β-RuCl$_{3}$ Structure: A3B_hP8_185_c_a-001
| Prototype | Cl$_{3}$Ru |
| AFLOW prototype label | A3B_hP8_185_c_a-001 |
| ICSD | 22092 |
| Pearson symbol | hP8 |
| Space group number | 185 |
| Space group symbol | $P6_3cm$ |
| AFLOW prototype command |
aflow --proto=A3B_hP8_185_c_a-001
--params=$a, \allowbreak c/a, \allowbreak z_{1}, \allowbreak x_{2}, \allowbreak z_{2}$ |
- The crystal structure of both $\alpha$- and $\beta$–RuCl$_{3}$ is somewhat uncertain:
- $\alpha$–RuCl$_{3}$ has been reported in the trigonal CrCl$_{3}$ ($D0_{4}$) structure (Fletcher, 1967) and in the monoclinic AlCl$_{3}$ structure (Johnson, 2015).
- (Fletcher, 1967) states that the structure of $\beta$–RuCl$_{3}$ is consistent with the hexagonal space groups $P6_{3}cm$ #185 (this structure), $P6c2$ #188, and $P6_{3}/mcm$ #193, in addition to the trigonal space group $P3c1$ #158, which we present here: trigonal $\beta$–RuCl$_{3}$ (A3B_hP8_158_d_a).
- Space group $P6_{3}cm$ #185 allows an arbitary choice of the origin of the $z$-axis. Here we set $z_{1} = 0$ for the ruthenium (2a) atoms.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \,\mathbf{\hat{y}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $z_{1} \, \mathbf{a}_{3}$ | = | $c z_{1} \,\mathbf{\hat{z}}$ | (2a) | Ru I |
| $\mathbf{B_{2}}$ | = | $\left(z_{1} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $c \left(z_{1} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (2a) | Ru I |
| $\mathbf{B_{3}}$ | = | $x_{2} \, \mathbf{a}_{1}+z_{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a x_{2} \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{2} \,\mathbf{\hat{y}}+c z_{2} \,\mathbf{\hat{z}}$ | (6c) | Cl I |
| $\mathbf{B_{4}}$ | = | $x_{2} \, \mathbf{a}_{2}+z_{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a x_{2} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{2} \,\mathbf{\hat{y}}+c z_{2} \,\mathbf{\hat{z}}$ | (6c) | Cl I |
| $\mathbf{B_{5}}$ | = | $- x_{2} \, \mathbf{a}_{1}- x_{2} \, \mathbf{a}_{2}+z_{2} \, \mathbf{a}_{3}$ | = | $- a x_{2} \,\mathbf{\hat{x}}+c z_{2} \,\mathbf{\hat{z}}$ | (6c) | Cl I |
| $\mathbf{B_{6}}$ | = | $- x_{2} \, \mathbf{a}_{1}+\left(z_{2} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a x_{2} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{2} \,\mathbf{\hat{y}}+c \left(z_{2} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (6c) | Cl I |
| $\mathbf{B_{7}}$ | = | $- x_{2} \, \mathbf{a}_{2}+\left(z_{2} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a x_{2} \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{2} \,\mathbf{\hat{y}}+c \left(z_{2} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (6c) | Cl I |
| $\mathbf{B_{8}}$ | = | $x_{2} \, \mathbf{a}_{1}+x_{2} \, \mathbf{a}_{2}+\left(z_{2} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{2} \,\mathbf{\hat{x}}+c \left(z_{2} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (6c) | Cl I |
References
- J. M. Fletcher, W. E. Gardner, A. C. Fox, and G. Topping, X-Ray, infrared, and magnetic studies of α- and β-ruthenium trichloride, J. Chem. Soc. A pp. 1038–1045 (1967), doi:10.1039/J19670001038.
Prototype Generator
aflow --proto=A3B_hP8_185_c_a --params=$a,c/a,z_{1},x_{2},z_{2}$