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Studies of the K-Ba-Ga-Sn system produced the clathrate compounds K
0.8(2)Ba
15.2(2)Ga
31.0(5)Sn
105.0(5) [
a = 17.0178 (4) Å], K
4.3(3)Ba
11.7(3)Ga
27.4(4)Sn
108.6(4) [
a = 17.0709 (6) Å] and K
12.9(2)Ba
3.1(2)Ga
19.5(4)Sn
116.5(4) [
a = 17.1946 (8) Å], with the type-II structure (cubic, space group
Fdm), and K
7.7(1)Ba
0.3(1)Ga
8.3(4)Sn
37.7(4) [
a = 11.9447 (4) Å], with the type-I structure (cubic, space group
Pmn). For the type-II structures, only the smaller (Ga,Sn)
24 pentagonal dodecahedral cages are filled, while the (Ga,Sn)
28 hexakaidecahedral cages remain empty. The unit-cell volume is directly correlated with the K:Ba ratio, since an increasing amount of monovalent K occupying the cages causes a decreasing substitution of the smaller Ga in the framework. All three formulae have an electron count that is in good agreement with the Zintl-Klemm rules. For the type-I compound, all framework sites are occupied by a mixture of Ga and Sn atoms, with Ga showing a preference for Wyckoff site 6
c. The (Ga,Sn)
20 pentagonal dodecahedral cages are occupied by statistically disordered K and Ba atoms, while the (Ga,Sn)
24 tetrakaidecahedral cages encapsulate only K atoms. Large anisotropic displacement parameters for K in the latter cages suggest an off-centering of the guest atoms.
Supporting information
For all compounds, data collection: SMART (Bruker, 2002); cell refinement: SMART (Bruker, 2002); data reduction: SAINT (Bruker, 2002); program(s) used to solve structure: SHELXTL (Sheldrick, 2008); program(s) used to refine structure: SHELXTL (Sheldrick, 2008); molecular graphics: CrystalMaker (Palmer, 2007); software used to prepare material for publication: SHELXTL (Sheldrick, 2008).
(K1Ba15Ga31Sn105) Potassium barium gallium tin
top
Crystal data top
K0.8Ba15.2Ga31.0Sn105.0 | Dx = 5.638 Mg m−3 |
Mr = 16732.79 | Mo Kα radiation, λ = 0.71073 Å |
Cubic, Fd3m | Cell parameters from 4013 reflections |
Hall symbol: F 4d 2 3 -1d | θ = 3.4–30.8° |
a = 17.0178 (4) Å | µ = 20.14 mm−1 |
V = 4928.4 (2) Å3 | T = 200 K |
Z = 1 | Block, silver |
F(000) = 7074 | 0.10 × 0.09 × 0.08 mm |
Data collection top
Bruker SMART APEX CCD area-detector diffractometer | 415 independent reflections |
Radiation source: fine-focus sealed tube | 386 reflections with I > 2σ(I) |
Graphite monochromator | Rint = 0.048 |
ω scans | θmax = 30.9°, θmin = 2.1° |
Absorption correction: multi-scan (SADABS; Sheldrick, 2008) | h = −24→24 |
Tmin = 0.145, Tmax = 0.192 | k = −24→23 |
18133 measured reflections | l = −23→23 |
Refinement top
Refinement on F2 | 0 restraints |
