The structures of one-dimensional ionic conductors Kx(Ga1 − yAly)2 + xTi2 − xO7 (x ≃ 0.14, y ≃ 0.10, 0.23, 0.39) were refined by single-crystal X-ray diffraction. A one-dimensional tunnel-like space with a large cross section is formed by the linkage of coordination polyhedra of the metal and oxygen ions; K ions are distributed in the tunnel. Significant differences were seen in structures with different Al content; these differences could be explained by considerations in crystal chemistry. The probability density functions (PDFs) of the K ion were obtained using up to fourth-order terms of the atomic displacement parameters. The joint PDFs for the K ion have clarified that a K conduction path deviates slightly from the central axis of the tunnel in all the samples. In contrast with the usual one-dimensional ionic conductors, no distinct bottleneck effect was observed from the joint-PDFs and one-particle potentials.
Supporting information
For all compounds, program(s) used to refine structure: (Jana2000; Petricek and Dusek, 2000); software used to prepare material for publication: (Jana2000; Petricek and Dusek, 2000).
Crystal data top
Al0.21Ga1.93K0.152O7Ti1.86 | Dx = 4.706 (3) Mg m−3 |
Mr = 347.2 | Mo Kα radiation, λ = 0.71069 Å |
Tetragonal, I4/m | Cell parameters from 20 reflections |
Hall symbol: -I 4 | θ = 30–37° |
a = 18.0971 (16) Å | µ = 13.58 mm−1 |
c = 2.9916 (19) Å | T = 298 K |
V = 979.8 (6) Å3 | Prism, colorless |
Z = 8 | 0.22 × 0.08 × 0.08 mm |
F(000) = 1299 | |
Data collection top
Rigaku AFC-5S diffractometer | Rint = 0.034 |
Graphite monochromator | θmax = 50.1°, θmin = 1.6° |
ω/2θ scans | h = −38→39 |
Absorption correction: numerical ? | k = 0→39 |
Tmin = 0.292, Tmax = 0.467 | l = 0→6 |
5602 measured reflections | 3 standard reflections every 100 reflections |
2817 independent reflections | intensity decay: <0.8% |
2350 reflections with I > 2σ(I) | |
Refinement top
Refinement on F2 | Weighting scheme based on measured s.u.'s w = 1/(σ2(I) + 0.0001I2) |
R[F2 > 2σ(F2)] = 0.031 | (Δ/σ)max = 0.001 |
wR(F2) = 0.051 | Δρmax = 1.35 e Å−3 |
S = 1.10 | Δρmin = −1.39 e Å−3 |
2817 reflections | Extinction correction: B-C type 1 Gaussian isotropic (Becker & Coppens, 1974) |
86 parameters | Extinction coefficient: 0.0397 (6) |
Crystal data top
Al0.21Ga1.93K0.152O7Ti1.86 | Z = 8 |
Mr = 347.2 | Mo Kα radiation |
