B-IncStrDB

Superspace description of the homologous series Ga₂O₃(ZnO)_m

Authors:

Michiue, Yuichi; Kimizuka, Noboru

Journal:

Acta Crystallographica, Section B 66 117-129 (2010)

DOI:

https://doi.org/10.1107/S0108768109053713

B-IncStrDB ID: bEH53SvGTCe Entry date: 2022-01-21 Last revision: 2022-01-21

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m_6

Chemical data

Structural Formula Sum: Ga0.25 O1.25 Zn0.75 [ Help ]

Formula weight: 84.5 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
3	x1,-x2,x3,x4+1/2
4	-x1,-x2,x3,x4+1/2
5	-x1,-x2,-x3,-x4
6	x1,-x2,-x3,-x4
7	-x1,x2,-x3,-x4+1/2
8	x1,x2,-x3,-x4+1/2
9	x1+1/2,x2+1/2,x3,x4
10	-x1+1/2,x2+1/2,x3,x4
11	x1+1/2,-x2+1/2,x3,x4+1/2
12	-x1+1/2,-x2+1/2,x3,x4+1/2
13	-x1+1/2,-x2+1/2,-x3,-x4
14	x1+1/2,-x2+1/2,-x3,-x4
15	-x1+1/2,x2+1/2,-x3,-x4+1/2
16	x1+1/2,x2+1/2,-x3,-x4+1/2

a: 3.2465(9) Å [ Help ]

b: 19.640(5) Å [ Help ]

c: 3.0979(8) Å [ Help ]

α: 90 ° [ Help ]

β: 90 ° [ Help ]

γ: 90 ° [ Help ]

Volume: 197.53(9) Å³ [ Help ]

Z: 8 [ Help ]

Cell determination reflection Nb.: 25 [ Help ]

θ(min) for cell determination: 12.6 ° [ Help ]

θ(max) for cell determination: 15.7 ° [ Help ]

Cell measurement temperature: 298 K [ Help ]

Modulation dimension: 1 [ Help ]

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	0.0	1.0
0.0	0.0	1.0	0.0

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

Wave vector id	q_x	q_y	q_z
1	0.00000	0.00000	1.12500

μ: 24.6 mm^-1 [ Help ]

Absorption correction type: psi-scan [ Help ]

Absorption correction remarks: Absorption correction given as psi-scan [ Help ]

Minimum transmission factor: 0.18 [ Help ]

Maximum transmission factor: 0.61 [ Help ]

Refinement details

Total nb. of reflections: 3699 [ Help ]

Nb. of observed reflections: 1349 [ Help ]

Intense reflections threshold: I>2σ(I) [ Help ]

Refinement based on: Fsqd [ Help ]

R(all): 0.1801 [ Help ]

R(obs): 0.0439 [ Help ]

wR(obs): 0.0683 [ Help ]

wR(all): 0.0988 [ Help ]

S(all): 1.03 [ Help ]

Nb. of reflections: 3699 [ Help ]

Nb. of parameters: 115 [ Help ]

Number of restraints: 0 [ Help ]

Number of constraints: 4 [ Help ]

Weighting scheme: sigma [ Help ]

Weighting scheme remarks: w=1/(σ²(I)+0.0001I²) [ Help ]

Δ/σ(max): 0.0169 [ Help ]

Δ/σ(mean): 0.0016 [ Help ]

Δρ(max): 2.29 e_Å^-3 [ Help ]

Δρ(min): -2.27 e_Å^-3 [ Help ]

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

Extinction coefficient: 404(14) [ Help ]

Structural Information

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

Atom symbol	Atom site label	Subsystem	x	y	z	Uiso/equiv	ADP type	Coords from (d)iffraction or (c)alculated	Coords restraints or constraints	Occupancy	Disordered cluster	Disordered group
Zn	M1	1	0	0.38426(4)	0	0.01344(16)	Uani	d	.	0.75	.	.
Ga	M1g	1	0	0.38426(4)	0	0.01344(16)	Uani	d	.	0.25	.	.
Zn	M1a	1	0	-0.10985(19)	0.049(5)	0.034(2)	Uani	d	.	0.1769(16)	.	.
Ga	M1ag	1	0	-0.10985(19)	0.049(5)	0.034(2)	Uani	d	.	0.0590(5)	.	.
Zn	M1b	1	0.5	-0.13516(11)	0	0.0113(6)	Uani	d	.	0.396(3)	.	.
Ga	M1bg	1	0.5	-0.13516(11)	0	0.0113(6)	Uani	d	.	0.1320(11)	.	.
Zn	M1c	1	0	0.87414(6)	0	0.0089(3)	Uani	d	.	0.75	.	.
Ga	M1cg	1	0	0.87414(6)	0	0.0089(3)	Uani	d	.	0.25	.	.
Zn	M2	1	0	0.88428(2)	0.5	0.01097(10)	Uani	d	.	0.75	.	.
Ga	M2g	1	0	0.88428(2)	0.5	0.01097(10)	Uani	d	.	0.25	.	.
O	O1	2	0	0.63435(13)	0.25	0.0155(6)	Uani	d	.	1	.	.
O	O2	2	0	0.13556(14)	0.75	0.0254(9)	Uani	d	.	1	.	.