Least-squares matrix: full | Primary atom site location: structure-invariant direct methods |
R[F2 > 2σ(F2)] = 0.025 | Secondary atom site location: difference Fourier map |
wR(F2) = 0.097 | w = 1/[σ2(Fo2) + (0.0394P)2 + 347.9131P] where P = (Fo2 + 2Fc2)/3 |
S = 1.35 | (Δ/σ)max < 0.001 |
415 reflections | Δρmax = 2.66 e Å−3 |
15 parameters | Δρmin = −1.88 e Å−3 |
Special details top
Geometry. All esds (except the esd in the dihedral angle between two l.s. planes) are
estimated using the full covariance matrix. The cell esds are taken into
account individually in the estimation of esds in distances, angles and torsion
angles; correlations between esds in cell parameters are only used when they
are defined by crystal symmetry. An approximate (isotropic) treatment of cell
esds is used for estimating esds involving l.s. planes. |
Refinement. Refinement of F2 against ALL reflections. The weighted R-factor wR and
goodness of fit S are based on F2, conventional R-factors R are based on F,
with F set to zero for negative F2. The threshold expression of F2 >
2sigma(F2) is used only for calculating R-factors(gt) etc. and is not
relevant to the choice of reflections for refinement. R-factors based on F2
are statistically about twice as large as those based on F, and R-factors based
on ALL data will be even larger. |
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top | x | y | z | Uiso*/Ueq | Occ. (<1) |
Ba | 0.0000 | 0.0000 | 0.0000 | 0.0187 (5) | 0.951 (11) |
K | 0.0000 | 0.0000 | 0.0000 | 0.0187 (5) | 0.049 (11) |
Sn1 | 0.06791 (3) | 0.06791 (3) | 0.37267 (4) | 0.0141 (2) | 0.70 |
Ga1 | 0.06791 (3) | 0.06791 (3) | 0.37267 (4) | 0.0141 (2) | 0.30 |
Sn2 | 0.21823 (4) | 0.21823 (4) | 0.21823 (4) | 0.0149 (3) | |
Sn3 | 0.1250 | 0.1250 | 0.1250 | 0.0123 (8) | 0.73 (4) |
Ga3 | 0.1250 | 0.1250 | 0.1250 | 0.0123 (8) | 0.27 (4) |
Atomic displacement parameters (Å2) top | U11 | U22 | U33 | U12 | U13 | U23 |
Ba | 0.0187 (5) | 0.0187 (5) | 0.0187 (5) | −0.0027 (3) | −0.0027 (3) | −0.0027 (3) |
K | 0.0187 (5) | 0.0187 (5) | 0.0187 (5) | −0.0027 (3) | −0.0027 (3) | −0.0027 (3) |
Sn1 | 0.0136 (3) | 0.0136 (3) | 0.0151 (4) | 0.0017 (2) | 0.00021 (17) | 0.00021 (17) |
Ga1 | 0.0136 (3) | 0.0136 (3) | 0.0151 (4) | 0.0017 (2) | 0.00021 (17) | 0.00021 (17) |
Sn2 | 0.0149 (3) | 0.0149 (3) | 0.0149 (3) | 0.0019 (2) | 0.0019 (2) | 0.0019 (2) |
Sn3 | 0.0123 (8) | 0.0123 (8) | 0.0123 (8) | 0.000 | 0.000 | 0.000 |
Ga3 | 0.0123 (8) | 0.0123 (8) | 0.0123 (8) | 0.000 | 0.000 | 0.000 |
Geometric parameters (Å, º) top
Ba—Sn3 | 3.6845 (1) | Sn2—Sn3 | 2.7481 (12) |
