B-IncStrDB

Identification of a secondary phase Ga₂O₃(ZnO)_m in Ga-doped ZnO thermoelectric materials by a (3 + 1)-dimensional superspace model

Authors:

Michiue, Yuichi; Mori, Takao

Journal:

Journal of Applied Crystallography 51 924-927 (2018)

DOI:

https://doi.org/10.1107/S1600576718004119

B-IncStrDB ID: VSa3aiHRFyn Entry date: 2022-01-20 Last revision: 2022-01-20

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m15superspace

Chemical data

Structural Formula Sum: Ga0 O2.118 Zn2.118 [ Help ]

Formula weight: 172.4 Da [ Help ]

Crystallographic data and experimental details

Crystal system: orthorhombic [ Help ]

Superspace group name: Cmmm(00γ)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,-x2,x3,x4+1/2
3	-x1,x2,-x3,-x4+1/2
4	x1,-x2,-x3,-x4
5	-x1,-x2,-x3,-x4
6	x1,x2,-x3,-x4+1/2
7	x1,-x2,x3,x4+1/2
8	-x1,x2,x3,x4
9	x1+1/2,x2+1/2,x3,x4
10	-x1+1/2,-x2+1/2,x3,x4+1/2
11	-x1+1/2,x2+1/2,-x3,-x4+1/2
12	x1+1/2,-x2+1/2,-x3,-x4
13	-x1+1/2,-x2+1/2,-x3,-x4
14	x1+1/2,x2+1/2,-x3,-x4+1/2
15	x1+1/2,-x2+1/2,x3,x4+1/2
16	-x1+1/2,x2+1/2,x3,x4

a: 3.2505(3) Å [ Help ]

b: 19.725(5) Å [ Help ]

c: 1.5071(4) Å [ Help ]

α: 90 ° [ Help ]

β: 90 ° [ Help ]

γ: 90 ° [ Help ]

Volume: 96.63(4) Å³ [ Help ]

Modulation dimension: 1 [ Help ]

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

Wave vector id	q_x	q_y	q_z
1	0.000000	0.000000	0.029412

Number of subsystems: 2 [ Help ]

Subsystem code: 1 [ Help ]

Subsystem description: 1-st subsystem [ 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: 2-nd subsystem [ 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	2.0
0.0	0.0	0.0	1.0

Z: 1 [ Help ]

Cell measurement temperature: 293 K [ Help ]

μ: 14.453 mm^-1 [ Help ]

Refinement details

R(obs): 0.0647 [ Help ]

wR(obs): 0.0802 [ Help ]

R(all): 0.0666 [ Help ]

wR(all): 0.0802 [ Help ]

S(all): 4.15 [ Help ]

Nb. of parameters: 35 [ Help ]

Number of restraints: 0 [ Help ]

Number of constraints: 0 [ Help ]

Weighting scheme: sigma [ Help ]

Δ/σ(max): 0.0384 [ Help ]

Δ/σ(mean): 0.0070 [ 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	Subsystem
M1	Zn	0	0.3802(3)	0	Uiso	0.01	8	0.5	d	.	.	.	1
M1a	Zn	0	0.590(7)	0	Uiso	0.01	4	0.0147	d	.	.	.	1
M1b	Zn	0.5	0.529(6)	0	Uiso	0.01	4	0.0147	d	.	.	.	1
M1c	Zn	0	-0.838(4)	0	Uiso	0.01	4	0.0294	d	.	.	.	1
O1	O	0	0.8610(10)	0.5	Uiso	0.02	8	0.5	d	.	.	.	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_1
1	1
2	2
3	3
4	4
5	5
6	6
7	7
8	8
9	9
10	10
11	11
12	12

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

Atom site label	Center (x0)	Width
M1a	0.75	0.0294
M1b	0.75	0.0294
M1c	0.25	0.0294

