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A unified description for the structures of the homologous series Ga2O3(ZnO)m, gallium zinc oxide, is presented using the superspace formalism. The structures were treated as a compositely modulated structure consisting of two subsystems. One is constructed with metal ions and the other with O ions. The ideal model is given, in which the displacive modulations of ions are well described by the zigzag function with large amplitudes. Alternative settings are also proposed which are analogous to the so-called modular structures. The validity of the model has been confirmed by refinements for phases with m = 6 and m = 9 in the homologous series. A few complex phenomena in real structures are taken into account by modifying the ideal model.
Supporting information
For both structures, program(s) used to refine structure: Jana2006 (Petricek, Dusek & Palatinus, 2006); software used to prepare material for publication: Jana2006 (Petricek, Dusek & Palatinus, 2006).
Crystal data top
Ga0.25O1.25Zn0.75 | F(000) = 314 |
Mr = 84.5 | Dx = 5.68 Mg m−3 |
Orthorhombic, Cmmm(00γ)0s0† | Mo Kα radiation, λ = 0.71069 Å |
q = 1.12500c*‡ | Cell parameters from 25 reflections |
a = 3.2465 (9) Å | θ = 12.6–15.7° |
b = 19.640 (5) Å | µ = 24.6 mm−1 |
c = 3.0979 (8) Å | T = 298 K |
V = 197.53 (9) Å3 | Irregular, colorless |
Z = 8 | 0.12 × 0.06 × 0.02 mm |
† Symmetry operations: (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.
‡ ; ![](http://publbio.iucr.org/publbio/opentex.php?tex=W%5E%7B2%7D%3D%5Cleft%28%5Cmatrix%7B%201%20%26%200%20%26%200%20%26%200%20%5Ccr%20%200%20%26%201%20%26%200%20%26%200%20%5Ccr%20%200%20%26%200%20%26%200%20%26%201%20%5Ccr%20%200%20%26%200%20%26%201%20%26%200%20%5Ccr%20%7D%5Cright%29&type=.png)
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Data collection top
Rigaku AFC-7R diffractometer | 1349 reflections with I > 2σ(I) |
Radiation source: Rotating anode | Rint = 0.122 |
Graphite monochromator | θmax = 45.0°, θmin = 2.7° |
ω scans | h = 0→6 |
Absorption correction: ψ scan Absorption correction given as ψ scan | k = 0→38 |
Tmin = 0.18, Tmax = 0.61 | l = −7→7 |
7287 measured reflections | 3 standard reflections every 200 reflections |
3699 independent reflections | intensity decay: 0.0% |
Refinement top
Refinement on F2 | 4 constraints |
R[F2 > 2σ(F2)] = 0.044 | Weighting scheme based on measured s.u.'s w = 1/(σ2(I) + 0.0001I2) |
wR(F2) = 0.099 | (Δ/σ)max = 0.017 |
S = 1.03 | Δρmax = 2.29 e Å−3 |
3699 reflections | Δρmin = −2.27 e Å−3 |
115 parameters | Extinction correction: B-C type 1 Gaussian isotropic (Becker & Coppens, 1974) |
0 restraints | Extinction coefficient: 404 (14) |
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top | x | y | z | Uiso*/Ueq | Occ. (<1) |
M1 | 0 | 0.38426 (4) | 0 | 0.01344 (16) | 0.75 |
M1g | 0 | 0.38426 (4) | 0 | 0.01344 (16) | 0.25 |
M1a | 0 | −0.10985 (19) | 0.049 (5) | 0.034 (2) | 0.1769 (16) |
M1ag | 0 | −0.10985 (19) | 0.049 (5) | 0.034 (2) | 0.0590 (5) |
M1b | 0.5 | −0.13516 (11) | 0 | 0.0113 (6) | 0.396 (3) |
M1bg | 0.5 | −0.13516 (11) | 0 | 0.0113 (6) | 0.1320 (11) |
M1c | 0 | 0.87414 (6) | 0 | 0.0089 (3) | 0.75 |
M1cg | 0 | 0.87414 (6) | 0 | 0.0089 (3) | 0.25 |
M2 | 0 | 0.88428 (2) | 0.5 | 0.01097 (10) | 0.75 |
M2g | 0 | 0.88428 (2) | 0.5 | 0.01097 (10) | 0.25 |
O1 | 0 | 0.63435 (13) | 0.25 | 0.0155 (6) | |
O2 | 0 | 0.13556 (14) | 0.75 | 0.0254 (9) | |
Atomic displacement parameters (Å2) top | U11 | U22 | U33 | U12 | U13 | U23 |
M1 | 0.0106 (3) | 0.0081 (2) | 0.0216 (3) | 0 | 0 | 0 |
M1g | 0.0106 (3) | 0.0081 (2) | 0.0216 (3) | 0 | 0 | 0 |
M1a | 0.068 (3) | 0.0092 (13) | 0.024 (7) | 0 | 0 | −0.004 (2) |
M1ag | 0.068 (3) | 0.0092 (13) | 0.024 (7) | 0 | 0 | −0.004 (2) |
M1b | 0.0178 (12) | 0.0078 (9) | 0.0083 (9) | 0 | 0 | 0 |
M1bg | 0.0178 (12) | 0.0078 (9) | 0.0083 (9) | 0 | 0 | 0 |
M1c | 0.0084 (5) | 0.0076 (5) | 0.0107 (5) | 0 | 0 | 0 |
M1cg | 0.0084 (5) | 0.0076 (5) | 0.0107 (5) | 0 | 0 | 0 |
M2 | 0.00950 (19) | 0.00838 (16) | 0.01504 (19) | 0 | 0 | 0 |
M2g | 0.00950 (19) | 0.00838 (16) | 0.01504 (19) | 0 | 0 | 0 |
O1 | 0.0143 (9) | 0.0115 (11) | 0.0207 (12) | 0 | 0 | 0 |
O2 | 0.0312 (17) | 0.0163 (13) | 0.0287 (16) | 0 | 0 | 0 |
Bond lengths (Å) top | Average | Minimum | Maximum |
M1—O1i | 44.91 (6) | 2.135 (10) | 11.748 (7) |
Symmetry code: (i) x1, x2, x3−1, x4. |
Crystal data top
Ga0.1818O1.0909Zn0.8181 | F(000) = 311 |
Mr = 83.6 | Dx = 5.68 Mg m−3 |
Orthorhombic, Cmcm(00γ)000† | Mo Kα radiation, λ = 0.71069 Å |
q = 1.09091c*‡ | Cell parameters from 25 reflections |
a = 3.2494 (14) Å | θ = 15.0–16.8° |
b = 19.722 (6) Å | µ = 24.7 mm−1 |
c = 3.0513 (11) Å | T = 298 K |
V = 195.54 (12) Å3 | Plate, colorless |
Z = 8 | 0.20 × 0.12 × 0.02 mm |
† Symmetry operations: (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.