Ba—Sn2i | 3.7917 (5) | Sn2—Sn1vi | 2.7684 (8) |
Ba—Sn1ii | 3.9110 (5) | Sn2—Sn1v | 2.7684 (8) |
Sn1—Sn1iii | 2.7179 (7) | Sn2—Sn1vii | 2.7684 (8) |
Sn1—Sn1iv | 2.7179 (7) | Sn3—Sn2viii | 2.7481 (12) |
Sn1—Sn1v | 2.7480 (15) | Sn3—Sn2ix | 2.7481 (12) |
Sn1—Sn2v | 2.7685 (8) | Sn3—Sn2v | 2.7481 (12) |
| | | |
Sn1iii—Sn1—Sn1iv | 119.627 (6) | Sn3—Sn2—Sn1vi | 106.95 (3) |
Sn1iii—Sn1—Sn1v | 109.77 (3) | Sn1vi—Sn2—Sn1v | 111.87 (3) |
Sn1iii—Sn1—Sn2v | 104.30 (3) | Sn2viii—Sn3—Sn2ix | 109.471 (1) |
Sn1v—Sn1—Sn2v | 108.31 (3) | | |
Symmetry codes: (i) −x, y−1/4, z−1/4; (ii) y, −z+1/4, −x+1/4; (iii) −z+1/2, −x, −y+1/2; (iv) −y, −z+1/2, −x+1/2; (v) −x+1/4, −y+1/4, z; (vi) −y+1/4, z, −x+1/4; (vii) z, −x+1/4, −y+1/4; (viii) x, −y+1/4, −z+1/4; (ix) −x+1/4, y, −z+1/4. |
(K4Ba12Ga27Sn109) Potassium barium gallium tin
top
Crystal data top
K4.3Ba11.7Ga27.4Sn108.6 | Dx = 5.533 Mg m−3 |
Mr = 16575.07 | Mo Kα radiation, λ = 0.71073 Å |
Cubic, Fd3m | Cell parameters from 973 reflections |
Hall symbol: F 4d 2 3 -1d | θ = 3.4–28.1° |
a = 17.0709 (6) Å | µ = 19.33 mm−1 |
V = 4974.7 (3) Å3 | T = 200 K |
Z = 1 | Block, silver |
F(000) = 7016 | 0.11 × 0.09 × 0.08 mm |
Data collection top
Bruker SMART APEX CCD area-detector diffractometer | 335 independent reflections |
Radiation source: fine-focus sealed tube | 316 reflections with I > 2σ(I) |
Graphite monochromator | Rint = 0.054 |
ω scans | θmax = 28.2°, θmin = 2.1° |
Absorption correction: multi-scan (SADABS; Sheldrick, 2008) | h = −22→22 |
Tmin = 0.115, Tmax = 0.209 | k = −22→22 |
16380 measured reflections | l = −22→22 |
Refinement top
Refinement on F2 | 0 restraints |
Least-squares matrix: full | Primary atom site location: structure-invariant direct methods |
R[F2 > 2σ(F2)] = 0.026 | Secondary atom site location: difference Fourier map |
wR(F2) = 0.093 | w = 1/[σ2(Fo2) + (0.0475P)2 + 195.9447P] where P = (Fo2 + 2Fc2)/3 |
S = 1.34 | (Δ/σ)max < 0.001 |
335 reflections | Δρmax = 2.28 e Å−3 |
15 parameters | Δρmin = −1.10 e Å−3 |
Special details top
Geometry. All esds (except the esd in the dihedral angle between two l.s. planes) are
estimated using the full covariance matrix. The cell esds are taken into
account individually in the estimation of esds in distances, angles and torsion
angles; correlations between esds in cell parameters are only used when they
are defined by crystal symmetry. An approximate (isotropic) treatment of cell
esds is used for estimating esds involving l.s. planes. |
Refinement. Refinement of F2 against ALL reflections. The weighted R-factor wR and
goodness of fit S are based on F2, conventional R-factors R are based on F,
