	1	d	.	.	.
Nb3	Nb	-0.3192(4)	0.3826(7)	0.25	Uani	0.0278(4)	8	1	d	.	.	.
Nb5	Nb	-0.1073(4)	0.6715(8)	-0.25	Uani	0.0278(4)	8	1	d	.	.	.
Nb6	Nb	-0.3904(4)	-0.1923(8)	0.25	Uani	0.0278(4)	8	1	d	.	.	.
O1	O	0.5	-0.020(3)	0.5	Uiso	0.053(4)	4	1	d	.	.	.
O2	O	-0.5	0.4714(8)	0.5	Uiso	0.053(4)	4	1	d	.	.	.
O3	O	-0.5	-0.228(5)	0.25	Uiso	0.053(4)	4	1	d	.	.	.
O4	O	0	0.710(5)	-0.25	Uiso	0.053(4)	4	1	d	.	.	.
O5	O	0.7839(13)	-0.009(4)	0.25	Uiso	0.0513(13)	8	1	d	.	.	.
O6	O	-0.3335(5)	0.380(2)	0	Uiso	0.0513(13)	8	1	d	.	.	.
O7	O	0.808(2)	0.107(2)	0	Uiso	0.0513(13)	8	1	d	.	.	.
O8	O	-0.104(2)	0.6623(17)	-0.5	Uiso	0.0513(13)	8	1	d	.	.	.
O9	O	-0.390(2)	-0.2103(19)	0	Uiso	0.0513(13)	8	1	d	.	.	.
O10	O	0.415(3)	-0.088(3)	0.25	Uiso	0.0513(13)	8	1	d	.	.	.
O11	O	0.420(3)	0.067(3)	0.25	Uiso	0.0513(13)	8	1	d	.	.	.
O12	O	-0.418(3)	0.414(3)	0.25	Uiso	0.0513(13)	8	1	d	.	.	.
O13	O	-0.574(3)	0.571(3)	0.25	Uiso	0.0513(13)	8	1	d	.	.	.
O14	O	-0.290(3)	-0.148(3)	0.25	Uiso	0.0513(13)	8	1	d	.	.	.
O15	O	0.713(3)	0.135(3)	0.25	Uiso	0.0513(13)	8	1	d	.	.	.
O17	O	0.849(3)	0.206(3)	0.25	Uiso	0.0513(13)	8	1	d	.	.	.
Bi1	Bi	-0.2522(6)	0.2465(8)	0	Uiso	0.0416(12)	8	0.380(18)	d	.	.	.
Pb1	Pb	-0.1673(7)	0.4634(11)	0	Uiso	0.0365(11)	8	0.36(2)	d	.	.	.
Pb2	Pb	-0.3356(13)	0.0241(12)	0	Uiso	0.0365(11)	8	0.229(17)	d	.	.	.
Pb3	Pb	-0.0203(9)	0.8315(9)	0	Uiso	0.0365(11)	8	0.310(10)	d	.	.	.
Nb2	Nb	0.5	-0.0089(9)	0.25	Uani	0.0277(9)	4	1	d	.	.	.
Nb4	Nb	0.8181(4)	0.0993(7)	0.25	Uani	0.0278(4)	8	1	d	.	.	.
Bi2	Bi	0	0.1315(19)	0	Uiso	0.0416(12)	4	0.22(2)	d	.	.	.
O16	O	-0.145(3)	0.777(3)	-0.25	Uiso	0.0513(13)	8	1	d	.	.	.
Bi4	Bi	-0.4715(10)	-0.3248(12)	0	Uiso	0.0416(12)	8	0.268(12)	d	.	.	.
Pb4	Pb	0.5	0.293(2)	0	Uiso	0.0365(11)	4	0.21(2)	d	.	.	.
Bi3	Bi	0.1908(14)	0.493(2)	0	Uiso	0.0416(12)	8	0.242(5)	d	.	.	.

