β-Ba$_{8}$Ga$_{16}$Sn$_{30}$ Clathrate Structure: A13B3C8D12_cP72_223_ak_c_i_k-001
| Prototype | Ba$_{4}$Ga$_{8}$Sn$_{15}$ |
| AFLOW prototype label | A13B3C8D12_cP72_223_ak_c_i_k-001 |
| ICSD | none |
| Pearson symbol | cP72 |
| Space group number | 223 |
| Space group symbol | $Pm\overline{3}n$ |
| AFLOW prototype command |
aflow --proto=A13B3C8D12_cP72_223_ak_c_i_k-001
--params=$a, \allowbreak x_{3}, \allowbreak y_{4}, \allowbreak z_{4}, \allowbreak y_{5}, \allowbreak z_{5}$ |
Other compounds with this structure
Ba$_{8}$Ga$_{16}$Ge$_{30}$
- There is a considerable amount of disorder in this system:
- The (2a) site is pure barium and labeled Ba.
- The (6c) site is pure gallium and labeled Ga.
- The (16i) site is 64.4% tin and 35.6% gallium. We label this as germanium, Ge, as that is another possible component of this compound and to avoid confusion with the other gallium and tin sites.
- The first (24k) site is 25% barium, with the remainder of the sites vacant. This can be seen as four-lobed atom clusters in the figure, when it is expanded beyond one unit cell. We label this site as barium, Ba.
- The final (24k) site is 74.8% tin and 25.2% gallium. We label this as tin, Sn.
- (Aliva, 2006) found another clathrate structure with this stoichiometry, $\alpha$–Ba$_{8}$Ga$_{16}$Sn$_{30}$.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&a \,\mathbf{\hat{x}}\\\mathbf{a_{2}}&=&a \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&a \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $0$ | = | $0$ | (2a) | Ba I |
| $\mathbf{B_{2}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}$ | (2a) | Ba I |
| $\mathbf{B_{3}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{z}}$ | (6c) | Ga I |
| $\mathbf{B_{4}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{3}{4}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{z}}$ | (6c) | Ga I |
| $\mathbf{B_{5}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}$ | (6c) | Ga I |
| $\mathbf{B_{6}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{3}{4}a \,\mathbf{\hat{y}}$ | (6c) | Ga I |
| $\mathbf{B_{7}}$ | = | $\frac{1}{2} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (6c) | Ga I |
| $\mathbf{B_{8}}$ | = | $\frac{1}{2} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{3}{4}a \,\mathbf{\hat{z}}$ | (6c) | Ga I |
| $\mathbf{B_{9}}$ | = | $x_{3} \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{2}+x_{3} \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{x}}+a x_{3} \,\mathbf{\hat{y}}+a x_{3} \,\mathbf{\hat{z}}$ | (16i) | Ge I |
| $\mathbf{B_{10}}$ | = | $- x_{3} \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}+x_{3} \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}- a x_{3} \,\mathbf{\hat{y}}+a x_{3} \,\mathbf{\hat{z}}$ | (16i) | Ge I |
| $\mathbf{B_{11}}$ | = | $- x_{3} \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{2}- x_{3} \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}+a x_{3} \,\mathbf{\hat{y}}- a x_{3} \,\mathbf{\hat{z}}$ | (16i) | Ge I |
| $\mathbf{B_{12}}$ | = | $x_{3} \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}- x_{3} \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{x}}- a x_{3} \,\mathbf{\hat{y}}- a x_{3} \,\mathbf{\hat{z}}$ | (16i) | Ge I |
| $\mathbf{B_{13}}$ | = | $\left(x_{3} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{3} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{3} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{3} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(x_{3} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(x_{3} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (16i) | Ge I |
| $\mathbf{B_{14}}$ | = | $- \left(x_{3} - \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{3} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{3} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{3} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(x_{3} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(x_{3} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (16i) | Ge I |
| $\mathbf{B_{15}}$ | = | $\left(x_{3} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{3} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{3} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(x_{3} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+a \left(x_{3} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (16i) | Ge I |
| $\mathbf{B_{16}}$ | = | $- \left(x_{3} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{3} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{3} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(x_{3} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+a \left(x_{3} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (16i) | Ge I |