with F set to zero for negative F2. The threshold expression of F2 >
2sigma(F2) is used only for calculating R-factors(gt) etc. and is not
relevant to the choice of reflections for refinement. R-factors based on F2
are statistically about twice as large as those based on F, and R-factors based
on ALL data will be even larger. |
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top | x | y | z | Uiso*/Ueq | Occ. (<1) |
Ba | 0.0000 | 0.0000 | 0.0000 | 0.0192 (6) | 0.727 (11) |
K | 0.0000 | 0.0000 | 0.0000 | 0.0192 (6) | 0.273 (11) |
Sn1 | 0.06794 (3) | 0.06794 (3) | 0.37276 (4) | 0.0145 (3) | 0.74 |
Ga1 | 0.06794 (3) | 0.06794 (3) | 0.37276 (4) | 0.0145 (3) | 0.26 |
Sn2 | 0.21811 (4) | 0.21811 (4) | 0.21811 (4) | 0.0142 (3) | |
Sn3 | 0.1250 | 0.1250 | 0.1250 | 0.0119 (9) | 0.71 (4) |
Ga3 | 0.1250 | 0.1250 | 0.1250 | 0.0119 (9) | 0.29 (4) |
Atomic displacement parameters (Å2) top | U11 | U22 | U33 | U12 | U13 | U23 |
Ba | 0.0192 (6) | 0.0192 (6) | 0.0192 (6) | −0.0027 (4) | −0.0027 (4) | −0.0027 (4) |
K | 0.0192 (6) | 0.0192 (6) | 0.0192 (6) | −0.0027 (4) | −0.0027 (4) | −0.0027 (4) |
Sn1 | 0.0143 (3) | 0.0143 (3) | 0.0150 (4) | 0.0014 (2) | −0.00003 (17) | −0.00003 (17) |
Ga1 | 0.0143 (3) | 0.0143 (3) | 0.0150 (4) | 0.0014 (2) | −0.00003 (17) | −0.00003 (17) |
Sn2 | 0.0142 (3) | 0.0142 (3) | 0.0142 (3) | 0.0017 (2) | 0.0017 (2) | 0.0017 (2) |
Sn3 | 0.0119 (9) | 0.0119 (9) | 0.0119 (9) | 0.000 | 0.000 | 0.000 |
Ga3 | 0.0119 (9) | 0.0119 (9) | 0.0119 (9) | 0.000 | 0.000 | 0.000 |
Geometric parameters (Å, º) top
Ba—Sn3 | 3.6960 (1) | Sn2—Sn3 | 2.7532 (11) |
Ba—Sn2i | 3.8022 (5) | Sn2—Sn1vi | 2.7798 (7) |
Ba—Sn1ii | 3.9239 (5) | Sn2—Sn1vii | 2.7798 (8) |
Sn1—Sn1iii | 2.7257 (7) | Sn2—Sn1v | 2.7798 (7) |
Sn1—Sn1iv | 2.7257 (7) | Sn3—Sn2ii | 2.7532 (11) |
Sn1—Sn1v | 2.7554 (15) | Sn3—Sn2viii | 2.7532 (11) |
Sn1—Sn2v | 2.7797 (7) | Sn3—Sn2v | 2.7532 (11) |
| | | |
Sn1iii—Sn1—Sn1iv | 119.611 (7) | Sn3—Sn2—Sn1vi | 107.02 (3) |
Sn1iii—Sn1—Sn1v | 109.82 (3) | Sn1vi—Sn2—Sn1vii | 111.81 (2) |
Sn1iii—Sn1—Sn2v | 104.27 (3) | Sn2—Sn3—Sn2ii | 109.471 (1) |
Sn1v—Sn1—Sn2v | 108.25 (3) | | |
Symmetry codes: (i) −x, y−1/4, z−1/4; (ii) x, −y+1/4, −z+1/4; (iii) −z+1/2, −x, −y+1/2; (iv) −y, −z+1/2, −x+1/2; (v) −x+1/4, −y+1/4, z; (vi) −y+1/4, z, −x+1/4; (vii) z, −x+1/4, −y+1/4; (viii) −x+1/4, y, −z+1/4. |
(K13Ba3Ga19Sn117) Potassium barium gallum tin
top
Crystal data top
K12.9Ba3.1Ga19.5Sn116.5 | Dx = 5.265 Mg m−3 |
Mr = 16117.07 | Mo Kα radiation, λ = 0.71073 Å |
Cubic, Fd3m | Cell parameters from 2939 reflections |
Hall symbol: F 4d 2 3 -1d | θ = 3.4–27.9° |
a = 17.1946 (8) Å | µ = 17.39 mm−1 |