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

Atom site label	Atom site symbol	U11	U22	U33	U12
Nb1	Nb	0.0337(17)	0.0154(17)	0.0340(9)	0
Nb3	Nb	0.0299(8)	0.0232(7)	0.0303(4)	0.0007(5)
Nb5	Nb	0.0299(8)	0.0232(7)	0.0303(4)	0.0007(5)
Nb6	Nb	0.0299(8)	0.0232(7)	0.0303(4)	0.0007(5)
Nb2	Nb	0.0337(17)	0.0154(17)	0.0340(9)	0
Nb4	Nb	0.0299(8)	0.0232(7)	0.0303(4)	0.0007(5)

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

Table: (Show/hide table) [ Help ]

_jana_atom_site_occ_Fourier_absolute_site_label	_jana_atom_site_occ_Fourier_absolute
Bi1	0.380(18)
Pb1	0.36(2)
Pb2	0.229(17)
Pb3	0.310(10)
Bi2	0.22(2)
Bi4	0.268(12)
Pb4	0.21(2)
Bi3	0.242(5)

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

Modulation code	Atom site label	Wave vector code
Bi1o1	Bi1	1
Pb1o1	Pb1	1
Pb2o1	Pb2	1
Pb3o1	Pb3	1
Bi2o1	Bi2	1
Bi4o1	Bi4	1
Pb4o1	Pb4	1
Bi3o1	Bi3	1

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

Modulation code	Cosine coefficient	Sine coefficient
Bi1o1	-0.061(7)	-0.015(11)
Pb1o1	-0.05(3)	-0.19(2)
Pb2o1	0.01(3)	-0.01(3)
Pb3o1	0.053(15)	0.08(3)
Bi2o1	-0.08(3)	0
Bi4o1	0.024(15)	-0.111(19)
Pb4o1	-0.06(3)	0
Bi3o1	0.02(4)	-0.08(3)

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

Modulation code	Atom site label	Displacement axis	Wave vector code
Nb1x1	Nb1	x	1
Nb1y1	Nb1	y	1
Nb1z1	Nb1	z	1
Nb3x1	Nb3	x	1
Nb3y1	Nb3	y	1
Nb3z1	Nb3	z	1
Nb5x1	Nb5	x	1
Nb5y1	Nb5	y	1
Nb5z1	Nb5	z	1
Nb6x1	Nb6	x	1
Nb6y1	Nb6	y	1
Nb6z1	Nb6	z	1
O1x1	O1	x	1
O1y1	O1	y	1
O1z1	O1	z	1
O2x1	O2	x	1
O2y1	O2	y	1
O2z1	O2	z	1
O3x1	O3	x	1
O3y1	O3	y	1
O3z1	O3	z	1
O4x1	O4	x	1
O4y1	O4	y	1
O4z1	O4	z	1
O5x1	O5	x	1
O5y1	O5	y	1
O5z1	O5	z	1
O6x1	O6	x	1
O6y1	O6	y	1
O6z1	O6	z	1
O7x1	O7	x	1
O7y1	O7	y	1
O7z1	O7	z	1
O8x1	O8	x	1
O8y1	O8	y	1
O8z1	O8	z	1
O9x1	O9	x	1
O9y1	O9	y	1
O9z1	O9	z	1
O10x1	O10	x	1
O10y1	O10	y	1
O10z1	O10	z	1
O11x1	O11	x	1
O11y1	O11	y	1
O11z1	O11	z	1
O12x1	O12	x	1
O12y1	O12	y	1
O12z1	O12	z	1
O13x1	O13	x	1
O13y1	O13	y	1
O13z1	O13	z	1
O14x1	O14	x	1
O14y1	O14	y	1
O14z1	O14	z	1
O15x1	O15	x	1
O15y1	O15	y	1
O15z1	O15	z	1
O17x1	O17	x	1
O17y1	O17	y	1
O17z1	O17	z	1
Bi1x1	Bi1	x	1
Bi1y1	Bi1	y	1
Bi1z1	Bi1	z	1
Pb1x1	Pb1	x	1
Pb1y1	Pb1	y	1
Pb1z1	Pb1	z	1
Pb2x1	Pb2	x	1
Pb2y1	Pb2	y	1
Pb2z1	Pb2	z	1
Pb3x1	Pb3	x	1
Pb3y1	Pb3	y	1
Pb3z1	Pb3	z	1
Nb2x1	Nb2	x	1
Nb2y1	Nb2	y	1
Nb2z1	Nb2	z	1
Nb4x1	Nb4	x	1
Nb4y1	Nb4	y	1
Nb4z1	Nb4	z	1
Bi2x1	Bi2	x	1
Bi2y1	Bi2	y	1
Bi2z1	Bi2	z	1
O16x1	O16	x	1
O16y1	O16	y	1
O16z1	O16	z	1
Bi4x1	Bi4	x	1
Bi4y1	Bi4	y	1
Bi4z1	Bi4	z	1
Pb4x1	Pb4	x	1
Pb4y1	Pb4	y	1
Pb4z1	Pb4	z	1
Bi3x1	Bi3	x	1
Bi3y1	Bi3	y	1
Bi3z1	Bi3	z	1

