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

Michiue, Y.; Kimizuka, N.; Kanke, Y.; Mori, T.

doi:10.1107/S0108768112016084

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

Y. Michiue, N. Kimizuka, Y. Kanke and T. Mori

The structure of (Ga₂O₃)₂(ZnO)₁₃ has been determined by a single-crystal X-ray diffraction technique. In the monoclinic structure of the space group C2/m with cell parameters a = 19.66 (4), b = 3.2487 (5), c = 27.31 (2) Å, and β = 105.9 (1)°, a unit cell is constructed by combining the halves of the unit cell of Ga₂O₃(ZnO)₆ and Ga₂O₃(ZnO)₇ in the homologous series Ga₂O₃(ZnO)_m. The homologous series (Ga₂O₃)₂(ZnO)_2n + 1 is derived and a unified description for structures in the series is presented using the (3+1)-dimensional superspace formalism. The phases are treated as compositely modulated structures consisting of two subsystems. One is constructed by metal ions and another is by O ions. In the (3 + 1)-dimensional model, displacive modulations of ions are described by the asymmetric zigzag function with large amplitudes, which was replaced by a combination of the sawtooth function in refinements. Similarities and differences between the two homologous series (Ga₂O₃)₂(ZnO)_2n + 1 and Ga₂O₃(ZnO)_m are clarified in (3 + 1)-dimensional superspace. The validity of the (3 + 1)-dimensional model is confirmed by the refinements of (Ga₂O₃)₂(ZnO)₁₃, while a few complex phenomena in the real structure are taken into account by modifying the model.

Keywords: gallium zinc oxide; homologous series; single-crystal X-ray diffraction; modulated structure; composite crystal; superspace formalism.

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Supporting information

	Crystallographic Information File (CIF) https://doi.org/10.1107/S0108768112016084/dk5003sup1.cif Contains datablocks global, I, II
	Structure factor file (CIF format) https://doi.org/10.1107/S0108768112016084/dk5003Isup2.hkl Contains datablock I
	Structure factor file (CIF format) https://doi.org/10.1107/S0108768112016084/dk5003IIsup3.hkl Contains datablock II
	Portable Document Format (PDF) file https://doi.org/10.1107/S0108768112016084/dk5003sup4.pdf Extra tables

B-IncStrDB reference: 6272EzStLP

Computing details top

Program(s) used to refine structure: Jana2006 (Petricek, Dusek & Palatinus, 2006) for (I). Software used to prepare material for publication: Jana2006 (Petricek, Dusek & Palatinus, 2006) for (I).

Figures top

(I) top

Crystal data top

Ga₄O₁₉Zn₁₃	F(000) = 2664
M_r = 1432.8	D_x = 5.671 Mg m⁻³
Monoclinic, C2/m	Mo Kα radiation, λ = 0.71069 Å
Hall symbol: -C 2y	Cell parameters from 16 reflections
a = 19.66 (4) Å	θ = 20.1–21.0°
b = 3.2487 (5) Å	µ = 24.61 mm⁻¹
c = 27.31 (2) Å	T = 295 K
β = 105.9 (1)°	Plate, colorless
V = 1678 (4) Å³	0.12 × 0.10 × 0.02 mm
Z = 4

Data collection top

Four-circle diffractometer	4676 reflections with I > 2σ(I)
Radiation source: X-ray tube	R_int = 0.088
Graphite monochromator	θ_max = 45.4°, θ_min = 2.7°
ω scans	h = 0→38
Absorption correction: ψ scans ?	k = −6→6
T_min = 0.466, T_max = 0.996	l = −54→52
14188 measured reflections	3 standard reflections every 150 reflections
7763 independent reflections	intensity decay: 2.3%