V = 5083.7 (4) Å3 | T = 200 K |
Z = 1 | Block, silver |
F(000) = 6848 | 0.09 × 0.09 × 0.08 mm |
Data collection top
Bruker SMART APEX CCD area-detector diffractometer | 335 independent reflections |
Radiation source: fine-focus sealed tube | 310 reflections with I > 2σ(I) |
Graphite monochromator | Rint = 0.054 |
ω scans | θmax = 28.0°, θmin = 2.1° |
Absorption correction: multi-scan (SADABS; Sheldrick, 2008) | h = −22→22 |
Tmin = 0.195, Tmax = 0.272 | k = −22→22 |
16727 measured reflections | l = −22→22 |
Refinement top
Refinement on F2 | 0 restraints |
Least-squares matrix: full | Primary atom site location: structure-invariant direct methods |
R[F2 > 2σ(F2)] = 0.029 | Secondary atom site location: difference Fourier map |
wR(F2) = 0.101 | w = 1/[σ2(Fo2) + (0.0478P)2 + 291.2296P] where P = (Fo2 + 2Fc2)/3 |
S = 1.34 | (Δ/σ)max < 0.001 |
335 reflections | Δρmax = 3.71 e Å−3 |
15 parameters | Δρmin = −1.15 e Å−3 |
Special details top
Geometry. All esds (except the esd in the dihedral angle between two l.s. planes) are
estimated using the full covariance matrix. The cell esds are taken into
account individually in the estimation of esds in distances, angles and torsion
angles; correlations between esds in cell parameters are only used when they
are defined by crystal symmetry. An approximate (isotropic) treatment of cell
esds is used for estimating esds involving l.s. planes. |
Refinement. Refinement of F2 against ALL reflections. The weighted R-factor wR and
goodness of fit S are based on F2, conventional R-factors R are based on F,
with F set to zero for negative F2. The threshold expression of F2 >
2sigma(F2) is used only for calculating R-factors(gt) etc. and is not
relevant to the choice of reflections for refinement. R-factors based on F2
are statistically about twice as large as those based on F, and R-factors based
on ALL data will be even larger. |
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top | x | y | z | Uiso*/Ueq | Occ. (<1) |
Ba | 0.0000 | 0.0000 | 0.0000 | 0.0229 (14) | 0.196 (12) |
K | 0.0000 | 0.0000 | 0.0000 | 0.0229 (14) | 0.804 (12) |
Sn1 | 0.06793 (3) | 0.06793 (3) | 0.37173 (4) | 0.0184 (3) | 0.81 |
Ga1 | 0.06793 (3) | 0.06793 (3) | 0.37173 (4) | 0.0184 (3) | 0.19 |
Sn2 | 0.21795 (4) | 0.21795 (4) | 0.21795 (4) | 0.0185 (4) | |
Sn3 | 0.1250 | 0.1250 | 0.1250 | 0.0152 (10) | 0.84 (4) |
Ga3 | 0.1250 | 0.1250 | 0.1250 | 0.0152 (10) | 0.16 (4) |
Atomic displacement parameters (Å2) top | U11 | U22 | U33 | U12 | U13 | U23 |
Ba | 0.0229 (14) | 0.0229 (14) | 0.0229 (14) | −0.0029 (8) | −0.0029 (8) | −0.0029 (8) |
