B-IncStrDB

Structure of (Ga₂O₃)₂(ZnO)₁₃ and a unified description of the homologous series(Ga₂O₃)₂(ZnO)_2n+1

Authors:

Michiue, Yuichi; Kimizuka, Noboru; Kanke, Yasushi; Mori, Yasushi

Journal:

Acta Crystallographica, Section B 68 250-260 (2012)

DOI:

https://doi.org/10.1107/s0108768112016084

B-IncStrDB ID: 6272EzStLP Entry date: 2012-04-11 Last revision: 2022-01-02

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(I)

Chemical data

Structural Formula Sum: Ga4 O19 Zn13 [ Help ]

Formula weight: 1432.8 Da [ Help ]

Crystallographic data and experimental details

Crystal system: monoclinic [ Help ]

Space group name (H-M): C 1 2/m 1 [ Help ]

Space group name (Hall): -C 2y [ Help ]

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

Operation code	Operation in algebraic form
1	x,y,z
2	-x,y,-z
3	-x,-y,-z
4	x,-y,z
5	x+1/2,y+1/2,z
6	-x+1/2,y+1/2,-z
7	-x+1/2,-y+1/2,-z
8	x+1/2,-y+1/2,z

a: 19.66(4) Å [ Help ]

b: 3.2487(5) Å [ Help ]

c: 27.31(2) Å [ Help ]

α: 90 ° [ Help ]

β: 105.9(10) ° [ Help ]

γ: 90 ° [ Help ]

Volume: 1678(4) Å³ [ Help ]

Z: 4 [ Help ]

Cell determination reflection Nb.: 16 [ Help ]

θ(min) for cell determination: 20.1 ° [ Help ]

θ(max) for cell determination: 21 ° [ Help ]

Cell measurement temperature: 295 K [ Help ]

μ: 24.607 mm^-1 [ Help ]

Absorption correction type: psi-scan [ Help ]

Minimum transmission factor: 0.466 [ Help ]

Maximum transmission factor: 0.996 [ Help ]

Refinement details

Total nb. of reflections: 7763 [ Help ]

Nb. of observed reflections: 4676 [ Help ]

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

Refinement based on: Fsqd [ Help ]

R(obs): 0.061 [ Help ]

wR(obs): 0.1355 [ Help ]

R(all): 0.1076 [ Help ]

wR(all): 0.1949 [ Help ]

S(all): 2.88 [ Help ]

S(obs): 2.61 [ Help ]

Nb. of reflections: 7763 [ Help ]

Nb. of parameters: 225 [ Help ]

Number of constraints: 111 [ Help ]

Weighting scheme: sigma [ Help ]

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

Δ/σ(max): 0.0120 [ Help ]

Δ/σ(mean): 0.0015 [ Help ]

Δρ(max): 3.59 e_Å^-3 [ Help ]

Δρ(min): -3.74 e_Å^-3 [ Help ]