Tetragonal, I4/m | µ = 13.58 mm−1 |
a = 18.0971 (16) Å | T = 298 K |
c = 2.9916 (19) Å | 0.22 × 0.08 × 0.08 mm |
V = 979.8 (6) Å3 | |
Data collection top
Rigaku AFC-5S diffractometer | 2350 reflections with I > 2σ(I) |
Absorption correction: numerical ? | Rint = 0.034 |
Tmin = 0.292, Tmax = 0.467 | 3 standard reflections every 100 reflections |
5602 measured reflections | intensity decay: <0.8% |
2817 independent reflections | |
Refinement top
R[F2 > 2σ(F2)] = 0.031 | 86 parameters |
wR(F2) = 0.051 | Δρmax = 1.35 e Å−3 |
S = 1.10 | Δρmin = −1.39 e Å−3 |
2817 reflections | |
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top | x | y | z | Uiso*/Ueq | Occ. (<1) |
K1 | 0 | 0 | 0.234 (3) | 0.089 (6) | 0.303 (3) |
Ga1 | 0.118144 (10) | 0.162373 (10) | 0.5 | 0.00472 (4) | 0.9326 (14) |
Al1 | 0.118144 | 0.162373 | 0.5 | 0.00472 | 0.0640 (16) |
Ga2 | 0.203530 (11) | 0.310781 (11) | 0 | 0.00525 (5) | 0.756 (5) |
Al2 | 0.203530 | 0.310781 | 0 | 0.00525 | 0.077 (14) |
Ti2 | 0.203530 | 0.310781 | 0 | 0.00525 | 0.166 (13) |
Ti3 | 0.221445 (15) | 0.035922 (14) | 0 | 0.00593 (6) | 0.730 (13) |
Ga3 | 0.221445 | 0.035922 | 0 | 0.00593 | 0.202 (6) |
Al3 | 0.221445 | 0.035922 | 0 | 0.00593 | 0.069 (14) |
Ti4 | 0.119442 (18) | 0.542960 (17) | 0 | 0.00905 (6) | 0.964 (2) |
Ga4 | 0.119442 | 0.542960 | 0 | 0.00905 | 0.036 (2) |
Ga5 | 0.057 (3) | 0.100 (3) | 0.5 | 0.01* | 0.0034 (8) |
O1 | 0.40977 (7) | 0.02065 (6) | 0 | 0.0059 (2) | |
O2 | 0.39445 (6) | 0.15152 (6) | 0.5 | 0.0057 (2) | |
O3 | 0.28044 (6) | 0.00190 (7) | 0.5 | 0.0063 (2) | |
O4 | 0.26450 (7) | 0.13104 (6) | 0 | 0.0061 (2) | |
O5 | 0.18949 (6) | 0.23637 (6) | 0.5 | 0.0053 (2) | |
O6 | 0.15538 (6) | 0.06769 (6) | 0.5 | 0.0062 (2) | |
O7 | 0.06143 (6) | 0.16830 (7) | 0 | 0.0070 (2) | |
Atomic displacement parameters (Å2) top | U11 | U22 | U33 | U12 | U13 | U23 |
K1 | 0.052 (2) | 0.052 (2) | 0.163 (19) | 0 | 0 | 0 |
Ga1 | 0.00498 (7) | 0.00556 (7) | 0.00361 (7) | −0.00019 (5) | 0 | 0 |
Ga2 | 0.00549 (8) | 0.00657 (8) | 0.00370 (8) | 0.00028 (5) | 0 | 0 |
Ti3 | 0.00858 (10) | 0.00475 (9) | 0.00446 (10) | 0.00003 (7) | 0 | 0 |
Ti4 | 0.01043 (11) | 0.00974 (11) | 0.00697 (11) | −0.00056 (8) | 0 | 0 |
O1 | 0.0081 (4) | 0.0042 (3) | 0.0054 (4) | −0.0015 (3) | 0 | 0 |
O2 | 0.0058 (4) | 0.0066 (4) | 0.0046 (4) | 0.0006 (3) | 0 | 0 |
O3 | 0.0050 (4) | 0.0079 (4) | 0.0060 (4) | 0.0026 (3) | 0 | 0 |
