B-IncStrDB

The structure refinement of compositely modulated Nb₂Zr_x-2O_2x+1 (x=12)

Authors:

Futterer, Klaus.; Schmid, Siegbert.; Thompson, John G.; Withers, Ray L.; Ishizawa, Nobuo; Kishimoto, Shunji

Journal:

Acta Crystallographica section B 51 688-697 (1995)

DOI:

https://doi.org/10.1107/S010876819401431X

B-IncStrDB ID: 2612EhisgU Entry date: 2010-11-08 Last revision: 2021-12-30

Download CIF

Open in JSmol

zrf.B

Chemical data

Structural Formula Sum: Nb2 Zr10 O25 [ Help ]

Crystallographic data and experimental details

a: 5.108(1) Å [ Help ]

b: 4.997(1) Å [ Help ]

c: 5.278(1) Å [ Help ]

α: 90 ° [ Help ]

β: 90 ° [ Help ]

γ: 90 ° [ Help ]

Number of subsystems: 2 [ Help ]

Modulation dimension: 1 [ Help ]

Subsystem code: 1 [ Help ]

Subsystem description: Metal subsytem [ Help ]

W matrix:

1.0	0.0	0.0	0.0
0.0	1.0	0.0	0.0
0.0	0.0	1.0	0.0
0.0	0.0	0.0	1.0

Subsystem code: 2 [ Help ]

Subsystem description: Oxygen subsystem [ Help ]

W matrix:

2.0	-1.0	0.0	1.0
0.0	1.0	0.0	0.0
0.0	0.0	1.0	0.0
1.0	0.0	0.0	0.0

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

Wave vector id	q_x	q_y	q_z
1	0.08333	1	0

Superspace group name: Amma(α10)0s0 [ Help ]

Symmetry operations of the superspace group: (Show/hide table) [ Help ]

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

Refinement details

Refinement remarks: Fourier amplitudes transformed to the CIF standard. Please, see the article. [ Help ]

Structural Information

Average Structure: (Show/hide table) [ Help ]

Atom site label	Atom symbol	Subsystem	Occupancy	Symmetry multiplicity	x	y	z	Uiso/equiv	ADP type
Zr	Zr	1	0.833	4	0.25	0	0.2160(2)	?	Uani
Nb	Nb	1	0.167	4	0.25	0	0.2160(2)	?	Uani
O	O	2	1	16	0.25	0.2696(6)	0.5	?	Uani

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

Atom site label	U11	U22	U33
Zr	0.0095(2)	0.0090(2)	0.0066(4)
Nb	0.0095(2)	0.0090(2)	0.0066(4)
O	0.017(2)	0.022(2)	0.025(2)

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

Wave vector code	q_x	q_y
1	0.08333	1
2	0.16667	2
3	0.25	3
4	0.33333	4

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

Modulation code	Atom site label	Displacement axis	Wave vector code
Zrx2	Zr	x	2
Zrx4	Zr	x	4
Zry1	Zr	y	1
Zry3	Zr	y	3
Zrz2	Zr	z	2
Zrz4	Zr	z	4
Nbx2	Nb	x	2
Nbx4	Nb	x	4
Nby1	Nb	y	1
Nby3	Nb	y	3
Nbz2	Nb	z	2
Nbz4	Nb	z	4
Ox2	O	x	2
Ox4	O	x	4
Oy2	O	y	2
Oy4	O	y	4
Oz1	O	z	1
Oz3	O	z	3

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

Modulation code	Sine coefficient	Cosine coefficient
Zrx2	0.0229(1)	0.00613(5)
Zrx4	0.0004(3)	0.0003(2)
Zry1	0.0157(2)	0.00206(3)
Zry3	0.0048(2)	0.00199(5)
Zrz2	0.0019(1)	0.00052(3)
Zrz4	-0.0003(3)	-0.0002(2)
Nbx2	0.0229(1)	0.00613(5)
Nbx4	0.0004(3)	0.0003(2)
Nby1	0.0157(2)	0.00206(3)
Nby3	0.0048(2)	0.00199(5)
Nbz2	0.0019(1)	0.00052(3)
Nbz4	-0.0003(3)	-0.0002(2)
Ox2	-0.0124(1)	-0.198(3)
Ox4	-0.061(2)	0.0076(3)
Oy2	0.00496(6)	0.079(3)
Oy4	0.005(1)	-0.0006(1)
Oz1	-0.0898(7)	-0.0843(6)
Oz3	-0.0158(6)	0.0191(7)

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

Modulation code	Atom site label	Tensor element	Wave vector code
OU112	O	U11	2
OU222	O	U22	2
OU332	O	U33	2
OU122	O	U12	2
OU131	O	U13	1
OU231	O	U23	1

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

Modulation code	Sine coefficient	Cosine coefficient
OU112	0.016(3)	-0.0010(2)
OU222	0.006(2)	-0.0004(1)
OU332	0.005(3)	-0.0003(2)
OU122	-0.015(2)	0.0009(1)
OU131	0.010(1)	-0.010(1)
OU231	0.003(1)	-0.004(1)

zr8.B1

Chemical data

Structural Formula Sum: Nb2 Zr10 O25 [ Help ]