Refinement top

Refinement on F²	111 constraints
R[F² > 2σ(F²)] = 0.061	Weighting scheme based on measured s.u.'s w = 1/(σ²(I) + 0.0001I²)
wR(F²) = 0.195	(Δ/σ)_max = 0.012
S = 2.88	Δρ_max = 3.59 e Å⁻³
7763 reflections	Δρ_min = −3.74 e Å⁻³
225 parameters	Extinction correction: B-C type 1 Gaussian isotropic (Becker & Coppens, 1974)
0 restraints	Extinction coefficient: 31E1 (2)

Crystal data top

Ga₄O₁₉Zn₁₃	V = 1678 (4) Å³
M_r = 1432.8	Z = 4
Monoclinic, C2/m	Mo Kα radiation
a = 19.66 (4) Å	µ = 24.61 mm⁻¹
b = 3.2487 (5) Å	T = 295 K
c = 27.31 (2) Å	0.12 × 0.10 × 0.02 mm
β = 105.9 (1)°

Data collection top

Four-circle diffractometer	4676 reflections with I > 2σ(I)
Absorption correction: ψ scans ?	R_int = 0.088
T_min = 0.466, T_max = 0.996	3 standard reflections every 150 reflections
14188 measured reflections	intensity decay: 2.3%
7763 independent reflections

Refinement top

R[F² > 2σ(F²)] = 0.061	225 parameters
wR(F²) = 0.195	0 restraints
S = 2.88	Δρ_max = 3.59 e Å⁻³
7763 reflections	Δρ_min = −3.74 e Å⁻³