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

Atom site label	U11	U22	U33	U23	Atom site symbol
M1	0.0106(3)	0.0081(2)	0.0216(3)	0	Zn
M1g	0.0106(3)	0.0081(2)	0.0216(3)	0	Ga
M1a	0.068(3)	0.0092(13)	0.024(7)	-0.004(2)	Zn
M1ag	0.068(3)	0.0092(13)	0.024(7)	-0.004(2)	Ga
M1b	0.0178(12)	0.0078(9)	0.0083(9)	0	Zn
M1bg	0.0178(12)	0.0078(9)	0.0083(9)	0	Ga
M1c	0.0084(5)	0.0076(5)	0.0107(5)	0	Zn
M1cg	0.0084(5)	0.0076(5)	0.0107(5)	0	Ga
M2	0.00950(19)	0.00838(16)	0.01504(19)	0	Zn
M2g	0.00950(19)	0.00838(16)	0.01504(19)	0	Ga
O1	0.0143(9)	0.0115(11)	0.0207(12)	0	O
O2	0.0312(17)	0.0163(13)	0.0287(16)	0	O

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_z
1	0.00000	1.12500
2	0.00000	2.25000
3	0.00000	3.37500
4	0.00000	4.50000

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
M1gx1	M1g	x	1
M1gy1	M1g	y	1
M1gz1	M1g	z	1
M1gx2	M1g	x	2
M1gy2	M1g	y	2
M1gz2	M1g	z	2
M1gx3	M1g	x	3
M1gy3	M1g	y	3
M1gz3	M1g	z	3
M2x1	M2	x	1
M2y1	M2	y	1
M2z1	M2	z	1
M2x2	M2	x	2
M2y2	M2	y	2
M2z2	M2	z	2
M2x3	M2	x	3
M2y3	M2	y	3
M2z3	M2	z	3
M2x4	M2	x	4
M2y4	M2	y	4
M2z4	M2	z	4
M2gx1	M2g	x	1
M2gy1	M2g	y	1
M2gz1	M2g	z	1
M2gx2	M2g	x	2
M2gy2	M2g	y	2
M2gz2	M2g	z	2
M2gx3	M2g	x	3
M2gy3	M2g	y	3
M2gz3	M2g	z	3
M2gx4	M2g	x	4
M2gy4	M2g	y	4
M2gz4	M2g	z	4
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
O2x1	O2	x	1
O2y1	O2	y	1
O2z1	O2	z	1
O2x2	O2	x	2
O2y2	O2	y	2
O2z2	O2	z	2
O2x3	O2	x	3
O2y3	O2	y	3
O2z3	O2	z	3
O2x4	O2	x	4
O2y4	O2	y	4
O2z4	O2	z	4

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

Modulation code	Cosine coefficient	Sine coefficient
M1x1	0	0
M1y1	0	-0.00109(4)
M1z1	0.0464(2)	0
M1x2	0	0
M1y2	0.00297(5)	0
M1z2	0	-0.0243(3)
M1x3	0	0
M1y3	0	0
M1z3	-0.0097(2)	0
M1gx1	0	0
M1gy1	0	-0.00109(4)
M1gz1	0.0464(2)	0
M1gx2	0	0
M1gy2	0.00297(5)	0
M1gz2	0	-0.0243(3)
M1gx3	0	0
M1gy3	0	0
M1gz3	-0.0097(2)	0
M2x1	0	0
M2y1	0	0.00341(3)
M2z1	-0.0594(2)	0
M2x2	0	0
M2y2	0.00027(3)	0
M2z2	0	-0.0247(2)
M2x3	0	0
M2y3	0	-0.00184(3)
M2z3	-0.0113(2)	0
M2x4	0	0
M2y4	0	0
M2z4	0	0.01022(15)
M2gx1	0	0
M2gy1	0	0.00341(3)
M2gz1	-0.0594(2)	0
M2gx2	0	0
M2gy2	0.00027(3)	0
M2gz2	0	-0.0247(2)
M2gx3	0	0
M2gy3	0	-0.00184(3)
M2gz3	-0.0113(2)	0
M2gx4	0	0
M2gy4	0	0
M2gz4	0	0.01022(15)
O1x1	0	0
O1y1	0.01080(17)	0
O1z1	0	0.0523(16)
O1x2	0	0
O1y2	-0.00131(18)	0
O1z2	0	-0.0468(14)
O1x3	0	0
O1y3	-0.00626(17)	0
O1z3	0	0.0416(15)
O1x4	0	0
O1y4	-0.00121(18)	0
O1z4	0	0.0167(14)
O2x1	0	0
O2y1	-0.0122(2)	0
O2z1	0	-0.0407(19)
O2x2	0	0
O2y2	0.00057(19)	0
O2z2	0	-0.0623(15)
O2x3	0	0
O2y3	0.00424(18)	0
O2z3	0	-0.0284(18)
O2x4	0	0
O2y4	0.00182(19)	0
O2z4	0	-0.0205(16)