K | 0.0229 (14) | 0.0229 (14) | 0.0229 (14) | −0.0029 (8) | −0.0029 (8) | −0.0029 (8) |
Sn1 | 0.0182 (4) | 0.0182 (4) | 0.0188 (4) | 0.0032 (3) | 0.0006 (2) | 0.0006 (2) |
Ga1 | 0.0182 (4) | 0.0182 (4) | 0.0188 (4) | 0.0032 (3) | 0.0006 (2) | 0.0006 (2) |
Sn2 | 0.0185 (4) | 0.0185 (4) | 0.0185 (4) | 0.0021 (3) | 0.0021 (3) | 0.0021 (3) |
Sn3 | 0.0152 (10) | 0.0152 (10) | 0.0152 (10) | 0.000 | 0.000 | 0.000 |
Ga3 | 0.0152 (10) | 0.0152 (10) | 0.0152 (10) | 0.000 | 0.000 | 0.000 |
Geometric parameters (Å, º) top
Ba—Sn3 | 3.7227 (2) | Sn2—Sn3 | 2.7683 (13) |
Ba—Sn2i | 3.8277 (5) | Sn2—Sn1vi | 2.7843 (9) |
Ba—Sn1ii | 3.9429 (5) | Sn2—Sn1vii | 2.7843 (9) |
Sn1—Sn1iii | 2.7586 (8) | Sn2—Sn1v | 2.7843 (8) |
Sn1—Sn1iv | 2.7586 (8) | Sn3—Sn2viii | 2.7682 (13) |
Sn1—Sn1v | 2.7758 (17) | Sn3—Sn2ix | 2.7682 (13) |
Sn1—Sn2v | 2.7844 (8) | Sn3—Sn2v | 2.7682 (13) |
| | | |
Sn1iii—Sn1—Sn1iv | 119.706 (6) | Sn3—Sn2—Sn1vi | 107.00 (3) |
Sn1iii—Sn1—Sn1v | 109.44 (3) | Sn1vi—Sn2—Sn1vii | 111.82 (3) |
Sn1iii—Sn1—Sn2v | 104.65 (4) | Sn2viii—Sn3—Sn2 | 109.471 (1) |
Sn1v—Sn1—Sn2v | 108.26 (3) | | |
Symmetry codes: (i) −x, y−1/4, z−1/4; (ii) −z+1/4, −x+1/4, y; (iii) −y, −z+1/2, −x+1/2; (iv) −z+1/2, −x, −y+1/2; (v) −x+1/4, −y+1/4, z; (vi) z, −x+1/4, −y+1/4; (vii) −y+1/4, z, −x+1/4; (viii) x, −y+1/4, −z+1/4; (ix) −x+1/4, y, −z+1/4. |
(K7Ba1Ga8Sn38) Potassium barium gallium tin
top
Crystal data top
K7.7Ba0.3Ga8.3Sn37.7 | Dx = 5.248 Mg m−3 |
Mr = 5385.77 | Mo Kα radiation, λ = 0.71073 Å |
Cubic, Pm3n | Cell parameters from 2232 reflections |
Hall symbol: -P 4n 2 3 | θ = 3.4–28.4° |
a = 11.9447 (4) Å | µ = 17.38 mm−1 |
V = 1704.22 (10) Å3 | T = 200 K |
Z = 1 | Block, silver |
F(000) = 2302 | 0.06 × 0.05 × 0.04 mm |
Data collection top
Bruker SMART APEX CCD area-detector diffractometer | 412 independent reflections |
Radiation source: fine-focus sealed tube | 358 reflections with I > 2σ(I) |
Graphite monochromator | Rint = 0.082 |
ω scans | θmax = 28.4°, θmin = 2.4° |
Absorption correction: multi-scan (SADABS; Sheldrick, 2008) | h = −16→16 |
Tmin = 0.329, Tmax = 0.554 | k = −15→16 |
21728 measured reflections | l = −15→16 |
Refinement top
Refinement on F2 | 0 restraints |
Least-squares matrix: full | Primary atom site location: structure-invariant direct methods |
R[F2 > 2σ(F2)] = 0.019 | Secondary atom site location: difference Fourier map |
wR(F2) = 0.044 | w = 1/[σ2(Fo2) + (0.0183P)2 + 5.4215P] where P = (Fo2 + 2Fc2)/3 |
S = 1.17 | (Δ/σ)max < 0.001 |
412 reflections | Δρmax = 0.71 e Å−3 |
20 parameters | Δρmin = −1.02 e Å−3 |
Special details top
Geometry. All esds (except the esd in the dihedral angle between two l.s. planes) are