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

Modulation code	Cosine coefficient	Sine coefficient
Nb1x1	0	0
Nb1y1	0	0
Nb1z1	0.0054(14)	0
Nb3x1	0	0
Nb3y1	0	0
Nb3z1	-0.0009(13)	0.0031(12)
Nb5x1	0	0
Nb5y1	0	0
Nb5z1	0.0043(8)	0.0006(9)
Nb6x1	0	0
Nb6y1	0	0
Nb6z1	0.0025(10)	-0.0057(8)
O1x1	0	0.0198(9)
O1y1	0.0011(10)	0
O1z1	0	0
O2x1	0	-0.0041(8)
O2y1	0.0006(10)	0
O2z1	0	0
O3x1	0	0
O3y1	0	0
O3z1	-0.006(2)	0
O4x1	0	0
O4y1	0	0
O4z1	0.009(3)	0
O5x1	0	0
O5y1	0	0
O5z1	0.027(2)	0.005(3)
O6x1	0.0031(9)	-0.0037(10)
O6y1	0.0111(16)	-0.0021(17)
O6z1	0	0
O7x1	-0.0155(10)	-0.0010(11)
O7y1	-0.0076(10)	-0.0031(11)
O7z1	0	0
O8x1	0.0080(8)	0.0067(10)
O8y1	0.0065(9)	0.0060(8)
O8z1	0	0
O9x1	0.0042(7)	0.0002(5)
O9y1	-0.0017(11)	-0.0044(12)
O9z1	0	0
O10x1	0	0
O10y1	0	0
O10z1	0.0092(18)	0.0337(16)
O11x1	0	0
O11y1	0	0
O11z1	0.0039(19)	0.0331(16)
O12x1	0	0
O12y1	0	0
O12z1	0.0033(15)	0.0083(13)
O13x1	0	0
O13y1	0	0
O13z1	-0.006(3)	-0.031(3)
O14x1	0	0
O14y1	0	0
O14z1	0.0128(18)	-0.0051(18)
O15x1	0	0
O15y1	0	0
O15z1	0.024(2)	-0.010(2)
O17x1	0	0
O17y1	0	0
O17z1	0.008(2)	-0.006(3)
Bi1x1	0.0109(7)	0.0057(7)
Bi1y1	-0.0108(8)	0.0052(7)
Bi1z1	0	0
Pb1x1	0.0059(14)	-0.0017(13)
Pb1y1	0.000(2)	-0.0219(13)
Pb1z1	0	0
Pb2x1	0.013(3)	0.0263(19)
Pb2y1	-0.008(3)	-0.006(2)
Pb2z1	0	0
Pb3x1	-0.0062(14)	0.015(2)
Pb3y1	0.0020(12)	0.0059(15)
Pb3z1	0	0
Nb2x1	0	0
Nb2y1	0	0
Nb2z1	-0.0042(8)	0
Nb4x1	0	0
Nb4y1	0	0
Nb4z1	-0.0022(7)	-0.0004(9)
Bi2x1	0	0.037(3)
Bi2y1	-0.017(3)	0
Bi2z1	0	0
O16x1	0	0
O16y1	0	0
O16z1	0.0140(19)	0.007(2)
Bi4x1	0.0017(13)	0.0154(18)
Bi4y1	-0.0081(15)	-0.011(2)
Bi4z1	0	0
Pb4x1	0	-0.007(3)
Pb4y1	0.020(3)	0
Pb4z1	0	0
Bi3x1	0.022(3)	0.019(3)
Bi3y1	-0.006(3)	-0.003(3)
Bi3z1	0	0