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

Modulation code	Atom site label	Tensor element	Wave vector code
M1U111	M1	U11	1
M1U221	M1	U22	1
M1U331	M1	U33	1
M1U121	M1	U12	1
M1U131	M1	U13	1
M1U231	M1	U23	1
M1U112	M1	U11	2
M1U222	M1	U22	2
M1U332	M1	U33	2
M1U122	M1	U12	2
M1U132	M1	U13	2
M1U232	M1	U23	2
M1U113	M1	U11	3
M1U223	M1	U22	3
M1U333	M1	U33	3
M1U123	M1	U12	3
M1U133	M1	U13	3
M1U233	M1	U23	3
M1gU111	M1g	U11	1
M1gU221	M1g	U22	1
M1gU331	M1g	U33	1
M1gU121	M1g	U12	1
M1gU131	M1g	U13	1
M1gU231	M1g	U23	1
M1gU112	M1g	U11	2
M1gU222	M1g	U22	2
M1gU332	M1g	U33	2
M1gU122	M1g	U12	2
M1gU132	M1g	U13	2
M1gU232	M1g	U23	2
M1gU113	M1g	U11	3
M1gU223	M1g	U22	3
M1gU333	M1g	U33	3
M1gU123	M1g	U12	3
M1gU133	M1g	U13	3
M1gU233	M1g	U23	3
M2U111	M2	U11	1
M2U221	M2	U22	1
M2U331	M2	U33	1
M2U121	M2	U12	1
M2U131	M2	U13	1
M2U231	M2	U23	1
M2U112	M2	U11	2
M2U222	M2	U22	2
M2U332	M2	U33	2
M2U122	M2	U12	2
M2U132	M2	U13	2
M2U232	M2	U23	2
M2U113	M2	U11	3
M2U223	M2	U22	3
M2U333	M2	U33	3
M2U123	M2	U12	3
M2U133	M2	U13	3
M2U233	M2	U23	3
M2U114	M2	U11	4
M2U224	M2	U22	4
M2U334	M2	U33	4
M2U124	M2	U12	4
M2U134	M2	U13	4
M2U234	M2	U23	4
M2gU111	M2g	U11	1
M2gU221	M2g	U22	1
M2gU331	M2g	U33	1
M2gU121	M2g	U12	1
M2gU131	M2g	U13	1
M2gU231	M2g	U23	1
M2gU112	M2g	U11	2
M2gU222	M2g	U22	2
M2gU332	M2g	U33	2
M2gU122	M2g	U12	2
M2gU132	M2g	U13	2
M2gU232	M2g	U23	2
M2gU113	M2g	U11	3
M2gU223	M2g	U22	3
M2gU333	M2g	U33	3
M2gU123	M2g	U12	3
M2gU133	M2g	U13	3
M2gU233	M2g	U23	3
M2gU114	M2g	U11	4
M2gU224	M2g	U22	4
M2gU334	M2g	U33	4
M2gU124	M2g	U12	4
M2gU134	M2g	U13	4
M2gU234	M2g	U23	4
O1U111	O1	U11	1
O1U221	O1	U22	1
O1U331	O1	U33	1
O1U121	O1	U12	1
O1U131	O1	U13	1
O1U231	O1	U23	1
O1U112	O1	U11	2
O1U222	O1	U22	2
O1U332	O1	U33	2
O1U122	O1	U12	2
O1U132	O1	U13	2
O1U232	O1	U23	2
O1U113	O1	U11	3
O1U223	O1	U22	3
O1U333	O1	U33	3
O1U123	O1	U12	3
O1U133	O1	U13	3
O1U233	O1	U23	3
O1U114	O1	U11	4
O1U224	O1	U22	4
O1U334	O1	U33	4
O1U124	O1	U12	4
O1U134	O1	U13	4
O1U234	O1	U23	4
O2U111	O2	U11	1
O2U221	O2	U22	1
O2U331	O2	U33	1
O2U121	O2	U12	1
O2U131	O2	U13	1
O2U231	O2	U23	1
O2U112	O2	U11	2
O2U222	O2	U22	2
O2U332	O2	U33	2
O2U122	O2	U12	2
O2U132	O2	U13	2
O2U232	O2	U23	2
O2U113	O2	U11	3
O2U223	O2	U22	3
O2U333	O2	U33	3
O2U123	O2	U12	3
O2U133	O2	U13	3
O2U233	O2	U23	3
O2U114	O2	U11	4
O2U224	O2	U22	4
O2U334	O2	U33	4
O2U124	O2	U12	4
O2U134	O2	U13	4
O2U234	O2	U23	4