| $\mathbf{B_{17}}$ | = | $- x_{3} \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}- x_{3} \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}- a x_{3} \,\mathbf{\hat{y}}- a x_{3} \,\mathbf{\hat{z}}$ | (16i) | Ge I |
| $\mathbf{B_{18}}$ | = | $x_{3} \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{2}- x_{3} \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{x}}+a x_{3} \,\mathbf{\hat{y}}- a x_{3} \,\mathbf{\hat{z}}$ | (16i) | Ge I |
| $\mathbf{B_{19}}$ | = | $x_{3} \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}+x_{3} \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{x}}- a x_{3} \,\mathbf{\hat{y}}+a x_{3} \,\mathbf{\hat{z}}$ | (16i) | Ge I |
| $\mathbf{B_{20}}$ | = | $- x_{3} \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{2}+x_{3} \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}+a x_{3} \,\mathbf{\hat{y}}+a x_{3} \,\mathbf{\hat{z}}$ | (16i) | Ge I |
| $\mathbf{B_{21}}$ | = | $- \left(x_{3} - \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{3} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{3} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(x_{3} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+a \left(x_{3} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (16i) | Ge I |
| $\mathbf{B_{22}}$ | = | $\left(x_{3} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{3} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{3} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(x_{3} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+a \left(x_{3} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (16i) | Ge I |
| $\mathbf{B_{23}}$ | = | $- \left(x_{3} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{3} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{3} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{3} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(x_{3} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(x_{3} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (16i) | Ge I |
| $\mathbf{B_{24}}$ | = | $\left(x_{3} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{3} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{3} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{3} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(x_{3} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(x_{3} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (16i) | Ge I |
| $\mathbf{B_{25}}$ | = | $y_{4} \, \mathbf{a}_{2}+z_{4} \, \mathbf{a}_{3}$ | = | $a y_{4} \,\mathbf{\hat{y}}+a z_{4} \,\mathbf{\hat{z}}$ | (24k) | Ba II |
| $\mathbf{B_{26}}$ | = | $- y_{4} \, \mathbf{a}_{2}+z_{4} \, \mathbf{a}_{3}$ | = | $- a y_{4} \,\mathbf{\hat{y}}+a z_{4} \,\mathbf{\hat{z}}$ | (24k) | Ba II |
| $\mathbf{B_{27}}$ | = | $y_{4} \, \mathbf{a}_{2}- z_{4} \, \mathbf{a}_{3}$ | = | $a y_{4} \,\mathbf{\hat{y}}- a z_{4} \,\mathbf{\hat{z}}$ | (24k) | Ba II |
| $\mathbf{B_{28}}$ | = | $- y_{4} \, \mathbf{a}_{2}- z_{4} \, \mathbf{a}_{3}$ | = | $- a y_{4} \,\mathbf{\hat{y}}- a z_{4} \,\mathbf{\hat{z}}$ | (24k) | Ba II |
| $\mathbf{B_{29}}$ | = | $z_{4} \, \mathbf{a}_{1}+y_{4} \, \mathbf{a}_{3}$ | = | $a z_{4} \,\mathbf{\hat{x}}+a y_{4} \,\mathbf{\hat{z}}$ | (24k) | Ba II |
| $\mathbf{B_{30}}$ | = | $z_{4} \, \mathbf{a}_{1}- y_{4} \, \mathbf{a}_{3}$ | = | $a z_{4} \,\mathbf{\hat{x}}- a y_{4} \,\mathbf{\hat{z}}$ | (24k) | Ba II |
| $\mathbf{B_{31}}$ | = | $- z_{4} \, \mathbf{a}_{1}+y_{4} \, \mathbf{a}_{3}$ | = | $- a z_{4} \,\mathbf{\hat{x}}+a y_{4} \,\mathbf{\hat{z}}$ | (24k) | Ba II |
| $\mathbf{B_{32}}$ | = | $- z_{4} \, \mathbf{a}_{1}- y_{4} \, \mathbf{a}_{3}$ | = | $- a z_{4} \,\mathbf{\hat{x}}- a y_{4} \,\mathbf{\hat{z}}$ | (24k) | Ba II |
| $\mathbf{B_{33}}$ | = | $y_{4} \, \mathbf{a}_{1}+z_{4} \, \mathbf{a}_{2}$ | = | $a y_{4} \,\mathbf{\hat{x}}+a z_{4} \,\mathbf{\hat{y}}$ | (24k) | Ba II |
| $\mathbf{B_{34}}$ | = | $- y_{4} \, \mathbf{a}_{1}+z_{4} \, \mathbf{a}_{2}$ | = | $- a y_{4} \,\mathbf{\hat{x}}+a z_{4} \,\mathbf{\hat{y}}$ | (24k) | Ba II |
| $\mathbf{B_{35}}$ | = | $y_{4} \, \mathbf{a}_{1}- z_{4} \, \mathbf{a}_{2}$ | = | $a y_{4} \,\mathbf{\hat{x}}- a z_{4} \,\mathbf{\hat{y}}$ | (24k) | Ba II |
| $\mathbf{B_{36}}$ | = | $- y_{4} \, \mathbf{a}_{1}- z_{4} \, \mathbf{a}_{2}$ | = | $- a y_{4} \,\mathbf{\hat{x}}- a z_{4} \,\mathbf{\hat{y}}$ | (24k) | Ba II |
| $\mathbf{B_{37}}$ | = | $\left(y_{4} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}- \left(z_{4} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{4} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}- a \left(z_{4} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24k) | Ba II |
| $\mathbf{B_{38}}$ | = | $- \left(y_{4} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}- \left(z_{4} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{4} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}- a \left(z_{4} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24k) | Ba II |