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

Modulation code	Atom site label	Displacement axis	Wave vector code
M1x1	M1	x	1
M1y1	M1	y	1
M1z1	M1	z	1
M1x2	M1	x	2
M1y2	M1	y	2
M1z2	M1	z	2
M1x3	M1	x	3
M1y3	M1	y	3
M1z3	M1	z	3
M1x4	M1	x	4
M1y4	M1	y	4
M1z4	M1	z	4
M1x5	M1	x	5
M1y5	M1	y	5
M1z5	M1	z	5
M1x6	M1	x	6
M1y6	M1	y	6
M1z6	M1	z	6
M1x7	M1	x	7
M1y7	M1	y	7
M1z7	M1	z	7
M1x8	M1	x	8
M1y8	M1	y	8
M1z8	M1	z	8
M1x9	M1	x	9
M1y9	M1	y	9
M1z9	M1	z	9
M1x10	M1	x	10
M1y10	M1	y	10
M1z10	M1	z	10
O1x1	O1	x	1
O1y1	O1	y	1
O1z1	O1	z	1
O1x2	O1	x	2
O1y2	O1	y	2
O1z2	O1	z	2
O1x3	O1	x	3
O1y3	O1	y	3
O1z3	O1	z	3
O1x4	O1	x	4
O1y4	O1	y	4
O1z4	O1	z	4
O1x5	O1	x	5
O1y5	O1	y	5
O1z5	O1	z	5
O1x6	O1	x	6
O1y6	O1	y	6
O1z6	O1	z	6
O1x7	O1	x	7
O1y7	O1	y	7
O1z7	O1	z	7
O1x8	O1	x	8
O1y8	O1	y	8
O1z8	O1	z	8
O1x9	O1	x	9
O1y9	O1	y	9
O1z9	O1	z	9
O1x10	O1	x	10
O1y10	O1	y	10
O1z10	O1	z	10
O1x11	O1	x	11
O1y11	O1	y	11
O1z11	O1	z	11
O1x12	O1	x	12
O1y12	O1	y	12
O1z12	O1	z	12

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

Modulation code	Cosine coefficient	Sine coefficient
M1x1	0	0
M1y1	0	-0.0136(5)
M1z1	0.1031	0
M1x2	0	0
M1y2	0.0011	0
M1z2	0	-0.0515
M1x3	0	0
M1y3	0	0.0036
M1z3	-0.0328	0
M1x4	0	0
M1y4	-0.0005	0
M1z4	0	0.0242
M1x5	0	0
M1y5	0	-0.0004
M1z5	-0.014	0
M1x6	0	0
M1y6	0	0
M1z6	0	-0.0151
M1x7	0	0
M1y7	0	0.0003
M1z7	0.0161	0
M1x8	0	0
M1y8	-0.0011	0
M1z8	0	0.0011
M1x9	0	0
M1y9	0	0
M1z9	0.0111	0
M1x10	0	0
M1y10	0	0
M1z10	0	-0.0014
O1x1	0	0
O1y1	0	-0.005(2)
O1z1	0.1023	0
O1x2	0	0
O1y2	0.0001	0
O1z2	0	-0.119
O1x3	0	0
O1y3	0	0.0074
O1z3	-0.0408	0
O1x4	0	0
O1y4	-0.0004	0
O1z4	0	-0.0245
O1x5	0	0
O1y5	0	-0.0007
O1z5	0.0362	0
O1x6	0	0
O1y6	0	0
O1z6	0	-0.0166
O1x7	0	0
O1y7	0	0.0012
O1z7	0.0201	0
O1x8	0	0
O1y8	-0.0004	0
O1z8	0	0.0048
O1x9	0	0
O1y9	0	-0.0007
O1z9	-0.0077	0
O1x10	0	0
O1y10	0.0001	0
O1z10	0	-0.0065
O1x11	0	0
O1y11	0	0.0011
O1z11	0.014	0
O1x12	0	0
O1y12	-0.0006	0
O1z12	0	0

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

Atom site label	Ax	Ay	Az	Center (x0)	Width
M1	0	-3	0	0	0.4706
O1	0	-3.375	0	0	0.5

m23superspace

Chemical data

Structural Formula Sum: Ga0 O2.08 Zn2.155 [ Help ]

Formula weight: 174.2 Da [ Help ]

Crystallographic data and experimental details

Crystal system: orthorhombic [ Help ]

Superspace group name: Cmmm(00γ)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,-x2,x3,x4+1/2
3	-x1,x2,-x3,-x4+1/2
4	x1,-x2,-x3,-x4
5	-x1,-x2,-x3,-x4
6	x1,x2,-x3,-x4+1/2
7	x1,-x2,x3,x4+1/2
8	-x1,x2,x3,x4
9	x1+1/2,x2+1/2,x3,x4
10	-x1+1/2,-x2+1/2,x3,x4+1/2
11	-x1+1/2,x2+1/2,-x3,-x4+1/2
12	x1+1/2,-x2+1/2,-x3,-x4
13	-x1+1/2,-x2+1/2,-x3,-x4
14	x1+1/2,x2+1/2,-x3,-x4+1/2
15	x1+1/2,-x2+1/2,x3,x4+1/2
16	-x1+1/2,x2+1/2,x3,x4

a: 3.2540(3) Å [ Help ]

b: 19.786(4) Å [ Help ]

c: 1.4996(3) Å [ Help ]

α: 90 ° [ Help ]

β: 90 ° [ Help ]

γ: 90 ° [ Help ]

Volume: 96.55(3) Å³ [ Help ]

Modulation dimension: 1 [ Help ]

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

Wave vector id	q_x	q_y	q_z
1	0.000000	0.000000	0.020000

Number of subsystems: 2 [ Help ]

