K$_{3}$Cu$_{3}$P$_{2}$: A3B3C2_hR8_166_d_ac_c-001
| Prototype | Cu$_{3}$K$_{3}$P$_{2}$ |
| AFLOW prototype label | A3B3C2_hR8_166_d_ac_c-001 |
| ICSD | 12163 |
| CCDC | 1595407 |
| Pearson symbol | hR8 |
| Space group number | 166 |
| Space group symbol | $R\overline{3}m$ |
| AFLOW prototype command |
aflow --proto=A3B3C2_hR8_166_d_ac_c-001
--params=$a, \allowbreak c/a, \allowbreak x_{2}, \allowbreak x_{3}$ |
Other compounds with this structure
K$_{3}$Ag$_{3}$As$_{2}$, K$_{3}$Au$_{3}$Sb$_{2}$, K$_{3}$Cu$_{3}$As$_{2}$, Rb$_{3}$Au$_{3}$Sb$_{2}$, Rb$_{3}$Cu$_{3}$As$_{2}$
- The AFLOW prototype label protocol moves the K I atom from the (1b) site, as given in (Savelsberg, 1978) to the (1a) site, shifting all atomic coordinates by ( 0 , 0 , 1/2 c).
- This structure is given in the rhombohedral setting of space group $R\overline{3}m$ #166. The hexagonal setting may be obtained by adding
--hexto the aflow command.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+\frac{1}{3}c \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{\sqrt{3}}a \,\mathbf{\hat{y}}+\frac{1}{3}c \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&- \frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+\frac{1}{3}c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $0$ | = | $0$ | (1a) | K I |
| $\mathbf{B_{2}}$ | = | $x_{2} \, \mathbf{a}_{1}+x_{2} \, \mathbf{a}_{2}+x_{2} \, \mathbf{a}_{3}$ | = | $c x_{2} \,\mathbf{\hat{z}}$ | (2c) | K II |
| $\mathbf{B_{3}}$ | = | $- x_{2} \, \mathbf{a}_{1}- x_{2} \, \mathbf{a}_{2}- x_{2} \, \mathbf{a}_{3}$ | = | $- c x_{2} \,\mathbf{\hat{z}}$ | (2c) | K 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) | P I |
| $\mathbf{B_{5}}$ | = | $- x_{3} \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}- x_{3} \, \mathbf{a}_{3}$ | = | $- c x_{3} \,\mathbf{\hat{z}}$ | (2c) | P I |
| $\mathbf{B_{6}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{12}a \,\mathbf{\hat{y}}+\frac{1}{6}c \,\mathbf{\hat{z}}$ | (3d) | Cu I |
| $\mathbf{B_{7}}$ | = | $\frac{1}{2} \, \mathbf{a}_{2}$ | = | $\frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+\frac{1}{6}c \,\mathbf{\hat{z}}$ | (3d) | Cu I |
| $\mathbf{B_{8}}$ | = | $\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- \frac{1}{4}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{12}a \,\mathbf{\hat{y}}+\frac{1}{6}c \,\mathbf{\hat{z}}$ | (3d) | Cu I |
References
- G. Savelsberg and H. Schäfer, Darstellung und Kristallstruktur von K$_{3}$Cu$_{3}$P$_{2}$, Z. Naturforsch. B 33, 590–592 (1978), doi:10.1515/znb-1978-0604.
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=A3B3C2_hR8_166_d_ac_c --params=$a,c/a,x_{2},x_{3}$