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Five single crystals of Y3Al5−xGaxO12 (0 ≤ x ≤ 5) garnet solid solutions with the compositions x = 0.0, 1.0, 2.0, 3.0 and 4.0 were synthesized using a flux method. The compositional dependence of the lattice constants of the garnet solid solutions shows a large deviation from Vegard's law. Investigation of the cation distributions of these garnets using single-crystal X-ray diffraction shows that Ga3+, which is larger than Al3+, preferentially occupies the tetrahedral (four-coordinate) site rather than the octahedral (six-coordinate) site. On the basis of the results obtained from structure refinements, geometric analyses of the polyhedral distortions were carried out. The results imply that the cation–cation repulsive force across the polyhedral shared edges decreases with increasing substitution of Ga3+. Moreover, the proportion of covalent bonding in the cation–oxygen bonds was estimated from the bond strength; the results indicate that the covalency of the Ga—O bond is greater than that of the Al—O bond. The peculiar cation distributions observed in the Y3Al5−xGaxO12 garnet solid solutions are most probably caused by the strong covalency of the Ga—O bond and also simultaneously induced by the need to decrease the cation–cation repulsive force. Crystal data: cubic, Ia3d, Z = 8, Mo Kα, λ = 0.71069 Å; at x = 0.0 (triyttrium pentaaluminium dodecaoxide): a0 = 12.0062 (5) Å, V = 1730.7 (2) Å3, Dx = 4.56 Mg m−3, Mr = 593.613, μ = 21.21 mm−1, F(000) = 2224, R = 0.029 for 294 reflections; at x = 1.0 (triyttrium tetraaluminium gallium dodecaoxide): a0 = 12.0432 (7) Å, V = 1746.7 (3) Å3, Dx = 4.84 Mg m−3, Mr = 636.351, μ = 24.09 mm−1, F(000) = 2368, R = 0.022 for 124 reflections; at x = 2.0 (triyttrium trialuminium digallium dodecaoxide): a0 = 12.0926 (9) Å, V = 1768.3 (4) Å3, Dx = 5.10 Mg m−3, Mr = 679.089, μ = 26.85 mm−1, F(000) = 2512, R = 0.018 for 144 reflections; at x = 3.0 (triyttrium dialuminium trigallium dodecaoxide): a0 = 12.1552 (6) Å, V = 1795.9 (3) Å3, Dx = 5.34 Mg m−3, Mr = 721.827, μ = 29.43 mm−1, F(000) = 2656, R = 0.018 for 184 reflections; at x = 4.0 (triyttrium aluminium tetragallium dodecaoxide): a0 = 12.2123 (8) Å, V = 1821.3 (4) Å3, Dx = 5.58 Mg m−3, Mr = 764.565, μ = 31.97 mm−1, F(000) = 2800, R = 0.014 for 159 reflections.

Supporting information

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Crystallographic Information File (CIF)
Contains datablocks text, x_0, x_1, x_2, x_3, x_4

