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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

cif

Crystallographic Information File (CIF) https://doi.org/10.1107/S0108768105031034/lc5028sup1.cif
Contains datablocks global, sample-I, sample-II, sample-III

hkl

Structure factor file (CIF format) https://doi.org/10.1107/S0108768105031034/lc5028sample-Isup2.hkl
Contains datablock sample-I

hkl

Structure factor file (CIF format) https://doi.org/10.1107/S0108768105031034/lc5028sample-IIsup3.hkl
Contains datablock sample-II

hkl

Structure factor file (CIF format) https://doi.org/10.1107/S0108768105031034/lc5028sample-IIIsup4.hkl
Contains datablock sample-III

pdf

Portable Document Format (PDF) file https://doi.org/10.1107/S0108768105031034/lc5028sup5.pdf
Coordinates and geometry

Computing details top

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).

Figures top
[Figure 1]
[Figure 2]
[Figure 3]
[Figure 4]
[Figure 5]
[Figure 6]
(sample-I) top
Crystal data top
Al0.21Ga1.93K0.152O7Ti1.86Dx = 4.706 (3) Mg m3
Mr = 347.2Mo Kα radiation, λ = 0.71069 Å
Tetragonal, I4/mCell parameters from 20 reflections
Hall symbol: -I 4θ = 30–37°
a = 18.0971 (16) ŵ = 13.58 mm1
c = 2.9916 (19) ÅT = 298 K
V = 979.8 (6) Å3Prism, colorless
Z = 80.22 × 0.08 × 0.08 mm
F(000) = 1299
Data collection top
Rigaku AFC-5S
diffractometer
Rint = 0.034
Graphite monochromatorθmax = 50.1°, θmin = 1.6°
ω/2θ scansh = 3839
Absorption correction: numerical
?
k = 039
Tmin = 0.292, Tmax = 0.467l = 06
5602 measured reflections3 standard reflections every 100 reflections
2817 independent reflections intensity decay: <0.8%
2350 reflections with I > 2σ(I)
Refinement top
Refinement on F2Weighting 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) = 0.051Δρmax = 1.35 e Å3
S = 1.10Δρmin = 1.39 e Å3
2817 reflectionsExtinction correction: B-C type 1 Gaussian isotropic (Becker & Coppens, 1974)
86 parametersExtinction coefficient: 0.0397 (6)
Crystal data top
Al0.21Ga1.93K0.152O7Ti1.86Z = 8
Mr = 347.2Mo Kα radiation
Tetragonal, I4/mµ = 13.58 mm1
a = 18.0971 (16) ÅT = 298 K
c = 2.9916 (19) Å0.22 × 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 = 0.4673 standard reflections every 100 reflections
5602 measured reflections intensity decay: <0.8%
2817 independent reflections
Refinement top
R[F2 > 2σ(F2)] = 0.03186 parameters
wR(F2) = 0.051Δρmax = 1.35 e Å3
S = 1.10Δρmin = 1.39 e Å3
2817 reflections
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzUiso*/UeqOcc. (<1)
K1000.234 (3)0.089 (6)0.303 (3)