Subsystem code: 1 [ Help ]

Subsystem description: 1-st subsystem [ 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: 2-nd subsystem [ 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	2.0
0.0	0.0	0.0	1.0

Z: 1 [ Help ]

Cell measurement temperature: 293 K [ Help ]

μ: 14.694 mm^-1 [ Help ]

Refinement details

R(obs): 0.0586 [ Help ]

wR(obs): 0.0672 [ Help ]

R(all): 0.0598 [ Help ]

wR(all): 0.0673 [ Help ]

S(all): 3.65 [ Help ]

Nb. of parameters: 35 [ Help ]

Number of restraints: 0 [ Help ]

Number of constraints: 0 [ Help ]

Weighting scheme: sigma [ Help ]

Δ/σ(max): 0.0407 [ Help ]

Δ/σ(mean): 0.0070 [ 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	Subsystem
M1	Zn	0	0.3802(2)	0	Uiso	0.01	8	0.5	d	.	.	.	1
M1a	Zn	0	0.115(7)	0	Uiso	0.01	4	0.0147	d	.	.	.	1
M1b	Zn	0.5	0.046(7)	0	Uiso	0.01	4	0.0147	d	.	.	.	1
M1c	Zn	0	-0.353(4)	0	Uiso	0.01	4	0.0294	d	.	.	.	1
O1	O	0	0.8657(9)	0.5	Uiso	0.02	8	0.5	d	.	.	.	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_1
1	1
2	2
3	3
4	4
5	5
6	6
7	7
8	8
9	9
10	10
11	11
12	12

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

Atom site label	Center (x0)	Width
M1a	0.75	0.0294
M1b	0.75	0.0294
M1c	0.25	0.0294

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

Modulation code	Atom site label	Displacement axis	Wave vector code
M1x1	M1	x	1
M1y1	M1	y	1
M1z1	M1	z	1
M1x2	M1	x	2
M1y2	M1	y	2
M1z2	M1	z	2
M1x3	M1	x	3
M1y3	M1	y	3
M1z3	M1	z	3
M1x4	M1	x	4
M1y4	M1	y	4
M1z4	M1	z	4
M1x5	M1	x	5
M1y5	M1	y	5
M1z5	M1	z	5
M1x6	M1	x	6
M1y6	M1	y	6
M1z6	M1	z	6
M1x7	M1	x	7
M1y7	M1	y	7
M1z7	M1	z	7
M1x8	M1	x	8
M1y8	M1	y	8
M1z8	M1	z	8
M1x9	M1	x	9
M1y9	M1	y	9
M1z9	M1	z	9
M1x10	M1	x	10
M1y10	M1	y	10
M1z10	M1	z	10
O1x1	O1	x	1
O1y1	O1	y	1
O1z1	O1	z	1
O1x2	O1	x	2
O1y2	O1	y	2
O1z2	O1	z	2
O1x3	O1	x	3
O1y3	O1	y	3
O1z3	O1	z	3
O1x4	O1	x	4
O1y4	O1	y	4
O1z4	O1	z	4
O1x5	O1	x	5
O1y5	O1	y	5
O1z5	O1	z	5
O1x6	O1	x	6
O1y6	O1	y	6
O1z6	O1	z	6
O1x7	O1	x	7
O1y7	O1	y	7
O1z7	O1	z	7
O1x8	O1	x	8
O1y8	O1	y	8
O1z8	O1	z	8
O1x9	O1	x	9
O1y9	O1	y	9
O1z9	O1	z	9
O1x10	O1	x	10
O1y10	O1	y	10
O1z10	O1	z	10
O1x11	O1	x	11
O1y11	O1	y	11
O1z11	O1	z	11
O1x12	O1	x	12
O1y12	O1	y	12
O1z12	O1	z	12

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

Modulation code	Cosine coefficient	Sine coefficient
M1x1	0	0
M1y1	0	-0.0231(4)
M1z1	0.1031	0
M1x2	0	0
M1y2	0.0011	0
M1z2	0	-0.0515
M1x3	0	0
M1y3	0	0.0036
M1z3	-0.0328	0
M1x4	0	0
M1y4	-0.0005	0
M1z4	0	0.0242
M1x5	0	0
M1y5	0	-0.0004
M1z5	-0.014	0
M1x6	0	0
M1y6	0	0
M1z6	0	-0.0151
M1x7	0	0
M1y7	0	0.0003
M1z7	0.0161	0
M1x8	0	0
M1y8	-0.0011	0
M1z8	0	0.0011
M1x9	0	0
M1y9	0	0
M1z9	0.0111	0
M1x10	0	0
M1y10	0	0
M1z10	0	-0.0014
O1x1	0	0
O1y1	0	-0.0109(16)
O1z1	0.1023	0
O1x2	0	0
O1y2	0.0001	0
O1z2	0	-0.119
O1x3	0	0
O1y3	0	0.0074
O1z3	-0.0408	0
O1x4	0	0
O1y4	-0.0004	0
O1z4	0	-0.0245
O1x5	0	0
O1y5	0	-0.0007
O1z5	0.0362	0
O1x6	0	0
O1y6	0	0
O1z6	0	-0.0166
O1x7	0	0
O1y7	0	0.0012
O1z7	0.0201	0
O1x8	0	0
O1y8	-0.0004	0
O1z8	0	0.0048
O1x9	0	0
O1y9	0	-0.0007
O1z9	-0.0077	0
O1x10	0	0
O1y10	0.0001	0
O1z10	0	-0.0065
O1x11	0	0
O1y11	0	0.0011
O1z11	0.014	0
O1x12	0	0
O1y12	-0.0006	0
O1z12	0	0