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

Extinction coefficient: 310(20) [ 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
Zn1	Zn	0.2117(5)	0	0.53326(5)	Uani	0.0099(3)	4	0.7647	d	?	?	?
Zn2	Zn	0.85726(5)	0	0.59388(5)	Uani	0.0108(3)	4	0.7647	d	?	?	?
Zn3	Zn	0.50166(6)	0	0.64777(5)	Uani	0.0149(3)	4	0.7647	d	?	?	?
Zn4	Zn	0.14303(5)	0	0.70417(4)	Uani	0.0099(3)	4	0.7647	d	?	?	?
Zn5	Zn	0.62577(6)	0	0.30013(5)	Uani	0.0099(3)	4	0.7647	d	?	?	?
Zn6	Zn	0.27143(5)	0	0.36026(5)	Uani	0.0103(3)	4	0.7647	d	?	?	?
Zn7	Zn	0.91592(5)	0	0.42068(5)	Uani	0.0102(3)	4	0.7647	d	?	?	?
Zn8	Zn	0.56414(5)	0	0.47553(5)	Uani	0.0097(3)	4	0.7647	d	?	?	?
Zn9	Zn	0.18938(6)	0	0.82541(5)	Uani	0.0112(3)	4	0.7647	d	?	?	?
Zn10	Zn	0.5881(6)	0	0.88032(6)	Uani	0.0159(3)	4	0.7647	d	?	?	?
Zn11	Zn	0.98503(6)	0	0.93459(5)	Uani	0.0128(3)	4	0.7647	d	?	?	?
Zn12	Zn	0.38574(6)	0	0.99567(5)	Uani	0.01(3)	4	0.7647	d	?	?	?
Zn13	Zn	0.77823(6)	0	0.05097(5)	Uani	0.0097(3)	4	0.7647	d	?	?	?
Zn14	Zn	0.1765(6)	0	0.11037(5)	Uani	0.0108(3)	4	0.7647	d	?	?	?
Zn15	Zn	0.57818(5)	0	0.17262(5)	Uani	0.0104(3)	4	0.7647	d	?	?	?
Zn16	Zn	0.78535(6)	0	0.76428(4)	Uani	0.0094(3)	4	0.7647	d	?	?	?
Zn17	Zn	0.97979(17)	0	0.23583(17)	Uani	0.044(16)	4	0.352(3)	d	?	?	?
Zn18	Zn	0.95397(10)	0.5	0.23574(8)	Uani	0.0098(5)	4	0.412(3)	d	?	?	?
Ga1	Ga	0.2117(5)	0	0.53326(5)	Uani	0.0099(3)	4	0.2353	d	?	?	?
Ga2	Ga	0.85726(5)	0	0.59388(5)	Uani	0.0108(3)	4	0.2353	d	?	?	?
Ga3	Ga	0.50166(6)	0	0.64777(5)	Uani	0.0149(3)	4	0.2353	d	?	?	?
Ga4	Ga	0.14303(5)	0	0.70417(4)	Uani	0.0099(3)	4	0.2353	d	?	?	?
Ga5	Ga	0.62577(6)	0	0.30013(5)	Uani	0.0099(3)	4	0.2353	d	?	?	?
Ga6	Ga	0.27143(5)	0	0.36026(5)	Uani	0.0103(3)	4	0.2353	d	?	?	?
Ga7	Ga	0.91592(5)	0	0.42068(5)	Uani	0.0102(3)	4	0.2353	d	?	?	?
Ga8	Ga	0.56414(5)	0	0.47553(5)	Uani	0.0097(3)	4	0.2353	d	?	?	?
Ga9	Ga	0.18938(6)	0	0.82541(5)	Uani	0.0112(3)	4	0.2353	d	?	?	?
Ga10	Ga	0.5881(6)	0	0.88032(6)	Uani	0.0159(3)	4	0.2353	d	?	?	?
Ga11	Ga	0.98503(6)	0	0.93459(5)	Uani	0.0128(3)	4	0.2353	d	?	?	?
Ga12	Ga	0.38574(6)	0	0.99567(5)	Uani	0.01(3)	4	0.2353	d	?	?	?
Ga13	Ga	0.77823(6)	0	0.05097(5)	Uani	0.0097(3)	4	0.2353	d	?	?	?
Ga14	Ga	0.1765(6)	0	0.11037(5)	Uani	0.0108(3)	4	0.2353	d	?	?	?
Ga15	Ga	0.57818(5)	0	0.17262(5)	Uani	0.0104(3)	4	0.2353	d	?	?	?
Ga16	Ga	0.78535(6)	0	0.76428(4)	Uani	0.0094(3)	4	0.2353	d	?	?	?
Ga17	Ga	0.97979(17)	0	0.23583(17)	Uani	0.044(16)	4	0.1084(10)	d	?	?	?
Ga18	Ga	0.95397(10)	0.5	0.23574(8)	Uani	0.0098(5)	4	0.1269(10)	d	?	?	?
O1	O	0.5357(4)	0	0.5535(3)	Uani	0.02(2)	4	1	d	?	?	?
O2	O	0.1868(3)	0	0.6049(3)	Uani	0.0116(17)	4	1	d	?	?	?
O3	O	0.8319(3)	0	0.6614(2)	Uani	0.0096(16)	4	1	d	?	?	?
O4	O	0.4744(4)	0	0.7066(4)	Uani	0.054(5)	4	1	d	?	?	?
O5	O	0.2994(3)	0	0.2959(2)	Uani	0.0072(15)	4	1	d	?	?	?
O6	O	0.9417(3)	0	0.3543(3)	Uani	0.0116(17)	4	1	d	?	?	?
O7	O	0.5881(3)	0	0.404(3)	Uani	0.0117(17)	4	1	d	?	?	?
O8	O	0.2351(4)	0	0.4553(3)	Uani	0.017(2)	4	1	d	?	?	?
O9	O	0.8873(4)	0	0.5004(3)	Uani	0.02(2)	4	1	d	?	?	?
O10	O	0.1093(4)	0	0.764(3)	Uani	0.022(2)	4	1	d	?	?	?
O11	O	0.5142(4)	0	0.8192(3)	Uani	0.042(4)	4	1	d	?	?	?
O12	O	0.907(3)	0	0.8665(3)	Uani	0.0127(17)	4	1	d	?	?	?
O13	O	0.3008(4)	0	0.9228(4)	Uani	0.024(3)	4	1	d	?	?	?
O14	O	0.6922(4)	0	0.976(4)	Uani	0.033(3)	4	1	d	?	?	?
O15	O	0.0804(5)	0	0.0222(5)	Uani	0.044(4)	4	1	d	?	?	?
O16	O	0.4632(4)	0	0.0664(3)	Uani	0.0134(18)	4	1	d	?	?	?
O17	O	0.8561(3)	0	0.1177(3)	Uani	0.0133(18)	4	1	d	?	?	?
O18	O	0.2552(3)	0	0.1759(2)	Uani	0.0093(16)	4	1	d	?	?	?
O19	O	0.6568(3)	0	0.2363(2)	Uani	0.0095(15)	4	1	d	?	?	?