ADSPD

Chemical data

Structural Formula Sum: Bi1 Nb5 O15 Pb1 [ Help ]

Formula weight: 1120.7 Da [ Help ]

Crystallographic data and experimental details

Crystal system: orthorhombic [ Help ]

Superspace group name: Xm2m(α00)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+1/2,x2+1/2,x3,x4
6	x1+1/2,x2+1/2,-x3,x4
7	-x1+1/2,x2+1/2,x3,-x4
8	-x1+1/2,x2+1/2,-x3,-x4
9	x1,x2,x3+1/2,x4+1/2
10	x1,x2,-x3+1/2,x4+1/2
11	-x1,x2,x3+1/2,-x4+1/2
12	-x1,x2,-x3+1/2,-x4+1/2
13	x1+1/2,x2+1/2,x3+1/2,x4+1/2
14	x1+1/2,x2+1/2,-x3+1/2,x4+1/2
15	-x1+1/2,x2+1/2,x3+1/2,-x4+1/2
16	-x1+1/2,x2+1/2,-x3+1/2,-x4+1/2

a: 17.65852(10) Å [ Help ]

b: 17.67709(10) Å [ Help ]

c: 7.75289(3) Å [ Help ]

α: 90 ° [ Help ]

β: 90 ° [ Help ]

γ: 90 ° [ Help ]

Volume: 2420.07(2) Å³ [ Help ]

Modulation dimension: 1 [ Help ]

Measured independent wave vectors: (Show/hide table) [ Help ]

Wave vector id	q_x	q_y	q_z
1	0.612154	0.000000	0.000000

Z: 8 [ Help ]

Cell measurement temperature: 300 K [ Help ]

μ: 32.674 mm^-1 [ Help ]

Refinement details

R(obs): 0.0578 [ Help ]

wR(obs): 0.0629 [ Help ]

R(all): 0.0724 [ Help ]

wR(all): 0.0656 [ Help ]

S(all): 3.04 [ Help ]

Nb. of parameters: 252 [ Help ]

Number of restraints: 29 [ Help ]

Number of constraints: 39 [ Help ]

Weighting scheme: sigma [ Help ]

Δ/σ(max): 0.0498 [ Help ]

Δ/σ(mean): 0.0053 [ Help ]

Δρ(max): 1.99 e_Å^-3 [ Help ]