sft

Structure factor file (SHELXL table format)
Supplementary material

sft

Structure factor file (SHELXL table format)
Supplementary material

sft

Structure factor file (SHELXL table format)
Supplementary material

sft

Structure factor file (SHELXL table format)
Supplementary material

sft

Structure factor file (SHELXL table format)
Supplementary material

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Supplementary material

Computing details top

(x_0) top
Crystal data top
Al5O12Y3Dx = 4.56 Mg m3
Mr = 593.61Mo Kα radiation, λ = 0.71069 Å
Cubic, Ia3dCell parameters from 25 reflections
Hall symbol: -I 4bd 2ab 3θ = 22.5–25.0°
a = 12.0062 (5) ŵ = 21.21 mm1
V = 1730.7 (2) Å3T = 296 K
Z = 8Sphere
F(000) = 22240.10 mm (radius)
Data collection top
Rigaku AFC-6
diffractometer
3294 measured reflections
ω–2θ scans294 reflections with |Fo| > 3σ(|Fo|)
Absorption correction: sphericalRint = 0.019
θmax = 60°
Refinement top
Refinement on F294 reflections
R[F2 > 2σ(F2)] = 0.0291/σ2(Fo)
wR(F2) = 0.026
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzBiso*/Beq
Y0.1250.00.250.32
Al10.00.00.00.37
Al20.3750.00.250.39
O0.0318 (3)0.0511 (3)0.1498 (3)0.31
(x_1) top
Crystal data top
Al4GaO12Y3Dx = 4.84 Mg m3
Mr = 636.35Mo Kα radiation, λ = 0.71069 Å
Cubic, Ia3dCell parameters from 25 reflections
Hall symbol: -I 4bd 2ab 3θ = 22.5–25.0°
a = 12.0432 (7) ŵ = 24.09 mm1
V = 1746.7 (3) Å3T = 296 K
Z = 8Sphere
F(000) = 23680.06 mm (radius)
Data collection top
Rigaku AFC-6
diffractometer
3309 measured reflections
ω–2θ scans124 reflections with |Fo| > 3σ(|Fo|)
Absorption correction: sphericalRint = 0.024
θmax = 60°
Refinement top
R[F2 > 2σ(F2)] = 0.022124 reflections
wR(F2) = 0.0161/σ2(Fo)
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzBiso*/BeqOcc. (<1)
Y0.1250.00.250.16
Al10.00.00.00.400.927
Ga10.00.00.00.400.073 (8)
Al20.3750.00.250.930.716
Ga20.3750.00.250.930.284
O0.0293 (4)0.0497 (4)0.1498 (4)0.69
(x_2) top
Crystal data top
Al3Ga2O12Y3Dx = 5.10 Mg m3
Mr = 679.09Mo Kα radiation, λ = 0.71069 Å
Cubic, Ia3dCell parameters from 25 reflections
Hall symbol: -I 4bd 2ab 3θ = 22.5–25.0°
a = 12.0926 (9) ŵ = 26.85 mm1
V = 1768.3 (4) Å3T = 296 K
Z = 8Sphere
F(000) = 25120.11 mm (radius)
Data collection top
Rigaku AFC-6
diffractometer
3359 measured reflections
ω–2θ scans144 reflections with |Fo| > 3σ(|Fo|)
Absorption correction: sphericalRint = 0.015
θmax = 60°
Refinement top
R[F2 > 2σ(F2)] = 0.018144 reflections
wR(F2) = 0.0171/σ2(Fo)
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzBiso*/BeqOcc. (<1)
Y0.1250.00.250.19
Al10.00.00.00.580.802
Ga10.00.00.00.580.198 (8)
Al20.3750.00.251.200.465
Ga20.3750.00.251.200.535
O0.0299 (4)0.0527 (4)0.1498 (4)0.54
(x_3) top
Crystal data top
Al2Ga3O12Y3Dx = 5.34 Mg m3
Mr = 721.83Mo Kα radiation, λ = 0.71069 Å
Cubic, Ia3dCell parameters from 25 reflections
Hall symbol: -I 4bd 2ab 3θ = 22.5–25.0°
a = 12.1552 (6) ŵ = 29.43 mm1
V = 1795.9 (3) Å3T = 296 K
Z = 8Sphere
F(000) = 26560.07 mm (radius)
Data collection top
Rigaku AFC-6
diffractometer
3400 measured reflections
ω–2θ scans184 reflections with |Fo| > 3σ(|Fo|)
Absorption correction: sphericalRint = 0.016
θmax = 60°
Refinement top