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

Atom site label	Atom site symbol	U11	U22	U33	U13
Zn1	Zn	0.006(3)	0.0045(4)	0.0173(5)	0.0003(3)
Zn2	Zn	0.0069(3)	0.0058(4)	0.0178(5)	0.0005(3)
Zn3	Zn	0.0066(4)	0.0086(5)	0.0275(6)	0.0014(4)
Zn4	Zn	0.0079(4)	0.0065(4)	0.014(5)	0.001(3)
Zn5	Zn	0.0082(4)	0.0079(5)	0.0133(4)	0.0023(3)
Zn6	Zn	0.0073(4)	0.0058(4)	0.0158(5)	-0.0002(3)
Zn7	Zn	0.0063(3)	0.0057(4)	0.0168(5)	0(3)
Zn8	Zn	0.0066(3)	0.0048(4)	0.0164(5)	0.0007(3)
Zn9	Zn	0.0116(4)	0.0057(4)	0.0174(5)	0.0059(4)
Zn10	Zn	0.0119(4)	0.0078(5)	0.0312(7)	0.0114(4)
Zn11	Zn	0.0115(4)	0.0055(4)	0.0243(6)	0.0096(4)
Zn12	Zn	0.0091(3)	0.0047(4)	0.0178(5)	0.0064(3)
Zn13	Zn	0.0098(4)	0.0056(4)	0.0149(5)	0.0054(3)
Zn14	Zn	0.0119(4)	0.005(4)	0.0174(5)	0.0068(3)
Zn15	Zn	0.009(4)	0.0074(4)	0.0144(5)	0.0024(3)
Zn16	Zn	0.008(4)	0.0061(4)	0.0132(5)	0.0015(3)
Zn17	Zn	0.0147(13)	0.07(4)	0.051(2)	0.0158(14)
Zn18	Zn	0.0067(7)	0.0118(9)	0.011(8)	0.0025(6)
Ga1	Ga	0.006(3)	0.0045(4)	0.0173(5)	0.0003(3)
Ga2	Ga	0.0069(3)	0.0058(4)	0.0178(5)	0.0005(3)
Ga3	Ga	0.0066(4)	0.0086(5)	0.0275(6)	0.0014(4)
Ga4	Ga	0.0079(4)	0.0065(4)	0.014(5)	0.001(3)
Ga5	Ga	0.0082(4)	0.0079(5)	0.0133(4)	0.0023(3)
Ga6	Ga	0.0073(4)	0.0058(4)	0.0158(5)	-0.0002(3)
Ga7	Ga	0.0063(3)	0.0057(4)	0.0168(5)	0(3)
Ga8	Ga	0.0066(3)	0.0048(4)	0.0164(5)	0.0007(3)
Ga9	Ga	0.0116(4)	0.0057(4)	0.0174(5)	0.0059(4)
Ga10	Ga	0.0119(4)	0.0078(5)	0.0312(7)	0.0114(4)
Ga11	Ga	0.0115(4)	0.0055(4)	0.0243(6)	0.0096(4)
Ga12	Ga	0.0091(3)	0.0047(4)	0.0178(5)	0.0064(3)
Ga13	Ga	0.0098(4)	0.0056(4)	0.0149(5)	0.0054(3)
Ga14	Ga	0.0119(4)	0.005(4)	0.0174(5)	0.0068(3)
Ga15	Ga	0.009(4)	0.0074(4)	0.0144(5)	0.0024(3)
Ga16	Ga	0.008(4)	0.0061(4)	0.0132(5)	0.0015(3)
Ga17	Ga	0.0147(13)	0.07(4)	0.051(2)	0.0158(14)
Ga18	Ga	0.0067(7)	0.0118(9)	0.011(8)	0.0025(6)
O1	O	0.013(3)	0.007(3)	0.034(5)	-0.002(3)
O2	O	0.01(2)	0.009(3)	0.015(3)	0.003(2)
O3	O	0.01(2)	0.009(3)	0.01(3)	0.0041(19)
O4	O	0.011(3)	0.108(13)	0.036(6)	-0.004(3)
O5	O	0.011(2)	0.008(3)	0.006(2)	0.007(18)
O6	O	0.009(2)	0.008(3)	0.016(3)	0.001(2)
O7	O	0.01(2)	0.009(3)	0.015(3)	0.001(2)
O8	O	0.014(3)	0.009(3)	0.024(4)	0(3)
O9	O	0.012(3)	0.01(3)	0.033(4)	-0.003(3)
O10	O	0.022(3)	0.041(6)	0.006(3)	0.011(2)
O11	O	0.018(3)	0.098(11)	0.016(3)	0.015(3)
O12	O	0.012(2)	0.01(3)	0.016(3)	0.004(2)
O13	O	0.02(3)	0.005(3)	0.042(5)	0.001(3)
O14	O	0.019(3)	0.004(3)	0.067(7)	-0.002(4)
O15	O	0.029(4)	0.005(3)	0.106(10)	0.029(6)
O16	O	0.014(3)	0.009(3)	0.017(3)	0.004(2)
O17	O	0.011(2)	0.018(4)	0.012(3)	0.005(2)
O18	O	0.011(2)	0.011(3)	0.008(2)	0.0064(19)
O19	O	0.013(2)	0.008(3)	0.007(2)	0.0025(19)

