Cu$_{2}$Ta$_{4}$O$_{11}$ Structure: A3B11C4_hR36_167_d_cef_be-001
| Prototype | Cu$_{2}$O$_{11}$Ta$_{4}$ |
| AFLOW prototype label | A3B11C4_hR36_167_d_cef_be-001 |
| ICSD | 194463 |
| CCDC | 1703148 |
| Pearson symbol | hR36 |
| Space group number | 167 |
| Space group symbol | $R\overline{3}c$ |
| AFLOW prototype command |
aflow --proto=A3B11C4_hR36_167_d_cef_be-001
--params=$a, \allowbreak c/a, \allowbreak x_{2}, \allowbreak x_{4}, \allowbreak x_{5}, \allowbreak x_{6}, \allowbreak y_{6}, \allowbreak z_{6}$ |
- Only two-thirds of the (6d) site are filled with copper atoms.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+\frac{1}{3}c \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{\sqrt{3}}a \,\mathbf{\hat{y}}+\frac{1}{3}c \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&- \frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+\frac{1}{3}c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $0$ | = | $0$ | (2b) | Ta I |
| $\mathbf{B_{2}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}c \,\mathbf{\hat{z}}$ | (2b) | Ta I |
| $\mathbf{B_{3}}$ | = | $x_{2} \, \mathbf{a}_{1}+x_{2} \, \mathbf{a}_{2}+x_{2} \, \mathbf{a}_{3}$ | = | $c x_{2} \,\mathbf{\hat{z}}$ | (4c) | O I |
| $\mathbf{B_{4}}$ | = | $- \left(x_{2} - \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{2} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{2} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- c \left(x_{2} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4c) | O I |
| $\mathbf{B_{5}}$ | = | $- x_{2} \, \mathbf{a}_{1}- x_{2} \, \mathbf{a}_{2}- x_{2} \, \mathbf{a}_{3}$ | = | $- c x_{2} \,\mathbf{\hat{z}}$ | (4c) | O I |
| $\mathbf{B_{6}}$ | = | $\left(x_{2} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{2} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{2} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $c \left(x_{2} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4c) | O I |
| $\mathbf{B_{7}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{12}a \,\mathbf{\hat{y}}+\frac{1}{6}c \,\mathbf{\hat{z}}$ | (6d) | Cu I |
| $\mathbf{B_{8}}$ | = | $\frac{1}{2} \, \mathbf{a}_{2}$ | = | $\frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+\frac{1}{6}c \,\mathbf{\hat{z}}$ | (6d) | Cu I |
| $\mathbf{B_{9}}$ | = | $\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- \frac{1}{4}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{12}a \,\mathbf{\hat{y}}+\frac{1}{6}c \,\mathbf{\hat{z}}$ | (6d) | Cu I |
| $\mathbf{B_{10}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{12}a \,\mathbf{\hat{y}}+\frac{1}{3}c \,\mathbf{\hat{z}}$ | (6d) | Cu I |
| $\mathbf{B_{11}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+\frac{1}{3}c \,\mathbf{\hat{z}}$ | (6d) | Cu I |
| $\mathbf{B_{12}}$ | = | $\frac{1}{2} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- \frac{1}{4}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{12}a \,\mathbf{\hat{y}}+\frac{1}{3}c \,\mathbf{\hat{z}}$ | (6d) | Cu I |
| $\mathbf{B_{13}}$ | = | $x_{4} \, \mathbf{a}_{1}- \left(x_{4} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{8}a \left(4 x_{4} - 1\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{8}a \left(4 x_{4} - 1\right) \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (6e) | O II |
| $\mathbf{B_{14}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+x_{4} \, \mathbf{a}_{2}- \left(x_{4} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{8}a \left(4 x_{4} - 1\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{8}a \left(4 x_{4} - 1\right) \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (6e) | O II |
| $\mathbf{B_{15}}$ | = | $- \left(x_{4} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}+x_{4} \, \mathbf{a}_{3}$ | = | $- a \left(x_{4} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (6e) | O II |