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

Modulation code	Cosine coefficient	Sine coefficient
M1U111	0	0.0015(3)
M1U221	0	-0.0002(3)
M1U331	0	0.0105(5)
M1U121	0	0
M1U131	0	0
M1U231	-0.0058(2)	0
M1U112	-0.0031(4)	0
M1U222	-0.0008(4)	0
M1U332	-0.0063(5)	0
M1U122	0	0
M1U132	0	0
M1U232	0	-0.0006(2)
M1U113	0	0
M1U223	0	0
M1U333	0	0
M1U123	0	0
M1U133	0	0
M1U233	0.0018(2)	0
M1gU111	0	0.0015(3)
M1gU221	0	-0.0002(3)
M1gU331	0	0.0105(5)
M1gU121	0	0
M1gU131	0	0
M1gU231	-0.0058(2)	0
M1gU112	-0.0031(4)	0
M1gU222	-0.0008(4)	0
M1gU332	-0.0063(5)	0
M1gU122	0	0
M1gU132	0	0
M1gU232	0	-0.0006(2)
M1gU113	0	0
M1gU223	0	0
M1gU333	0	0
M1gU123	0	0
M1gU133	0	0
M1gU233	0.0018(2)	0
M2U111	0	0.0012(2)
M2U221	0	-0.0004(2)
M2U331	0	-0.0032(3)
M2U121	0	0
M2U131	0	0
M2U231	0.0050(2)	0
M2U112	-0.0008(3)	0
M2U222	-0.0005(2)	0
M2U332	0.0027(2)	0
M2U122	0	0
M2U132	0	0
M2U232	0	-0.0013(2)
M2U113	0	-0.0012(2)
M2U223	0	0.0002(2)
M2U333	0	-0.0027(3)
M2U123	0	0
M2U133	0	0
M2U233	-0.0002(2)	0
M2U114	0	0
M2U224	0	0
M2U334	0	0
M2U124	0	0
M2U134	0	0
M2U234	0	0.00049(15)
M2gU111	0	0.0012(2)
M2gU221	0	-0.0004(2)
M2gU331	0	-0.0032(3)
M2gU121	0	0
M2gU131	0	0
M2gU231	0.0050(2)	0
M2gU112	-0.0008(3)	0
M2gU222	-0.0005(2)	0
M2gU332	0.0027(2)	0
M2gU122	0	0
M2gU132	0	0
M2gU232	0	-0.0013(2)
M2gU113	0	-0.0012(2)
M2gU223	0	0.0002(2)
M2gU333	0	-0.0027(3)
M2gU123	0	0
M2gU133	0	0
M2gU233	-0.0002(2)	0
M2gU114	0	0
M2gU224	0	0
M2gU334	0	0
M2gU124	0	0
M2gU134	0	0
M2gU234	0	0.00049(15)
O1U111	0.0043(17)	0
O1U221	0.0013(14)	0
O1U331	0.0021(18)	0
O1U121	0	0
O1U131	0	0
O1U231	0	-0.0078(15)
O1U112	0.0007(13)	0
O1U222	0.0002(14)	0
O1U332	-0.0116(19)	0
O1U122	0	0
O1U132	0	0
O1U232	0	-0.0002(12)
O1U113	0.0045(17)	0
O1U223	0.0031(14)	0
O1U333	-0.0010(19)	0
O1U123	0	0
O1U133	0	0
O1U233	0	0.0036(13)
O1U114	0.0016(15)	0
O1U224	0.0016(14)	0
O1U334	0.0070(16)	0
O1U124	0	0
O1U134	0	0
O1U234	0	0.0044(13)
O2U111	-0.038(3)	0
O2U221	0.0009(15)	0
O2U331	-0.007(2)	0
O2U121	0	0
O2U131	0	0
O2U231	0	0.0164(19)
O2U112	0.030(3)	0
O2U222	-0.0066(18)	0
O2U332	-0.015(3)	0
O2U122	0	0
O2U132	0	0
O2U232	0	-0.0027(15)
O2U113	-0.021(2)	0
O2U223	0.0003(15)	0
O2U333	-0.008(2)	0
O2U123	0	0
O2U133	0	0
O2U233	0	-0.0092(18)
O2U114	0.0079(16)	0
O2U224	0.0023(16)	0
O2U334	0.011(2)	0
O2U124	0	0
O2U134	0	0
O2U234	0	-0.0023(17)

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

Atom site label	Ay	Center (x0)	Width
M1	0.375	0	0.375
M1g	0.375	0	0.375
M2	0.5	0.5	0.5
M2g	0.5	0.5	0.5
O1	0.5625	0.75	0.5
O2	0.5625	0.25	0.5

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

Atom site label	Center (x0)	Width
M1a	0.805(6)	0.125
M1ag	0.8042	0.125
M1b	0.75	0.125
M1bg	0.75	0.125
M1c	0.25	0.125
M1cg	0.25	0.125

m_9

Chemical data

Structural Formula Sum: Ga0.1818 O1.0909 Zn0.8181 [ Help ]

Formula weight: 83.6 Da [ Help ]

Crystallographic data and experimental details

Crystal system: orthorhombic [ Help ]

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

a: 3.2494(14) Å [ Help ]

b: 19.722(6) Å [ Help ]

c: 3.0513(11) Å [ Help ]

α: 90 ° [ Help ]

β: 90 ° [ Help ]

γ: 90 ° [ Help ]

Volume: 195.54(12) Å³ [ Help ]

Z: 8 [ Help ]

Cell determination reflection Nb.: 25 [ Help ]

θ(min) for cell determination: 15.0 ° [ Help ]

θ(max) for cell determination: 16.8 ° [ Help ]

Cell measurement temperature: 298 K [ Help ]

Modulation dimension: 1 [ Help ]

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	0.0	1.0
0.0	0.0	1.0	0.0

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

Wave vector id	q_x	q_y	q_z
1	0.00000	0.00000	1.09091

μ: 24.7 mm^-1 [ Help ]

Absorption correction type: analytical [ Help ]

Absorption correction remarks: Tompa Analytical [ Help ]

Minimum transmission factor: 0.034 [ Help ]

Maximum transmission factor: 0.417 [ Help ]

Refinement details

Total nb. of reflections: 1862 [ Help ]

Nb. of observed reflections: 993 [ Help ]

Intense reflections threshold: I>2σ(I) [ Help ]

Refinement based on: Fsqd [ Help ]

R(all): 0.0827 [ Help ]

R(obs): 0.0340 [ Help ]

wR(obs): 0.0598 [ Help ]

wR(all): 0.0677 [ Help ]

S(all): 1.35 [ Help ]

Nb. of reflections: 1862 [ Help ]

Nb. of parameters: 149 [ Help ]

Number of restraints: 0 [ Help ]

Number of constraints: 5 [ Help ]

Weighting scheme: sigma [ Help ]

Weighting scheme remarks: w=1/(σ²(I)+0.0001I²) [ Help ]

Δ/σ(max): 0.0165 [ Help ]

Δ/σ(mean): 0.0015 [ Help ]

Δρ(max): 1.60 e_Å^-3 [ Help ]