Ga10.118144 (10)0.162373 (10)0.50.00472 (4)0.9326 (14)
Al10.1181440.1623730.50.004720.0640 (16)
Ga20.203530 (11)0.310781 (11)00.00525 (5)0.756 (5)
Al20.2035300.31078100.005250.077 (14)
Ti20.2035300.31078100.005250.166 (13)
Ti30.221445 (15)0.035922 (14)00.00593 (6)0.730 (13)
Ga30.2214450.03592200.005930.202 (6)
Al30.2214450.03592200.005930.069 (14)
Ti40.119442 (18)0.542960 (17)00.00905 (6)0.964 (2)
Ga40.1194420.54296000.009050.036 (2)
Ga50.057 (3)0.100 (3)0.50.01*0.0034 (8)
O10.40977 (7)0.02065 (6)00.0059 (2)
O20.39445 (6)0.15152 (6)0.50.0057 (2)
O30.28044 (6)0.00190 (7)0.50.0063 (2)
O40.26450 (7)0.13104 (6)00.0061 (2)
O50.18949 (6)0.23637 (6)0.50.0053 (2)
O60.15538 (6)0.06769 (6)0.50.0062 (2)
O70.06143 (6)0.16830 (7)00.0070 (2)
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
K10.052 (2)0.052 (2)0.163 (19)000
Ga10.00498 (7)0.00556 (7)0.00361 (7)0.00019 (5)00
Ga20.00549 (8)0.00657 (8)0.00370 (8)0.00028 (5)00
Ti30.00858 (10)0.00475 (9)0.00446 (10)0.00003 (7)00
Ti40.01043 (11)0.00974 (11)0.00697 (11)0.00056 (8)00
O10.0081 (4)0.0042 (3)0.0054 (4)0.0015 (3)00
O20.0058 (4)0.0066 (4)0.0046 (4)0.0006 (3)00
O30.0050 (4)0.0079 (4)0.0060 (4)0.0026 (3)00
O40.0088 (4)0.0048 (3)0.0048 (4)0.0013 (3)00
O50.0062 (4)0.0051 (3)0.0045 (4)0.0004 (3)00
O60.0065 (4)0.0072 (4)0.0049 (4)0.0024 (3)00
O70.0055 (4)0.0120 (4)0.0035 (4)0.0030 (3)00
Bond lengths (Å) top
Ga1—O51.8602 (11)Ti3—O6iv1.9993 (8)
Ga1—O61.8413 (12)Ti3—O61.9993 (8)
Ga1—O71.8172 (7)Ti3—O7v2.0072 (12)
Ga1—O7i1.8172 (7)Ti4—O1iii1.9602 (7)
Ga2—O2ii1.8998 (12)Ti4—O1ii1.9602 (7)
Ga2—O4iii1.9185 (7)Ti4—O1vi1.9819 (11)
Ga2—O4ii1.9185 (7)Ti4—O2vi1.9641 (8)
Ga2—O5iv2.0286 (8)Ti4—O2vii1.9641 (8)
Ga2—O52.0286 (8)Ti4—O3ii1.9855 (12)
Ga2—O5ii2.1158 (11)Ga5—O61.88 (6)
Ti3—O3iv1.9381 (7)Ga5—O6viii2.47 (6)
Ti3—O31.9381 (7)Ga5—O71.95 (4)
Ti3—O41.8895 (12)Ga5—O7i1.95 (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, z1/2; (iv) x, y, z1; (v) y, x, z; (vi) y, x+1, z; (vii) y, x+1, z+1; (viii) y, x, z.
(sample-II) top
Crystal data top
Al0.49Ga1.65K0.155O7Ti1.86Dx = 4.576 (2) Mg m3
Mr = 335.4Mo Kα radiation, λ = 0.71069 Å
Tetragonal, I4/mCell parameters from 20 reflections
Hall symbol: -I 4θ = 30–37°
a = 18.0606 (11) ŵ = 12.21 mm1
c = 2.9839 (13) ÅT = 298 K
V = 973.3 (4) Å3Prism, colorless
Z = 80.24 × 0.14 × 0.08 mm
F(000) = 1259
Data collection top
Rigaku AFC-5S
diffractometer
Rint = 0.038
Graphite monochromatorθmax = 50.1°, θmin = 1.6°
ω/2θ scansh = 3838
Absorption correction: numerical
?
k = 3738
Tmin = 0.250, Tmax = 0.423l = 06