II

Chemical data

Structural Formula Sum: Ga0.889 O4.222 Zn2.889 [ Help ]

Formula weight: 318.4 Da [ Help ]

Crystallographic data and experimental details

Crystal system: monoclinic [ Help ]

Superspace group name: C2/m(α0γ)00 [ 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

a: 19.66(4) Å [ Help ]

b: 3.2487(5) Å [ Help ]

c: 1.6065(12) Å [ Help ]

α: 90 ° [ Help ]

β: 105.9(10) ° [ Help ]

γ: 90 ° [ Help ]

Volume: 98.7(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	0	0.058824

Number of subsystems: 2 [ Help ]

Subsystem code: 1 [ Help ]

Subsystem description: 1st 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: 2nd 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: 23.236 mm^-1 [ Help ]

Refinement details

Total nb. of reflections: 7763 [ Help ]

Nb. of observed reflections: 4676 [ Help ]

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

Refinement based on: Fsqd [ Help ]

R(obs): 0.0656 [ Help ]

wR(obs): 0.1421 [ Help ]

R(all): 0.113 [ Help ]

wR(all): 0.2022 [ Help ]

S(all): 2.98 [ Help ]

S(obs): 2.72 [ Help ]

Nb. of reflections: 7763 [ Help ]

Nb. of parameters: 179 [ Help ]

Number of constraints: 13 [ Help ]

Weighting scheme: sigma [ Help ]

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

Δ/σ(max): 0.0350 [ Help ]

Δ/σ(mean): 0.0045 [ Help ]

Δρ(max): 3.28 e_Å^-3 [ Help ]

Δρ(min): -3.55 e_Å^-3 [ Help ]

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

Extinction coefficient: 310(20) [ 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
Zn1	Zn	0.1829(3)	0	-0.1054(8)	Uani	0.013(6)	4	0.7647	d	?	?	?	1
Zn1a	Zn	1.97979(18)	0	0.012(3)	Uani	0.044(16)	4	0.0208(2)	d	?	?	?	1
Zn1b	Zn	1.95398(10)	0.5	0.0088(14)	Uani	0.0095(5)	4	0.0241(2)	d	?	?	?	1
Zn2	Zn	0.38666(11)	0	0.0873(3)	Uani	0.0064(5)	4	0.7647	d	?	?	?	1
Ga1	Ga	0.1829(3)	0	-0.1054(8)	Uani	0.013(6)	4	0.2353	d	?	?	?	1
Ga1a	Ga	1.97979(18)	0	0.012(3)	Uani	0.044(16)	4	0.00641(6)	d	?	?	?	1
Ga1b	Ga	1.95398(10)	0.5	0.0088(14)	Uani	0.0095(5)	4	0.00743(6)	d	?	?	?	1
Ga2	Ga	0.38666(11)	0	0.0873(3)	Uani	0.0064(5)	4	0.2353	d	?	?	?	1
O1	O	0.8835(10)	0	0.428(2)	Uani	0.0166(12)	4	1	d	?	?	?	2
O2	O	0.8865(8)	0	0.566(2)	Uani	0.0204(10)	4	1	d	?	?	?	2

