α-Ba$_{8}$Ga$_{16}$Sn$_{30}$ Clathrate Structure: A4B4C6D13_cI54_217_c_c_d_ag-001
| Prototype | Ba$_{4}$Ga$_{8}$Sn$_{15}$ |
| AFLOW prototype label | A4B4C6D13_cI54_217_c_c_d_ag-001 |
| ICSD | none |
| Pearson symbol | cI54 |
| Space group number | 217 |
| Space group symbol | $I\overline{4}3m$ |
| AFLOW prototype command |
aflow --proto=A4B4C6D13_cI54_217_c_c_d_ag-001
--params=$a, \allowbreak x_{2}, \allowbreak x_{3}, \allowbreak x_{5}, \allowbreak z_{5}$ |
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 84.2% tin and 15.8% gallium. We label it Sn.
- The first (8c) site is pure barium, labeled Ba.
- The second (8c) site is 76.6% gallium and 23.4% tin, and is labeled Ga.
- The (12d) site is 81.60% tin and 18.4% gallium. We label this as germanium, Ge, since that is another possible component of this compound and to avoid confusion with the other tin/gallium sites.
- The (24g) site is 68.6% gallium and 31.4% tin, and is labeled Sn.
- The occupation of each of the Sn/Ga sites can be varied during crystal growth, and controls the semiconducting behavior of the sample (Avila, 2006).
- (Aliva, 2008) showed that this compound also exists as $\beta$–Ba$_{8}$Ga$_{16}$Sn$_{30}$, another clathrate structure.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&- \frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}- \frac{1}{2}a \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $0$ | = | $0$ | (2a) | Sn I |
| $\mathbf{B_{2}}$ | = | $2 x_{2} \, \mathbf{a}_{1}+2 x_{2} \, \mathbf{a}_{2}+2 x_{2} \, \mathbf{a}_{3}$ | = | $a x_{2} \,\mathbf{\hat{x}}+a x_{2} \,\mathbf{\hat{y}}+a x_{2} \,\mathbf{\hat{z}}$ | (8c) | Ba I |
| $\mathbf{B_{3}}$ | = | $- 2 x_{2} \, \mathbf{a}_{3}$ | = | $- a x_{2} \,\mathbf{\hat{x}}- a x_{2} \,\mathbf{\hat{y}}+a x_{2} \,\mathbf{\hat{z}}$ | (8c) | Ba I |
| $\mathbf{B_{4}}$ | = | $- 2 x_{2} \, \mathbf{a}_{2}$ | = | $- a x_{2} \,\mathbf{\hat{x}}+a x_{2} \,\mathbf{\hat{y}}- a x_{2} \,\mathbf{\hat{z}}$ | (8c) | Ba I |
| $\mathbf{B_{5}}$ | = | $- 2 x_{2} \, \mathbf{a}_{1}$ | = | $a x_{2} \,\mathbf{\hat{x}}- a x_{2} \,\mathbf{\hat{y}}- a x_{2} \,\mathbf{\hat{z}}$ | (8c) | Ba I |
| $\mathbf{B_{6}}$ | = | $2 x_{3} \, \mathbf{a}_{1}+2 x_{3} \, \mathbf{a}_{2}+2 x_{3} \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{x}}+a x_{3} \,\mathbf{\hat{y}}+a x_{3} \,\mathbf{\hat{z}}$ | (8c) | Ga I |
| $\mathbf{B_{7}}$ | = | $- 2 x_{3} \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}- a x_{3} \,\mathbf{\hat{y}}+a x_{3} \,\mathbf{\hat{z}}$ | (8c) | Ga I |
| $\mathbf{B_{8}}$ | = | $- 2 x_{3} \, \mathbf{a}_{2}$ | = | $- a x_{3} \,\mathbf{\hat{x}}+a x_{3} \,\mathbf{\hat{y}}- a x_{3} \,\mathbf{\hat{z}}$ | (8c) | Ga I |
| $\mathbf{B_{9}}$ | = | $- 2 x_{3} \, \mathbf{a}_{1}$ | = | $a x_{3} \,\mathbf{\hat{x}}- a x_{3} \,\mathbf{\hat{y}}- a x_{3} \,\mathbf{\hat{z}}$ | (8c) | Ga I |
| $\mathbf{B_{10}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}$ | (12d) | Ge I |
| $\mathbf{B_{11}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{z}}$ | (12d) | Ge I |
| $\mathbf{B_{12}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}$ | (12d) | Ge I |
| $\mathbf{B_{13}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}$ | (12d) | Ge I |
| $\mathbf{B_{14}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (12d) | Ge I |
