Ce$_{5}$Co$_{19}$ Structure: A5B19_hR24_166_a2c_b3c2h-001
| Prototype | Ce$_{5}$Co$_{19}$ |
| AFLOW prototype label | A5B19_hR24_166_a2c_b3c2h-001 |
| ICSD | 620646 |
| CCDC | 1748866 |
| Pearson symbol | hR24 |
| Space group number | 166 |
| Space group symbol | $R\overline{3}m$ |
| AFLOW prototype command |
aflow --proto=A5B19_hR24_166_a2c_b3c2h-001
--params=$a, \allowbreak c/a, \allowbreak x_{3}, \allowbreak x_{4}, \allowbreak x_{5}, \allowbreak x_{6}, \allowbreak x_{7}, \allowbreak x_{8}, \allowbreak z_{8}, \allowbreak x_{9}, \allowbreak z_{9}$ |
Other compounds with this structure
Ce$_{5}$Co$_{19}$, La$_{5}$Co$_{19}$, Nd$_{5}$Co$_{19}$, Nd$_{5}$Ni$_{19}$, Pr$_{5}$Co$_{19}$, Pr$_{5}$Ni$_{19}$, Sm$_{5}$Co$_{19}$, Y$_{5}$Co$_{19}$
- This is the binary version of the Ce$_{5}$Ga$_{7}$Rh$_{12}$ structure.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+\frac{1}{3}c \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{\sqrt{3}}a \,\mathbf{\hat{y}}+\frac{1}{3}c \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&- \frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+\frac{1}{3}c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $0$ | = | $0$ | (1a) | Ce I |
| $\mathbf{B_{2}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}c \,\mathbf{\hat{z}}$ | (1b) | Co I |
| $\mathbf{B_{3}}$ | = | $x_{3} \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{2}+x_{3} \, \mathbf{a}_{3}$ | = | $c x_{3} \,\mathbf{\hat{z}}$ | (2c) | Ce II |
| $\mathbf{B_{4}}$ | = | $- x_{3} \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}- x_{3} \, \mathbf{a}_{3}$ | = | $- c x_{3} \,\mathbf{\hat{z}}$ | (2c) | Ce II |
| $\mathbf{B_{5}}$ | = | $x_{4} \, \mathbf{a}_{1}+x_{4} \, \mathbf{a}_{2}+x_{4} \, \mathbf{a}_{3}$ | = | $c x_{4} \,\mathbf{\hat{z}}$ | (2c) | Ce III |
| $\mathbf{B_{6}}$ | = | $- x_{4} \, \mathbf{a}_{1}- x_{4} \, \mathbf{a}_{2}- x_{4} \, \mathbf{a}_{3}$ | = | $- c x_{4} \,\mathbf{\hat{z}}$ | (2c) | Ce III |
| $\mathbf{B_{7}}$ | = | $x_{5} \, \mathbf{a}_{1}+x_{5} \, \mathbf{a}_{2}+x_{5} \, \mathbf{a}_{3}$ | = | $c x_{5} \,\mathbf{\hat{z}}$ | (2c) | Co II |
| $\mathbf{B_{8}}$ | = | $- x_{5} \, \mathbf{a}_{1}- x_{5} \, \mathbf{a}_{2}- x_{5} \, \mathbf{a}_{3}$ | = | $- c x_{5} \,\mathbf{\hat{z}}$ | (2c) | Co II |
| $\mathbf{B_{9}}$ | = | $x_{6} \, \mathbf{a}_{1}+x_{6} \, \mathbf{a}_{2}+x_{6} \, \mathbf{a}_{3}$ | = | $c x_{6} \,\mathbf{\hat{z}}$ | (2c) | Co III |
| $\mathbf{B_{10}}$ | = | $- x_{6} \, \mathbf{a}_{1}- x_{6} \, \mathbf{a}_{2}- x_{6} \, \mathbf{a}_{3}$ | = | $- c x_{6} \,\mathbf{\hat{z}}$ | (2c) | Co III |
| $\mathbf{B_{11}}$ | = | $x_{7} \, \mathbf{a}_{1}+x_{7} \, \mathbf{a}_{2}+x_{7} \, \mathbf{a}_{3}$ | = | $c x_{7} \,\mathbf{\hat{z}}$ | (2c) | Co IV |
| $\mathbf{B_{12}}$ | = | $- x_{7} \, \mathbf{a}_{1}- x_{7} \, \mathbf{a}_{2}- x_{7} \, \mathbf{a}_{3}$ | = | $- c x_{7} \,\mathbf{\hat{z}}$ | (2c) | Co IV |
| $\mathbf{B_{13}}$ | = | $x_{8} \, \mathbf{a}_{1}+x_{8} \, \mathbf{a}_{2}+z_{8} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{8} - z_{8}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(x_{8} - z_{8}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(2 x_{8} + z_{8}\right) \,\mathbf{\hat{z}}$ | (6h) | Co V |
| $\mathbf{B_{14}}$ | = | $z_{8} \, \mathbf{a}_{1}+x_{8} \, \mathbf{a}_{2}+x_{8} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{8} - z_{8}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(x_{8} - z_{8}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(2 x_{8} + z_{8}\right) \,\mathbf{\hat{z}}$ | (6h) | Co V |