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

Atom site label	Atom site symbol	U11	U22	U33	U13
Zn1	Zn	0.008(8)	0.0097(9)	0.0223(11)	0.0057(8)
Zn1a	Zn	0.0149(13)	0.073(4)	0.048(2)	0.0152(14)
Zn1b	Zn	0.0066(7)	0.0121(10)	0.01(8)	0.0024(6)
Zn2	Zn	0.0075(7)	0.0044(9)	0.006(10)	-0.0003(7)
Ga1	Ga	0.008(8)	0.0097(9)	0.0223(11)	0.0057(8)
Ga1a	Ga	0.0149(13)	0.073(4)	0.048(2)	0.0152(14)
Ga1b	Ga	0.0066(7)	0.0121(10)	0.01(8)	0.0024(6)
Ga2	Ga	0.0075(7)	0.0044(9)	0.006(10)	-0.0003(7)
O1	O	0.0164(17)	0.011(2)	0.021(2)	0.0027(15)
O2	O	0.0129(11)	0.019(2)	0.0255(18)	-0.001(12)

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

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

Atom site label	Center (x0)	Width
Zn1a	0.23598(17)	0.0588
Zn1b	0.23581(8)	0.0588
Ga1a	0.23598(17)	0.0588
Ga1b	0.23581(8)	0.0588

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

Modulation code	Atom site label	Displacement axis	Wave vector code
Zn1x1	Zn1	x	1
Zn1y1	Zn1	y	1
Zn1z1	Zn1	z	1
Zn1x2	Zn1	x	2
Zn1y2	Zn1	y	2
Zn1z2	Zn1	z	2
Zn1x3	Zn1	x	3
Zn1y3	Zn1	y	3
Zn1z3	Zn1	z	3
Zn1x4	Zn1	x	4
Zn1y4	Zn1	y	4
Zn1z4	Zn1	z	4
Zn1x5	Zn1	x	5
Zn1y5	Zn1	y	5
Zn1z5	Zn1	z	5
Zn2x1	Zn2	x	1
Zn2y1	Zn2	y	1
Zn2z1	Zn2	z	1
Zn2x2	Zn2	x	2
Zn2y2	Zn2	y	2
Zn2z2	Zn2	z	2
Zn2x3	Zn2	x	3
Zn2y3	Zn2	y	3
Zn2z3	Zn2	z	3
Zn2x4	Zn2	x	4
Zn2y4	Zn2	y	4
Zn2z4	Zn2	z	4
Zn2x5	Zn2	x	5
Zn2y5	Zn2	y	5
Zn2z5	Zn2	z	5
Ga1x1	Ga1	x	1
Ga1y1	Ga1	y	1
Ga1z1	Ga1	z	1
Ga1x2	Ga1	x	2
Ga1y2	Ga1	y	2
Ga1z2	Ga1	z	2
Ga1x3	Ga1	x	3
Ga1y3	Ga1	y	3
Ga1z3	Ga1	z	3
Ga1x4	Ga1	x	4
Ga1y4	Ga1	y	4
Ga1z4	Ga1	z	4
Ga1x5	Ga1	x	5
Ga1y5	Ga1	y	5
Ga1z5	Ga1	z	5
Ga2x1	Ga2	x	1
Ga2y1	Ga2	y	1
Ga2z1	Ga2	z	1
Ga2x2	Ga2	x	2
Ga2y2	Ga2	y	2
Ga2z2	Ga2	z	2
Ga2x3	Ga2	x	3
Ga2y3	Ga2	y	3
Ga2z3	Ga2	z	3
Ga2x4	Ga2	x	4
Ga2y4	Ga2	y	4
Ga2z4	Ga2	z	4
Ga2x5	Ga2	x	5
Ga2y5	Ga2	y	5
Ga2z5	Ga2	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
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

