Ba$_{3}$Ir$_{4}$Ge$_{16}$ Structure: A3B16C4_tI46_139_ad_2ejm_g2-001
| Prototype | Ba$_{3}$Ge$_{16}$Ir$_{4}$ |
| AFLOW prototype label | A3B16C4_tI46_139_ad_2ejm_g2-001 |
| ICSD | 194235 |
| CCDC | 1702931 |
| Pearson symbol | tI46 |
| Space group number | 139 |
| Space group symbol | $I4/mmm$ |
| AFLOW prototype command |
aflow --proto=A3B16C4_tI46_139_ad_2ejm_g2-001
--params=$a, \allowbreak c/a, \allowbreak z_{3}, \allowbreak z_{4}, \allowbreak z_{5}, \allowbreak x_{6}, \allowbreak x_{7}, \allowbreak z_{7}$ |
Other compounds with this structure
Ba$_{3}$Rh$_{4}$Ge$_{16}$
- BaIr$_{2}$Ge$_{7}$ and Ba$_{3}$Ir$_{4}$Ge$_{16}$ are structures with the barium atoms surrounded by germanium rings and germanium-iridium cages. They are superconducting at 2.5 and 5.2K, respectively.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&- \frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}- \frac{1}{2}c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $0$ | = | $0$ | (2a) | Ba I |
| $\mathbf{B_{2}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (4d) | Ba II |
| $\mathbf{B_{3}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (4d) | Ba II |
| $\mathbf{B_{4}}$ | = | $z_{3} \, \mathbf{a}_{1}+z_{3} \, \mathbf{a}_{2}$ | = | $c z_{3} \,\mathbf{\hat{z}}$ | (4e) | Ge I |
| $\mathbf{B_{5}}$ | = | $- z_{3} \, \mathbf{a}_{1}- z_{3} \, \mathbf{a}_{2}$ | = | $- c z_{3} \,\mathbf{\hat{z}}$ | (4e) | Ge I |
| $\mathbf{B_{6}}$ | = | $z_{4} \, \mathbf{a}_{1}+z_{4} \, \mathbf{a}_{2}$ | = | $c z_{4} \,\mathbf{\hat{z}}$ | (4e) | Ge II |
| $\mathbf{B_{7}}$ | = | $- z_{4} \, \mathbf{a}_{1}- z_{4} \, \mathbf{a}_{2}$ | = | $- c z_{4} \,\mathbf{\hat{z}}$ | (4e) | Ge II |
| $\mathbf{B_{8}}$ | = | $\left(z_{5} + \frac{1}{2}\right) \, \mathbf{a}_{1}+z_{5} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{y}}+c z_{5} \,\mathbf{\hat{z}}$ | (8g) | Ir I |
| $\mathbf{B_{9}}$ | = | $z_{5} \, \mathbf{a}_{1}+\left(z_{5} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+c z_{5} \,\mathbf{\hat{z}}$ | (8g) | Ir I |
| $\mathbf{B_{10}}$ | = | $- \left(z_{5} - \frac{1}{2}\right) \, \mathbf{a}_{1}- z_{5} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{y}}- c z_{5} \,\mathbf{\hat{z}}$ | (8g) | Ir I |
| $\mathbf{B_{11}}$ | = | $- z_{5} \, \mathbf{a}_{1}- \left(z_{5} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- c z_{5} \,\mathbf{\hat{z}}$ | (8g) | Ir I |
| $\mathbf{B_{12}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+x_{6} \, \mathbf{a}_{2}+\left(x_{6} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{6} \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}$ | (8j) | Ge III |
| $\mathbf{B_{13}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}- x_{6} \, \mathbf{a}_{2}- \left(x_{6} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{6} \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}$ | (8j) | Ge III |
| $\mathbf{B_{14}}$ | = | $x_{6} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+\left(x_{6} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+a x_{6} \,\mathbf{\hat{y}}$ | (8j) | Ge III |
