CsCuCl$_{3}$ Structure: A3BC_hP30_178_bc_b_a-001
| Prototype | Cl$_{3}$CsCu |
| AFLOW prototype label | A3BC_hP30_178_bc_b_a-001 |
| ICSD | 78435 |
| Pearson symbol | hP30 |
| Space group number | 178 |
| Space group symbol | $P6_122$ |
| AFLOW prototype command |
aflow --proto=A3BC_hP30_178_bc_b_a-001
--params=$a, \allowbreak c/a, \allowbreak x_{1}, \allowbreak x_{2}, \allowbreak x_{3}, \allowbreak x_{4}, \allowbreak y_{4}, \allowbreak z_{4}$ |
- (Christy, 1994) call this a
hexagonal perovskite
structure. - This chiral structure can also be found in the enantiomorphic space group $P6_{5}22$ #179. (Kousaka, 2014).
- We use the data taken at ambient pressure.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \,\mathbf{\hat{y}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $x_{1} \, \mathbf{a}_{1}$ | = | $\frac{1}{2}a x_{1} \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{1} \,\mathbf{\hat{y}}$ | (6a) | Cu I |
| $\mathbf{B_{2}}$ | = | $x_{1} \, \mathbf{a}_{2}+\frac{1}{3} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a x_{1} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{1} \,\mathbf{\hat{y}}+\frac{1}{3}c \,\mathbf{\hat{z}}$ | (6a) | Cu I |
| $\mathbf{B_{3}}$ | = | $- x_{1} \, \mathbf{a}_{1}- x_{1} \, \mathbf{a}_{2}+\frac{2}{3} \, \mathbf{a}_{3}$ | = | $- a x_{1} \,\mathbf{\hat{x}}+\frac{2}{3}c \,\mathbf{\hat{z}}$ | (6a) | Cu I |
| $\mathbf{B_{4}}$ | = | $- x_{1} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a x_{1} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{1} \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (6a) | Cu I |
| $\mathbf{B_{5}}$ | = | $- x_{1} \, \mathbf{a}_{2}+\frac{5}{6} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a x_{1} \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{1} \,\mathbf{\hat{y}}+\frac{5}{6}c \,\mathbf{\hat{z}}$ | (6a) | Cu I |
| $\mathbf{B_{6}}$ | = | $x_{1} \, \mathbf{a}_{1}+x_{1} \, \mathbf{a}_{2}+\frac{1}{6} \, \mathbf{a}_{3}$ | = | $a x_{1} \,\mathbf{\hat{x}}+\frac{1}{6}c \,\mathbf{\hat{z}}$ | (6a) | Cu I |
| $\mathbf{B_{7}}$ | = | $x_{2} \, \mathbf{a}_{1}+2 x_{2} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{3}{2}a x_{2} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{2} \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (6b) | Cl I |
| $\mathbf{B_{8}}$ | = | $- 2 x_{2} \, \mathbf{a}_{1}- x_{2} \, \mathbf{a}_{2}+\frac{7}{12} \, \mathbf{a}_{3}$ | = | $- \frac{3}{2}a x_{2} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{2} \,\mathbf{\hat{y}}+\frac{7}{12}c \,\mathbf{\hat{z}}$ | (6b) | Cl I |
| $\mathbf{B_{9}}$ | = | $x_{2} \, \mathbf{a}_{1}- x_{2} \, \mathbf{a}_{2}+\frac{11}{12} \, \mathbf{a}_{3}$ | = | $- \sqrt{3}a x_{2} \,\mathbf{\hat{y}}+\frac{11}{12}c \,\mathbf{\hat{z}}$ | (6b) | Cl I |
| $\mathbf{B_{10}}$ | = | $- x_{2} \, \mathbf{a}_{1}- 2 x_{2} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $- \frac{3}{2}a x_{2} \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{2} \,\mathbf{\hat{y}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ | (6b) | Cl I |
| $\mathbf{B_{11}}$ | = | $2 x_{2} \, \mathbf{a}_{1}+x_{2} \, \mathbf{a}_{2}+\frac{1}{12} \, \mathbf{a}_{3}$ | = | $\frac{3}{2}a x_{2} \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{2} \,\mathbf{\hat{y}}+\frac{1}{12}c \,\mathbf{\hat{z}}$ | (6b) | Cl I |