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

Atom site label	Ax	Ay	Az	Center (x0)	Width
M1	0	-4.5	0	0	0.48
O1	0	-4.875	0	0	0.5

m28superspace

Chemical data

Structural Formula Sum: Ga0 O2.067 Zn2.067 [ Help ]

Formula weight: 168.2 Da [ Help ]

Crystallographic data and experimental details

Crystal system: orthorhombic [ Help ]

Superspace group name: Cmmm(00γ)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,-x2,x3,x4+1/2
3	-x1,x2,-x3,-x4+1/2
4	x1,-x2,-x3,-x4
5	-x1,-x2,-x3,-x4
6	x1,x2,-x3,-x4+1/2
7	x1,-x2,x3,x4+1/2
8	-x1,x2,x3,x4
9	x1+1/2,x2+1/2,x3,x4
10	-x1+1/2,-x2+1/2,x3,x4+1/2
11	-x1+1/2,x2+1/2,-x3,-x4+1/2
12	x1+1/2,-x2+1/2,-x3,-x4
13	-x1+1/2,-x2+1/2,-x3,-x4
14	x1+1/2,x2+1/2,-x3,-x4+1/2
15	x1+1/2,-x2+1/2,x3,x4+1/2
16	-x1+1/2,x2+1/2,x3,x4

a: 3.2543(3) Å [ Help ]

b: 19.799(2) Å [ Help ]

c: 1.4973(3) Å [ Help ]

α: 90 ° [ Help ]

β: 90 ° [ Help ]

γ: 90 ° [ Help ]

Volume: 96.47(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	0.000000	0.000000	0.016667

Number of subsystems: 2 [ Help ]

Subsystem code: 1 [ Help ]

Subsystem description: 1-st subsystem [ 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: 2-nd subsystem [ 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	2.0
0.0	0.0	0.0	1.0

Z: 1 [ Help ]

Cell measurement temperature: 293 K [ Help ]

μ: 14.128 mm^-1 [ Help ]

Refinement details

R(obs): 0.0630 [ Help ]

wR(obs): 0.0606 [ Help ]

R(all): 0.0665 [ Help ]

wR(all): 0.0607 [ Help ]

S(all): 3.96 [ Help ]

Nb. of parameters: 32 [ Help ]

Number of restraints: 0 [ Help ]

Number of constraints: 0 [ Help ]

Weighting scheme: sigma [ Help ]

Δ/σ(max): 0.0407 [ Help ]

Δ/σ(mean): 0.0061 [ 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	Subsystem
M1	Zn	0	0.3828(3)	0	Uiso	0.01	8	0.5	d	.	.	.	1
M1a	Zn	0	0.068(8)	0	Uiso	0.01	4	0.0083	d	.	.	.	1
M1b	Zn	0.5	-0.050(8)	0	Uiso	0.01	4	0.0083	d	.	.	.	1
M1c	Zn	0	-0.304(5)	0	Uiso	0.01	4	0.0167	d	.	.	.	1
O1	O	0	0.8839(16)	0.5	Uiso	0.02	8	0.5	d	.	.	.	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_1
1	1
2	2
3	3
4	4
5	5
6	6
7	7
8	8
9	9
10	10
11	11
12	12

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

Atom site label	Center (x0)	Width
M1a	0.75	0.0167
M1b	0.75	0.0167
M1c	0.25	0.0167