O4 | 0.0088 (4) | 0.0048 (3) | 0.0048 (4) | −0.0013 (3) | 0 | 0 |
O5 | 0.0062 (4) | 0.0051 (3) | 0.0045 (4) | −0.0004 (3) | 0 | 0 |
O6 | 0.0065 (4) | 0.0072 (4) | 0.0049 (4) | 0.0024 (3) | 0 | 0 |
O7 | 0.0055 (4) | 0.0120 (4) | 0.0035 (4) | 0.0030 (3) | 0 | 0 |
Bond lengths (Å) top
Ga1—O5 | 1.8602 (11) | Ti3—O6iv | 1.9993 (8) |
Ga1—O6 | 1.8413 (12) | Ti3—O6 | 1.9993 (8) |
Ga1—O7 | 1.8172 (7) | Ti3—O7v | 2.0072 (12) |
Ga1—O7i | 1.8172 (7) | Ti4—O1iii | 1.9602 (7) |
Ga2—O2ii | 1.8998 (12) | Ti4—O1ii | 1.9602 (7) |
Ga2—O4iii | 1.9185 (7) | Ti4—O1vi | 1.9819 (11) |
Ga2—O4ii | 1.9185 (7) | Ti4—O2vi | 1.9641 (8) |
Ga2—O5iv | 2.0286 (8) | Ti4—O2vii | 1.9641 (8) |
Ga2—O5 | 2.0286 (8) | Ti4—O3ii | 1.9855 (12) |
Ga2—O5ii | 2.1158 (11) | Ga5—O6 | 1.88 (6) |
Ti3—O3iv | 1.9381 (7) | Ga5—O6viii | 2.47 (6) |
Ti3—O3 | 1.9381 (7) | Ga5—O7 | 1.95 (4) |
Ti3—O4 | 1.8895 (12) | Ga5—O7i | 1.95 (4) |
Symmetry codes: (i) x, y, z+1; (ii) −x+1/2, −y+1/2, −z+1/2; (iii) −x+1/2, −y+1/2, −z−1/2; (iv) x, y, z−1; (v) y, −x, −z; (vi) y, −x+1, −z; (vii) y, −x+1, −z+1; (viii) −y, x, z. |
Crystal data top
Al0.49Ga1.65K0.155O7Ti1.86 | Dx = 4.576 (2) Mg m−3 |
Mr = 335.4 | Mo Kα radiation, λ = 0.71069 Å |
Tetragonal, I4/m | Cell parameters from 20 reflections |
Hall symbol: -I 4 | θ = 30–37° |
a = 18.0606 (11) Å | µ = 12.21 mm−1 |
c = 2.9839 (13) Å | T = 298 K |
V = 973.3 (4) Å3 | Prism, colorless |
Z = 8 | 0.24 × 0.14 × 0.08 mm |
F(000) = 1259 | |
Data collection top
Rigaku AFC-5S diffractometer | Rint = 0.038 |
Graphite monochromator | θmax = 50.1°, θmin = 1.6° |
ω/2θ scans | h = −38→38 |
Absorption correction: numerical ? | k = −37→38 |
Tmin = 0.250, Tmax = 0.423 | l = 0→6 |
5591 measured reflections | 3 standard reflections every 100 reflections |
2811 independent reflections | intensity decay: <1.2% |
2378 reflections with I > 2σ(I) | |
Refinement top
Refinement on F2 | Weighting scheme based on measured s.u.'s w = 1/(σ2(I) + 0.0001I2) |
R[F2 > 2σ(F2)] = 0.032 | (Δ/σ)max = 0.001 |
wR(F2) = 0.055 | Δρmax = 2.22 e Å−3 |
S = 1.17 | Δρmin = −1.41 e Å−3 |
2811 reflections | Extinction correction: B-C type 1 Gaussian isotropic (Becker & Coppens, 1974) |
86 parameters | Extinction coefficient: 0.0609 (9) |
Crystal data top
Al0.49Ga1.65K0.155O7Ti1.86 | Z = 8 |
Mr = 335.4 | Mo Kα radiation |
Tetragonal, I4/m | µ = 12.21 mm−1 |
