ThB$_{2}$C Structure: A2BC_hR12_166_g_d_ac-001
| Prototype | BCTh$_{2}$ |
| AFLOW prototype label | A2BC_hR12_166_g_d_ac-001 |
| ICSD | 68414 |
| Pearson symbol | hR12 |
| Space group number | 166 |
| Space group symbol | $R\overline{3}m$ |
| AFLOW prototype command |
aflow --proto=A2BC_hR12_166_g_d_ac-001
--params=$a, \allowbreak c/a, \allowbreak x_{2}, \allowbreak x_{4}$ |
Other compounds with this structure
$\beta$-UB$_{2}$C (HT)
- We take the coordinates from the neutron powder diffraction data at 298K.
- Hexagonal settings of this structure can be obtained with the option
--hex.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+\frac{1}{3}c \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{\sqrt{3}}a \,\mathbf{\hat{y}}+\frac{1}{3}c \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&- \frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+\frac{1}{3}c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $0$ | = | $0$ | (1a) | Th 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) | Th 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) | Th II |
| $\mathbf{B_{4}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{12}a \,\mathbf{\hat{y}}+\frac{1}{6}c \,\mathbf{\hat{z}}$ | (3d) | C I |
| $\mathbf{B_{5}}$ | = | $\frac{1}{2} \, \mathbf{a}_{2}$ | = | $\frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+\frac{1}{6}c \,\mathbf{\hat{z}}$ | (3d) | C I |
| $\mathbf{B_{6}}$ | = | $\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- \frac{1}{4}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{12}a \,\mathbf{\hat{y}}+\frac{1}{6}c \,\mathbf{\hat{z}}$ | (3d) | C I |
| $\mathbf{B_{7}}$ | = | $x_{4} \, \mathbf{a}_{1}- x_{4} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \left(2 x_{4} - 1\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{12}a \left(6 x_{4} + 1\right) \,\mathbf{\hat{y}}+\frac{1}{6}c \,\mathbf{\hat{z}}$ | (6g) | B I |
| $\mathbf{B_{8}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+x_{4} \, \mathbf{a}_{2}- x_{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \left(2 x_{4} + 1\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{12}a \left(6 x_{4} - 1\right) \,\mathbf{\hat{y}}+\frac{1}{6}c \,\mathbf{\hat{z}}$ | (6g) | B I |
| $\mathbf{B_{9}}$ | = | $- x_{4} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+x_{4} \, \mathbf{a}_{3}$ | = | $- a x_{4} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+\frac{1}{6}c \,\mathbf{\hat{z}}$ | (6g) | B I |
| $\mathbf{B_{10}}$ | = | $- x_{4} \, \mathbf{a}_{1}+x_{4} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- \frac{1}{4}a \left(2 x_{4} + 1\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{12}a \left(6 x_{4} - 1\right) \,\mathbf{\hat{y}}+\frac{1}{6}c \,\mathbf{\hat{z}}$ | (6g) | B I |
| $\mathbf{B_{11}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}- x_{4} \, \mathbf{a}_{2}+x_{4} \, \mathbf{a}_{3}$ | = | $- \frac{1}{4}a \left(2 x_{4} - 1\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{12}a \left(6 x_{4} + 1\right) \,\mathbf{\hat{y}}+\frac{1}{6}c \,\mathbf{\hat{z}}$ | (6g) | B I |
| $\mathbf{B_{12}}$ | = | $x_{4} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}- x_{4} \, \mathbf{a}_{3}$ | = | $a x_{4} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+\frac{1}{6}c \,\mathbf{\hat{z}}$ | (6g) | B I |
References
- P. Rogl and P. Fischer, Single-crystal X-ray and powder neutron diffraction of ThB$_{2}$C (ThB$_{2}$C-type), J. Solid State Chem. 78, 294–300 (1989), doi:10.1016/0022-4596(89)90110-2.
Found in
- P. Rogl and P. Fischer, Powder neutron diffraction of $\alpha$UB$_{2}$C ($\alpha$UB$_{2}$C-type), J. Solid State Chem. 90, 285–290 (1991), doi:10.1016/0022-4596(91)90144-7.
Prototype Generator
aflow --proto=A2BC_hR12_166_g_d_ac --params=$a,c/a,x_{2},x_{4}$