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å²) top

	x	y	z	U_iso*/U_eq	Occ. (<1)
Zn1	0.21170 (5)	0	0.53326 (5)	0.0099 (3)	0.7647
Zn2	0.85726 (5)	0	0.59388 (5)	0.0108 (3)	0.7647
Zn3	0.50166 (6)	0	0.64777 (5)	0.0149 (3)	0.7647
Zn4	0.14303 (5)	0	0.70417 (4)	0.0099 (3)	0.7647
Zn5	0.62577 (6)	0	0.30013 (5)	0.0099 (3)	0.7647
Zn6	0.27143 (5)	0	0.36026 (5)	0.0103 (3)	0.7647
Zn7	0.91592 (5)	0	0.42068 (5)	0.0102 (3)	0.7647
Zn8	0.56414 (5)	0	0.47553 (5)	0.0097 (3)	0.7647
Zn9	0.18938 (6)	0	0.82541 (5)	0.0112 (3)	0.7647
Zn10	0.58810 (6)	0	0.88032 (6)	0.0159 (3)	0.7647
Zn11	0.98503 (6)	0	0.93459 (5)	0.0128 (3)	0.7647
Zn12	0.38574 (6)	0	0.99567 (5)	0.0100 (3)	0.7647
Zn13	0.77823 (6)	0	0.05097 (5)	0.0097 (3)	0.7647
Zn14	0.17650 (6)	0	0.11037 (5)	0.0108 (3)	0.7647
Zn15	0.57818 (5)	0	0.17262 (5)	0.0104 (3)	0.7647
Zn16	0.78535 (6)	0	0.76428 (4)	0.0094 (3)	0.7647
Zn17	0.97979 (17)	0	0.23583 (17)	0.0440 (16)	0.352 (3)
Zn18	0.95397 (10)	0.5	0.23574 (8)	0.0098 (5)	0.412 (3)
Ga1	0.21170 (5)	0	0.53326 (5)	0.0099 (3)	0.2353
Ga2	0.85726 (5)	0	0.59388 (5)	0.0108 (3)	0.2353
Ga3	0.50166 (6)	0	0.64777 (5)	0.0149 (3)	0.2353
Ga4	0.14303 (5)	0	0.70417 (4)	0.0099 (3)	0.2353
Ga5	0.62577 (6)	0	0.30013 (5)	0.0099 (3)	0.2353
Ga6	0.27143 (5)	0	0.36026 (5)	0.0103 (3)	0.2353
Ga7	0.91592 (5)	0	0.42068 (5)	0.0102 (3)	0.2353
Ga8	0.56414 (5)	0	0.47553 (5)	0.0097 (3)	0.2353
Ga9	0.18938 (6)	0	0.82541 (5)	0.0112 (3)	0.2353
Ga10	0.58810 (6)	0	0.88032 (6)	0.0159 (3)	0.2353
Ga11	0.98503 (6)	0	0.93459 (5)	0.0128 (3)	0.2353
Ga12	0.38574 (6)	0	0.99567 (5)	0.0100 (3)	0.2353
Ga13	0.77823 (6)	0	0.05097 (5)	0.0097 (3)	0.2353
Ga14	0.17650 (6)	0	0.11037 (5)	0.0108 (3)	0.2353
Ga15	0.57818 (5)	0	0.17262 (5)	0.0104 (3)	0.2353
Ga16	0.78535 (6)	0	0.76428 (4)	0.0094 (3)	0.2353
Ga17	0.97979 (17)	0	0.23583 (17)	0.0440 (16)	0.1084 (10)
Ga18	0.95397 (10)	0.5	0.23574 (8)	0.0098 (5)	0.1269 (10)
O1	0.5357 (4)	0	0.5535 (3)	0.020 (2)
O2	0.1868 (3)	0	0.6049 (3)	0.0116 (17)
O3	0.8319 (3)	0	0.6614 (2)	0.0096 (16)
O4	0.4744 (4)	0	0.7066 (4)	0.054 (5)
O5	0.2994 (3)	0	0.2959 (2)	0.0072 (15)
O6	0.9417 (3)	0	0.3543 (3)	0.0116 (17)
O7	0.5881 (3)	0	0.4040 (3)	0.0117 (17)
O8	0.2351 (4)	0	0.4553 (3)	0.017 (2)
O9	0.8873 (4)	0	0.5004 (3)	0.020 (2)
O10	0.1093 (4)	0	0.7640 (3)	0.022 (2)
O11	0.5142 (4)	0	0.8192 (3)	0.042 (4)
O12	0.9070 (3)	0	0.8665 (3)	0.0127 (17)
O13	0.3008 (4)	0	0.9228 (4)	0.024 (3)
O14	0.6922 (4)	0	0.9760 (4)	0.033 (3)
O15	0.0804 (5)	0	0.0222 (5)	0.044 (4)
O16	0.4632 (4)	0	0.0664 (3)	0.0134 (18)
O17	0.8561 (3)	0	0.1177 (3)	0.0133 (18)
O18	0.2552 (3)	0	0.1759 (2)	0.0093 (16)
O19	0.6568 (3)	0	0.2363 (2)	0.0095 (15)