Δρ(min): -2.07 e_Å^-3 [ 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
Nb1	Nb	-0.5	0.4858(8)	0.25	Uani	0.0277(9)	4	1	d	.	.	.
Nb3	Nb	-0.3192(4)	0.3826(7)	0.25	Uani	0.0278(4)	8	1	d	.	.	.
Nb5	Nb	-0.1073(4)	0.6715(8)	-0.25	Uani	0.0278(4)	8	1	d	.	.	.
Nb6	Nb	-0.3904(4)	-0.1923(8)	0.25	Uani	0.0278(4)	8	1	d	.	.	.
O1	O	0.5	-0.020(3)	0.5	Uiso	0.053(4)	4	1	d	.	.	.
O2	O	-0.5	0.4714(8)	0.5	Uiso	0.053(4)	4	1	d	.	.	.
O3	O	-0.5	-0.228(5)	0.25	Uiso	0.053(4)	4	1	d	.	.	.
O4	O	0	0.710(5)	-0.25	Uiso	0.053(4)	4	1	d	.	.	.
O5	O	0.7839(13)	-0.009(4)	0.25	Uiso	0.0513(13)	8	1	d	.	.	.
O6	O	-0.3335(5)	0.380(2)	0	Uiso	0.0513(13)	8	1	d	.	.	.
O7	O	0.808(2)	0.107(2)	0	Uiso	0.0513(13)	8	1	d	.	.	.
O8	O	-0.104(2)	0.6623(17)	-0.5	Uiso	0.0513(13)	8	1	d	.	.	.
O9	O	-0.390(2)	-0.2103(19)	0	Uiso	0.0513(13)	8	1	d	.	.	.
O10	O	0.415(3)	-0.088(3)	0.25	Uiso	0.0513(13)	8	1	d	.	.	.
O11	O	0.420(3)	0.067(3)	0.25	Uiso	0.0513(13)	8	1	d	.	.	.
O12	O	-0.418(3)	0.414(3)	0.25	Uiso	0.0513(13)	8	1	d	.	.	.
O13	O	-0.574(3)	0.571(3)	0.25	Uiso	0.0513(13)	8	1	d	.	.	.
O14	O	-0.290(3)	-0.148(3)	0.25	Uiso	0.0513(13)	8	1	d	.	.	.
O15	O	0.713(3)	0.135(3)	0.25	Uiso	0.0513(13)	8	1	d	.	.	.
O17	O	0.849(3)	0.206(3)	0.25	Uiso	0.0513(13)	8	1	d	.	.	.
Bi1	Bi	-0.2522(6)	0.2465(8)	0	Uiso	0.0416(12)	8	0.380(18)	d	.	.	.
Pb1	Pb	-0.1673(7)	0.4634(11)	0	Uiso	0.0365(11)	8	0.36(2)	d	.	.	.
Pb2	Pb	-0.3356(13)	0.0241(12)	0	Uiso	0.0365(11)	8	0.229(17)	d	.	.	.
Pb3	Pb	-0.0203(9)	0.8315(9)	0	Uiso	0.0365(11)	8	0.310(10)	d	.	.	.
Nb2	Nb	0.5	-0.0089(9)	0.25	Uani	0.0277(9)	4	1	d	.	.	.
Nb4	Nb	0.8181(4)	0.0993(7)	0.25	Uani	0.0278(4)	8	1	d	.	.	.
Bi2	Bi	0	0.1315(19)	0	Uiso	0.0416(12)	4	0.22(2)	d	.	.	.
O16	O	-0.145(3)	0.777(3)	-0.25	Uiso	0.0513(13)	8	1	d	.	.	.
Bi4	Bi	-0.4715(10)	-0.3248(12)	0	Uiso	0.0416(12)	8	0.268(12)	d	.	.	.
Pb4	Pb	0.5	0.293(2)	0	Uiso	0.0365(11)	4	0.21(2)	d	.	.	.
Bi3	Bi	0.1908(14)	0.493(2)	0	Uiso	0.0416(12)	8	0.242(5)	d	.	.	.

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

Atom site label	Atom site symbol	U11	U22	U33	U12
Nb1	Nb	0.0337(17)	0.0154(17)	0.0340(9)	0
Nb3	Nb	0.0299(8)	0.0232(7)	0.0303(4)	0.0007(5)
Nb5	Nb	0.0299(8)	0.0232(7)	0.0303(4)	0.0007(5)
Nb6	Nb	0.0299(8)	0.0232(7)	0.0303(4)	0.0007(5)
Nb2	Nb	0.0337(17)	0.0154(17)	0.0340(9)	0
Nb4	Nb	0.0299(8)	0.0232(7)	0.0303(4)	0.0007(5)

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

Table: (Show/hide table) [ Help ]

_jana_atom_site_occ_Fourier_absolute_site_label	_jana_atom_site_occ_Fourier_absolute
Bi1	0.380(18)
Pb1	0.36(2)
Pb2	0.229(17)
Pb3	0.310(10)
Bi2	0.22(2)
Bi4	0.268(12)
Pb4	0.21(2)
Bi3	0.242(5)

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

Modulation code	Atom site label	Wave vector code
Bi1o1	Bi1	1
Pb1o1	Pb1	1
Pb2o1	Pb2	1
Pb3o1	Pb3	1
Bi2o1	Bi2	1
Bi4o1	Bi4	1
Pb4o1	Pb4	1
Bi3o1	Bi3	1