Δρ(min): -1.21 e_Å^-3 [ Help ]

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

Extinction coefficient: 59E1(2) [ Help ]

Structural Information

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

Atom symbol	Atom site label	Subsystem	x	y	z	Uiso/equiv	ADP type	Coords from (d)iffraction or (c)alculated	Coords restraints or constraints	Occupancy	Disordered cluster	Disordered group
Zn	M1	1	0	0.63438(3)	0.25	0.01132(14)	Uani	d	.	0.8181	.	.
Ga	M1g	1	0	0.63438(3)	0.25	0.01132(14)	Uani	d	.	0.1919	.	.
Zn	M1a	1	0	-0.04159(19)	0.25	0.0422(12)	Uani	d	.	0.456(4)	.	.
Ga	M1ag	1	0	-0.04159(19)	0.25	0.0422(12)	Uani	d	.	0.1013(8)	.	.
Zn	M1b	1	0.5	-0.06856(18)	0.25	0.0154(9)	Uani	d	.	0.362(4)	.	.
Ga	M1bg	1	0.5	-0.06856(18)	0.25	0.0154(9)	Uani	d	.	0.0805(8)	.	.
Zn	M2	1	0	0.13443(2)	0.75	0.01253(12)	Uani	d	.	0.8181	.	.
Ga	M2g	1	0	0.13443(2)	0.75	0.01253(12)	Uani	d	.	0.1919	.	.
O	O1	2	0	0.38420(13)	0	0.0173(7)	Uani	d	.	1	.	.
O	O2	2	0	0.88545(15)	0.5	0.0217(8)	Uani	d	.	1	.	.

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

Atom site label	U11	U22	U33	Atom site symbol
M1	0.00793(18)	0.0099(3)	0.0161(2)	Zn
M1g	0.00793(18)	0.0099(3)	0.0161(2)	Ga
M1a	0.076(3)	0.0118(17)	0.0391(19)	Zn
M1ag	0.076(3)	0.0118(17)	0.0391(19)	Ga
M1b	0.0270(16)	0.0081(16)	0.0113(14)	Zn
M1bg	0.0270(16)	0.0081(16)	0.0113(14)	Ga
M2	0.00863(16)	0.0098(3)	0.0192(2)	Zn
M2g	0.00863(16)	0.0098(3)	0.0192(2)	Ga
O1	0.0109(10)	0.0158(14)	0.0251(13)	O
O2	0.0241(14)	0.0134(13)	0.0276(14)	O

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_z
1	0.00000	1.09091
2	0.00000	2.18182
3	0.00000	3.27273
4	0.00000	4.36364
5	0.00000	5.45455
6	0.00000	6.54545

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
M1gx1	M1g	x	1
M1gy1	M1g	y	1
M1gz1	M1g	z	1
M1gx2	M1g	x	2
M1gy2	M1g	y	2
M1gz2	M1g	z	2
M1gx3	M1g	x	3
M1gy3	M1g	y	3
M1gz3	M1g	z	3
M1gx4	M1g	x	4
M1gy4	M1g	y	4
M1gz4	M1g	z	4
M1gx5	M1g	x	5
M1gy5	M1g	y	5
M1gz5	M1g	z	5
M2x1	M2	x	1
M2y1	M2	y	1
M2z1	M2	z	1
M2x2	M2	x	2
M2y2	M2	y	2
M2z2	M2	z	2
M2x3	M2	x	3
M2y3	M2	y	3
M2z3	M2	z	3
M2x4	M2	x	4
M2y4	M2	y	4
M2z4	M2	z	4
M2x5	M2	x	5
M2y5	M2	y	5
M2z5	M2	z	5
M2gx1	M2g	x	1
M2gy1	M2g	y	1
M2gz1	M2g	z	1
M2gx2	M2g	x	2
M2gy2	M2g	y	2
M2gz2	M2g	z	2
M2gx3	M2g	x	3
M2gy3	M2g	y	3
M2gz3	M2g	z	3
M2gx4	M2g	x	4
M2gy4	M2g	y	4
M2gz4	M2g	z	4
M2gx5	M2g	x	5
M2gy5	M2g	y	5
M2gz5	M2g	z	5
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
O2x1	O2	x	1
O2y1	O2	y	1
O2z1	O2	z	1
O2x2	O2	x	2
O2y2	O2	y	2
O2z2	O2	z	2
O2x3	O2	x	3
O2y3	O2	y	3
O2z3	O2	z	3
O2x4	O2	x	4
O2y4	O2	y	4
O2z4	O2	z	4
O2x5	O2	x	5
O2y5	O2	y	5
O2z5	O2	z	5
O2x6	O2	x	6
O2y6	O2	y	6
O2z6	O2	z	6