| $\mathbf{B_{16}}$ | = | $- x_{4} \, \mathbf{a}_{1}+\left(x_{4} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $- \frac{1}{8}a \left(4 x_{4} + 3\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{24}a \left(12 x_{4} + 1\right) \,\mathbf{\hat{y}}+\frac{5}{12}c \,\mathbf{\hat{z}}$ | (6e) | O II |
| $\mathbf{B_{17}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}- x_{4} \, \mathbf{a}_{2}+\left(x_{4} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{8}a \left(4 x_{4} - 1\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{24}a \left(12 x_{4} + 5\right) \,\mathbf{\hat{y}}+\frac{5}{12}c \,\mathbf{\hat{z}}$ | (6e) | O II |
| $\mathbf{B_{18}}$ | = | $\left(x_{4} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}- x_{4} \, \mathbf{a}_{3}$ | = | $a \left(x_{4} + \frac{1}{4}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+\frac{5}{12}c \,\mathbf{\hat{z}}$ | (6e) | O II |
| $\mathbf{B_{19}}$ | = | $x_{5} \, \mathbf{a}_{1}- \left(x_{5} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{8}a \left(4 x_{5} - 1\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{8}a \left(4 x_{5} - 1\right) \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (6e) | Ta II |
| $\mathbf{B_{20}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+x_{5} \, \mathbf{a}_{2}- \left(x_{5} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{8}a \left(4 x_{5} - 1\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{8}a \left(4 x_{5} - 1\right) \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (6e) | Ta II |
| $\mathbf{B_{21}}$ | = | $- \left(x_{5} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}+x_{5} \, \mathbf{a}_{3}$ | = | $- a \left(x_{5} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (6e) | Ta II |
| $\mathbf{B_{22}}$ | = | $- x_{5} \, \mathbf{a}_{1}+\left(x_{5} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $- \frac{1}{8}a \left(4 x_{5} + 3\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{24}a \left(12 x_{5} + 1\right) \,\mathbf{\hat{y}}+\frac{5}{12}c \,\mathbf{\hat{z}}$ | (6e) | Ta II |
| $\mathbf{B_{23}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}- x_{5} \, \mathbf{a}_{2}+\left(x_{5} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{8}a \left(4 x_{5} - 1\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{24}a \left(12 x_{5} + 5\right) \,\mathbf{\hat{y}}+\frac{5}{12}c \,\mathbf{\hat{z}}$ | (6e) | Ta II |
| $\mathbf{B_{24}}$ | = | $\left(x_{5} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}- x_{5} \, \mathbf{a}_{3}$ | = | $a \left(x_{5} + \frac{1}{4}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+\frac{5}{12}c \,\mathbf{\hat{z}}$ | (6e) | Ta II |
| $\mathbf{B_{25}}$ | = | $x_{6} \, \mathbf{a}_{1}+y_{6} \, \mathbf{a}_{2}+z_{6} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{6} - z_{6}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(x_{6} - 2 y_{6} + z_{6}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(x_{6} + y_{6} + z_{6}\right) \,\mathbf{\hat{z}}$ | (12f) | O III |
| $\mathbf{B_{26}}$ | = | $z_{6} \, \mathbf{a}_{1}+x_{6} \, \mathbf{a}_{2}+y_{6} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(y_{6} - z_{6}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(2 x_{6} - y_{6} - z_{6}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(x_{6} + y_{6} + z_{6}\right) \,\mathbf{\hat{z}}$ | (12f) | O III |
| $\mathbf{B_{27}}$ | = | $y_{6} \, \mathbf{a}_{1}+z_{6} \, \mathbf{a}_{2}+x_{6} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{6} - y_{6}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(x_{6} + y_{6} - 2 z_{6}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(x_{6} + y_{6} + z_{6}\right) \,\mathbf{\hat{z}}$ | (12f) | O III |