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

Modulation code	Cosine coefficient	Sine coefficient
Zn1x1	0	0
Zn1y1	0	0
Zn1z1	0	0
Zn1x2	0	-0.0058(4)
Zn1y2	0	0
Zn1z2	0	-0.26(6)
Zn1x3	0.0105(3)	0.0132(8)
Zn1y3	0	0
Zn1z3	0.096(5)	0.411(12)
Zn1x4	-0.0171(5)	-0.0122(6)
Zn1y4	0	0
Zn1z4	-0.22(8)	-0.295(9)
Zn1x5	0.0108(3)	0.0035(2)
Zn1y5	0	0
Zn1z5	0.156(4)	0.088(3)
Zn2x1	0	0
Zn2y1	0	0
Zn2z1	0	0
Zn2x2	0	-0.005(4)
Zn2y2	0	0
Zn2z2	0	-0.065(5)
Zn2x3	-0.00342(8)	-0.0051(7)
Zn2y3	0	0
Zn2z3	-0.0127(11)	-0.019(11)
Zn2x4	-0.00423(13)	-0.0004(7)
Zn2y4	0	0
Zn2z4	0.01(2)	0.022(11)
Zn2x5	-0.00236(9)	0.0003(3)
Zn2y5	0	0
Zn2z5	0.0478(14)	0.019(4)
Ga1x1	0	0
Ga1y1	0	0
Ga1z1	0	0
Ga1x2	0	-0.0058(4)
Ga1y2	0	0
Ga1z2	0	-0.26(6)
Ga1x3	0.0105(3)	0.0132(8)
Ga1y3	0	0
Ga1z3	0.096(5)	0.411(12)
Ga1x4	-0.0171(5)	-0.0122(6)
Ga1y4	0	0
Ga1z4	-0.22(8)	-0.295(9)
Ga1x5	0.0108(3)	0.0035(2)
Ga1y5	0	0
Ga1z5	0.156(4)	0.088(3)
Ga2x1	0	0
Ga2y1	0	0
Ga2z1	0	0
Ga2x2	0	-0.005(4)
Ga2y2	0	0
Ga2z2	0	-0.065(5)
Ga2x3	-0.00342(8)	-0.0051(7)
Ga2y3	0	0
Ga2z3	-0.0127(11)	-0.019(11)
Ga2x4	-0.00423(13)	-0.0004(7)
Ga2y4	0	0
Ga2z4	0.01(2)	0.022(11)
Ga2x5	-0.00236(9)	0.0003(3)
Ga2y5	0	0
Ga2z5	0.0478(14)	0.019(4)
O1x1	0	0
O1y1	0	0
O1z1	0	0
O1x2	0	-0.0121(4)
O1y2	0	0
O1z2	0	-0.089(6)
O1x3	0.0009(3)	-0.0028(10)
O1y3	0	0
O1z3	-0.024(5)	-0.115(15)
O1x4	-0.0001(3)	0.0041(10)
O1y4	0	0
O1z4	0.087(4)	0.114(16)
O1x5	0.0025(3)	-0.0024(6)
O1y5	0	0
O1z5	0.006(4)	-0.08(9)
O2x1	0	0
O2y1	0	0
O2z1	0	0
O2x2	0	0.0156(14)
O2y2	0	0
O2z2	0	-0.2(2)
O2x3	0.0004(4)	0.009(3)
O2y3	0	0
O2z3	-0.052(6)	-0.21(5)
O2x4	-0.0003(6)	0.006(3)
O2y4	0	0
O2z4	-0.158(9)	-0.17(5)
O2x5	-0.0002(5)	0.0022(12)
O2y5	0	0
O2z5	-0.087(7)	-0.06(2)

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

Atom site label	Ax	Center (x0)	Width
Zn1	1.5882	-0.03561(5)	0.4706
Zn2	-1.4118	0.505138(19)	0.4706
Ga1	1.5882	-0.03561(5)	0.4706
Ga2	-1.4118	0.505138(19)	0.4706
O1	1.9737	-0.00378(13)	0.5263
O2	-1.5987	0.5035(12)	0.4737