| $\mathbf{B_{39}}$ | = | $\left(y_{4} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+\left(z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{4} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+a \left(z_{4} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24k) | Ba II |
| $\mathbf{B_{40}}$ | = | $- \left(y_{4} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+\left(z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{4} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+a \left(z_{4} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24k) | Ba II |
| $\mathbf{B_{41}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\left(z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(y_{4} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+a \left(z_{4} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(y_{4} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24k) | Ba II |
| $\mathbf{B_{42}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\left(z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(y_{4} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+a \left(z_{4} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+a \left(y_{4} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24k) | Ba II |
| $\mathbf{B_{43}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}- \left(z_{4} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(y_{4} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- a \left(z_{4} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(y_{4} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24k) | Ba II |
| $\mathbf{B_{44}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}- \left(z_{4} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(y_{4} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- a \left(z_{4} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+a \left(y_{4} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24k) | Ba II |
| $\mathbf{B_{45}}$ | = | $\left(z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{4} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $a \left(z_{4} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(y_{4} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}$ | (24k) | Ba II |
| $\mathbf{B_{46}}$ | = | $\left(z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{4} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $a \left(z_{4} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(y_{4} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}$ | (24k) | Ba II |
| $\mathbf{B_{47}}$ | = | $- \left(z_{4} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{4} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- a \left(z_{4} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(y_{4} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}$ | (24k) | Ba II |
| $\mathbf{B_{48}}$ | = | $- \left(z_{4} - \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{4} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- a \left(z_{4} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(y_{4} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}$ | (24k) | Ba II |
| $\mathbf{B_{49}}$ | = | $y_{5} \, \mathbf{a}_{2}+z_{5} \, \mathbf{a}_{3}$ | = | $a y_{5} \,\mathbf{\hat{y}}+a z_{5} \,\mathbf{\hat{z}}$ | (24k) | Sn I |
| $\mathbf{B_{50}}$ | = | $- y_{5} \, \mathbf{a}_{2}+z_{5} \, \mathbf{a}_{3}$ | = | $- a y_{5} \,\mathbf{\hat{y}}+a z_{5} \,\mathbf{\hat{z}}$ | (24k) | Sn I |
| $\mathbf{B_{51}}$ | = | $y_{5} \, \mathbf{a}_{2}- z_{5} \, \mathbf{a}_{3}$ | = | $a y_{5} \,\mathbf{\hat{y}}- a z_{5} \,\mathbf{\hat{z}}$ | (24k) | Sn I |
| $\mathbf{B_{52}}$ | = | $- y_{5} \, \mathbf{a}_{2}- z_{5} \, \mathbf{a}_{3}$ | = | $- a y_{5} \,\mathbf{\hat{y}}- a z_{5} \,\mathbf{\hat{z}}$ | (24k) | Sn I |
| $\mathbf{B_{53}}$ | = | $z_{5} \, \mathbf{a}_{1}+y_{5} \, \mathbf{a}_{3}$ | = | $a z_{5} \,\mathbf{\hat{x}}+a y_{5} \,\mathbf{\hat{z}}$ | (24k) | Sn I |
| $\mathbf{B_{54}}$ | = | $z_{5} \, \mathbf{a}_{1}- y_{5} \, \mathbf{a}_{3}$ | = | $a z_{5} \,\mathbf{\hat{x}}- a y_{5} \,\mathbf{\hat{z}}$ | (24k) | Sn I |
| $\mathbf{B_{55}}$ | = | $- z_{5} \, \mathbf{a}_{1}+y_{5} \, \mathbf{a}_{3}$ | = | $- a z_{5} \,\mathbf{\hat{x}}+a y_{5} \,\mathbf{\hat{z}}$ | (24k) | Sn I |
| $\mathbf{B_{56}}$ | = | $- z_{5} \, \mathbf{a}_{1}- y_{5} \, \mathbf{a}_{3}$ | = | $- a z_{5} \,\mathbf{\hat{x}}- a y_{5} \,\mathbf{\hat{z}}$ | (24k) | Sn I |
| $\mathbf{B_{57}}$ | = | $y_{5} \, \mathbf{a}_{1}+z_{5} \, \mathbf{a}_{2}$ | = | $a y_{5} \,\mathbf{\hat{x}}+a z_{5} \,\mathbf{\hat{y}}$ | (24k) | Sn I |