| $\mathbf{B_{15}}$ | = | $- x_{6} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}- \left(x_{6} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- a x_{6} \,\mathbf{\hat{y}}$ | (8j) | Ge III |
| $\mathbf{B_{16}}$ | = | $\left(x_{7} + z_{7}\right) \, \mathbf{a}_{1}+\left(x_{7} + z_{7}\right) \, \mathbf{a}_{2}+2 x_{7} \, \mathbf{a}_{3}$ | = | $a x_{7} \,\mathbf{\hat{x}}+a x_{7} \,\mathbf{\hat{y}}+c z_{7} \,\mathbf{\hat{z}}$ | (16m) | Ge IV |
| $\mathbf{B_{17}}$ | = | $- \left(x_{7} - z_{7}\right) \, \mathbf{a}_{1}- \left(x_{7} - z_{7}\right) \, \mathbf{a}_{2}- 2 x_{7} \, \mathbf{a}_{3}$ | = | $- a x_{7} \,\mathbf{\hat{x}}- a x_{7} \,\mathbf{\hat{y}}+c z_{7} \,\mathbf{\hat{z}}$ | (16m) | Ge IV |
| $\mathbf{B_{18}}$ | = | $\left(x_{7} + z_{7}\right) \, \mathbf{a}_{1}- \left(x_{7} - z_{7}\right) \, \mathbf{a}_{2}$ | = | $- a x_{7} \,\mathbf{\hat{x}}+a x_{7} \,\mathbf{\hat{y}}+c z_{7} \,\mathbf{\hat{z}}$ | (16m) | Ge IV |
| $\mathbf{B_{19}}$ | = | $- \left(x_{7} - z_{7}\right) \, \mathbf{a}_{1}+\left(x_{7} + z_{7}\right) \, \mathbf{a}_{2}$ | = | $a x_{7} \,\mathbf{\hat{x}}- a x_{7} \,\mathbf{\hat{y}}+c z_{7} \,\mathbf{\hat{z}}$ | (16m) | Ge IV |
| $\mathbf{B_{20}}$ | = | $\left(x_{7} - z_{7}\right) \, \mathbf{a}_{1}- \left(x_{7} + z_{7}\right) \, \mathbf{a}_{2}$ | = | $- a x_{7} \,\mathbf{\hat{x}}+a x_{7} \,\mathbf{\hat{y}}- c z_{7} \,\mathbf{\hat{z}}$ | (16m) | Ge IV |
| $\mathbf{B_{21}}$ | = | $- \left(x_{7} + z_{7}\right) \, \mathbf{a}_{1}+\left(x_{7} - z_{7}\right) \, \mathbf{a}_{2}$ | = | $a x_{7} \,\mathbf{\hat{x}}- a x_{7} \,\mathbf{\hat{y}}- c z_{7} \,\mathbf{\hat{z}}$ | (16m) | Ge IV |
| $\mathbf{B_{22}}$ | = | $\left(x_{7} - z_{7}\right) \, \mathbf{a}_{1}+\left(x_{7} - z_{7}\right) \, \mathbf{a}_{2}+2 x_{7} \, \mathbf{a}_{3}$ | = | $a x_{7} \,\mathbf{\hat{x}}+a x_{7} \,\mathbf{\hat{y}}- c z_{7} \,\mathbf{\hat{z}}$ | (16m) | Ge IV |
| $\mathbf{B_{23}}$ | = | $- \left(x_{7} + z_{7}\right) \, \mathbf{a}_{1}- \left(x_{7} + z_{7}\right) \, \mathbf{a}_{2}- 2 x_{7} \, \mathbf{a}_{3}$ | = | $- a x_{7} \,\mathbf{\hat{x}}- a x_{7} \,\mathbf{\hat{y}}- c z_{7} \,\mathbf{\hat{z}}$ | (16m) | Ge IV |
References
- S. Ishida, Y. Yanagi, K. Oka, K. Kataoka, H. Fujihisa, H. Kito, Y. Yoshida, A. Iyo, I. Hase, Y. Gotoh, and H. Eisaki, Crystal Structure and Superconductivity of BaIr$_{2}$Ge$_{7}$ and Ba$_{3}$Ir$_{4}$Ge$_{16}$ with Two-Dimensional Ba-Ge Networks, J. Am. Chem. Soc. 136, 5245–5248 (2014), doi:10.1021/ja5011527.
Found in
- C. Pei, T. Ying, Y. Zhao, L. Gao, W. Cao, C. Li, H. Hosono, and Y. Qi, Pressure-induced reemergence of superconductivity in BaIr$_{2}$Ge$_{7}$ and Ba$_{3}$Ir$_{4}$Ge$_{16}$ with cage structures, Matter Radiat. Extremes 7, 038404 (2022), doi:10.1063/5.0088235.
First cited in
- N. Anderson, M. J. Mehl, H. Eckert, S. Divilov, X. Campilongo, S. Curtarolo, The AFLOW Library of Crystallographic Prototypes: Part 5. Submitted to Computational Materials Science (2026).
Geometry files
Prototype Generator
aflow --proto=A3B16C4_tI46_139_ad_2ejm_g --params=$a,c/a,z_{3},z_{4},z_{5},x_{6},x_{7},z_{7}$