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

Modulation code	Atom site label	Displacement axis	Wave vector code
M1x1	M1	x	1
M1y1	M1	y	1
M1z1	M1	z	1
M1x2	M1	x	2
M1y2	M1	y	2
M1z2	M1	z	2
M1x3	M1	x	3
M1y3	M1	y	3
M1z3	M1	z	3
M1x4	M1	x	4
M1y4	M1	y	4
M1z4	M1	z	4
M1x5	M1	x	5
M1y5	M1	y	5
M1z5	M1	z	5
M1x6	M1	x	6
M1y6	M1	y	6
M1z6	M1	z	6
M1x7	M1	x	7
M1y7	M1	y	7
M1z7	M1	z	7
M1x8	M1	x	8
M1y8	M1	y	8
M1z8	M1	z	8
M1x9	M1	x	9
M1y9	M1	y	9
M1z9	M1	z	9
M1x10	M1	x	10
M1y10	M1	y	10
M1z10	M1	z	10
O1x1	O1	x	1
O1y1	O1	y	1
O1z1	O1	z	1
O1x2	O1	x	2
O1y2	O1	y	2
O1z2	O1	z	2
O1x3	O1	x	3
O1y3	O1	y	3
O1z3	O1	z	3
O1x4	O1	x	4
O1y4	O1	y	4
O1z4	O1	z	4
O1x5	O1	x	5
O1y5	O1	y	5
O1z5	O1	z	5
O1x6	O1	x	6
O1y6	O1	y	6
O1z6	O1	z	6
O1x7	O1	x	7
O1y7	O1	y	7
O1z7	O1	z	7
O1x8	O1	x	8
O1y8	O1	y	8
O1z8	O1	z	8
O1x9	O1	x	9
O1y9	O1	y	9
O1z9	O1	z	9
O1x10	O1	x	10
O1y10	O1	y	10
O1z10	O1	z	10
O1x11	O1	x	11
O1y11	O1	y	11
O1z11	O1	z	11
O1x12	O1	x	12
O1y12	O1	y	12
O1z12	O1	z	12

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

Modulation code	Cosine coefficient	Sine coefficient
M1x1	0	0
M1y1	0	-0.0311(3)
M1z1	0.1031	0
M1x2	0	0
M1y2	0.0011	0
M1z2	0	-0.0515
M1x3	0	0
M1y3	0	0.0036
M1z3	-0.0328	0
M1x4	0	0
M1y4	-0.0005	0
M1z4	0	0.0242
M1x5	0	0
M1y5	0	-0.0004
M1z5	-0.014	0
M1x6	0	0
M1y6	0	0
M1z6	0	-0.0151
M1x7	0	0
M1y7	0	0.0003
M1z7	0.0161	0
M1x8	0	0
M1y8	-0.0011	0
M1z8	0	0.0011
M1x9	0	0
M1y9	0	0
M1z9	0.0111	0
M1x10	0	0
M1y10	0	0
M1z10	0	-0.0014
O1x1	0	0
O1y1	0	-0.0142(9)
O1z1	0.1023	0
O1x2	0	0
O1y2	0.0001	0
O1z2	0	-0.119
O1x3	0	0
O1y3	0	0.0074
O1z3	-0.0408	0
O1x4	0	0
O1y4	-0.0004	0
O1z4	0	-0.0245
O1x5	0	0
O1y5	0	-0.0007
O1z5	0.0362	0
O1x6	0	0
O1y6	0	0
O1z6	0	-0.0166
O1x7	0	0
O1y7	0	0.0012
O1z7	0.0201	0
O1x8	0	0
O1y8	-0.0004	0
O1z8	0	0.0048
O1x9	0	0
O1y9	0	-0.0007
O1z9	-0.0077	0
O1x10	0	0
O1y10	0.0001	0
O1z10	0	-0.0065
O1x11	0	0
O1y11	0	0.0011
O1z11	0.014	0
O1x12	0	0
O1y12	-0.0006	0
O1z12	0	0

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

Atom site label	Ax	Ay	Az	Center (x0)	Width
M1	0	-5.4375	0	0	0.4833
O1	0	-5.8125	0	0	0.5

m33superspace

Chemical data

Structural Formula Sum: Ga0 O2.057 Zn2.057 [ Help ]

Formula weight: 167.4 Da [ Help ]

Crystallographic data and experimental details

Crystal system: orthorhombic [ Help ]

Superspace group name: Cmmm(00γ)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,-x2,x3,x4+1/2
3	-x1,x2,-x3,-x4+1/2
4	x1,-x2,-x3,-x4
5	-x1,-x2,-x3,-x4
6	x1,x2,-x3,-x4+1/2
7	x1,-x2,x3,x4+1/2
8	-x1,x2,x3,x4
9	x1+1/2,x2+1/2,x3,x4
10	-x1+1/2,-x2+1/2,x3,x4+1/2
11	-x1+1/2,x2+1/2,-x3,-x4+1/2
12	x1+1/2,-x2+1/2,-x3,-x4
13	-x1+1/2,-x2+1/2,-x3,-x4
14	x1+1/2,x2+1/2,-x3,-x4+1/2
15	x1+1/2,-x2+1/2,x3,x4+1/2
16	-x1+1/2,x2+1/2,x3,x4

a: 3.2514(2) Å [ Help ]

b: 19.797(2) Å [ Help ]

c: 1.4924(2) Å [ Help ]