5591 measured reflections3 standard reflections every 100 reflections
2811 independent reflections intensity decay: <1.2%
2378 reflections with I > 2σ(I)
Refinement top
Refinement on F2Weighting 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) = 0.055Δρmax = 2.22 e Å3
S = 1.17Δρmin = 1.41 e Å3
2811 reflectionsExtinction correction: B-C type 1 Gaussian isotropic (Becker & Coppens, 1974)
86 parametersExtinction coefficient: 0.0609 (9)
Crystal data top
Al0.49Ga1.65K0.155O7Ti1.86Z = 8
Mr = 335.4Mo Kα radiation
Tetragonal, I4/mµ = 12.21 mm1
a = 18.0606 (11) ÅT = 298 K
c = 2.9839 (13) Å0.24 × 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 = 0.4233 standard reflections every 100 reflections
5591 measured reflections intensity decay: <1.2%
2811 independent reflections
Refinement top
R[F2 > 2σ(F2)] = 0.03286 parameters
wR(F2) = 0.055Δρmax = 2.22 e Å3
S = 1.17Δρmin = 1.41 e Å3
2811 reflections
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzUiso*/UeqOcc. (<1)
K1000.225 (6)0.092 (11)0.310 (4)
Ga10.117996 (11)0.162518 (11)0.50.00521 (4)0.8351 (15)
Al10.1179960.1625180.50.005210.1596 (17)
Ga20.203739 (12)0.310893 (12)00.00607 (5)0.610 (6)
Al20.2037390.31089300.006070.167 (16)
Ti20.2037390.31089300.006070.223 (15)
Ti30.221305 (15)0.036084 (14)00.00640 (6)0.659 (15)
Ga30.2213050.03608400.006400.178 (7)
Al30.2213050.03608400.006400.163 (16)
Ti40.119804 (17)0.542926 (17)00.00966 (6)0.978 (3)
Ga40.1198040.54292600.009660.022 (3)
Ga50.062 (2)0.104 (2)0.50.01*0.0053 (8)
O10.40946 (6)0.02052 (6)00.0064 (2)
O20.39415 (6)0.15200 (6)0.50.0065 (2)
O30.28021 (6)0.00199 (6)0.50.0068 (2)
O40.26458 (6)0.13112 (6)00.0070 (2)
O50.18948 (6)0.23623 (6)0.50.0066 (2)
O60.15515 (6)0.06782 (6)0.50.0070 (2)
O70.06154 (6)0.16841 (7)00.0081 (2)
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
K10.051 (2)0.051 (2)0.18 (3)000
Ga10.00533 (7)0.00602 (7)0.00428 (7)0.00021 (5)00
Ga20.00595 (9)0.00739 (9)0.00485 (9)0.00022 (6)00
Ti30.00853 (11)0.00525 (10)0.00542 (11)0.00006 (7)00
Ti40.01099 (11)0.01015 (10)0.00785 (11)0.00049 (7)00
O10.0076 (3)0.0055 (3)0.0059 (4)0.0013 (3)00
O20.0053 (3)0.0077 (4)0.0066 (4)0.0013 (3)00
O30.0058 (3)0.0081 (4)0.0063 (4)0.0023 (3)00
O40.0084 (4)0.0056 (3)0.0071 (4)0.0010 (3)00
O50.0066 (3)0.0055 (3)0.0076 (4)0.0010 (3)00
O60.0061 (3)0.0078 (4)0.0069 (4)0.0016 (3)00
O70.0064 (3)0.0115 (4)0.0063 (4)0.0028 (3)00
Bond lengths (Å) top
Ga1—O51.8545 (11)Ti3—O6iv1.9955 (8)
Ga1—O61.8372 (12)Ti3—O61.9955 (8)
Ga1—O71.8102 (7)Ti3—O7v2.0053 (12)
Ga1—O7i1.8102 (7)Ti4—O1iii1.9540 (7)
Ga2—O2ii1.8906 (11)Ti4—O1ii1.9540 (7)