| $\mathbf{B_{58}}$ | = | $- y_{5} \, \mathbf{a}_{1}+z_{5} \, \mathbf{a}_{2}$ | = | $- a y_{5} \,\mathbf{\hat{x}}+a z_{5} \,\mathbf{\hat{y}}$ | (24k) | Sn I |
| $\mathbf{B_{59}}$ | = | $y_{5} \, \mathbf{a}_{1}- z_{5} \, \mathbf{a}_{2}$ | = | $a y_{5} \,\mathbf{\hat{x}}- a z_{5} \,\mathbf{\hat{y}}$ | (24k) | Sn I |
| $\mathbf{B_{60}}$ | = | $- y_{5} \, \mathbf{a}_{1}- z_{5} \, \mathbf{a}_{2}$ | = | $- a y_{5} \,\mathbf{\hat{x}}- a z_{5} \,\mathbf{\hat{y}}$ | (24k) | Sn I |
| $\mathbf{B_{61}}$ | = | $\left(y_{5} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}- \left(z_{5} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{5} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}- a \left(z_{5} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24k) | Sn I |
| $\mathbf{B_{62}}$ | = | $- \left(y_{5} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}- \left(z_{5} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{5} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}- a \left(z_{5} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24k) | Sn I |
| $\mathbf{B_{63}}$ | = | $\left(y_{5} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+\left(z_{5} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{5} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+a \left(z_{5} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24k) | Sn I |
| $\mathbf{B_{64}}$ | = | $- \left(y_{5} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+\left(z_{5} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{5} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+a \left(z_{5} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24k) | Sn I |
| $\mathbf{B_{65}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\left(z_{5} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(y_{5} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+a \left(z_{5} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(y_{5} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24k) | Sn I |
| $\mathbf{B_{66}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\left(z_{5} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(y_{5} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+a \left(z_{5} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+a \left(y_{5} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24k) | Sn I |
| $\mathbf{B_{67}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}- \left(z_{5} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(y_{5} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- a \left(z_{5} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(y_{5} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24k) | Sn I |
| $\mathbf{B_{68}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}- \left(z_{5} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(y_{5} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- a \left(z_{5} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+a \left(y_{5} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24k) | Sn I |
| $\mathbf{B_{69}}$ | = | $\left(z_{5} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{5} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $a \left(z_{5} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(y_{5} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}$ | (24k) | Sn I |
| $\mathbf{B_{70}}$ | = | $\left(z_{5} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{5} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $a \left(z_{5} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(y_{5} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}$ | (24k) | Sn I |
| $\mathbf{B_{71}}$ | = | $- \left(z_{5} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{5} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- a \left(z_{5} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(y_{5} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}$ | (24k) | Sn I |
| $\mathbf{B_{72}}$ | = | $- \left(z_{5} - \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{5} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- a \left(z_{5} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(y_{5} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}$ | (24k) | Sn I |
References
- M. A. Avila, K. Suekuni, K. Umeo, H. Fukuoka, S. Yamanaka, and T. Takabatake, Ba$_{8}$Ga$_{16}$Sn$_{30}$ with type-I clathrate structure: Drastic suppression of heat conduction, Appl. Phys. Lett. 92, 041901 (2007), doi:10.1063/1.2831926.
- M. A. Avila, K. Suekuni, K. Umeo, H. Fukuoka, S. Yamanaka, and T. Takabatake, Glasslike versus crystalline thermal conductivity in carrier-tuned Ba$_{8}$Ga$_{16}$X$_{30}$ clathrates (X=Ge,Sn), Phys. Rev. B 74, 125109 (2006), doi:10.1103/PhysRevB.74.125109.
Prototype Generator
aflow --proto=A13B3C8D12_cP72_223_ak_c_i_k --params=$a,x_{3},y_{4},z_{4},y_{5},z_{5}$