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

Modulation code	Cosine coefficient	Sine coefficient
M1x1	0	0
M1y1	0.00576(4)	0
M1z1	0	0.0509(2)
M1x2	0	0
M1y2	-0.00146(4)	0
M1z2	0	0.02017(18)
M1x3	0	0
M1y3	0.00219(4)	0
M1z3	0	0.0158(2)
M1x4	0	0
M1y4	-0.00062(5)	0
M1z4	0	0.02014(18)
M1x5	0	0
M1y5	0	0
M1z5	0	-0.01453(18)
M1gx1	0	0
M1gy1	0.00576(4)	0
M1gz1	0	0.0509(2)
M1gx2	0	0
M1gy2	-0.00146(4)	0
M1gz2	0	0.02017(18)
M1gx3	0	0
M1gy3	0.00219(4)	0
M1gz3	0	0.0158(2)
M1gx4	0	0
M1gy4	-0.00062(5)	0
M1gz4	0	0.02014(18)
M1gx5	0	0
M1gy5	0	0
M1gz5	0	-0.01453(18)
M2x1	0	0
M2y1	-0.00641(3)	0
M2z1	0	-0.0522(2)
M2x2	0	0
M2y2	-0.00133(3)	0
M2z2	0	0.03131(18)
M2x3	0	0
M2y3	-0.00498(3)	0
M2z3	0	-0.0169(2)
M2x4	0	0
M2y4	-0.00106(4)	0
M2z4	0	0.00403(17)
M2x5	0	0
M2y5	-0.00072(4)	0
M2z5	0	-0.0006(2)
M2gx1	0	0
M2gy1	-0.00641(3)	0
M2gz1	0	-0.0522(2)
M2gx2	0	0
M2gy2	-0.00133(3)	0
M2gz2	0	0.03131(18)
M2gx3	0	0
M2gy3	-0.00498(3)	0
M2gz3	0	-0.0169(2)
M2gx4	0	0
M2gy4	-0.00106(4)	0
M2gz4	0	0.00403(17)
M2gx5	0	0
M2gy5	-0.00072(4)	0
M2gz5	0	-0.0006(2)
O1x1	0	0
O1y1	0	-0.00868(19)
O1z1	0.0582(14)	0
O1x2	0	0
O1y2	0.00021(19)	0
O1z2	0	0.0562(13)
O1x3	0	0
O1y3	0	-0.00812(18)
O1z3	-0.0243(13)	0
O1x4	0	0
O1y4	-0.00071(18)	0
O1z4	0	0.0146(12)
O1x5	0	0
O1y5	0	0.00187(19)
O1z5	0.0282(14)	0
O1x6	0	0
O1y6	0.00000(14)	0
O1z6	0	0
O2x1	0	0
O2y1	0	0.0108(2)
O2z1	-0.0443(14)	0
O2x2	0	0
O2y2	-0.0001(2)	0
O2z2	0	0.0628(14)
O2x3	0	0
O2y3	0	0.00675(19)
O2z3	0.0165(14)	0
O2x4	0	0
O2y4	-0.00002(19)	0
O2z4	0	0.0098(13)
O2x5	0	0
O2y5	0	0.00051(19)
O2z5	-0.0080(13)	0
O2x6	0	0
O2y6	0	0
O2z6	0	0.0084(8)

