Co$_{5}$Ge$_{7}$ Structure: A5B7_tI24_107_ac_abd-001
| Prototype | Co$_{5}$Ge$_{7}$ |
| AFLOW prototype label | A5B7_tI24_107_ac_abd-001 |
| ICSD | 197263 |
| Pearson symbol | tI24 |
| Space group number | 107 |
| Space group symbol | $I4mm$ |
| AFLOW prototype command |
aflow --proto=A5B7_tI24_107_ac_abd-001
--params=$a, \allowbreak c/a, \allowbreak z_{1}, \allowbreak z_{2}, \allowbreak z_{3}, \allowbreak x_{4}, \allowbreak z_{4}, \allowbreak x_{5}, \allowbreak z_{5}$ |
Other compounds with this structure
Ir$_{5}$Ge$_{7}$
- The origin of the $z$ axis is arbitrary. We have chosen to place the Ge(2a) atom at the origin, taking $z_{1} = 0$. (Schubert, 1960) instead set $z_{4} = 0$.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&- \frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}- \frac{1}{2}c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $z_{1} \, \mathbf{a}_{1}+z_{1} \, \mathbf{a}_{2}$ | = | $c z_{1} \,\mathbf{\hat{z}}$ | (2a) | Co I |
| $\mathbf{B_{2}}$ | = | $z_{2} \, \mathbf{a}_{1}+z_{2} \, \mathbf{a}_{2}$ | = | $c z_{2} \,\mathbf{\hat{z}}$ | (2a) | Ge I |
| $\mathbf{B_{3}}$ | = | $\left(z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{1}+z_{3} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{y}}+c z_{3} \,\mathbf{\hat{z}}$ | (4b) | Ge II |
| $\mathbf{B_{4}}$ | = | $z_{3} \, \mathbf{a}_{1}+\left(z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+c z_{3} \,\mathbf{\hat{z}}$ | (4b) | Ge II |
| $\mathbf{B_{5}}$ | = | $\left(x_{4} + z_{4}\right) \, \mathbf{a}_{1}+\left(x_{4} + z_{4}\right) \, \mathbf{a}_{2}+2 x_{4} \, \mathbf{a}_{3}$ | = | $a x_{4} \,\mathbf{\hat{x}}+a x_{4} \,\mathbf{\hat{y}}+c z_{4} \,\mathbf{\hat{z}}$ | (8c) | Co II |
| $\mathbf{B_{6}}$ | = | $- \left(x_{4} - z_{4}\right) \, \mathbf{a}_{1}- \left(x_{4} - z_{4}\right) \, \mathbf{a}_{2}- 2 x_{4} \, \mathbf{a}_{3}$ | = | $- a x_{4} \,\mathbf{\hat{x}}- a x_{4} \,\mathbf{\hat{y}}+c z_{4} \,\mathbf{\hat{z}}$ | (8c) | Co II |
| $\mathbf{B_{7}}$ | = | $\left(x_{4} + z_{4}\right) \, \mathbf{a}_{1}- \left(x_{4} - z_{4}\right) \, \mathbf{a}_{2}$ | = | $- a x_{4} \,\mathbf{\hat{x}}+a x_{4} \,\mathbf{\hat{y}}+c z_{4} \,\mathbf{\hat{z}}$ | (8c) | Co II |
| $\mathbf{B_{8}}$ | = | $- \left(x_{4} - z_{4}\right) \, \mathbf{a}_{1}+\left(x_{4} + z_{4}\right) \, \mathbf{a}_{2}$ | = | $a x_{4} \,\mathbf{\hat{x}}- a x_{4} \,\mathbf{\hat{y}}+c z_{4} \,\mathbf{\hat{z}}$ | (8c) | Co II |
| $\mathbf{B_{9}}$ | = | $z_{5} \, \mathbf{a}_{1}+\left(x_{5} + z_{5}\right) \, \mathbf{a}_{2}+x_{5} \, \mathbf{a}_{3}$ | = | $a x_{5} \,\mathbf{\hat{x}}+c z_{5} \,\mathbf{\hat{z}}$ | (8d) | Ge III |
| $\mathbf{B_{10}}$ | = | $z_{5} \, \mathbf{a}_{1}- \left(x_{5} - z_{5}\right) \, \mathbf{a}_{2}- x_{5} \, \mathbf{a}_{3}$ | = | $- a x_{5} \,\mathbf{\hat{x}}+c z_{5} \,\mathbf{\hat{z}}$ | (8d) | Ge III |
| $\mathbf{B_{11}}$ | = | $\left(x_{5} + z_{5}\right) \, \mathbf{a}_{1}+z_{5} \, \mathbf{a}_{2}+x_{5} \, \mathbf{a}_{3}$ | = | $a x_{5} \,\mathbf{\hat{y}}+c z_{5} \,\mathbf{\hat{z}}$ | (8d) | Ge III |
| $\mathbf{B_{12}}$ | = | $- \left(x_{5} - z_{5}\right) \, \mathbf{a}_{1}+z_{5} \, \mathbf{a}_{2}- x_{5} \, \mathbf{a}_{3}$ | = | $- a x_{5} \,\mathbf{\hat{y}}+c z_{5} \,\mathbf{\hat{z}}$ | (8d) | Ge III |
References
- K. Schubert, T. R. Anantharaman, H. O. K. Ata, H. G. Meissner, M. Pötzschke, W. Rossteutscher, and E. Stolz, Einige strukturelle Ergebnisse an metallischen Phasen (6), Naturwissenschaften 47, 512 (1960), doi:10.1007/BF00641115.
Found in
- P. Villars and K. Cenzual, Pearson's Crystal Data – Crystal Structure Database for Inorganic Compounds (2013). ASM International.
Prototype Generator
aflow --proto=A5B7_tI24_107_ac_abd --params=$a,c/a,z_{1},z_{2},z_{3},x_{4},z_{4},x_{5},z_{5}$