a = 18.0606 (11) Å | T = 298 K |
c = 2.9839 (13) Å | 0.24 × 0.14 × 0.08 mm |
V = 973.3 (4) Å3 | |
Data collection top
Rigaku AFC-5S diffractometer | 2378 reflections with I > 2σ(I) |
Absorption correction: numerical ? | Rint = 0.038 |
Tmin = 0.250, Tmax = 0.423 | 3 standard reflections every 100 reflections |
5591 measured reflections | intensity decay: <1.2% |
2811 independent reflections | |
Refinement top
R[F2 > 2σ(F2)] = 0.032 | 86 parameters |
wR(F2) = 0.055 | Δρmax = 2.22 e Å−3 |
S = 1.17 | Δρmin = −1.41 e Å−3 |
2811 reflections | |
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top | x | y | z | Uiso*/Ueq | Occ. (<1) |
K1 | 0 | 0 | 0.225 (6) | 0.092 (11) | 0.310 (4) |
Ga1 | 0.117996 (11) | 0.162518 (11) | 0.5 | 0.00521 (4) | 0.8351 (15) |
Al1 | 0.117996 | 0.162518 | 0.5 | 0.00521 | 0.1596 (17) |
Ga2 | 0.203739 (12) | 0.310893 (12) | 0 | 0.00607 (5) | 0.610 (6) |
Al2 | 0.203739 | 0.310893 | 0 | 0.00607 | 0.167 (16) |
Ti2 | 0.203739 | 0.310893 | 0 | 0.00607 | 0.223 (15) |
Ti3 | 0.221305 (15) | 0.036084 (14) | 0 | 0.00640 (6) | 0.659 (15) |
Ga3 | 0.221305 | 0.036084 | 0 | 0.00640 | 0.178 (7) |
Al3 | 0.221305 | 0.036084 | 0 | 0.00640 | 0.163 (16) |
Ti4 | 0.119804 (17) | 0.542926 (17) | 0 | 0.00966 (6) | 0.978 (3) |
Ga4 | 0.119804 | 0.542926 | 0 | 0.00966 | 0.022 (3) |
Ga5 | 0.062 (2) | 0.104 (2) | 0.5 | 0.01* | 0.0053 (8) |
O1 | 0.40946 (6) | 0.02052 (6) | 0 | 0.0064 (2) | |
O2 | 0.39415 (6) | 0.15200 (6) | 0.5 | 0.0065 (2) | |
O3 | 0.28021 (6) | 0.00199 (6) | 0.5 | 0.0068 (2) | |
O4 | 0.26458 (6) | 0.13112 (6) | 0 | 0.0070 (2) | |
O5 | 0.18948 (6) | 0.23623 (6) | 0.5 | 0.0066 (2) | |
O6 | 0.15515 (6) | 0.06782 (6) | 0.5 | 0.0070 (2) | |
O7 | 0.06154 (6) | 0.16841 (7) | 0 | 0.0081 (2) | |
Atomic displacement parameters (Å2) top | U11 | U22 | U33 | U12 | U13 | U23 |
K1 | 0.051 (2) | 0.051 (2) | 0.18 (3) | 0 | 0 | 0 |
Ga1 | 0.00533 (7) | 0.00602 (7) | 0.00428 (7) | −0.00021 (5) | 0 | 0 |
Ga2 | 0.00595 (9) | 0.00739 (9) | 0.00485 (9) | 0.00022 (6) | 0 | 0 |
Ti3 | 0.00853 (11) | 0.00525 (10) | 0.00542 (11) | 0.00006 (7) | 0 | 0 |
Ti4 | 0.01099 (11) | 0.01015 (10) | 0.00785 (11) | −0.00049 (7) | 0 | 0 |
O1 | 0.0076 (3) | 0.0055 (3) | 0.0059 (4) | −0.0013 (3) | 0 | 0 |
O2 | 0.0053 (3) | 0.0077 (4) | 0.0066 (4) | 0.0013 (3) | 0 | 0 |
O3 | 0.0058 (3) | 0.0081 (4) | 0.0063 (4) | 0.0023 (3) | 0 | 0 |