Atomic displacement parameters (Å²) top

	U¹¹	U²²	U³³	U¹²	U¹³	U²³
Zn1	0.0060 (3)	0.0045 (4)	0.0173 (5)	0	0.0003 (3)	0
Zn2	0.0069 (3)	0.0058 (4)	0.0178 (5)	0	0.0005 (3)	0
Zn3	0.0066 (4)	0.0086 (5)	0.0275 (6)	0	0.0014 (4)	0
Zn4	0.0079 (4)	0.0065 (4)	0.0140 (5)	0	0.0010 (3)	0
Zn5	0.0082 (4)	0.0079 (5)	0.0133 (4)	0	0.0023 (3)	0
Zn6	0.0073 (4)	0.0058 (4)	0.0158 (5)	0	−0.0002 (3)	0
Zn7	0.0063 (3)	0.0057 (4)	0.0168 (5)	0	0.0000 (3)	0
Zn8	0.0066 (3)	0.0048 (4)	0.0164 (5)	0	0.0007 (3)	0
Zn9	0.0116 (4)	0.0057 (4)	0.0174 (5)	0	0.0059 (4)	0
Zn10	0.0119 (4)	0.0078 (5)	0.0312 (7)	0	0.0114 (4)	0
Zn11	0.0115 (4)	0.0055 (4)	0.0243 (6)	0	0.0096 (4)	0
Zn12	0.0091 (3)	0.0047 (4)	0.0178 (5)	0	0.0064 (3)	0
Zn13	0.0098 (4)	0.0056 (4)	0.0149 (5)	0	0.0054 (3)	0
Zn14	0.0119 (4)	0.0050 (4)	0.0174 (5)	0	0.0068 (3)	0
Zn15	0.0090 (4)	0.0074 (4)	0.0144 (5)	0	0.0024 (3)	0
Zn16	0.0080 (4)	0.0061 (4)	0.0132 (5)	0	0.0015 (3)	0
Zn17	0.0147 (13)	0.070 (4)	0.051 (2)	0	0.0158 (14)	0
Zn18	0.0067 (7)	0.0118 (9)	0.0110 (8)	0	0.0025 (6)	0
Ga1	0.0060 (3)	0.0045 (4)	0.0173 (5)	0	0.0003 (3)	0
Ga2	0.0069 (3)	0.0058 (4)	0.0178 (5)	0	0.0005 (3)	0
Ga3	0.0066 (4)	0.0086 (5)	0.0275 (6)	0	0.0014 (4)	0
Ga4	0.0079 (4)	0.0065 (4)	0.0140 (5)	0	0.0010 (3)	0
Ga5	0.0082 (4)	0.0079 (5)	0.0133 (4)	0	0.0023 (3)	0
Ga6	0.0073 (4)	0.0058 (4)	0.0158 (5)	0	−0.0002 (3)	0
Ga7	0.0063 (3)	0.0057 (4)	0.0168 (5)	0	0.0000 (3)	0
Ga8	0.0066 (3)	0.0048 (4)	0.0164 (5)	0	0.0007 (3)	0
Ga9	0.0116 (4)	0.0057 (4)	0.0174 (5)	0	0.0059 (4)	0
Ga10	0.0119 (4)	0.0078 (5)	0.0312 (7)	0	0.0114 (4)	0
Ga11	0.0115 (4)	0.0055 (4)	0.0243 (6)	0	0.0096 (4)	0
Ga12	0.0091 (3)	0.0047 (4)	0.0178 (5)	0	0.0064 (3)	0
Ga13	0.0098 (4)	0.0056 (4)	0.0149 (5)	0	0.0054 (3)	0
Ga14	0.0119 (4)	0.0050 (4)	0.0174 (5)	0	0.0068 (3)	0
Ga15	0.0090 (4)	0.0074 (4)	0.0144 (5)	0	0.0024 (3)	0
Ga16	0.0080 (4)	0.0061 (4)	0.0132 (5)	0	0.0015 (3)	0
Ga17	0.0147 (13)	0.070 (4)	0.051 (2)	0	0.0158 (14)	0
Ga18	0.0067 (7)	0.0118 (9)	0.0110 (8)	0	0.0025 (6)	0
O1	0.013 (3)	0.007 (3)	0.034 (5)	0	−0.002 (3)	0
O2	0.010 (2)	0.009 (3)	0.015 (3)	0	0.003 (2)	0
O3	0.010 (2)	0.009 (3)	0.010 (3)	0	0.0041 (19)	0
O4	0.011 (3)	0.108 (13)	0.036 (6)	0	−0.004 (3)	0
O5	0.011 (2)	0.008 (3)	0.006 (2)	0	0.0070 (18)	0
O6	0.009 (2)	0.008 (3)	0.016 (3)	0	0.001 (2)	0
O7	0.010 (2)	0.009 (3)	0.015 (3)	0	0.001 (2)	0
O8	0.014 (3)	0.009 (3)	0.024 (4)	0	0.000 (3)	0
O9	0.012 (3)	0.010 (3)	0.033 (4)	0	−0.003 (3)	0
O10	0.022 (3)	0.041 (6)	0.006 (3)	0	0.011 (2)	0
O11	0.018 (3)	0.098 (11)	0.016 (3)	0	0.015 (3)	0
O12	0.012 (2)	0.010 (3)	0.016 (3)	0	0.004 (2)	0
O13	0.020 (3)	0.005 (3)	0.042 (5)	0	0.001 (3)	0
O14	0.019 (3)	0.004 (3)	0.067 (7)	0	−0.002 (4)	0
O15	0.029 (4)	0.005 (3)	0.106 (10)	0	0.029 (6)	0
O16	0.014 (3)	0.009 (3)	0.017 (3)	0	0.004 (2)	0
O17	0.011 (2)	0.018 (4)	0.012 (3)	0	0.005 (2)	0
O18	0.011 (2)	0.011 (3)	0.008 (2)	0	0.0064 (19)	0
O19	0.013 (2)	0.008 (3)	0.007 (2)	0	0.0025 (19)	0