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

Modulation code	Atom site label	Tensor element	Wave vector code
M1U111	M1	U11	1
M1U221	M1	U22	1
M1U331	M1	U33	1
M1U121	M1	U12	1
M1U131	M1	U13	1
M1U231	M1	U23	1
M1U112	M1	U11	2
M1U222	M1	U22	2
M1U332	M1	U33	2
M1U122	M1	U12	2
M1U132	M1	U13	2
M1U232	M1	U23	2
M1U113	M1	U11	3
M1U223	M1	U22	3
M1U333	M1	U33	3
M1U123	M1	U12	3
M1U133	M1	U13	3
M1U233	M1	U23	3
M1U114	M1	U11	4
M1U224	M1	U22	4
M1U334	M1	U33	4
M1U124	M1	U12	4
M1U134	M1	U13	4
M1U234	M1	U23	4
M1U115	M1	U11	5
M1U225	M1	U22	5
M1U335	M1	U33	5
M1U125	M1	U12	5
M1U135	M1	U13	5
M1U235	M1	U23	5
M1gU111	M1g	U11	1
M1gU221	M1g	U22	1
M1gU331	M1g	U33	1
M1gU121	M1g	U12	1
M1gU131	M1g	U13	1
M1gU231	M1g	U23	1
M1gU112	M1g	U11	2
M1gU222	M1g	U22	2
M1gU332	M1g	U33	2
M1gU122	M1g	U12	2
M1gU132	M1g	U13	2
M1gU232	M1g	U23	2
M1gU113	M1g	U11	3
M1gU223	M1g	U22	3
M1gU333	M1g	U33	3
M1gU123	M1g	U12	3
M1gU133	M1g	U13	3
M1gU233	M1g	U23	3
M1gU114	M1g	U11	4
M1gU224	M1g	U22	4
M1gU334	M1g	U33	4
M1gU124	M1g	U12	4
M1gU134	M1g	U13	4
M1gU234	M1g	U23	4
M1gU115	M1g	U11	5
M1gU225	M1g	U22	5
M1gU335	M1g	U33	5
M1gU125	M1g	U12	5
M1gU135	M1g	U13	5
M1gU235	M1g	U23	5
M2U111	M2	U11	1
M2U221	M2	U22	1
M2U331	M2	U33	1
M2U121	M2	U12	1
M2U131	M2	U13	1
M2U231	M2	U23	1
M2U112	M2	U11	2
M2U222	M2	U22	2
M2U332	M2	U33	2
M2U122	M2	U12	2
M2U132	M2	U13	2
M2U232	M2	U23	2
M2U113	M2	U11	3
M2U223	M2	U22	3
M2U333	M2	U33	3
M2U123	M2	U12	3
M2U133	M2	U13	3
M2U233	M2	U23	3
M2U114	M2	U11	4
M2U224	M2	U22	4
M2U334	M2	U33	4
M2U124	M2	U12	4
M2U134	M2	U13	4
M2U234	M2	U23	4
M2U115	M2	U11	5
M2U225	M2	U22	5
M2U335	M2	U33	5
M2U125	M2	U12	5
M2U135	M2	U13	5
M2U235	M2	U23	5
M2gU111	M2g	U11	1
M2gU221	M2g	U22	1
M2gU331	M2g	U33	1
M2gU121	M2g	U12	1
M2gU131	M2g	U13	1
M2gU231	M2g	U23	1
M2gU112	M2g	U11	2
M2gU222	M2g	U22	2
M2gU332	M2g	U33	2
M2gU122	M2g	U12	2
M2gU132	M2g	U13	2
M2gU232	M2g	U23	2
M2gU113	M2g	U11	3
M2gU223	M2g	U22	3
M2gU333	M2g	U33	3
M2gU123	M2g	U12	3
M2gU133	M2g	U13	3
M2gU233	M2g	U23	3
M2gU114	M2g	U11	4
M2gU224	M2g	U22	4
M2gU334	M2g	U33	4
M2gU124	M2g	U12	4
M2gU134	M2g	U13	4
M2gU234	M2g	U23	4
M2gU115	M2g	U11	5
M2gU225	M2g	U22	5
M2gU335	M2g	U33	5
M2gU125	M2g	U12	5
M2gU135	M2g	U13	5
M2gU235	M2g	U23	5
O1U111	O1	U11	1
O1U221	O1	U22	1
O1U331	O1	U33	1
O1U121	O1	U12	1
O1U131	O1	U13	1
O1U231	O1	U23	1
O1U112	O1	U11	2
O1U222	O1	U22	2
O1U332	O1	U33	2
O1U122	O1	U12	2
O1U132	O1	U13	2
O1U232	O1	U23	2
O1U113	O1	U11	3
O1U223	O1	U22	3
O1U333	O1	U33	3
O1U123	O1	U12	3
O1U133	O1	U13	3
O1U233	O1	U23	3
O1U114	O1	U11	4
O1U224	O1	U22	4
O1U334	O1	U33	4
O1U124	O1	U12	4
O1U134	O1	U13	4
O1U234	O1	U23	4
O1U115	O1	U11	5
O1U225	O1	U22	5
O1U335	O1	U33	5
O1U125	O1	U12	5
O1U135	O1	U13	5
O1U235	O1	U23	5
O1U116	O1	U11	6
O1U226	O1	U22	6
O1U336	O1	U33	6
O1U126	O1	U12	6
O1U136	O1	U13	6
O1U236	O1	U23	6
O2U111	O2	U11	1
O2U221	O2	U22	1
O2U331	O2	U33	1
O2U121	O2	U12	1
O2U131	O2	U13	1
O2U231	O2	U23	1
O2U112	O2	U11	2
O2U222	O2	U22	2
O2U332	O2	U33	2
O2U122	O2	U12	2
O2U132	O2	U13	2
O2U232	O2	U23	2
O2U113	O2	U11	3
O2U223	O2	U22	3
O2U333	O2	U33	3
O2U123	O2	U12	3
O2U133	O2	U13	3
O2U233	O2	U23	3
O2U114	O2	U11	4
O2U224	O2	U22	4
O2U334	O2	U33	4
O2U124	O2	U12	4
O2U134	O2	U13	4
O2U234	O2	U23	4
O2U115	O2	U11	5
O2U225	O2	U22	5
O2U335	O2	U33	5
O2U125	O2	U12	5
O2U135	O2	U13	5
O2U235	O2	U23	5
O2U116	O2	U11	6
O2U226	O2	U22	6
O2U336	O2	U33	6
O2U126	O2	U12	6
O2U136	O2	U13	6
O2U236	O2	U23	6

