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
| Crystallographic Information File (CIF) Contains datablocks text, x_0, x_1, x_2, x_3, x_4 |
| Structure factor file (SHELXL table format) Supplementary material |
| Structure factor file (SHELXL table format) Supplementary material |
| Structure factor file (SHELXL table format) Supplementary material |
| Structure factor file (SHELXL table format) Supplementary material |
| Structure factor file (SHELXL table format) Supplementary material |
| Portable Document Format (PDF) file Supplementary material |
Crystal data top
Al5O12Y3 | Dx = 4.56 Mg m−3 |
Mr = 593.61 | Mo Kα radiation, λ = 0.71069 Å |
Cubic, Ia3d | Cell parameters from 25 reflections |
Hall symbol: -I 4bd 2ab 3 | θ = 22.5–25.0° |
a = 12.0062 (5) Å | µ = 21.21 mm−1 |
V = 1730.7 (2) Å3 | T = 296 K |
Z = 8 | Sphere |
F(000) = 2224 | 0.10 mm (radius) |
Data collection top
Rigaku AFC-6 diffractometer | 3294 measured reflections |
ω–2θ scans | 294 reflections with |Fo| > 3σ(|Fo|) |
Absorption correction: spherical | Rint = 0.019 |
| θmax = 60° |
Refinement top
Refinement on F | 294 reflections |
R[F2 > 2σ(F2)] = 0.029 | 1/σ2(Fo) |
wR(F2) = 0.026 | |
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top | x | y | z | Biso*/Beq | |
Y | 0.125 | 0.0 | 0.25 | 0.32 | |
Al1 | 0.0 | 0.0 | 0.0 | 0.37 | |
Al2 | 0.375 | 0.0 | 0.25 | 0.39 | |
O | −0.0318 (3) | 0.0511 (3) | 0.1498 (3) | 0.31 | |
Crystal data top
Al4GaO12Y3 | Dx = 4.84 Mg m−3 |
Mr = 636.35 | Mo Kα radiation, λ = 0.71069 Å |
Cubic, Ia3d | Cell parameters from 25 reflections |
Hall symbol: -I 4bd 2ab 3 | θ = 22.5–25.0° |
a = 12.0432 (7) Å | µ = 24.09 mm−1 |
V = 1746.7 (3) Å3 | T = 296 K |
Z = 8 | Sphere |
F(000) = 2368 | 0.06 mm (radius) |
Data collection top
Rigaku AFC-6 diffractometer | 3309 measured reflections |
ω–2θ scans | 124 reflections with |Fo| > 3σ(|Fo|) |
Absorption correction: spherical | Rint = 0.024 |
| θmax = 60° |
Refinement top
R[F2 > 2σ(F2)] = 0.022 | 124 reflections |
wR(F2) = 0.016 | 1/σ2(Fo) |
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top | x | y | z | Biso*/Beq | Occ. (<1) |
Y | 0.125 | 0.0 | 0.25 | 0.16 | |
Al1 | 0.0 | 0.0 | 0.0 | 0.40 | 0.927 |
Ga1 | 0.0 | 0.0 | 0.0 | 0.40 | 0.073 (8) |
Al2 | 0.375 | 0.0 | 0.25 | 0.93 | 0.716 |
Ga2 | 0.375 | 0.0 | 0.25 | 0.93 | 0.284 |
O | −0.0293 (4) | 0.0497 (4) | 0.1498 (4) | 0.69 | |
Crystal data top
Al3Ga2O12Y3 | Dx = 5.10 Mg m−3 |
Mr = 679.09 | Mo Kα radiation, λ = 0.71069 Å |
Cubic, Ia3d | Cell parameters from 25 reflections |
Hall symbol: -I 4bd 2ab 3 | θ = 22.5–25.0° |
a = 12.0926 (9) Å | µ = 26.85 mm−1 |
V = 1768.3 (4) Å3 | T = 296 K |
Z = 8 | Sphere |
F(000) = 2512 | 0.11 mm (radius) |
Data collection top
Rigaku AFC-6 diffractometer | 3359 measured reflections |
ω–2θ scans | 144 reflections with |Fo| > 3σ(|Fo|) |
Absorption correction: spherical | Rint = 0.015 |
| θmax = 60° |
Refinement top
R[F2 > 2σ(F2)] = 0.018 | 144 reflections |
wR(F2) = 0.017 | 1/σ2(Fo) |
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top | x | y | z | Biso*/Beq | Occ. (<1) |
Y | 0.125 | 0.0 | 0.25 | 0.19 | |
Al1 | 0.0 | 0.0 | 0.0 | 0.58 | 0.802 |