R[F2 > 2σ(F2)] = 0.018184 reflections
wR(F2) = 0.0131/σ2(Fo)
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzBiso*/BeqOcc. (<1)
Y0.1250.00.250.30
Al10.00.00.00.470.591
Ga10.00.00.00.470.409 (6)
Al20.3750.00.250.680.273
Ga20.3750.00.250.680.727
O0.0278 (3)0.0523 (3)0.1495 (3)0.54
(x_4) top
Crystal data top
AlGa4O12Y3Dx = 5.58 Mg m3
Mr = 764.57Mo Kα radiation, λ = 0.71069 Å
Cubic, Ia3dCell parameters from 25 reflections
Hall symbol: -I 4bd 2ab 3θ = 22.5–25.0°
a = 12.2123 (8) ŵ = 31.97 mm1
V = 1821.3 (4) Å3T = 296 K
Z = 8Sphere
F(000) = 28000.07 mm (radius)
Data collection top
Rigaku AFC-6
diffractometer
3074 measured reflections
ω–2θ scans159 reflections with |Fo| > 3σ(|Fo|)
Absorption correction: sphericalRint = 0.010
θmax = 60°
Refinement top
R[F2 > 2σ(F2)] = 0.014159 reflections
wR(F2) = 0.0091/σ2(Fo)
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzBiso*/BeqOcc. (<1)
Y0.1250.00.250.34
Al10.00.00.00.430.354
Ga10.00.00.00.430.646 (5)
Al20.3750.00.250.710.097
Ga20.3750.00.250.710.903
O0.0279 (3)0.0540 (2)0.1498 (3)0.61
Refined anisotropic temperature factors (times 105). The form of the anisotropic temperature factors is defined as exp[-(h2beta_11_+k2beta_22_+l2beta_33_+2hkbeta_12_+2lhbeta_13 +2klbeta_23)] top
β_11_β_22_β_33_β_12_β_13_β_23_
dodecahedral site (24c)42 (7)62 (5)620018 (10)
octahedral site (16a)65 (7)656514 (24)1414
tetrahedral site (24d)45 (25)78 (16)78000
oxygen (96h)79 (23)43 (19)41 (20)1(19)19 (17)-9(18)
Refined anisotropic temperature factors (times 105). The form of the anisotropic temperature factors is defined as exp[-(h2beta_11_+k2beta_22_+l2beta_33_+2hkbeta_12_+2lhbeta_13 +2klbeta_23)] top
β_11_β_22_β_33_β_12_β_13_β_23_
dodecahedral site (24c)23 (12)31 (8)31005(23)
octahedral site (16a)69 (11)696923 (51)2323
tetrahedral site (24d)177 (39)151 (28)151 (28)000
oxygen (96h)87 (32)108 (28)164 (37)92 (27)11 (25)-4(30)
Refined anisotropic temperature factors (times 105). The form of the anisotropic temperature factors is defined as exp[-(h2beta_11_+k2beta_22_+l2beta_33_+2hkbeta_12_+2lhbeta_13 +2klbeta_23)] top
β_11_β_22_β_33_β_12_β_13_β_23_
dodecahedral site (24c)16 (14)41 (9)4100-21 (42)
octahedral site (16a)98 (11)989861 (46)6161
tetrahedral site (24d)217 (42)200 (28)200000
oxygen (96h)87 (27)62 (22)127 (29)36 (23)-30 (21)-50 (24)
Refined anisotropic temperature factors (times 105). The form of the anisotropic temperature factors is defined as exp[-(h2beta_11_+k2beta_22_+l2beta_33_+2hkbeta_12_+2lhbeta_13 +2klbeta_23)] top
β_11_β_22_β_33_β_12_β_13_β_23_
dodecahedral site (24c)29 (13)62 (9)62005(24)
octahedral site (16a)80 (5)808028 (29)2828
tetrahedral site (24d)125 (26)109 (15)109000
oxygen (96h)68 (18)94 (17)113 (20)40 (17)2(15)-28 (18)
Refined anisotropic temperature factors (times 105). The form of the anisotropic temperature factors is defined as exp[-(h2beta_11_+k2beta_22_+l2beta_33_+2hkbeta_12_+2lhbeta_13 +2klbeta_23)] top
β_11_β_22_β_33_β_12_β_13_β_23_
dodecahedral site (24c)44 (3)64 (2)640025 (17)
octahedral site (16a)72 (3)7272-3(20)-3-3
tetrahedral site (24d)104 (6)126 (4)126000
oxygen (96h)107 (16)92 (14)107 (16)-5(14)15 (12)-19 (4)
 
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