| $\mathbf{B_{12}}$ | = | $- x_{2} \, \mathbf{a}_{1}+x_{2} \, \mathbf{a}_{2}+\frac{5}{12} \, \mathbf{a}_{3}$ | = | $\sqrt{3}a x_{2} \,\mathbf{\hat{y}}+\frac{5}{12}c \,\mathbf{\hat{z}}$ | (6b) | Cl I |
| $\mathbf{B_{13}}$ | = | $x_{3} \, \mathbf{a}_{1}+2 x_{3} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{3}{2}a x_{3} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{3} \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (6b) | Cs I |
| $\mathbf{B_{14}}$ | = | $- 2 x_{3} \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}+\frac{7}{12} \, \mathbf{a}_{3}$ | = | $- \frac{3}{2}a x_{3} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{3} \,\mathbf{\hat{y}}+\frac{7}{12}c \,\mathbf{\hat{z}}$ | (6b) | Cs I |
| $\mathbf{B_{15}}$ | = | $x_{3} \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}+\frac{11}{12} \, \mathbf{a}_{3}$ | = | $- \sqrt{3}a x_{3} \,\mathbf{\hat{y}}+\frac{11}{12}c \,\mathbf{\hat{z}}$ | (6b) | Cs I |
| $\mathbf{B_{16}}$ | = | $- x_{3} \, \mathbf{a}_{1}- 2 x_{3} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $- \frac{3}{2}a x_{3} \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{3} \,\mathbf{\hat{y}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ | (6b) | Cs I |
| $\mathbf{B_{17}}$ | = | $2 x_{3} \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{2}+\frac{1}{12} \, \mathbf{a}_{3}$ | = | $\frac{3}{2}a x_{3} \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{3} \,\mathbf{\hat{y}}+\frac{1}{12}c \,\mathbf{\hat{z}}$ | (6b) | Cs I |
| $\mathbf{B_{18}}$ | = | $- x_{3} \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{2}+\frac{5}{12} \, \mathbf{a}_{3}$ | = | $\sqrt{3}a x_{3} \,\mathbf{\hat{y}}+\frac{5}{12}c \,\mathbf{\hat{z}}$ | (6b) | Cs I |
| $\mathbf{B_{19}}$ | = | $x_{4} \, \mathbf{a}_{1}+y_{4} \, \mathbf{a}_{2}+z_{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{4} + y_{4}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \left(x_{4} - y_{4}\right) \,\mathbf{\hat{y}}+c z_{4} \,\mathbf{\hat{z}}$ | (12c) | Cl II |
| $\mathbf{B_{20}}$ | = | $- y_{4} \, \mathbf{a}_{1}+\left(x_{4} - y_{4}\right) \, \mathbf{a}_{2}+\left(z_{4} + \frac{1}{3}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{4} - 2 y_{4}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{4} \,\mathbf{\hat{y}}+c \left(z_{4} + \frac{1}{3}\right) \,\mathbf{\hat{z}}$ | (12c) | Cl II |
| $\mathbf{B_{21}}$ | = | $- \left(x_{4} - y_{4}\right) \, \mathbf{a}_{1}- x_{4} \, \mathbf{a}_{2}+\left(z_{4} + \frac{2}{3}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(2 x_{4} - y_{4}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a y_{4} \,\mathbf{\hat{y}}+\frac{1}{3}c \left(3 z_{4} + 2\right) \,\mathbf{\hat{z}}$ | (12c) | Cl II |
| $\mathbf{B_{22}}$ | = | $- x_{4} \, \mathbf{a}_{1}- y_{4} \, \mathbf{a}_{2}+\left(z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{4} + y_{4}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \left(x_{4} - y_{4}\right) \,\mathbf{\hat{y}}+c \left(z_{4} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (12c) | Cl II |
| $\mathbf{B_{23}}$ | = | $y_{4} \, \mathbf{a}_{1}- \left(x_{4} - y_{4}\right) \, \mathbf{a}_{2}+\left(z_{4} + \frac{5}{6}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(- x_{4} + 2 y_{4}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{4} \,\mathbf{\hat{y}}+\frac{1}{6}c \left(6 z_{4} + 5\right) \,\mathbf{\hat{z}}$ | (12c) | Cl II |