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

Modulation code	Atom site label	Tensor element	Wave vector code
Zn1U111	Zn1	U11	1
Zn1U221	Zn1	U22	1
Zn1U331	Zn1	U33	1
Zn1U121	Zn1	U12	1
Zn1U131	Zn1	U13	1
Zn1U231	Zn1	U23	1
Zn1U112	Zn1	U11	2
Zn1U222	Zn1	U22	2
Zn1U332	Zn1	U33	2
Zn1U122	Zn1	U12	2
Zn1U132	Zn1	U13	2
Zn1U232	Zn1	U23	2
Zn1U113	Zn1	U11	3
Zn1U223	Zn1	U22	3
Zn1U333	Zn1	U33	3
Zn1U123	Zn1	U12	3
Zn1U133	Zn1	U13	3
Zn1U233	Zn1	U23	3
Zn1U114	Zn1	U11	4
Zn1U224	Zn1	U22	4
Zn1U334	Zn1	U33	4
Zn1U124	Zn1	U12	4
Zn1U134	Zn1	U13	4
Zn1U234	Zn1	U23	4
Zn2U111	Zn2	U11	1
Zn2U221	Zn2	U22	1
Zn2U331	Zn2	U33	1
Zn2U121	Zn2	U12	1
Zn2U131	Zn2	U13	1
Zn2U231	Zn2	U23	1
Zn2U112	Zn2	U11	2
Zn2U222	Zn2	U22	2
Zn2U332	Zn2	U33	2
Zn2U122	Zn2	U12	2
Zn2U132	Zn2	U13	2
Zn2U232	Zn2	U23	2
Zn2U113	Zn2	U11	3
Zn2U223	Zn2	U22	3
Zn2U333	Zn2	U33	3
Zn2U123	Zn2	U12	3
Zn2U133	Zn2	U13	3
Zn2U233	Zn2	U23	3
Zn2U114	Zn2	U11	4
Zn2U224	Zn2	U22	4
Zn2U334	Zn2	U33	4
Zn2U124	Zn2	U12	4
Zn2U134	Zn2	U13	4
Zn2U234	Zn2	U23	4
Ga1U111	Ga1	U11	1
Ga1U221	Ga1	U22	1
Ga1U331	Ga1	U33	1
Ga1U121	Ga1	U12	1
Ga1U131	Ga1	U13	1
Ga1U231	Ga1	U23	1
Ga1U112	Ga1	U11	2
Ga1U222	Ga1	U22	2
Ga1U332	Ga1	U33	2
Ga1U122	Ga1	U12	2
Ga1U132	Ga1	U13	2
Ga1U232	Ga1	U23	2
Ga1U113	Ga1	U11	3
Ga1U223	Ga1	U22	3
Ga1U333	Ga1	U33	3
Ga1U123	Ga1	U12	3
Ga1U133	Ga1	U13	3
Ga1U233	Ga1	U23	3
Ga1U114	Ga1	U11	4
Ga1U224	Ga1	U22	4
Ga1U334	Ga1	U33	4
Ga1U124	Ga1	U12	4
Ga1U134	Ga1	U13	4
Ga1U234	Ga1	U23	4
Ga2U111	Ga2	U11	1
Ga2U221	Ga2	U22	1
Ga2U331	Ga2	U33	1
Ga2U121	Ga2	U12	1
Ga2U131	Ga2	U13	1
Ga2U231	Ga2	U23	1
Ga2U112	Ga2	U11	2
Ga2U222	Ga2	U22	2
Ga2U332	Ga2	U33	2
Ga2U122	Ga2	U12	2
Ga2U132	Ga2	U13	2
Ga2U232	Ga2	U23	2
Ga2U113	Ga2	U11	3
Ga2U223	Ga2	U22	3
Ga2U333	Ga2	U33	3
Ga2U123	Ga2	U12	3
Ga2U133	Ga2	U13	3
Ga2U233	Ga2	U23	3
Ga2U114	Ga2	U11	4
Ga2U224	Ga2	U22	4
Ga2U334	Ga2	U33	4
Ga2U124	Ga2	U12	4
Ga2U134	Ga2	U13	4
Ga2U234	Ga2	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