O4 | 0.0084 (4) | 0.0056 (3) | 0.0071 (4) | −0.0010 (3) | 0 | 0 |
O5 | 0.0066 (3) | 0.0055 (3) | 0.0076 (4) | −0.0010 (3) | 0 | 0 |
O6 | 0.0061 (3) | 0.0078 (4) | 0.0069 (4) | 0.0016 (3) | 0 | 0 |
O7 | 0.0064 (3) | 0.0115 (4) | 0.0063 (4) | 0.0028 (3) | 0 | 0 |
Bond lengths (Å) top
Ga1—O5 | 1.8545 (11) | Ti3—O6iv | 1.9955 (8) |
Ga1—O6 | 1.8372 (12) | Ti3—O6 | 1.9955 (8) |
Ga1—O7 | 1.8102 (7) | Ti3—O7v | 2.0053 (12) |
Ga1—O7i | 1.8102 (7) | Ti4—O1iii | 1.9540 (7) |
Ga2—O2ii | 1.8906 (11) | Ti4—O1ii | 1.9540 (7) |
Ga2—O4iii | 1.9105 (7) | Ti4—O1vi | 1.9887 (11) |
Ga2—O4ii | 1.9105 (7) | Ti4—O2vi | 1.9636 (7) |
Ga2—O5iv | 2.0274 (7) | Ti4—O2vii | 1.9636 (7) |
Ga2—O5 | 2.0274 (7) | Ti4—O3ii | 1.9796 (11) |
Ga2—O5ii | 2.1081 (11) | Ga5—O6 | 1.80 (4) |
Ti3—O3iv | 1.9332 (7) | Ga5—O6viii | 2.52 (4) |
Ti3—O3 | 1.9332 (7) | Ga5—O7 | 1.89 (2) |
Ti3—O4 | 1.8860 (11) | Ga5—O7i | 1.89 (2) |
Symmetry codes: (i) x, y, z+1; (ii) −x+1/2, −y+1/2, −z+1/2; (iii) −x+1/2, −y+1/2, −z−1/2; (iv) x, y, z−1; (v) y, −x, −z; (vi) y, −x+1, −z; (vii) y, −x+1, −z+1; (viii) −y, x, z. |
Crystal data top
Al0.84Ga1.30K0.157O7Ti1.86 | Dx = 4.408 (2) Mg m−3 |
Mr = 320.4 | Mo Kα radiation, λ = 0.71069 Å |
Tetragonal, I4/m | Cell parameters from 20 reflections |
Hall symbol: -I 4 | θ = 30–37° |
a = 18.0088 (12) Å | µ = 10.45 mm−1 |
c = 2.9759 (14) Å | T = 298 K |
V = 965.1 (5) Å3 | Prism, colorless |
Z = 8 | 0.20 × 0.03 × 0.02 mm |
F(000) = 1209 | |
Data collection top
Rigaku AFC-5S diffractometer | Rint = 0.055 |
Graphite monochromator | θmax = 50.2°, θmin = 1.6° |
ω/2θ scans | h = −38→38 |
Absorption correction: numerical ? | k = 0→38 |
Tmin = 0.646, Tmax = 0.834 | l = 0→6 |
5056 measured reflections | 3 standard reflections every 50 reflections |
2709 independent reflections | intensity decay: <3.9% |
1749 reflections with I > 2σ(I) | |
Refinement top
Refinement on F2 | Weighting scheme based on measured s.u.'s w = 1/(σ2(I) + 0.0001I2) |
R[F2 > 2σ(F2)] = 0.043 | (Δ/σ)max = 0.017 |
wR(F2) = 0.072 | Δρmax = 2.28 e Å−3 |
S = 0.99 | Δρmin = −1.99 e Å−3 |
2709 reflections | Extinction correction: B-C type 2 (Becker & Coppens, 1974) |
86 parameters | Extinction coefficient: 0.059 (2) |
Crystal data top
Al0.84Ga1.30K0.157O7Ti1.86 | Z = 8 |
Mr = 320.4 | Mo Kα radiation |
Tetragonal, I4/m | µ = 10.45 mm−1 |
a = 18.0088 (12) Å | T = 298 K |
c = 2.9759 (14) Å | 0.20 × 0.03 × 0.02 mm |