‡ ; ![](http://publbio.iucr.org/publbio/opentex.php?tex=W%5E%7B2%7D%3D%5Cleft%28%5Cmatrix%7B%201%20%26%200%20%26%200%20%26%200%20%5Ccr%20%200%20%26%201%20%26%200%20%26%200%20%5Ccr%20%200%20%26%200%20%26%200%20%26%201%20%5Ccr%20%200%20%26%200%20%26%201%20%26%200%20%5Ccr%20%7D%5Cright%29&type=.png)
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Data collection top
Rigaku AFC-7R diffractometer | 993 reflections with I > 2σ(I) |
Radiation source: Rotating anode | Rint = 0.048 |
Graphite monochromator | θmax = 30.1°, θmin = 2.8° |
ω scans | h = 0→4 |
Absorption correction: analytical Tompa Analytical | k = −27→0 |
Tmin = 0.034, Tmax = 0.417 | l = −7→7 |
3662 measured reflections | 3 standard reflections every 200 reflections |
1862 independent reflections | intensity decay: 0.0% |
Refinement top
Refinement on F2 | 5 constraints |
R[F2 > 2σ(F2)] = 0.034 | Weighting scheme based on measured s.u.'s w = 1/(σ2(I) + 0.0001I2) |
wR(F2) = 0.068 | (Δ/σ)max = 0.017 |
S = 1.35 | Δρmax = 1.60 e Å−3 |
1862 reflections | Δρmin = −1.21 e Å−3 |
149 parameters | Extinction correction: B-C type 1 Gaussian isotropic (Becker & Coppens, 1974) |
0 restraints | Extinction coefficient: 590 (20) |
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top | x | y | z | Uiso*/Ueq | Occ. (<1) |
M1 | 0 | 0.63438 (3) | 0.25 | 0.01132 (14) | 0.8181 |
M1g | 0 | 0.63438 (3) | 0.25 | 0.01132 (14) | 0.1919 |
M1a | 0 | −0.04159 (19) | 0.25 | 0.0422 (12) | 0.456 (4) |
M1ag | 0 | −0.04159 (19) | 0.25 | 0.0422 (12) | 0.1013 (8) |
M1b | 0.5 | −0.06856 (18) | 0.25 | 0.0154 (9) | 0.362 (4) |
M1bg | 0.5 | −0.06856 (18) | 0.25 | 0.0154 (9) | 0.0805 (8) |
M2 | 0 | 0.13443 (2) | 0.75 | 0.01253 (12) | 0.8181 |
M2g | 0 | 0.13443 (2) | 0.75 | 0.01253 (12) | 0.1919 |
O1 | 0 | 0.38420 (13) | 0 | 0.0173 (7) | |
O2 | 0 | 0.88545 (15) | 0.5 | 0.0217 (8) | |
Atomic displacement parameters (Å2) top | U11 | U22 | U33 | U12 | U13 | U23 |
M1 | 0.00793 (18) | 0.0099 (3) | 0.0161 (2) | 0 | 0 | 0 |
M1g | 0.00793 (18) | 0.0099 (3) | 0.0161 (2) | 0 | 0 | 0 |
M1a | 0.076 (3) | 0.0118 (17) | 0.0391 (19) | 0 | 0 | 0 |
M1ag | 0.076 (3) | 0.0118 (17) | 0.0391 (19) | 0 | 0 | 0 |
M1b | 0.0270 (16) | 0.0081 (16) | 0.0113 (14) | 0 | 0 | 0 |
M1bg | 0.0270 (16) | 0.0081 (16) | 0.0113 (14) | 0 | 0 | 0 |
M2 | 0.00863 (16) | 0.0098 (3) | 0.0192 (2) | 0 | 0 | 0 |
M2g | 0.00863 (16) | 0.0098 (3) | 0.0192 (2) | 0 | 0 | 0 |
O1 | 0.0109 (10) | 0.0158 (14) | 0.0251 (13) | 0 | 0 | 0 |
O2 | 0.0241 (14) | 0.0134 (13) | 0.0276 (14) | 0 | 0 | 0 |
Bond lengths (Å) top | Average | Minimum | Maximum |
M1—O1 | 53.5 (4) | 1.91 (4) | 11.75 (3) |
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