Crystallographic data and experimental details

a: 5.108(1) Å [ Help ]

b: 4.997(1) Å [ Help ]

c: 5.278(1) Å [ Help ]

α: 90 ° [ Help ]

β: 90 ° [ Help ]

γ: 90 ° [ Help ]

Number of subsystems: 2 [ Help ]

Modulation dimension: 1 [ Help ]

Subsystem code: 1 [ Help ]

Subsystem description: Metal subsytem [ Help ]

W matrix:

1.0	0.0	0.0	0.0
0.0	1.0	0.0	0.0
0.0	0.0	1.0	0.0
0.0	0.0	0.0	1.0

Subsystem code: 2 [ Help ]

Subsystem description: Oxygen subsystem [ Help ]

W matrix:

2.0	-1.0	0.0	1.0
0.0	1.0	0.0	0.0
0.0	0.0	1.0	0.0
1.0	0.0	0.0	0.0

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

Wave vector id	q_x	q_y	q_z
1	0.08333	1	0

Superspace group name: Amma(α10)0s0 [ Help ]

Symmetry operations of the superspace group: (Show/hide table) [ Help ]

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

Refinement details

Refinement remarks: Fourier amplitudes transformed to the CIF standard. Please, see the article. [ Help ]

Structural Information

Average Structure: (Show/hide table) [ Help ]

Atom site label	Atom symbol	Subsystem	Occupancy	Symmetry multiplicity	x	y	z	Uiso/equiv	ADP type
Zr	Zr	1	0.833	4	0.25	0	0.2155(1)	?	Uani
Nb	Nb	1	0.167	4	0.25	0	0.2155(1)	?	Uani
O	O	2	1	16	0.25	0.2699(8)	0.5	?	Uani

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

Atom site label	U11	U22	U33
Zr	0.0067(6)	0.0092(6)	0.0027(5)
Nb	0.0067(6)	0.0092(6)	0.0027(5)
O	0.018(3)	0.028(3)	0.026(3)

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

Wave vector code	q_x	q_y
1	0.08333	1
2	0.16667	2
3	0.25	3
4	0.33333	4

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

Modulation code	Atom site label	Displacement axis	Wave vector code
Zrx2	Zr	x	2
Zrx4	Zr	x	4
Zry1	Zr	y	1
Zry3	Zr	y	3
Zrz2	Zr	z	2
Zrz4	Zr	z	4
Nbx2	Nb	x	2
Nbx4	Nb	x	4
Nby1	Nb	y	1
Nby3	Nb	y	3
Nbz2	Nb	z	2
Nbz4	Nb	z	4
Ox2	O	x	2
Ox4	O	x	4
Oy2	O	y	2
Oy4	O	y	4
Oz1	O	z	1
Oz3	O	z	3

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

Modulation code	Sine coefficient	Cosine coefficient
Zrx2	0.0241(3)	0.00644(8)
Zrx4	0.0017(9)	0.0010(5)
Zry1	0.0158(6)	0.00208(8)
Zry3	0.0059(6)	0.0024(2)
Zrz2	0.0016(3)	0.00044(8)
Zrz4	-0.0017(9)	-0.0010(5)
Nbx2	0.0241(3)	0.00644(8)
Nbx4	0.0017(9)	0.0010(5)
Nby1	0.0158(6)	0.00208(8)
Nby3	0.0059(6)	0.0024(2)
Nbz2	0.0016(3)	0.00044(8)
Nbz4	-0.0017(9)	-0.0010(5)
Ox2	-0.0120(1)	-0.191(2)
Ox4	-0.058(3)	0.0073(4)
Oy2	0.0050(1)	0.079(2)
Oy4	0.003(2)	-0.0004(3)
Oz1	-0.0919(7)	-0.0863(7)
Oz3	-0.014(1)	0.017(2)

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

Modulation code	Atom site label	Tensor element	Wave vector code
OU112	O	U11	2
OU222	O	U22	2
OU332	O	U33	2
OU122	O	U12	2
OU131	O	U13	1
OU231	O	U23	1

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

Modulation code	Sine coefficient	Cosine coefficient
OU112	0.024(4)	-0.0015(3)
OU222	0.009(4)	-0.0006(3)
OU332	0.000(4)	0.0000(3)
OU122	-0.017(3)	0.0011(2)
OU131	0.014(2)	-0.015(2)
OU231	0.007(2)	-0.007(2)

zr8.B2

Chemical data

Structural Formula Sum: Nb2 Zr10 O25 [ Help ]

Crystallographic data and experimental details

a: 5.108(1) Å [ Help ]

b: 4.997(1) Å [ Help ]

c: 5.278(1) Å [ Help ]

α: 90 ° [ Help ]

β: 90 ° [ Help ]

γ: 90 ° [ Help ]

Number of subsystems: 2 [ Help ]

Modulation dimension: 1 [ Help ]

Subsystem code: 1 [ Help ]

Subsystem description: Metal subsytem [ Help ]

W matrix:

1.0	0.0	0.0	0.0
0.0	1.0	0.0	0.0
0.0	0.0	1.0	0.0
0.0	0.0	0.0	1.0

Subsystem code: 2 [ Help ]

Subsystem description: Oxygen subsystem [ Help ]

W matrix:

2.0	-1.0	0.0	1.0
0.0	1.0	0.0	0.0
0.0	0.0	1.0	0.0
1.0	0.0	0.0	0.0

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

Wave vector id	q_x	q_y	q_z
1	0.08333	1	0

Superspace group name: Amma(α10)0s0 [ Help ]

Symmetry operations of the superspace group: (Show/hide table) [ Help ]

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

Refinement details

Refinement remarks: Fourier amplitudes transformed to the CIF standard. Please, see the article. [ Help ]

Structural Information

Average Structure: (Show/hide table) [ Help ]

Atom site label	Atom symbol	Subsystem	Occupancy	Symmetry multiplicity	x	y	z	Uiso/equiv	ADP type
Zr	Zr	1	0.833	4	0.25	0	0.2157(2)	?	Uani
Nb	Nb	1	0.167	4	0.25	0	0.2157(2)	?	Uani
O	O	2	1	16	0.25	0.2698(8)	0.5	?	Uani

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

Atom site label	U11	U22	U33
Zr	0.0078(6)	0.0106(6)	0.0041(5)
Nb	0.0078(6)	0.0106(6)	0.0041(5)
O	0.021(3)	0.030(3)	0.028(3)

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

Wave vector code	q_x	q_y
1	0.08333	1
2	0.16667	2
3	0.25	3
4	0.33333	4

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

Modulation code	Atom site label	Wave vector code
Zro2	Zr	2
Zro4	Zr	4
Nbo2	Nb	2
Nbo4	Nb	4

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

Modulation code	Sine coefficient	Cosine coefficient
Zro2	0.014(15)	0.004(4)
Zro4	-0.23(9)	-0.13(5)
Nbo2	-0.014(15)	-0.004(4)
Nbo4	0.23(9)	0.13(5)

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

Modulation code	Atom site label	Displacement axis	Wave vector code
Zrx2	Zr	x	2
Zrx4	Zr	x	4
Zry1	Zr	y	1
Zry3	Zr	y	3
Zrz2	Zr	z	2
Zrz4	Zr	z	4
Nbx2	Nb	x	2
Nbx4	Nb	x	4
Nby1	Nb	y	1
Nby3	Nb	y	3
Nbz2	Nb	z	2
Nbz4	Nb	z	4
Ox2	O	x	2
Ox4	O	x	4
Oy2	O	y	2
Oy4	O	y	4
Oz1	O	z	1
Oz3	O	z	3

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

Modulation code	Sine coefficient	Cosine coefficient
Zrx2	0.0247(5)	0.0066(1)
Zrx4	0.0009(9)	0.0005(5)
Zry1	0.0159(7)	0.00209(9)
Zry3	0.0063(6)	0.0026(3)
Zrz2	0.0016(3)	0.00044(8)
Zrz4	-0.001(2)	-0.001(1)
Nbx2	0.0247(5)	0.0066(1)
Nbx4	0.0009(9)	0.0005(5)
Nby1	0.0159(7)	0.00209(9)
Nby3	0.0063(6)	0.0026(3)
Nbz2	0.0016(3)	0.00044(8)
Nbz4	-0.001(2)	-0.001(1)
Ox2	-0.0121(1)	-0.192(2)
Ox4	-0.058(3)	0.0073(4)
Oy2	0.0050(1)	0.079(2)
Oy4	0.003(2)	-0.0004(3)
Oz1	-0.0919(7)	-0.0863(7)
Oz3	-0.0140(6)	0.0170(8)

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

Modulation code	Atom site label	Tensor element	Wave vector code
OU112	O	U11	2
OU222	O	U22	2
OU332	O	U33	2
OU122	O	U12	2
OU131	O	U13	1
OU231	O	U23	1

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

Modulation code	Sine coefficient	Cosine coefficient
OU112	0.026(4)	-0.0016(3)
OU222	0.010(4)	-0.0006(3)
OU332	0.000(4)	0.0000(3)
OU122	-0.017(4)	0.0011(3)
OU131	0.014(2)	-0.015(2)
OU231	0.008(2)	-0.008(2)

The structure refinement of compositely modulated Nb2Zrx-2O2x+1 (x=12)

Futterer, Klaus.; Schmid, Siegbert.; Thompson, John G.; Withers, Ray L.; Ishizawa, Nobuo; Kishimoto, Shunji

Acta Crystallographica section B 51 688-697 (1995)

https://doi.org/10.1107/S010876819401431X

Download CIF

Open in JSmol

zrf.B

Chemical data

Crystallographic data and experimental details

Refinement details

Structural Information

zr8.B1

Chemical data

Crystallographic data and experimental details

Refinement details

Structural Information

zr8.B2

Chemical data

Crystallographic data and experimental details

Refinement details

Structural Information

The structure refinement of compositely modulated Nb₂Zr_x-2O_2x+1 (x=12)