V = 965.1 (5) Å3 | |
Data collection top
Rigaku AFC-5S diffractometer | 1749 reflections with I > 2σ(I) |
Absorption correction: numerical ? | Rint = 0.055 |
Tmin = 0.646, Tmax = 0.834 | 3 standard reflections every 50 reflections |
5056 measured reflections | intensity decay: <3.9% |
2709 independent reflections | |
Refinement top
R[F2 > 2σ(F2)] = 0.043 | 86 parameters |
wR(F2) = 0.072 | Δρmax = 2.28 e Å−3 |
S = 0.99 | Δρmin = −1.99 e Å−3 |
2709 reflections | |
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top | x | y | z | Uiso*/Ueq | Occ. (<1) |
K1 | 0 | 0 | 0.226 (3) | 0.085 (5) | 0.314 (5) |
Ga1 | 0.11781 (2) | 0.16271 (2) | 0.5 | 0.00546 (8) | 0.7059 (19) |
Al1 | 0.11781 | 0.16271 | 0.5 | 0.00546 | 0.286 (2) |
Ga2 | 0.20407 (2) | 0.31096 (2) | 0 | 0.00668 (10) | 0.475 (9) |
Al2 | 0.20407 | 0.31096 | 0 | 0.00668 | 0.35 (2) |
Ti2 | 0.20407 | 0.31096 | 0 | 0.00668 | 0.17 (2) |
Ti3 | 0.22114 (3) | 0.03631 (3) | 0 | 0.00678 (10) | 0.69 (2) |
Ga3 | 0.22114 | 0.03631 | 0 | 0.00678 | 0.105 (10) |
Al3 | 0.22114 | 0.03631 | 0 | 0.00678 | 0.20 (2) |
Ti4 | 0.12029 (3) | 0.54304 (3) | 0 | 0.01008 (10) | 0.997 (3) |
Ga4 | 0.12029 | 0.54304 | 0 | 0.01008 | 0.003 (3) |
Ga5 | 0.064 (2) | 0.102 (2) | 0.5 | 0.01* | 0.0080 (11) |
O1 | 0.40921 (10) | 0.02046 (10) | 0 | 0.0066 (4) | |
O2 | 0.39374 (10) | 0.15235 (10) | 0.5 | 0.0067 (4) | |
O3 | 0.28003 (10) | 0.00222 (10) | 0.5 | 0.0071 (4) | |
O4 | 0.26498 (10) | 0.13137 (10) | 0 | 0.0076 (4) | |
O5 | 0.18961 (10) | 0.23608 (10) | 0.5 | 0.0067 (4) | |
O6 | 0.15496 (10) | 0.06837 (11) | 0.5 | 0.0077 (4) | |
O7 | 0.06206 (10) | 0.16859 (11) | 0 | 0.0089 (4) | |
Atomic displacement parameters (Å2) top | U11 | U22 | U33 | U12 | U13 | U23 |
K1 | 0.058 (4) | 0.058 (4) | 0.140 (12) | 0 | 0 | 0 |
Ga1 | 0.00552 (13) | 0.00609 (13) | 0.00476 (13) | −0.00040 (10) | 0 | 0 |
Ga2 | 0.00605 (16) | 0.00833 (17) | 0.00566 (18) | 0.00032 (12) | 0 | 0 |
Ti3 | 0.00868 (19) | 0.00566 (17) | 0.00600 (19) | −0.00025 (13) | 0 | 0 |
Ti4 | 0.01162 (19) | 0.01070 (18) | 0.00792 (17) | −0.00049 (14) | 0 | 0 |
O1 | 0.0075 (6) | 0.0055 (6) | 0.0069 (7) | −0.0010 (5) | 0 | 0 |
O2 | 0.0059 (6) | 0.0071 (6) | 0.0070 (7) | 0.0008 (5) | 0 | 0 |
O3 | 0.0061 (6) | 0.0078 (6) | 0.0075 (7) | 0.0028 (5) | 0 | 0 |
O4 | 0.0091 (7) | 0.0052 (6) | 0.0086 (7) | −0.0011 (5) | 0 | 0 |
O5 | 0.0059 (6) | 0.0058 (6) | 0.0085 (7) | −0.0004 (5) | 0 | 0 |