| $\mathbf{B_{15}}$ | = | $x_{8} \, \mathbf{a}_{1}+z_{8} \, \mathbf{a}_{2}+x_{8} \, \mathbf{a}_{3}$ | = | $- \frac{1}{\sqrt{3}}a \left(x_{8} - z_{8}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(2 x_{8} + z_{8}\right) \,\mathbf{\hat{z}}$ | (6h) | Co V |
| $\mathbf{B_{16}}$ | = | $- z_{8} \, \mathbf{a}_{1}- x_{8} \, \mathbf{a}_{2}- x_{8} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{8} - z_{8}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(x_{8} - z_{8}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(2 x_{8} + z_{8}\right) \,\mathbf{\hat{z}}$ | (6h) | Co V |
| $\mathbf{B_{17}}$ | = | $- x_{8} \, \mathbf{a}_{1}- x_{8} \, \mathbf{a}_{2}- z_{8} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{8} - z_{8}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(x_{8} - z_{8}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(2 x_{8} + z_{8}\right) \,\mathbf{\hat{z}}$ | (6h) | Co V |
| $\mathbf{B_{18}}$ | = | $- x_{8} \, \mathbf{a}_{1}- z_{8} \, \mathbf{a}_{2}- x_{8} \, \mathbf{a}_{3}$ | = | $\frac{1}{\sqrt{3}}a \left(x_{8} - z_{8}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(2 x_{8} + z_{8}\right) \,\mathbf{\hat{z}}$ | (6h) | Co V |
| $\mathbf{B_{19}}$ | = | $x_{9} \, \mathbf{a}_{1}+x_{9} \, \mathbf{a}_{2}+z_{9} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{9} - z_{9}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(x_{9} - z_{9}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(2 x_{9} + z_{9}\right) \,\mathbf{\hat{z}}$ | (6h) | Co VI |
| $\mathbf{B_{20}}$ | = | $z_{9} \, \mathbf{a}_{1}+x_{9} \, \mathbf{a}_{2}+x_{9} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{9} - z_{9}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(x_{9} - z_{9}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(2 x_{9} + z_{9}\right) \,\mathbf{\hat{z}}$ | (6h) | Co VI |
| $\mathbf{B_{21}}$ | = | $x_{9} \, \mathbf{a}_{1}+z_{9} \, \mathbf{a}_{2}+x_{9} \, \mathbf{a}_{3}$ | = | $- \frac{1}{\sqrt{3}}a \left(x_{9} - z_{9}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(2 x_{9} + z_{9}\right) \,\mathbf{\hat{z}}$ | (6h) | Co VI |
| $\mathbf{B_{22}}$ | = | $- z_{9} \, \mathbf{a}_{1}- x_{9} \, \mathbf{a}_{2}- x_{9} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{9} - z_{9}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(x_{9} - z_{9}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(2 x_{9} + z_{9}\right) \,\mathbf{\hat{z}}$ | (6h) | Co VI |
| $\mathbf{B_{23}}$ | = | $- x_{9} \, \mathbf{a}_{1}- x_{9} \, \mathbf{a}_{2}- z_{9} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{9} - z_{9}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(x_{9} - z_{9}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(2 x_{9} + z_{9}\right) \,\mathbf{\hat{z}}$ | (6h) | Co VI |
| $\mathbf{B_{24}}$ | = | $- x_{9} \, \mathbf{a}_{1}- z_{9} \, \mathbf{a}_{2}- x_{9} \, \mathbf{a}_{3}$ | = | $\frac{1}{\sqrt{3}}a \left(x_{9} - z_{9}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(2 x_{9} + z_{9}\right) \,\mathbf{\hat{z}}$ | (6h) | Co VI |
References
- A. E. Ray, A. T. Biermann, R. S. Harmer, and J. E. Davison, Ueberpruefung der Zustandsschaubilder der binaeren Systeme Cer-Kobalt, Praseodym-Kobalt und Neodym-Kobalt, Kobalt 4, 90–93 (1973).
Found in
- Y. Khan, The crystal structure of R$_{5}$Co$_{19}$, Acta Crystallogr. Sect. B 30, 1533–1537 (1974), doi:10.1107/S0567740874005206.
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=A5B19_hR24_166_a2c_b3c2h --params=$a,c/a,x_{3},x_{4},x_{5},x_{6},x_{7},x_{8},z_{8},x_{9},z_{9}$