Ga2—O4iii1.9105 (7)Ti4—O1vi1.9887 (11)
Ga2—O4ii1.9105 (7)Ti4—O2vi1.9636 (7)
Ga2—O5iv2.0274 (7)Ti4—O2vii1.9636 (7)
Ga2—O52.0274 (7)Ti4—O3ii1.9796 (11)
Ga2—O5ii2.1081 (11)Ga5—O61.80 (4)
Ti3—O3iv1.9332 (7)Ga5—O6viii2.52 (4)
Ti3—O31.9332 (7)Ga5—O71.89 (2)
Ti3—O41.8860 (11)Ga5—O7i1.89 (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, z1/2; (iv) x, y, z1; (v) y, x, z; (vi) y, x+1, z; (vii) y, x+1, z+1; (viii) y, x, z.
(sample-III) top
Crystal data top
Al0.84Ga1.30K0.157O7Ti1.86Dx = 4.408 (2) Mg m3
Mr = 320.4Mo Kα radiation, λ = 0.71069 Å
Tetragonal, I4/mCell parameters from 20 reflections
Hall symbol: -I 4θ = 30–37°
a = 18.0088 (12) ŵ = 10.45 mm1
c = 2.9759 (14) ÅT = 298 K
V = 965.1 (5) Å3Prism, colorless
Z = 80.20 × 0.03 × 0.02 mm
F(000) = 1209
Data collection top
Rigaku AFC-5S
diffractometer
Rint = 0.055
Graphite monochromatorθmax = 50.2°, θmin = 1.6°
ω/2θ scansh = 3838
Absorption correction: numerical
?
k = 038
Tmin = 0.646, Tmax = 0.834l = 06
5056 measured reflections3 standard reflections every 50 reflections
2709 independent reflections intensity decay: <3.9%
1749 reflections with I > 2σ(I)
Refinement top
Refinement on F2Weighting 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) = 0.072Δρmax = 2.28 e Å3
S = 0.99Δρmin = 1.99 e Å3
2709 reflectionsExtinction correction: B-C type 2 (Becker & Coppens, 1974)
86 parametersExtinction coefficient: 0.059 (2)
Crystal data top
Al0.84Ga1.30K0.157O7Ti1.86Z = 8
Mr = 320.4Mo Kα radiation
Tetragonal, I4/mµ = 10.45 mm1
a = 18.0088 (12) ÅT = 298 K
c = 2.9759 (14) Å0.20 × 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 = 0.8343 standard reflections every 50 reflections
5056 measured reflections intensity decay: <3.9%
2709 independent reflections
Refinement top
R[F2 > 2σ(F2)] = 0.04386 parameters
wR(F2) = 0.072Δρmax = 2.28 e Å3
S = 0.99Δρmin = 1.99 e Å3
2709 reflections
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzUiso*/UeqOcc. (<1)
K1000.226 (3)0.085 (5)0.314 (5)
Ga10.11781 (2)0.16271 (2)0.50.00546 (8)0.7059 (19)
Al10.117810.162710.50.005460.286 (2)
Ga20.20407 (2)0.31096 (2)00.00668 (10)0.475 (9)
Al20.204070.3109600.006680.35 (2)
Ti20.204070.3109600.006680.17 (2)
Ti30.22114 (3)0.03631 (3)00.00678 (10)0.69 (2)
Ga30.221140.0363100.006780.105 (10)
Al30.221140.0363100.006780.20 (2)
Ti40.12029 (3)0.54304 (3)00.01008 (10)0.997 (3)
Ga40.120290.5430400.010080.003 (3)
Ga50.064 (2)0.102 (2)0.50.01*0.0080 (11)
O10.40921 (10)0.02046 (10)00.0066 (4)
O20.39374 (10)0.15235 (10)0.50.0067 (4)
O30.28003 (10)0.00222 (10)0.50.0071 (4)