| $\mathbf{B_{24}}$ | = | $\left(x_{4} - y_{4}\right) \, \mathbf{a}_{1}+x_{4} \, \mathbf{a}_{2}+\left(z_{4} + \frac{1}{6}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(2 x_{4} - y_{4}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a y_{4} \,\mathbf{\hat{y}}+c \left(z_{4} + \frac{1}{6}\right) \,\mathbf{\hat{z}}$ | (12c) | Cl II |
| $\mathbf{B_{25}}$ | = | $y_{4} \, \mathbf{a}_{1}+x_{4} \, \mathbf{a}_{2}- \left(z_{4} - \frac{1}{3}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{4} + y_{4}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \left(x_{4} - y_{4}\right) \,\mathbf{\hat{y}}- c \left(z_{4} - \frac{1}{3}\right) \,\mathbf{\hat{z}}$ | (12c) | Cl II |
| $\mathbf{B_{26}}$ | = | $\left(x_{4} - y_{4}\right) \, \mathbf{a}_{1}- y_{4} \, \mathbf{a}_{2}- z_{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{4} - 2 y_{4}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{4} \,\mathbf{\hat{y}}- c z_{4} \,\mathbf{\hat{z}}$ | (12c) | Cl II |
| $\mathbf{B_{27}}$ | = | $- x_{4} \, \mathbf{a}_{1}- \left(x_{4} - y_{4}\right) \, \mathbf{a}_{2}- \left(z_{4} - \frac{2}{3}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(2 x_{4} - y_{4}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a y_{4} \,\mathbf{\hat{y}}- \frac{1}{3}c \left(3 z_{4} - 2\right) \,\mathbf{\hat{z}}$ | (12c) | Cl II |
| $\mathbf{B_{28}}$ | = | $- y_{4} \, \mathbf{a}_{1}- x_{4} \, \mathbf{a}_{2}- \left(z_{4} - \frac{5}{6}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{4} + y_{4}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \left(x_{4} - y_{4}\right) \,\mathbf{\hat{y}}- \frac{1}{6}c \left(6 z_{4} - 5\right) \,\mathbf{\hat{z}}$ | (12c) | Cl II |
| $\mathbf{B_{29}}$ | = | $- \left(x_{4} - y_{4}\right) \, \mathbf{a}_{1}+y_{4} \, \mathbf{a}_{2}- \left(z_{4} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(- x_{4} + 2 y_{4}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{4} \,\mathbf{\hat{y}}- c \left(z_{4} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (12c) | Cl II |
| $\mathbf{B_{30}}$ | = | $x_{4} \, \mathbf{a}_{1}+\left(x_{4} - y_{4}\right) \, \mathbf{a}_{2}- \left(z_{4} - \frac{1}{6}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(2 x_{4} - y_{4}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a y_{4} \,\mathbf{\hat{y}}- c \left(z_{4} - \frac{1}{6}\right) \,\mathbf{\hat{z}}$ | (12c) | Cl II |
References
- A. G. Christy, R. J. Angel, J. Haines, and S. M. Clark, Crystal structural variation and phase transition in caesium trichlorocuprate at high pressure, J. Phys.: Condens. Matter 6, 3125–3136 (1994), doi:10.1088/0953-8984/6/17/005.
- Y. Kousaka, T. Koyama, M. Miyagawa, K. Tanaka, J. Akimitsu, and K. Inoue, Crystal Growth of Chiral Magnetic Material in CsCuCl$_{3}$, J. Phys.: Conf. Ser. 502, 012019 (2014), doi:10.1088/1742-6596/502/1/012019. 1st Conference on Light and Particle Beams in Materials Science 2013.
Found in
- P. Villars, K. Cenzual, J. Daams, R. Gladyshevskii, O. Shcherban, V. Dubenskyy, N. Melnichenko-Koblyuk, O. Pavlyuk, I. Savesyuk, S. Stoiko, and L. Sysa, Landolt-Börnstein - Group III Condensed Matter 43A4} (Springer-Verlag, Berlin Heidelberg, 2006), chap. Structure Types. Part 4: Space Groups (189)P-62m- (174)P-6 $\cdot$ CsCuCl$_{3$, doi:10.1007/10920527_420.
Prototype Generator
aflow --proto=A3BC_hP30_178_bc_b_a --params=$a,c/a,x_{1},x_{2},x_{3},x_{4},y_{4},z_{4}$