α: 90 ° [ Help ]

β: 90 ° [ Help ]

γ: 90 ° [ Help ]

Volume: 96.063(18) Å³ [ Help ]

Modulation dimension: 1 [ Help ]

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

Wave vector id	q_x	q_y	q_z
1	0.000000	0.000000	0.014286

Number of subsystems: 2 [ Help ]

Subsystem code: 1 [ Help ]

Subsystem description: 1-st subsystem [ 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: 2-nd subsystem [ 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	2.0
0.0	0.0	0.0	1.0

Z: 1 [ Help ]

Cell measurement temperature: 293 K [ Help ]

μ: 14.12 mm^-1 [ Help ]

Refinement details

R(obs): 0.0700 [ Help ]

wR(obs): 0.0610 [ Help ]

R(all): 0.0737 [ Help ]

wR(all): 0.0611 [ Help ]

S(all): 3.53 [ Help ]

Nb. of parameters: 32 [ Help ]

Number of restraints: 0 [ Help ]

Number of constraints: 0 [ Help ]

Weighting scheme: sigma [ Help ]

Δ/σ(max): 0.0472 [ Help ]

Δ/σ(mean): 0.0064 [ 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	Subsystem
M1	Zn	0	0.3832(3)	0	Uiso	0.01	8	0.5	d	.	.	.	1
M1a	Zn	0	1.018(9)	0	Uiso	0.01	4	0.0071	d	.	.	.	1
M1b	Zn	0.5	0.892(8)	0	Uiso	0.01	4	0.0071	d	.	.	.	1
M1c	Zn	0	-0.254(5)	0	Uiso	0.01	4	0.0143	d	.	.	.	1
O1	O	0	0.8809(16)	0.5	Uiso	0.02	8	0.5	d	.	.	.	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_1
1	1
2	2
3	3
4	4
5	5
6	6
7	7
8	8
9	9
10	10
11	11
12	12

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

Atom site label	Center (x0)	Width
M1a	0.75	0.0143
M1b	0.75	0.0143
M1c	0.25	0.0143

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

Modulation code	Atom site label	Displacement axis	Wave vector code
M1x1	M1	x	1
M1y1	M1	y	1
M1z1	M1	z	1
M1x2	M1	x	2
M1y2	M1	y	2
M1z2	M1	z	2
M1x3	M1	x	3
M1y3	M1	y	3
M1z3	M1	z	3
M1x4	M1	x	4
M1y4	M1	y	4
M1z4	M1	z	4
M1x5	M1	x	5
M1y5	M1	y	5
M1z5	M1	z	5
M1x6	M1	x	6
M1y6	M1	y	6
M1z6	M1	z	6
M1x7	M1	x	7
M1y7	M1	y	7
M1z7	M1	z	7
M1x8	M1	x	8
M1y8	M1	y	8
M1z8	M1	z	8
M1x9	M1	x	9
M1y9	M1	y	9
M1z9	M1	z	9
M1x10	M1	x	10
M1y10	M1	y	10
M1z10	M1	z	10
O1x1	O1	x	1
O1y1	O1	y	1
O1z1	O1	z	1
O1x2	O1	x	2
O1y2	O1	y	2
O1z2	O1	z	2
O1x3	O1	x	3
O1y3	O1	y	3
O1z3	O1	z	3
O1x4	O1	x	4
O1y4	O1	y	4
O1z4	O1	z	4
O1x5	O1	x	5
O1y5	O1	y	5
O1z5	O1	z	5
O1x6	O1	x	6
O1y6	O1	y	6
O1z6	O1	z	6
O1x7	O1	x	7
O1y7	O1	y	7
O1z7	O1	z	7
O1x8	O1	x	8
O1y8	O1	y	8
O1z8	O1	z	8
O1x9	O1	x	9
O1y9	O1	y	9
O1z9	O1	z	9
O1x10	O1	x	10
O1y10	O1	y	10
O1z10	O1	z	10
O1x11	O1	x	11
O1y11	O1	y	11
O1z11	O1	z	11
O1x12	O1	x	12
O1y12	O1	y	12
O1z12	O1	z	12