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

Modulation code	Cosine coefficient	Sine coefficient
Bi1o1	-0.061(7)	-0.015(11)
Pb1o1	-0.05(3)	-0.19(2)
Pb2o1	0.01(3)	-0.01(3)
Pb3o1	0.053(15)	0.08(3)
Bi2o1	-0.08(3)	0
Bi4o1	0.024(15)	-0.111(19)
Pb4o1	-0.06(3)	0
Bi3o1	0.02(4)	-0.08(3)

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

Modulation code	Atom site label	Displacement axis	Wave vector code
Nb1x1	Nb1	x	1
Nb1y1	Nb1	y	1
Nb1z1	Nb1	z	1
Nb3x1	Nb3	x	1
Nb3y1	Nb3	y	1
Nb3z1	Nb3	z	1
Nb5x1	Nb5	x	1
Nb5y1	Nb5	y	1
Nb5z1	Nb5	z	1
Nb6x1	Nb6	x	1
Nb6y1	Nb6	y	1
Nb6z1	Nb6	z	1
O1x1	O1	x	1
O1y1	O1	y	1
O1z1	O1	z	1
O2x1	O2	x	1
O2y1	O2	y	1
O2z1	O2	z	1
O3x1	O3	x	1
O3y1	O3	y	1
O3z1	O3	z	1
O4x1	O4	x	1
O4y1	O4	y	1
O4z1	O4	z	1
O5x1	O5	x	1
O5y1	O5	y	1
O5z1	O5	z	1
O6x1	O6	x	1
O6y1	O6	y	1
O6z1	O6	z	1
O7x1	O7	x	1
O7y1	O7	y	1
O7z1	O7	z	1
O8x1	O8	x	1
O8y1	O8	y	1
O8z1	O8	z	1
O9x1	O9	x	1
O9y1	O9	y	1
O9z1	O9	z	1
O10x1	O10	x	1
O10y1	O10	y	1
O10z1	O10	z	1
O11x1	O11	x	1
O11y1	O11	y	1
O11z1	O11	z	1
O12x1	O12	x	1
O12y1	O12	y	1
O12z1	O12	z	1
O13x1	O13	x	1
O13y1	O13	y	1
O13z1	O13	z	1
O14x1	O14	x	1
O14y1	O14	y	1
O14z1	O14	z	1
O15x1	O15	x	1
O15y1	O15	y	1
O15z1	O15	z	1
O17x1	O17	x	1
O17y1	O17	y	1
O17z1	O17	z	1
Bi1x1	Bi1	x	1
Bi1y1	Bi1	y	1
Bi1z1	Bi1	z	1
Pb1x1	Pb1	x	1
Pb1y1	Pb1	y	1
Pb1z1	Pb1	z	1
Pb2x1	Pb2	x	1
Pb2y1	Pb2	y	1
Pb2z1	Pb2	z	1
Pb3x1	Pb3	x	1
Pb3y1	Pb3	y	1
Pb3z1	Pb3	z	1
Nb2x1	Nb2	x	1
Nb2y1	Nb2	y	1
Nb2z1	Nb2	z	1
Nb4x1	Nb4	x	1
Nb4y1	Nb4	y	1
Nb4z1	Nb4	z	1
Bi2x1	Bi2	x	1
Bi2y1	Bi2	y	1
Bi2z1	Bi2	z	1
O16x1	O16	x	1
O16y1	O16	y	1
O16z1	O16	z	1
Bi4x1	Bi4	x	1
Bi4y1	Bi4	y	1
Bi4z1	Bi4	z	1
Pb4x1	Pb4	x	1
Pb4y1	Pb4	y	1
Pb4z1	Pb4	z	1
Bi3x1	Bi3	x	1
Bi3y1	Bi3	y	1
Bi3z1	Bi3	z	1