| $\mathbf{B_{28}}$ | = | $- \left(z_{6} - \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{6} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{6} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{6} - z_{6}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(x_{6} - 2 y_{6} + z_{6}\right) \,\mathbf{\hat{y}}- \frac{1}{6}c \left(2 x_{6} + 2 y_{6} + 2 z_{6} - 3\right) \,\mathbf{\hat{z}}$ | (12f) | O III |
| $\mathbf{B_{29}}$ | = | $- \left(y_{6} - \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{6} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{6} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(y_{6} - z_{6}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(2 x_{6} - y_{6} - z_{6}\right) \,\mathbf{\hat{y}}- \frac{1}{6}c \left(2 x_{6} + 2 y_{6} + 2 z_{6} - 3\right) \,\mathbf{\hat{z}}$ | (12f) | O III |
| $\mathbf{B_{30}}$ | = | $- \left(x_{6} - \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(z_{6} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(y_{6} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{6} - y_{6}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(x_{6} + y_{6} - 2 z_{6}\right) \,\mathbf{\hat{y}}- \frac{1}{6}c \left(2 x_{6} + 2 y_{6} + 2 z_{6} - 3\right) \,\mathbf{\hat{z}}$ | (12f) | O III |
| $\mathbf{B_{31}}$ | = | $- x_{6} \, \mathbf{a}_{1}- y_{6} \, \mathbf{a}_{2}- z_{6} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{6} - z_{6}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(x_{6} - 2 y_{6} + z_{6}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(x_{6} + y_{6} + z_{6}\right) \,\mathbf{\hat{z}}$ | (12f) | O III |
| $\mathbf{B_{32}}$ | = | $- z_{6} \, \mathbf{a}_{1}- x_{6} \, \mathbf{a}_{2}- y_{6} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(y_{6} - z_{6}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(2 x_{6} - y_{6} - z_{6}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(x_{6} + y_{6} + z_{6}\right) \,\mathbf{\hat{z}}$ | (12f) | O III |
| $\mathbf{B_{33}}$ | = | $- y_{6} \, \mathbf{a}_{1}- z_{6} \, \mathbf{a}_{2}- x_{6} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{6} - y_{6}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(x_{6} + y_{6} - 2 z_{6}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(x_{6} + y_{6} + z_{6}\right) \,\mathbf{\hat{z}}$ | (12f) | O III |
| $\mathbf{B_{34}}$ | = | $\left(z_{6} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{6} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{6} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{6} - z_{6}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(x_{6} - 2 y_{6} + z_{6}\right) \,\mathbf{\hat{y}}+\frac{1}{6}c \left(2 x_{6} + 2 y_{6} + 2 z_{6} + 3\right) \,\mathbf{\hat{z}}$ | (12f) | O III |
| $\mathbf{B_{35}}$ | = | $\left(y_{6} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{6} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(z_{6} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(y_{6} - z_{6}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(2 x_{6} - y_{6} - z_{6}\right) \,\mathbf{\hat{y}}+\frac{1}{6}c \left(2 x_{6} + 2 y_{6} + 2 z_{6} + 3\right) \,\mathbf{\hat{z}}$ | (12f) | O III |
| $\mathbf{B_{36}}$ | = | $\left(x_{6} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(z_{6} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(y_{6} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{6} - y_{6}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(x_{6} + y_{6} - 2 z_{6}\right) \,\mathbf{\hat{y}}+\frac{1}{6}c \left(2 x_{6} + 2 y_{6} + 2 z_{6} + 3\right) \,\mathbf{\hat{z}}$ | (12f) | O III |
References
- N. King, R. D. Sommer, P. Watkins-Curry, J. Y. Chan, and P. A. Maggard, Synthesis, Structure, and Thermal Instability of the Cu$_{2}$Ta$_{4}$O$_{11}$ Phase, Crystal Growth & Design 15, 552–558 (2015), doi:10.1021/cg500987c.
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=A3B11C4_hR36_167_d_cef_be --params=$a,c/a,x_{2},x_{4},x_{5},x_{6},y_{6},z_{6}$