O6 | 0.0054 (6) | 0.0094 (7) | 0.0084 (7) | 0.0011 (5) | 0 | 0 |
O7 | 0.0073 (6) | 0.0121 (7) | 0.0073 (7) | 0.0023 (6) | 0 | 0 |
Bond lengths (Å) top
Ga1—O5 | 1.8487 (18) | Ti3—O6iv | 1.9919 (12) |
Ga1—O6 | 1.8260 (19) | Ti3—O6 | 1.9919 (12) |
Ga1—O7 | 1.7981 (11) | Ti3—O7v | 2.009 (2) |
Ga1—O7i | 1.7981 (11) | Ti4—O1iii | 1.9504 (12) |
Ga2—O2ii | 1.8813 (18) | Ti4—O1ii | 1.9504 (12) |
Ga2—O4iii | 1.8983 (11) | Ti4—O1vi | 1.9928 (19) |
Ga2—O4ii | 1.8983 (11) | Ti4—O2vi | 1.9605 (12) |
Ga2—O5iv | 2.0249 (12) | Ti4—O2vii | 1.9605 (12) |
Ga2—O5 | 2.0249 (12) | Ti4—O3ii | 1.9716 (19) |
Ga2—O5ii | 2.0937 (18) | Ga5—O6 | 1.75 (4) |
Ti3—O3iv | 1.9276 (12) | Ga5—O6viii | 2.57 (4) |
Ti3—O3 | 1.9276 (12) | Ga5—O7 | 1.91 (3) |
Ti3—O4 | 1.8850 (18) | Ga5—O7i | 1.91 (3) |
Symmetry codes: (i) x, y, z+1; (ii) −x+1/2, −y+1/2, −z+1/2; (iii) −x+1/2, −y+1/2, −z−1/2; (iv) x, y, z−1; (v) y, −x, −z; (vi) y, −x+1, −z; (vii) y, −x+1, −z+1; (viii) −y, x, z. |
Experimental details
| (sample-I) | (sample-II) | (sample-III) |
Crystal data |
Chemical formula | Al0.21Ga1.93K0.152O7Ti1.86 | Al0.49Ga1.65K0.155O7Ti1.86 | Al0.84Ga1.30K0.157O7Ti1.86 |
Mr | 347.2 | 335.4 | 320.4 |
Crystal system, space group | Tetragonal, I4/m | Tetragonal, I4/m | Tetragonal, I4/m |
Temperature (K) | 298 | 298 | 298 |
a, c (Å) | 18.0971 (16), 2.9916 (19) | 18.0606 (11), 2.9839 (13) | 18.0088 (12), 2.9759 (14) |
V (Å3) | 979.8 (6) | 973.3 (4) | 965.1 (5) |
Z | 8 | 8 | 8 |
Radiation type | Mo Kα | Mo Kα | Mo Kα |
µ (mm−1) | 13.58 | 12.21 | 10.45 |
Crystal size (mm) | 0.22 × 0.08 × 0.08 | 0.24 × 0.14 × 0.08 | 0.20 × 0.03 × 0.02 |
|
Data collection |
Diffractometer | Rigaku AFC-5S diffractometer | Rigaku AFC-5S diffractometer | Rigaku AFC-5S diffractometer |
Absorption correction | Numerical | Numerical | Numerical |
Tmin, Tmax | 0.292, 0.467 | 0.250, 0.423 | 0.646, 0.834 |
No. of measured, independent and observed [I > 2σ(I)] reflections | 5602, 2817, 2350 | 5591, 2811, 2378 | 5056, 2709, 1749 |
Rint | 0.034 | 0.038 | 0.055 |
(sin θ/λ)max (Å−1) | 1.080 | 1.080 | 1.080 |
|
Refinement |
R[F2 > 2σ(F2)], wR(F2), S | 0.031, 0.051, 1.10 | 0.032, 0.055, 1.17 | 0.043, 0.072, 0.99 |
No. of reflections | 2817 | 2811 | 2709 |
No. of parameters | 86 | 86 | 86 |
No. of restraints | ? | ? | ? |
Δρmax, Δρmin (e Å−3) | 1.35, −1.39 | 2.22, −1.41 | 2.28, −1.99 |