O40.26498 (10)0.13137 (10)00.0076 (4)
O50.18961 (10)0.23608 (10)0.50.0067 (4)
O60.15496 (10)0.06837 (11)0.50.0077 (4)
O70.06206 (10)0.16859 (11)00.0089 (4)
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
K10.058 (4)0.058 (4)0.140 (12)000
Ga10.00552 (13)0.00609 (13)0.00476 (13)0.00040 (10)00
Ga20.00605 (16)0.00833 (17)0.00566 (18)0.00032 (12)00
Ti30.00868 (19)0.00566 (17)0.00600 (19)0.00025 (13)00
Ti40.01162 (19)0.01070 (18)0.00792 (17)0.00049 (14)00
O10.0075 (6)0.0055 (6)0.0069 (7)0.0010 (5)00
O20.0059 (6)0.0071 (6)0.0070 (7)0.0008 (5)00
O30.0061 (6)0.0078 (6)0.0075 (7)0.0028 (5)00
O40.0091 (7)0.0052 (6)0.0086 (7)0.0011 (5)00
O50.0059 (6)0.0058 (6)0.0085 (7)0.0004 (5)00
O60.0054 (6)0.0094 (7)0.0084 (7)0.0011 (5)00
O70.0073 (6)0.0121 (7)0.0073 (7)0.0023 (6)00
Bond lengths (Å) top
Ga1—O51.8487 (18)Ti3—O6iv1.9919 (12)
Ga1—O61.8260 (19)Ti3—O61.9919 (12)
Ga1—O71.7981 (11)Ti3—O7v2.009 (2)
Ga1—O7i1.7981 (11)Ti4—O1iii1.9504 (12)
Ga2—O2ii1.8813 (18)Ti4—O1ii1.9504 (12)
Ga2—O4iii1.8983 (11)Ti4—O1vi1.9928 (19)
Ga2—O4ii1.8983 (11)Ti4—O2vi1.9605 (12)
Ga2—O5iv2.0249 (12)Ti4—O2vii1.9605 (12)
Ga2—O52.0249 (12)Ti4—O3ii1.9716 (19)
Ga2—O5ii2.0937 (18)Ga5—O61.75 (4)
Ti3—O3iv1.9276 (12)Ga5—O6viii2.57 (4)
Ti3—O31.9276 (12)Ga5—O71.91 (3)
Ti3—O41.8850 (18)Ga5—O7i1.91 (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, z1/2; (iv) x, y, z1; (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 formulaAl0.21Ga1.93K0.152O7Ti1.86Al0.49Ga1.65K0.155O7Ti1.86Al0.84Ga1.30K0.157O7Ti1.86
Mr347.2335.4320.4
Crystal system, space groupTetragonal, I4/mTetragonal, I4/mTetragonal, I4/m
Temperature (K)298298298
a, c (Å)18.0971 (16), 2.9916 (19)18.0606 (11), 2.9839 (13)18.0088 (12), 2.9759 (14)
V3)979.8 (6)973.3 (4)965.1 (5)
Z888
Radiation typeMo KαMo KαMo Kα
µ (mm1)13.5812.2110.45
Crystal size (mm)0.22 × 0.08 × 0.080.24 × 0.14 × 0.080.20 × 0.03 × 0.02
Data collection
DiffractometerRigaku AFC-5S
diffractometer
Rigaku AFC-5S
diffractometer
Rigaku AFC-5S
diffractometer
Absorption correctionNumericalNumericalNumerical
Tmin, Tmax0.292, 0.4670.250, 0.4230.646, 0.834
No. of measured, independent and
observed [I > 2σ(I)] reflections
5602, 2817, 2350 5591, 2811, 2378 5056, 2709, 1749
Rint0.0340.0380.055
(sin θ/λ)max1)1.0801.0801.080
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 reflections281728112709
No. of parameters868686
No. of restraints???
Δρmax, Δρmin (e Å3)1.35, 1.392.22, 1.412.28, 1.99

Computer programs: (Jana2000; Petricek and Dusek, 2000).

 

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