Geometric parameters (Å, º) top

Zn1—O2	2.143 (8)	Zn10—O11	1.889 (9)
Zn1—O8	2.297 (9)	Zn10—O16ⁱⁱⁱ	1.986 (9)
Zn1—O8ⁱ	1.911 (4)	Zn10—O17^iv	1.952 (5)
Zn1—O8ⁱⁱ	1.911 (4)	Zn10—O17^v	1.952 (5)
Zn1—O9ⁱⁱⁱ	1.911 (11)	Zn11—O12	2.062 (9)
Zn2—O3	2.037 (8)	Zn11—O15ⁱⁱⁱ	1.970 (14)
Zn2—O7^iv	1.939 (4)	Zn11—O16^iv	1.921 (5)
Zn2—O7^v	1.939 (4)	Zn11—O16^v	1.921 (5)
Zn2—O8ⁱⁱⁱ	1.940 (10)	Zn12—O13	2.221 (11)
Zn3—O4	1.829 (11)	Zn12—O14^vi	1.897 (12)
Zn3—O6^iv	1.979 (5)	Zn12—O15ⁱ	1.870 (7)
Zn3—O6^v	1.979 (5)	Zn12—O15ⁱⁱ	1.870 (7)
Zn3—O7ⁱⁱⁱ	1.936 (9)	Zn12—O16^vii	2.106 (9)
Zn4—O5ⁱ	1.981 (5)	Zn13—O13ⁱⁱⁱ	1.881 (11)
Zn4—O5ⁱⁱ	1.981 (5)	Zn13—O14^viii	2.270 (11)
Zn4—O6ⁱⁱⁱ	1.967 (9)	Zn13—O14^iv	1.937 (6)
Zn4—O10	1.924 (9)	Zn13—O14^v	1.937 (6)
Zn5—O3^iv	1.990 (4)	Zn13—O17	2.034 (9)
Zn5—O3^v	1.990 (4)	Zn14—O12ⁱⁱⁱ	1.914 (10)
Zn5—O4ⁱⁱⁱ	1.926 (12)	Zn14—O13ⁱ	1.970 (6)
Zn5—O19	1.998 (8)	Zn14—O13ⁱⁱ	1.970 (6)
Zn6—O2ⁱ	1.947 (4)	Zn14—O18	2.019 (8)
Zn6—O2ⁱⁱ	1.947 (4)	Zn15—O11ⁱⁱⁱ	1.890 (11)
Zn6—O3ⁱⁱⁱ	1.954 (11)	Zn15—O12^iv	2.008 (5)
Zn6—O5	1.979 (7)	Zn15—O12^v	2.008 (5)
Zn7—O1^iv	1.917 (4)	Zn15—O19	1.985 (8)
Zn7—O1^v	1.917 (4)	Zn16—O5ⁱⁱⁱ	1.995 (9)
Zn7—O2ⁱⁱⁱ	1.947 (11)	Zn16—O18ⁱⁱⁱ	2.005 (8)
Zn7—O6	2.012 (8)	Zn16—O19^iv	1.986 (5)
Zn7—O9	2.393 (10)	Zn16—O19^v	1.986 (5)
Zn8—O1	2.344 (10)	Zn17—O4^iv	2.268 (7)
Zn8—O1ⁱⁱⁱ	1.904 (11)	Zn17—O4^v	2.268 (7)
Zn8—O7	2.131 (8)	Zn17—O10ⁱⁱⁱ	1.753 (11)
Zn8—O9^iv	1.907 (4)	Zn17—O11^iv	2.238 (7)
Zn8—O9^v	1.907 (4)	Zn17—O11^v	2.238 (7)
Zn9—O10	1.962 (9)	Zn18—O4^v	1.802 (10)
Zn9—O17ⁱⁱⁱ	1.994 (8)	Zn18—O10ⁱⁱⁱ	2.047 (6)
Zn9—O18ⁱ	1.962 (4)	Zn18—O10^ix	2.047 (6)
Zn9—O18ⁱⁱ	1.962 (4)	Zn18—O11^v	1.776 (10)