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

Modulation code	Cosine coefficient	Sine coefficient
M1x1	0	0
M1y1	0	-0.0415(3)
M1z1	0.1031	0
M1x2	0	0
M1y2	0.0011	0
M1z2	0	-0.0515
M1x3	0	0
M1y3	0	0.0036
M1z3	-0.0328	0
M1x4	0	0
M1y4	-0.0005	0
M1z4	0	0.0242
M1x5	0	0
M1y5	0	-0.0004
M1z5	-0.014	0
M1x6	0	0
M1y6	0	0
M1z6	0	-0.0151
M1x7	0	0
M1y7	0	0.0003
M1z7	0.0161	0
M1x8	0	0
M1y8	-0.0011	0
M1z8	0	0.0011
M1x9	0	0
M1y9	0	0
M1z9	0.0111	0
M1x10	0	0
M1y10	0	0
M1z10	0	-0.0014
O1x1	0	0
O1y1	0	-0.0230(9)
O1z1	0.1023	0
O1x2	0	0
O1y2	0.0001	0
O1z2	0	-0.119
O1x3	0	0
O1y3	0	0.0074
O1z3	-0.0408	0
O1x4	0	0
O1y4	-0.0004	0
O1z4	0	-0.0245
O1x5	0	0
O1y5	0	-0.0007
O1z5	0.0362	0
O1x6	0	0
O1y6	0	0
O1z6	0	-0.0166
O1x7	0	0
O1y7	0	0.0012
O1z7	0.0201	0
O1x8	0	0
O1y8	-0.0004	0
O1z8	0	0.0048
O1x9	0	0
O1y9	0	-0.0007
O1z9	-0.0077	0
O1x10	0	0
O1y10	0.0001	0
O1z10	0	-0.0065
O1x11	0	0
O1y11	0	0.0011
O1z11	0.014	0
O1x12	0	0
O1y12	-0.0006	0
O1z12	0	0

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

Atom site label	Ax	Ay	Az	Center (x0)	Width
M1	0	-6.375	0	0	0.4857
O1	0	-6.75	0	0	0.5

m38superspace

Chemical data

Structural Formula Sum: Ga0 O2.05 Zn2.05 [ Help ]

Formula weight: 166.8 Da [ Help ]

Crystallographic data and experimental details

Crystal system: orthorhombic [ Help ]

Superspace group name: Cmmm(00γ)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,-x2,x3,x4+1/2
3	-x1,x2,-x3,-x4+1/2
4	x1,-x2,-x3,-x4
5	-x1,-x2,-x3,-x4
6	x1,x2,-x3,-x4+1/2
7	x1,-x2,x3,x4+1/2
8	-x1,x2,x3,x4
9	x1+1/2,x2+1/2,x3,x4
10	-x1+1/2,-x2+1/2,x3,x4+1/2
11	-x1+1/2,x2+1/2,-x3,-x4+1/2
12	x1+1/2,-x2+1/2,-x3,-x4
13	-x1+1/2,-x2+1/2,-x3,-x4
14	x1+1/2,x2+1/2,-x3,-x4+1/2
15	x1+1/2,-x2+1/2,x3,x4+1/2
16	-x1+1/2,x2+1/2,x3,x4

a: 3.2515(2) Å [ Help ]

b: 19.809(2) Å [ Help ]

c: 1.4917(2) Å [ Help ]

α: 90 ° [ Help ]

β: 90 ° [ Help ]

γ: 90 ° [ Help ]

Volume: 96.076(19) Å³ [ Help ]

Modulation dimension: 1 [ Help ]

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

Wave vector id	q_x	q_y	q_z
1	0.000000	0.000000	0.012500

Number of subsystems: 2 [ Help ]

Subsystem code: 1 [ Help ]

Subsystem description: 1-st subsystem [ 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: 2-nd subsystem [ 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	2.0
0.0	0.0	0.0	1.0

Z: 1 [ Help ]

Cell measurement temperature: 293 K [ Help ]

μ: 14.07 mm^-1 [ Help ]

Refinement details

R(obs): 0.0603 [ Help ]

wR(obs): 0.0538 [ Help ]

R(all): 0.0717 [ Help ]

wR(all): 0.0540 [ Help ]

S(all): 3.52 [ Help ]

Nb. of parameters: 28 [ Help ]

Number of restraints: 0 [ Help ]

Number of constraints: 0 [ Help ]

Weighting scheme: sigma [ Help ]

Δ/σ(max): 0.0414 [ Help ]

Δ/σ(mean): 0.0141 [ Help ]

Δρ(max): 1.85 e_Å^-3 [ Help ]

Δρ(min): -1.88 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	Subsystem
M1	Zn	0	0.3828(3)	0	Uiso	0.01	8	0.5	d	.	.	.	1
M1a	Zn	0	0.969(11)	0	Uiso	0.01	4	0.0062	d	.	.	.	1
M1b	Zn	0.5	0.832(9)	0	Uiso	0.01	4	0.0062	d	.	.	.	1
M1c	Zn	0	-0.204(6)	0	Uiso	0.01	4	0.0125	d	.	.	.	1
O1	O	0	0.8849(14)	0.5	Uiso	0.02	8	0.5	d	.	.	.	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_1
1	1
2	2
3	3
4	4
5	5
6	6
7	7
8	8
9	9
10	10
11	11
12	12