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

Modulation code	Cosine coefficient	Sine coefficient
M1U111	0.0000(3)	0
M1U221	-0.0001(5)	0
M1U331	-0.0014(3)	0
M1U121	0	0
M1U131	0	0
M1U231	0	-0.0043(2)
M1U112	0.0009(3)	0
M1U222	0.0001(4)	0
M1U332	-0.0042(4)	0
M1U122	0	0
M1U132	0	0
M1U232	0	0.0002(2)
M1U113	0.0002(3)	0
M1U223	0.0002(4)	0
M1U333	-0.0034(3)	0
M1U123	0	0
M1U133	0	0
M1U233	0	-0.0006(2)
M1U114	-0.0002(3)	0
M1U224	-0.0002(5)	0
M1U334	-0.0029(4)	0
M1U124	0	0
M1U134	0	0
M1U234	0	0.0007(2)
M1U115	0	0
M1U225	0	0
M1U335	0	0
M1U125	0	0
M1U135	0	0
M1U235	0	0.0001(2)
M1gU111	0.0000(3)	0
M1gU221	-0.0001(5)	0
M1gU331	-0.0014(3)	0
M1gU121	0	0
M1gU131	0	0
M1gU231	0	-0.0043(2)
M1gU112	0.0009(3)	0
M1gU222	0.0001(4)	0
M1gU332	-0.0042(4)	0
M1gU122	0	0
M1gU132	0	0
M1gU232	0	0.0002(2)
M1gU113	0.0002(3)	0
M1gU223	0.0002(4)	0
M1gU333	-0.0034(3)	0
M1gU123	0	0
M1gU133	0	0
M1gU233	0	-0.0006(2)
M1gU114	-0.0002(3)	0
M1gU224	-0.0002(5)	0
M1gU334	-0.0029(4)	0
M1gU124	0	0
M1gU134	0	0
M1gU234	0	0.0007(2)
M1gU115	0	0
M1gU225	0	0
M1gU335	0	0
M1gU125	0	0
M1gU135	0	0
M1gU235	0	0.0001(2)
M2U111	0.0005(2)	0
M2U221	-0.0006(3)	0
M2U331	0.0028(3)	0
M2U121	0	0
M2U131	0	0
M2U231	0	0.0055(2)
M2U112	0.0023(2)	0
M2U222	-0.0002(3)	0
M2U332	-0.0016(2)	0
M2U122	0	0
M2U132	0	0
M2U232	0	0.0008(2)
M2U113	-0.0002(2)	0
M2U223	0.0001(3)	0
M2U333	0.0005(3)	0
M2U123	0	0
M2U133	0	0
M2U233	0	0.0010(2)
M2U114	-0.0012(2)	0
M2U224	-0.0004(3)	0
M2U334	-0.0035(2)	0
M2U124	0	0
M2U134	0	0
M2U234	0	0.0010(2)
M2U115	-0.0015(2)	0
M2U225	0.0001(3)	0
M2U335	-0.0038(3)	0
M2U125	0	0
M2U135	0	0
M2U235	0	-0.0009(2)
M2gU111	0.0005(2)	0
M2gU221	-0.0006(3)	0
M2gU331	0.0028(3)	0
M2gU121	0	0
M2gU131	0	0
M2gU231	0	0.0055(2)
M2gU112	0.0023(2)	0
M2gU222	-0.0002(3)	0
M2gU332	-0.0016(2)	0
M2gU122	0	0
M2gU132	0	0
M2gU232	0	0.0008(2)
M2gU113	-0.0002(2)	0
M2gU223	0.0001(3)	0
M2gU333	0.0005(3)	0
M2gU123	0	0
M2gU133	0	0
M2gU233	0	0.0010(2)
M2gU114	-0.0012(2)	0
M2gU224	-0.0004(3)	0
M2gU334	-0.0035(2)	0
M2gU124	0	0
M2gU134	0	0
M2gU234	0	0.0010(2)
M2gU115	-0.0015(2)	0
M2gU225	0.0001(3)	0
M2gU335	-0.0038(3)	0
M2gU125	0	0
M2gU135	0	0
M2gU235	0	-0.0009(2)
O1U111	0	-0.0034(13)
O1U221	0	-0.001(2)
O1U331	0	-0.0009(16)
O1U121	0	0
O1U131	0	0
O1U231	-0.0113(16)	0
O1U112	-0.0037(13)	0
O1U222	0.002(2)	0
O1U332	0.018(2)	0
O1U122	0	0
O1U132	0	0
O1U232	0	-0.0012(15)
O1U113	0	0.0014(15)
O1U223	0	0.0020(19)
O1U333	0	0.0017(16)
O1U123	0	0
O1U133	0	0
O1U233	-0.0084(16)	0
O1U114	0.0018(15)	0
O1U224	0.005(2)	0
O1U334	0.0092(19)	0
O1U124	0	0
O1U134	0	0
O1U234	0	-0.0021(13)
O1U115	0	-0.0054(15)
O1U225	0	-0.001(2)
O1U335	0	0.0001(14)
O1U125	0	0
O1U135	0	0
O1U235	-0.0075(16)	0
O1U116	-0.0016(10)	0
O1U226	0.0023(13)	0
O1U336	0.0030(13)	0
O1U126	0	0
O1U136	0	0
O1U236	0	0
O2U111	0	0.028(2)
O2U221	0	0.001(2)
O2U331	0	0.0048(18)
O2U121	0	0
O2U131	0	0
O2U231	0.0147(16)	0
O2U112	-0.024(2)	0
O2U222	0.005(2)	0
O2U332	0.007(2)	0
O2U122	0	0
O2U132	0	0
O2U232	0	-0.0012(16)
O2U113	0	-0.0205(18)
O2U223	0	0.000(2)
O2U333	0	-0.0070(19)
O2U123	0	0
O2U133	0	0
O2U233	0.0078(15)	0
O2U114	0.0132(17)	0
O2U224	0.0023(18)	0
O2U334	0.0086(16)	0
O2U124	0	0
O2U134	0	0
O2U234	0	-0.0041(15)
O2U115	0	0.0054(14)
O2U225	0	-0.001(2)
O2U335	0	0.0006(18)
O2U125	0	0
O2U135	0	0
O2U235	0.0029(14)	0
O2U116	0	0
O2U226	0	0
O2U336	0	0
O2U126	0	0
O2U136	0	0
O2U236	0	0.0014(11)

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

Atom site label	Ay	Center (x0)	Width
M1	-0.5625	0.75	0.4091
M1g	-0.5625	0.75	0.4091
M2	-0.6875	0.25	0.5
M2g	-0.6875	0.25	0.5
O1	-0.75	0	0.5
O2	-0.75	0.5	0.5

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

Atom site label	Center (x0)	Width
M1a	0	0.0909
M1ag	0	0.0909
M1b	0	0.0909
M1bg	0	0.0909

Superspace description of the homologous series Ga2O3(ZnO)m

Michiue, Yuichi; Kimizuka, Noboru

Acta Crystallographica, Section B 66 117-129 (2010)

https://doi.org/10.1107/S0108768109053713

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m_6

Chemical data

Crystallographic data and experimental details

Refinement details

Structural Information

m_9

Chemical data

Crystallographic data and experimental details

Refinement details

Structural Information

Superspace description of the homologous series Ga₂O₃(ZnO)_m