O2—Zn1—O8	178.4 (2)

Symmetry codes: (i) −x+1/2, y−1/2, −z+1; (ii) −x+1/2, y+1/2, −z+1; (iii) −x+1, y, −z+1; (iv) −x+3/2, y−1/2, −z+1; (v) −x+3/2, y+1/2, −z+1; (vi) −x+1, y, −z+2; (vii) x, y, z+1; (viii) x, y, z−1; (ix) −x+1, y+1, −z+1.

(II) top

Crystal data top

Ga_0.889O_4.222Zn_2.889	V = 98.7 (2) Å³
M_r = 318.4	Z = 1
Monoclinic, C2/m(α0γ)00†	F(000) = 157
q = 0.058824c*‡	D_x = 5.355 Mg m⁻³
a = 19.66 (4) Å	? radiation, λ = 0.71069 Å
b = 3.2487 (5) Å	µ = 23.24 mm⁻¹
c = 1.6065 (12) Å	T = 293 K
β = 105.9 (1)°	× × mm

† Symmetry operations: (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.

‡

;

Data collection top

Radiation source: X-ray tube	θ_max = 45.4°, θ_min = 2.7°
14188 measured reflections	h = 0→38
7763 independent reflections	k = −6→6
4676 reflections with I > 2σ(I)	l = −3→3
R_int = 0.088

Refinement top

Refinement on F²	13 constraints
R[F² > 2σ(F²)] = 0.066	Weighting scheme based on measured s.u.'s w = 1/(σ²(I) + 0.0001I²)
wR(F²) = 0.202	(Δ/σ)_max = 0.035
S = 2.98	Δρ_max = 3.28 e Å⁻³
7763 reflections	Δρ_min = −3.55 e Å⁻³
179 parameters	Extinction correction: B-C type 1 Gaussian isotropic (Becker & Coppens, 1974)
0 restraints	Extinction coefficient: 31E1 (2)

Crystal data top

Ga_0.889O_4.222Zn_2.889	β = 105.9 (1)°
M_r = 318.4	V = 98.7 (2) Å³
Monoclinic, C2/m(α0γ)00†	Z = 1
q = 0.058824c*‡	? radiation, λ = 0.71069 Å
a = 19.66 (4) Å	µ = 23.24 mm⁻¹
b = 3.2487 (5) Å	T = 293 K
c = 1.6065 (12) Å	× × mm

;

Data collection top

14188 measured reflections	4676 reflections with I > 2σ(I)
7763 independent reflections	R_int = 0.088

Refinement top

R[F² > 2σ(F²)] = 0.066	179 parameters
wR(F²) = 0.202	0 restraints
S = 2.98	Δρ_max = 3.28 e Å⁻³
7763 reflections	Δρ_min = −3.55 e Å⁻³