| $\mathbf{B_{15}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (12d) | Ge I |
| $\mathbf{B_{16}}$ | = | $\left(x_{5} + z_{5}\right) \, \mathbf{a}_{1}+\left(x_{5} + z_{5}\right) \, \mathbf{a}_{2}+2 x_{5} \, \mathbf{a}_{3}$ | = | $a x_{5} \,\mathbf{\hat{x}}+a x_{5} \,\mathbf{\hat{y}}+a z_{5} \,\mathbf{\hat{z}}$ | (24g) | Sn II |
| $\mathbf{B_{17}}$ | = | $- \left(x_{5} - z_{5}\right) \, \mathbf{a}_{1}- \left(x_{5} - z_{5}\right) \, \mathbf{a}_{2}- 2 x_{5} \, \mathbf{a}_{3}$ | = | $- a x_{5} \,\mathbf{\hat{x}}- a x_{5} \,\mathbf{\hat{y}}+a z_{5} \,\mathbf{\hat{z}}$ | (24g) | Sn II |
| $\mathbf{B_{18}}$ | = | $\left(x_{5} - z_{5}\right) \, \mathbf{a}_{1}- \left(x_{5} + z_{5}\right) \, \mathbf{a}_{2}$ | = | $- a x_{5} \,\mathbf{\hat{x}}+a x_{5} \,\mathbf{\hat{y}}- a z_{5} \,\mathbf{\hat{z}}$ | (24g) | Sn II |
| $\mathbf{B_{19}}$ | = | $- \left(x_{5} + z_{5}\right) \, \mathbf{a}_{1}+\left(x_{5} - z_{5}\right) \, \mathbf{a}_{2}$ | = | $a x_{5} \,\mathbf{\hat{x}}- a x_{5} \,\mathbf{\hat{y}}- a z_{5} \,\mathbf{\hat{z}}$ | (24g) | Sn II |
| $\mathbf{B_{20}}$ | = | $2 x_{5} \, \mathbf{a}_{1}+\left(x_{5} + z_{5}\right) \, \mathbf{a}_{2}+\left(x_{5} + z_{5}\right) \, \mathbf{a}_{3}$ | = | $a z_{5} \,\mathbf{\hat{x}}+a x_{5} \,\mathbf{\hat{y}}+a x_{5} \,\mathbf{\hat{z}}$ | (24g) | Sn II |
| $\mathbf{B_{21}}$ | = | $- 2 x_{5} \, \mathbf{a}_{1}- \left(x_{5} - z_{5}\right) \, \mathbf{a}_{2}- \left(x_{5} - z_{5}\right) \, \mathbf{a}_{3}$ | = | $a z_{5} \,\mathbf{\hat{x}}- a x_{5} \,\mathbf{\hat{y}}- a x_{5} \,\mathbf{\hat{z}}$ | (24g) | Sn II |
| $\mathbf{B_{22}}$ | = | $\left(x_{5} - z_{5}\right) \, \mathbf{a}_{2}- \left(x_{5} + z_{5}\right) \, \mathbf{a}_{3}$ | = | $- a z_{5} \,\mathbf{\hat{x}}- a x_{5} \,\mathbf{\hat{y}}+a x_{5} \,\mathbf{\hat{z}}$ | (24g) | Sn II |
| $\mathbf{B_{23}}$ | = | $- \left(x_{5} + z_{5}\right) \, \mathbf{a}_{2}+\left(x_{5} - z_{5}\right) \, \mathbf{a}_{3}$ | = | $- a z_{5} \,\mathbf{\hat{x}}+a x_{5} \,\mathbf{\hat{y}}- a x_{5} \,\mathbf{\hat{z}}$ | (24g) | Sn II |
| $\mathbf{B_{24}}$ | = | $\left(x_{5} + z_{5}\right) \, \mathbf{a}_{1}+2 x_{5} \, \mathbf{a}_{2}+\left(x_{5} + z_{5}\right) \, \mathbf{a}_{3}$ | = | $a x_{5} \,\mathbf{\hat{x}}+a z_{5} \,\mathbf{\hat{y}}+a x_{5} \,\mathbf{\hat{z}}$ | (24g) | Sn II |
| $\mathbf{B_{25}}$ | = | $- \left(x_{5} - z_{5}\right) \, \mathbf{a}_{1}- 2 x_{5} \, \mathbf{a}_{2}- \left(x_{5} - z_{5}\right) \, \mathbf{a}_{3}$ | = | $- a x_{5} \,\mathbf{\hat{x}}+a z_{5} \,\mathbf{\hat{y}}- a x_{5} \,\mathbf{\hat{z}}$ | (24g) | Sn II |
| $\mathbf{B_{26}}$ | = | $- \left(x_{5} + z_{5}\right) \, \mathbf{a}_{1}+\left(x_{5} - z_{5}\right) \, \mathbf{a}_{3}$ | = | $a x_{5} \,\mathbf{\hat{x}}- a z_{5} \,\mathbf{\hat{y}}- a x_{5} \,\mathbf{\hat{z}}$ | (24g) | Sn II |
| $\mathbf{B_{27}}$ | = | $\left(x_{5} - z_{5}\right) \, \mathbf{a}_{1}- \left(x_{5} + z_{5}\right) \, \mathbf{a}_{3}$ | = | $- a x_{5} \,\mathbf{\hat{x}}- a z_{5} \,\mathbf{\hat{y}}+a x_{5} \,\mathbf{\hat{z}}$ | (24g) | Sn II |
References
- 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.
- 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.
Found in
- 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.
Prototype Generator
aflow --proto=A4B4C6D13_cI54_217_c_c_d_ag --params=$a,x_{2},x_{3},x_{5},z_{5}$