Ga1 | 0.0 | 0.0 | 0.0 | 0.58 | 0.198 (8) |
Al2 | 0.375 | 0.0 | 0.25 | 1.20 | 0.465 |
Ga2 | 0.375 | 0.0 | 0.25 | 1.20 | 0.535 |
O | −0.0299 (4) | 0.0527 (4) | 0.1498 (4) | 0.54 | |
Crystal data top
Al2Ga3O12Y3 | Dx = 5.34 Mg m−3 |
Mr = 721.83 | Mo Kα radiation, λ = 0.71069 Å |
Cubic, Ia3d | Cell parameters from 25 reflections |
Hall symbol: -I 4bd 2ab 3 | θ = 22.5–25.0° |
a = 12.1552 (6) Å | µ = 29.43 mm−1 |
V = 1795.9 (3) Å3 | T = 296 K |
Z = 8 | Sphere |
F(000) = 2656 | 0.07 mm (radius) |
Data collection top
Rigaku AFC-6 diffractometer | 3400 measured reflections |
ω–2θ scans | 184 reflections with |Fo| > 3σ(|Fo|) |
Absorption correction: spherical | Rint = 0.016 |
| θmax = 60° |
Refinement top
R[F2 > 2σ(F2)] = 0.018 | 184 reflections |
wR(F2) = 0.013 | 1/σ2(Fo) |
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top | x | y | z | Biso*/Beq | Occ. (<1) |
Y | 0.125 | 0.0 | 0.25 | 0.30 | |
Al1 | 0.0 | 0.0 | 0.0 | 0.47 | 0.591 |
Ga1 | 0.0 | 0.0 | 0.0 | 0.47 | 0.409 (6) |
Al2 | 0.375 | 0.0 | 0.25 | 0.68 | 0.273 |
Ga2 | 0.375 | 0.0 | 0.25 | 0.68 | 0.727 |
O | −0.0278 (3) | 0.0523 (3) | 0.1495 (3) | 0.54 | |
Crystal data top
AlGa4O12Y3 | Dx = 5.58 Mg m−3 |
Mr = 764.57 | Mo Kα radiation, λ = 0.71069 Å |
Cubic, Ia3d | Cell parameters from 25 reflections |
Hall symbol: -I 4bd 2ab 3 | θ = 22.5–25.0° |
a = 12.2123 (8) Å | µ = 31.97 mm−1 |
V = 1821.3 (4) Å3 | T = 296 K |
Z = 8 | Sphere |
F(000) = 2800 | 0.07 mm (radius) |
Data collection top
Rigaku AFC-6 diffractometer | 3074 measured reflections |
ω–2θ scans | 159 reflections with |Fo| > 3σ(|Fo|) |
Absorption correction: spherical | Rint = 0.010 |
| θmax = 60° |
Refinement top
R[F2 > 2σ(F2)] = 0.014 | 159 reflections |
wR(F2) = 0.009 | 1/σ2(Fo) |
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top | x | y | z | Biso*/Beq | Occ. (<1) |
Y | 0.125 | 0.0 | 0.25 | 0.34 | |
Al1 | 0.0 | 0.0 | 0.0 | 0.43 | 0.354 |
Ga1 | 0.0 | 0.0 | 0.0 | 0.43 | 0.646 (5) |
Al2 | 0.375 | 0.0 | 0.25 | 0.71 | 0.097 |
Ga2 | 0.375 | 0.0 | 0.25 | 0.71 | 0.903 |
O | −0.0279 (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) | 62 | 0 | 0 | 18 (10) |
octahedral site (16a) | 65 (7) | 65 | 65 | 14 (24) | 14 | 14 |
tetrahedral site (24d) | 45 (25) | 78 (16) | 78 | 0 | 0 | 0 |
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) | 31 | 0 | 0 | 5(23) |
octahedral site (16a) | 69 (11) | 69 | 69 | 23 (51) | 23 | 23 |
tetrahedral site (24d) | 177 (39) | 151 (28) | 151 (28) | 0 | 0 | 0 |
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) | 41 | 0 | 0 | -21 (42) |
octahedral site (16a) | 98 (11) | 98 | 98 | 61 (46) | 61 | 61 |
tetrahedral site (24d) | 217 (42) | 200 (28) | 200 | 0 | 0 | 0 |
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) | 62 | 0 | 0 | 5(24) |
octahedral site (16a) | 80 (5) | 80 | 80 | 28 (29) | 28 | 28 |
tetrahedral site (24d) | 125 (26) | 109 (15) | 109 | 0 | 0 | 0 |
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) | 64 | 0 | 0 | 25 (17) |
octahedral site (16a) | 72 (3) | 72 | 72 | -3(20) | -3 | -3 |
tetrahedral site (24d) | 104 (6) | 126 (4) | 126 | 0 | 0 | 0 |
oxygen (96h) | 107 (16) | 92 (14) | 107 (16) | -5(14) | 15 (12) | -19 (4) |