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å²) top

	x	y	z	U_iso*/U_eq	Occ. (<1)
Zn1	0.1829 (3)	0	−0.1054 (8)	0.0130 (6)	0.7647
Zn1a	1.97979 (18)	0	0.012 (3)	0.0440 (16)	0.0208 (2)
Zn1b	1.95398 (10)	0.5	0.0088 (14)	0.0095 (5)	0.0241 (2)
Zn2	0.38666 (11)	0	0.0873 (3)	0.0064 (5)	0.7647
Ga1	0.1829 (3)	0	−0.1054 (8)	0.0130 (6)	0.2353
Ga1a	1.97979 (18)	0	0.012 (3)	0.0440 (16)	0.00641 (6)
Ga1b	1.95398 (10)	0.5	0.0088 (14)	0.0095 (5)	0.00743 (6)
Ga2	0.38666 (11)	0	0.0873 (3)	0.0064 (5)	0.2353
O1	0.8835 (10)	0	0.428 (2)	0.0166 (12)
O2	0.8865 (8)	0	0.566 (2)	0.0204 (10)

Atomic displacement parameters (Å²) top

	U¹¹	U²²	U³³	U¹²	U¹³	U²³
Zn1	0.0080 (8)	0.0097 (9)	0.0223 (11)	0	0.0057 (8)	0
Zn1a	0.0149 (13)	0.073 (4)	0.048 (2)	0	0.0152 (14)	0
Zn1b	0.0066 (7)	0.0121 (10)	0.0100 (8)	0	0.0024 (6)	0
Zn2	0.0075 (7)	0.0044 (9)	0.0060 (10)	0	−0.0003 (7)	0
Ga1	0.0080 (8)	0.0097 (9)	0.0223 (11)	0	0.0057 (8)	0
Ga1a	0.0149 (13)	0.073 (4)	0.048 (2)	0	0.0152 (14)	0
Ga1b	0.0066 (7)	0.0121 (10)	0.0100 (8)	0	0.0024 (6)	0
Ga2	0.0075 (7)	0.0044 (9)	0.0060 (10)	0	−0.0003 (7)	0
O1	0.0164 (17)	0.011 (2)	0.021 (2)	0	0.0027 (15)	0
O2	0.0129 (11)	0.019 (2)	0.0255 (18)	0	−0.0010 (12)	0

Experimental details

	(I)	(II)
Crystal data
Chemical formula	Ga₄O₁₉Zn₁₃	Ga_0.889O_4.222Zn_2.889
M_r	1432.8	318.4
Crystal system, space group	Monoclinic, C2/m	Monoclinic, C2/m(α0γ)00†
Temperature (K)	295	293
a, b, c (Å)	19.66 (4), 3.2487 (5), 27.31 (2)	?
β (°)	90, 105.9 (1), 90	19.66 (4), 3.2487 (5), 1.6065 (12)
V (Å³)	1678 (4)	90, 105.9 (1), 90
Z	4	98.7 (2)
Radiation type	Mo Kα	?
µ (mm⁻¹)	24.61	?
Crystal size (mm)	0.12 × 0.10 × 0.02

Data collection
Diffractometer	Four-circle diffractometer	?
Absorption correction	ψ scans	–
T_min, T_max	0.466, 0.996	–
No. of measured, independent and observed [I > 2σ(I)] reflections	14188, 7763, 4676	14188, 7763, 4676
R_int	0.088	0.088
(sin θ/λ)_max (Å⁻¹)	1.002	1.002

Refinement
R[F² > 2σ(F²)], wR(F²), S	0.061, 0.195, 2.88	0.066, 0.202, 2.98
No. of reflections	7763	7763
No. of parameters	225	179
Δρ_max, Δρ_min (e Å⁻³)	3.59, −3.74	3.28, −3.55

Computer programs: Jana2006 (Petricek, Dusek & Palatinus, 2006).

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