estimated using the full covariance matrix. The cell esds are taken into
account individually in the estimation of esds in distances, angles and torsion
angles; correlations between esds in cell parameters are only used when they
are defined by crystal symmetry. An approximate (isotropic) treatment of cell
esds is used for estimating esds involving l.s. planes. |
Refinement. Refinement of F2 against ALL reflections. The weighted R-factor wR and
goodness of fit S are based on F2, conventional R-factors R are based on F,
with F set to zero for negative F2. The threshold expression of F2 >
2sigma(F2) is used only for calculating R-factors(gt) etc. and is not
relevant to the choice of reflections for refinement. R-factors based on F2
are statistically about twice as large as those based on F, and R-factors based
on ALL data will be even larger. |
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top | x | y | z | Uiso*/Ueq | Occ. (<1) |
Sn1 | 0.38232 (4) | 0.5000 | 0.18776 (4) | 0.01392 (15) | 0.84 |
Ga1 | 0.38232 (4) | 0.5000 | 0.18776 (4) | 0.01392 (15) | 0.16 |
Sn2 | 0.18322 (2) | 0.18322 (2) | 0.18322 (2) | 0.01306 (18) | 0.896 (8) |
Ga2 | 0.18322 (2) | 0.18322 (2) | 0.18322 (2) | 0.01306 (18) | 0.104 (8) |
Sn3 | 0.2500 | 0.5000 | 0.0000 | 0.0148 (2) | 0.54 |
Ga3 | 0.2500 | 0.5000 | 0.0000 | 0.0148 (2) | 0.46 |
K1 | 0.5000 | 0.254 (3) | 0.0235 (19) | 0.038 (5) | 0.25 |
K2 | 0.0000 | 0.0000 | 0.0000 | 0.0255 (8) | 0.86 |
Ba2 | 0.0000 | 0.0000 | 0.0000 | 0.0255 (8) | 0.14 |
Atomic displacement parameters (Å2) top | U11 | U22 | U33 | U12 | U13 | U23 |
Sn1 | 0.0138 (2) | 0.0135 (2) | 0.0144 (2) | 0.000 | 0.00024 (17) | 0.000 |
Ga1 | 0.0138 (2) | 0.0135 (2) | 0.0144 (2) | 0.000 | 0.00024 (17) | 0.000 |
Sn2 | 0.01306 (18) | 0.01306 (18) | 0.01306 (18) | −0.00054 (11) | −0.00054 (11) | −0.00054 (11) |
Ga2 | 0.01306 (18) | 0.01306 (18) | 0.01306 (18) | −0.00054 (11) | −0.00054 (11) | −0.00054 (11) |
Sn3 | 0.0140 (5) | 0.0153 (3) | 0.0153 (3) | 0.000 | 0.000 | 0.000 |
Ga3 | 0.0140 (5) | 0.0153 (3) | 0.0153 (3) | 0.000 | 0.000 | 0.000 |
K1 | 0.035 (8) | 0.027 (6) | 0.051 (11) | 0.000 | 0.000 | −0.015 (8) |
K2 | 0.0255 (8) | 0.0255 (8) | 0.0255 (8) | 0.000 | 0.000 | 0.000 |
Ba2 | 0.0255 (8) | 0.0255 (8) | 0.0255 (8) | 0.000 | 0.000 | 0.000 |
Geometric parameters (Å, º) top
Sn1—Sn3 | 2.7436 (4) | K1—Sn1vii | 4.12 (3) |
Sn1—Sn2i | 2.7888 (3) | K1—Sn1ix | 4.14 (2) |
Sn1—Sn2ii | 2.7888 (3) | K1—Sn3x | 4.20 (3) |
Sn1—Sn1iii | 2.8114 (9) | K1—Sn2ii | 4.197 (17) |
Sn2—Sn2ii | 2.7631 (10) | K1—Sn2xi | 4.322 (15) |
Sn2—Sn1ii | 2.7888 (3) | K1—Sn1viii | 4.36 (3) |