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

Modulation code	Cosine coefficient	Sine coefficient
Nb1x1	0	0
Nb1y1	0	0
Nb1z1	0.0054(14)	0
Nb3x1	0	0
Nb3y1	0	0
Nb3z1	-0.0009(13)	0.0031(12)
Nb5x1	0	0
Nb5y1	0	0
Nb5z1	0.0043(8)	0.0006(9)
Nb6x1	0	0
Nb6y1	0	0
Nb6z1	0.0025(10)	-0.0057(8)
O1x1	0	0.0198(9)
O1y1	0.0011(10)	0
O1z1	0	0
O2x1	0	-0.0041(8)
O2y1	0.0006(10)	0
O2z1	0	0
O3x1	0	0
O3y1	0	0
O3z1	-0.006(2)	0
O4x1	0	0
O4y1	0	0
O4z1	0.009(3)	0
O5x1	0	0
O5y1	0	0
O5z1	0.027(2)	0.005(3)
O6x1	0.0031(9)	-0.0037(10)
O6y1	0.0111(16)	-0.0021(17)
O6z1	0	0
O7x1	-0.0155(10)	-0.0010(11)
O7y1	-0.0076(10)	-0.0031(11)
O7z1	0	0
O8x1	0.0080(8)	0.0067(10)
O8y1	0.0065(9)	0.0060(8)
O8z1	0	0
O9x1	0.0042(7)	0.0002(5)
O9y1	-0.0017(11)	-0.0044(12)
O9z1	0	0
O10x1	0	0
O10y1	0	0
O10z1	0.0092(18)	0.0337(16)
O11x1	0	0
O11y1	0	0
O11z1	0.0039(19)	0.0331(16)
O12x1	0	0
O12y1	0	0
O12z1	0.0033(15)	0.0083(13)
O13x1	0	0
O13y1	0	0
O13z1	-0.006(3)	-0.031(3)
O14x1	0	0
O14y1	0	0
O14z1	0.0128(18)	-0.0051(18)
O15x1	0	0
O15y1	0	0
O15z1	0.024(2)	-0.010(2)
O17x1	0	0
O17y1	0	0
O17z1	0.008(2)	-0.006(3)
Bi1x1	0.0109(7)	0.0057(7)
Bi1y1	-0.0108(8)	0.0052(7)
Bi1z1	0	0
Pb1x1	0.0059(14)	-0.0017(13)
Pb1y1	0.000(2)	-0.0219(13)
Pb1z1	0	0
Pb2x1	0.013(3)	0.0263(19)
Pb2y1	-0.008(3)	-0.006(2)
Pb2z1	0	0
Pb3x1	-0.0062(14)	0.015(2)
Pb3y1	0.0020(12)	0.0059(15)
Pb3z1	0	0
Nb2x1	0	0
Nb2y1	0	0
Nb2z1	-0.0042(8)	0
Nb4x1	0	0
Nb4y1	0	0
Nb4z1	-0.0022(7)	-0.0004(9)
Bi2x1	0	0.037(3)
Bi2y1	-0.017(3)	0
Bi2z1	0	0
O16x1	0	0
O16y1	0	0
O16z1	0.0140(19)	0.007(2)
Bi4x1	0.0017(13)	0.0154(18)
Bi4y1	-0.0081(15)	-0.011(2)
Bi4z1	0	0
Pb4x1	0	-0.007(3)
Pb4y1	0.020(3)	0
Pb4z1	0	0
Bi3x1	0.022(3)	0.019(3)
Bi3y1	-0.006(3)	-0.003(3)
Bi3z1	0	0

Unusual Strong Incommensurate Modulation in a Tungsten-Bronze-Type Relaxor PbBiNb5O15

Lin, Kun; Zhou, Zhengyang; Liu, Laijun; Ma, Hongqiang; Chen, Jun; Deng, Jinxia; Sun, Junliang; You, Li; Kasai, Hidetaka; Kato, Kenichi; Takata, Masaki; Xing, Xianran

Journal of the American Chemical Society 137 13468-13471 (2015)

https://dx.doi.org/10.1021/jacs.5b08230

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Unusual Strong Incommensurate Modulation in a Tungsten-Bronze-Type Relaxor PbBiNb₅O₁₅