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

Modulation code	Cosine coefficient	Sine coefficient
Zn1U111	0	0
Zn1U221	0	0
Zn1U331	0	0
Zn1U121	0	0
Zn1U131	0	0
Zn1U231	0	0
Zn1U112	0.007(2)	-0.0043(11)
Zn1U222	-0.012(3)	0.0059(13)
Zn1U332	-0.01(3)	-0.0013(16)
Zn1U122	0	0
Zn1U132	0.003(2)	-0.0037(11)
Zn1U232	0	0
Zn1U113	-0.006(2)	0.006(19)
Zn1U223	0.011(3)	-0.01(2)
Zn1U333	0.015(4)	-0.007(3)
Zn1U123	0	0
Zn1U133	0.001(2)	0.002(19)
Zn1U233	0	0
Zn1U114	0.0004(10)	-0.003(11)
Zn1U224	-0.004(12)	0.0056(13)
Zn1U334	-0.0111(15)	0.0027(16)
Zn1U124	0	0
Zn1U134	-0.0035(10)	-0.0011(11)
Zn1U234	0	0
Zn2U111	0	0
Zn2U221	0	0
Zn2U331	0	0
Zn2U121	0	0
Zn2U131	0	0
Zn2U231	0	0
Zn2U112	-0.002(2)	-0.0002(2)
Zn2U222	0.005(3)	0.0003(3)
Zn2U332	0.038(3)	0.004(3)
Zn2U122	0	0
Zn2U132	0.003(2)	-0.00004(19)
Zn2U232	0	0
Zn2U113	-0.002(3)	-0.0001(2)
Zn2U223	0.008(4)	-0.0002(3)
Zn2U333	0.044(4)	0.0018(3)
Zn2U123	0	0
Zn2U133	0.004(3)	-0.0004(2)
Zn2U233	0	0
Zn2U114	-0.0006(12)	0
Zn2U224	0.0031(17)	0
Zn2U334	0.0174(18)	0
Zn2U124	0	0
Zn2U134	0.0026(13)	0
Zn2U234	0	0
Ga1U111	0	0
Ga1U221	0	0
Ga1U331	0	0
Ga1U121	0	0
Ga1U131	0	0
Ga1U231	0	0
Ga1U112	0.007(2)	-0.0043(11)
Ga1U222	-0.012(3)	0.0059(13)
Ga1U332	-0.01(3)	-0.0013(16)
Ga1U122	0	0
Ga1U132	0.003(2)	-0.0037(11)
Ga1U232	0	0
Ga1U113	-0.006(2)	0.006(19)
Ga1U223	0.011(3)	-0.01(2)
Ga1U333	0.015(4)	-0.007(3)
Ga1U123	0	0
Ga1U133	0.001(2)	0.002(19)
Ga1U233	0	0
Ga1U114	0.0004(10)	-0.003(11)
Ga1U224	-0.004(12)	0.0056(13)
Ga1U334	-0.0111(15)	0.0027(16)
Ga1U124	0	0
Ga1U134	-0.0035(10)	-0.0011(11)
Ga1U234	0	0
Ga2U111	0	0
Ga2U221	0	0
Ga2U331	0	0
Ga2U121	0	0
Ga2U131	0	0
Ga2U231	0	0
Ga2U112	-0.002(2)	-0.0002(2)
Ga2U222	0.005(3)	0.0003(3)
Ga2U332	0.038(3)	0.004(3)
Ga2U122	0	0
Ga2U132	0.003(2)	-0.00004(19)
Ga2U232	0	0
Ga2U113	-0.002(3)	-0.0001(2)
Ga2U223	0.008(4)	-0.0002(3)
Ga2U333	0.044(4)	0.0018(3)
Ga2U123	0	0
Ga2U133	0.004(3)	-0.0004(2)
Ga2U233	0	0
Ga2U114	-0.0006(12)	0
Ga2U224	0.0031(17)	0
Ga2U334	0.0174(18)	0
Ga2U124	0	0
Ga2U134	0.0026(13)	0
Ga2U234	0	0
O1U111	0	0
O1U221	0	0
O1U331	0	0
O1U121	0	0
O1U131	0	0
O1U231	0	0
O1U112	0.003(6)	-0.0053(17)
O1U222	0.008(8)	-0.018(3)
O1U332	0.061(7)	-0.005(2)
O1U122	0	0
O1U132	0.014(5)	-0.0015(16)
O1U232	0	0
O1U113	0(7)	0.006(2)
O1U223	-0.031(11)	0.021(4)
O1U333	-0.041(9)	0(2)
O1U123	0	0
O1U133	-0.02(7)	0.0046(18)
O1U233	0	0
O1U114	0.005(4)	-0.003(2)
O1U224	0.019(6)	-0.002(3)
O1U334	0.037(6)	-0.001(3)
O1U124	0	0
O1U134	0.014(4)	0.001(2)
O1U234	0	0
O2U111	0	0
O2U221	0	0
O2U331	0	0
O2U121	0	0
O2U131	0	0
O2U231	0	0
O2U112	-0.003(3)	0.0016(12)
O2U222	-0.025(4)	0.011(2)
O2U332	-0.001(3)	0.0032(17)
O2U122	0	0
O2U132	-0.002(2)	-0.0005(12)
O2U232	0	0
O2U113	-0.004(2)	0.0014(15)
O2U223	-0.017(4)	0.013(3)
O2U333	-0.015(3)	0.009(2)
O2U123	0	0
O2U133	0.004(2)	-0.0031(14)
O2U233	0	0

Structure of (Ga2O3)2(ZnO)13 and a unified description of the homologous series(Ga2O3)2(ZnO)2n+1

Michiue, Yuichi; Kimizuka, Noboru; Kanke, Yasushi; Mori, Yasushi

Acta Crystallographica, Section B 68 250-260 (2012)

https://doi.org/10.1107/s0108768112016084

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(I)

Chemical data

Crystallographic data and experimental details

Refinement details

Structural Information

II

Chemical data

Crystallographic data and experimental details

Refinement details

Structural Information

Structure of (Ga₂O₃)₂(ZnO)₁₃ and a unified description of the homologous series(Ga₂O₃)₂(ZnO)_2n+1