Sn2—Sn1iv | 2.7888 (3) | K1—Sn3xii | 4.46 (2) |
Sn2—Sn1v | 2.7888 (3) | K1—Sn2vii | 4.598 (11) |
Sn3—Sn1iv | 2.7437 (4) | K1—Sn1xiii | 4.627 (6) |
Sn3—Sn1vi | 2.7437 (4) | K1—Sn2xiv | 4.68 (2) |
Sn3—Sn1vii | 2.7437 (4) | K1—Sn1xv | 4.91 (2) |
K1—Sn1iii | 3.80 (3) | K2—Sn2xvi | 3.7906 (5) |
K1—Sn1v | 3.94 (3) | K2—Sn1ii | 3.9857 (4) |
K1—Sn3viii | 4.07 (4) | | |
| | | |
Sn3—Sn1—Sn2ii | 106.859 (14) | Sn2ii—Sn2—Sn1ii | 107.224 (13) |
Sn2i—Sn1—Sn2ii | 103.394 (18) | Sn1ii—Sn2—Sn1iv | 111.622 (12) |
Sn3—Sn1—Sn1iii | 125.174 (9) | Sn1—Sn3—Sn1iv | 109.380 (9) |
Sn2i—Sn1—Sn1iii | 106.302 (10) | Sn1iv—Sn3—Sn1vi | 109.655 (18) |
Symmetry codes: (i) −y+1/2, x+1/2, −z+1/2; (ii) −y+1/2, −x+1/2, −z+1/2; (iii) −x+1, −y+1, z; (iv) −x+1/2, −z+1/2, y−1/2; (v) −z+1/2, y−1/2, −x+1/2; (vi) −x+1/2, z+1/2, y−1/2; (vii) x, y, −z; (viii) y, z, x; (ix) −z+1/2, −y+1/2, x−1/2; (x) −x+1, −y+1, −z; (xi) −x+1, y, z; (xii) −y+1, −z, −x; (xiii) x+1/2, −z+1/2, −y+1/2; (xiv) −y+1/2, −x+1/2, z−1/2; (xv) −y+1, z, −x; (xvi) −x, −y, −z. |
Distribution of the two framework-building elements (Sn,Ga), interatomic
distance range (Å) and unit-cell volume (Å3) in the three refined
type-II compounds topFormula | Sn:Ga (site 96g) | Sn:Ga (site 8a) | Sn:Ga (site 32e) | Sn/Ga—Sn/(Ga) | K/Ba—Sn/Ga | Unit-cell volume |
K0.8 (2)Ba15.2 (2)Ga31.0 (5)Sn105.0 (5) | 70:30 | 73:27 | 100:0 | 2.7179 (7)–2.7685 (8) | 3.6845 (5)–3.9110 (1) | 4928.4 (2) |
K4.3 (3)Ba11.7 (3)Ga27.4 (4)Sn108.6 (4) | 74:26 | 71:29 | 100:0 | 2.7257 (7)–2.7797 (7) | 3.6960 (1)–3.9239 (5) | 4974.7 (3) |
K12.9 (2)Ba3.1 (2)Ga19.5 (4)Sn116.5 (4) | 80:20 | 84:16 | 100:0 | 2.7586 (8)–2.7844 (8) | 3.7227 (2)–3.9429 (5) | 5083.7 (4) |
Bond distance ranges (Å) in selected type-I and type-VIII clathrate compounds topFormula | Sn/Ga—Sn/Ga | K—Sn/Ga | Reference |
K7.7 (1)Ba0.3 (1)Ga8.3 (4)Sn37.7 (4) | 2.7436 (4)–2.8114 (9) | 3.7906 (5)–3.9857 (4) [(Ga,Sn)20 cages] 3.80 (3)–4.91 (2) [(Ga,Sn)24 cages] | |
K8.0Ga7.9 (2)Sn37.9 (2) | 2.738–2.840 | 3.796–4.002 [(Ga,Sn)20 cages] 3.999–4.625 [(Ga,Sn)24 cages] | Tanaka et al. (2010) |
K8Ba8.1(1.8)Sn38.0(1.8) | 2.733–2.813 | 3.785–3.992 [(Ga,Sn)20 cages] 3.983–4.623 [(Ga,Sn)24 cages] | Kröner et al. (1998b) |
Ba8Ga16.8Sn29.2 | 2.660–2.730 | 3.678–4.491 | von Schnering et al. (1998) |
Ba8Ga14.5Sn31.5 | 2.660–2.730 | 3.710–4.129 | Schäfer et al. (2011) |
Ba8Ga17.4Sn28.6 | 2.642–2.764 | 3.635–3.845 | Eisenmann et al. (1986) |
Ba8Ga17.2Sn28.8 | 2.649–2.766 | 3.632–3.852 | Carrillo-Cabrera et al. (2002) |
Ba8Ga13.2Sn23.8 | 2.645–2.762 | 3.626–3.848 | Schäfer et al. (2011) |
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