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

Atom site label	Center (x0)	Width
M1a	0.75	0.0125
M1b	0.75	0.0125
M1c	0.25	0.0125

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

Modulation code	Atom site label	Displacement axis	Wave vector code
M1x1	M1	x	1
M1y1	M1	y	1
M1z1	M1	z	1
M1x2	M1	x	2
M1y2	M1	y	2
M1z2	M1	z	2
M1x3	M1	x	3
M1y3	M1	y	3
M1z3	M1	z	3
M1x4	M1	x	4
M1y4	M1	y	4
M1z4	M1	z	4
M1x5	M1	x	5
M1y5	M1	y	5
M1z5	M1	z	5
M1x6	M1	x	6
M1y6	M1	y	6
M1z6	M1	z	6
M1x7	M1	x	7
M1y7	M1	y	7
M1z7	M1	z	7
M1x8	M1	x	8
M1y8	M1	y	8
M1z8	M1	z	8
M1x9	M1	x	9
M1y9	M1	y	9
M1z9	M1	z	9
M1x10	M1	x	10
M1y10	M1	y	10
M1z10	M1	z	10
O1x1	O1	x	1
O1y1	O1	y	1
O1z1	O1	z	1
O1x2	O1	x	2
O1y2	O1	y	2
O1z2	O1	z	2
O1x3	O1	x	3
O1y3	O1	y	3
O1z3	O1	z	3
O1x4	O1	x	4
O1y4	O1	y	4
O1z4	O1	z	4
O1x5	O1	x	5
O1y5	O1	y	5
O1z5	O1	z	5
O1x6	O1	x	6
O1y6	O1	y	6
O1z6	O1	z	6
O1x7	O1	x	7
O1y7	O1	y	7
O1z7	O1	z	7
O1x8	O1	x	8
O1y8	O1	y	8
O1z8	O1	z	8
O1x9	O1	x	9
O1y9	O1	y	9
O1z9	O1	z	9
O1x10	O1	x	10
O1y10	O1	y	10
O1z10	O1	z	10
O1x11	O1	x	11
O1y11	O1	y	11
O1z11	O1	z	11
O1x12	O1	x	12
O1y12	O1	y	12
O1z12	O1	z	12

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

Modulation code	Cosine coefficient	Sine coefficient
M1x1	0	0
M1y1	0	-0.0496(3)
M1z1	0.1031	0
M1x2	0	0
M1y2	0.0011	0
M1z2	0	-0.0515
M1x3	0	0
M1y3	0	0.0036
M1z3	-0.0328	0
M1x4	0	0
M1y4	-0.0005	0
M1z4	0	0.0242
M1x5	0	0
M1y5	0	-0.0004
M1z5	-0.014	0
M1x6	0	0
M1y6	0	0
M1z6	0	-0.0151
M1x7	0	0
M1y7	0	0.0003
M1z7	0.0161	0
M1x8	0	0
M1y8	-0.0011	0
M1z8	0	0.0011
M1x9	0	0
M1y9	0	0
M1z9	0.0111	0
M1x10	0	0
M1y10	0	0
M1z10	0	-0.0014
O1x1	0	0
O1y1	0	-0.0282(8)
O1z1	0.1023	0
O1x2	0	0
O1y2	0.0001	0
O1z2	0	-0.119
O1x3	0	0
O1y3	0	0.0074
O1z3	-0.0408	0
O1x4	0	0
O1y4	-0.0004	0
O1z4	0	-0.0245
O1x5	0	0
O1y5	0	-0.0007
O1z5	0.0362	0
O1x6	0	0
O1y6	0	0
O1z6	0	-0.0166
O1x7	0	0
O1y7	0	0.0012
O1z7	0.0201	0
O1x8	0	0
O1y8	-0.0004	0
O1z8	0	0.0048
O1x9	0	0
O1y9	0	-0.0007
O1z9	-0.0077	0
O1x10	0	0
O1y10	0.0001	0
O1z10	0	-0.0065
O1x11	0	0
O1y11	0	0.0011
O1z11	0.014	0
O1x12	0	0
O1y12	-0.0006	0
O1z12	0	0

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

Atom site label	Ax	Ay	Az	Center (x0)	Width
M1	0	-7.3125	0	0	0.4875
O1	0	-7.6875	0	0	0.5

Identification of a secondary phase Ga2O3(ZnO)m in Ga-doped ZnO thermoelectric materials by a (3 + 1)-dimensional superspace model

Michiue, Yuichi; Mori, Takao

Journal of Applied Crystallography 51 924-927 (2018)

https://doi.org/10.1107/S1600576718004119

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m15superspace

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m23superspace

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m28superspace

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m33superspace

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m38superspace

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Identification of a secondary phase Ga₂O₃(ZnO)_m in Ga-doped ZnO thermoelectric materials by a (3 + 1)-dimensional superspace model