KBe$_{2}$BO$_{3}$F$_{2}$ Structure: AB2C2DE3_hR9_155_a_c_c_b_d-001
| Prototype | BBe$_{2}$F$_{2}$KO$_{3}$ |
| AFLOW prototype label | AB2C2DE3_hR9_155_a_c_c_b_d-001 |
| ICSD | 77277 |
| Pearson symbol | hR9 |
| Space group number | 155 |
| Space group symbol | $R32$ |
| AFLOW prototype command |
aflow --proto=AB2C2DE3_hR9_155_a_c_c_b_d-001
--params=$a, \allowbreak c/a, \allowbreak x_{3}, \allowbreak x_{4}, \allowbreak y_{5}$ |
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+\frac{1}{3}c \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{\sqrt{3}}a \,\mathbf{\hat{y}}+\frac{1}{3}c \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&- \frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+\frac{1}{3}c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $0$ | = | $0$ | (1a) | B I |
| $\mathbf{B_{2}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}c \,\mathbf{\hat{z}}$ | (1b) | K I |
| $\mathbf{B_{3}}$ | = | $x_{3} \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{2}+x_{3} \, \mathbf{a}_{3}$ | = | $c x_{3} \,\mathbf{\hat{z}}$ | (2c) | Be I |
| $\mathbf{B_{4}}$ | = | $- x_{3} \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}- x_{3} \, \mathbf{a}_{3}$ | = | $- c x_{3} \,\mathbf{\hat{z}}$ | (2c) | Be I |
| $\mathbf{B_{5}}$ | = | $x_{4} \, \mathbf{a}_{1}+x_{4} \, \mathbf{a}_{2}+x_{4} \, \mathbf{a}_{3}$ | = | $c x_{4} \,\mathbf{\hat{z}}$ | (2c) | F I |
| $\mathbf{B_{6}}$ | = | $- x_{4} \, \mathbf{a}_{1}- x_{4} \, \mathbf{a}_{2}- x_{4} \, \mathbf{a}_{3}$ | = | $- c x_{4} \,\mathbf{\hat{z}}$ | (2c) | F I |
| $\mathbf{B_{7}}$ | = | $y_{5} \, \mathbf{a}_{2}- y_{5} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a y_{5} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a y_{5} \,\mathbf{\hat{y}}$ | (3d) | O I |
| $\mathbf{B_{8}}$ | = | $- y_{5} \, \mathbf{a}_{1}+y_{5} \, \mathbf{a}_{3}$ | = | $- a y_{5} \,\mathbf{\hat{x}}$ | (3d) | O I |
| $\mathbf{B_{9}}$ | = | $y_{5} \, \mathbf{a}_{1}- y_{5} \, \mathbf{a}_{2}$ | = | $\frac{1}{2}a y_{5} \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a y_{5} \,\mathbf{\hat{y}}$ | (3d) | O I |
References
- L. Mei, X. Huang, Y. Want, Q. Wu, and C. Chen, Crystal Structure of KBe$_{2}$BO$_{3}$F$_{2}$, Z. Kristallogr. 210, 93–95 (1995), doi:10.1524/zkri.1995.210.2.93.
Prototype Generator
aflow --proto=AB2C2DE3_hR9_155_a_c_c_b_d --params=$a,c/a,x_{3},x_{4},y_{5}$