KBe2BO3F2 Structure : AB2C2DE3_hR9_155_b_c_c_a_e
| Prototype | : | BBe2F2KO3 |
| AFLOW prototype label | : | AB2C2DE3_hR9_155_b_c_c_a_e |
| Strukturbericht designation | : | None |
| Pearson symbol | : | hR9 |
| Space group number | : | 155 |
| Space group symbol | : | $R32$ |
| AFLOW prototype command | : | aflow --proto=AB2C2DE3_hR9_155_b_c_c_a_e --params=$a$,$c/a$,$x_{3}$,$x_{4}$,$y_{5}$ |
Rhombohedral primitive vectors:
\[ \begin{array}{ccc} \mathbf{a}_1 & = & ~ \frac12 \, a \, \mathbf{\hat{x}} - \frac{1}{2\sqrt{3}} \, a \, \mathbf{\hat{y}} + \frac13 \, c \, \mathbf{\hat{z}} \\ \mathbf{a}_2 & = & \frac{1}{\sqrt{3}} \, a \, \mathbf{\hat{y}} + \frac13 \, c \, \mathbf{\hat{z}} \\ \mathbf{a}_3 & = & - \frac12 \, a \, \mathbf{\hat{x}} - \frac{1}{2\sqrt{3}} \, a \, \mathbf{\hat{y}} + \frac13 \, c \, \mathbf{\hat{z}} \\ \end{array} \]
Basis vectors:
\[ \begin{array}{ccccccc} & & \text{Lattice Coordinates} & & \text{Cartesian Coordinates} &\text{Wyckoff Position} & \text{Atom Type} \\ \mathbf{B}_{1} & = & 0 \, \mathbf{a}_{1} + 0 \, \mathbf{a}_{2} + 0 \, \mathbf{a}_{3} & = & 0 \, \mathbf{\hat{x}} + 0 \, \mathbf{\hat{y}} + 0 \, \mathbf{\hat{z}} & \left(1a\right) & \text{K} \\ \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}} & \left(1b\right) & \text{B} \\ \mathbf{B}_{3} & = & x_{3} \, \mathbf{a}_{1} + x_{3} \, \mathbf{a}_{2} + x_{3} \, \mathbf{a}_{3} & = & x_{3}c \, \mathbf{\hat{z}} & \left(2c\right) & \text{Be} \\ \mathbf{B}_{4} & = & -x_{3} \, \mathbf{a}_{1}-x_{3} \, \mathbf{a}_{2}-x_{3} \, \mathbf{a}_{3} & = & -x_{3}c \, \mathbf{\hat{z}} & \left(2c\right) & \text{Be} \\ \mathbf{B}_{5} & = & x_{4} \, \mathbf{a}_{1} + x_{4} \, \mathbf{a}_{2} + x_{4} \, \mathbf{a}_{3} & = & x_{4}c \, \mathbf{\hat{z}} & \left(2c\right) & \text{F} \\ \mathbf{B}_{6} & = & -x_{4} \, \mathbf{a}_{1}-x_{4} \, \mathbf{a}_{2}-x_{4} \, \mathbf{a}_{3} & = & -x_{4}c \, \mathbf{\hat{z}} & \left(2c\right) & \text{F} \\ \mathbf{B}_{7} & = & \frac{1}{2} \, \mathbf{a}_{1} + y_{5} \, \mathbf{a}_{2}-y_{5} \, \mathbf{a}_{3} & = & \left(\frac{1}{4} +\frac{1}{2}y_{5}\right)a \, \mathbf{\hat{x}} + \left(- \frac{1}{4\sqrt{3}} +\frac{\sqrt{3}}{2}y_{5}\right)a \, \mathbf{\hat{y}} + \frac{1}{6}c \, \mathbf{\hat{z}} & \left(3e\right) & \text{O} \\ \mathbf{B}_{8} & = & -y_{5} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{2} + y_{5} \, \mathbf{a}_{3} & = & -y_{5}a \, \mathbf{\hat{x}} + \frac{1}{2\sqrt{3}}a \, \mathbf{\hat{y}} + \frac{1}{6}c \, \mathbf{\hat{z}} & \left(3e\right) & \text{O} \\ \mathbf{B}_{9} & = & y_{5} \, \mathbf{a}_{1}-y_{5} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \left(- \frac{1}{4} +\frac{1}{2}y_{5}\right)a \, \mathbf{\hat{x}}-\left(\frac{\sqrt{3}}{2}y_{5}+\frac{1}{4\sqrt{3}}\right)a \, \mathbf{\hat{y}} + \frac{1}{6}c \, \mathbf{\hat{z}} & \left(3e\right) & \text{O} \\ \end{array} \]References
- L. Mei, X. Huang, Y. Wang, Q. Wu, and C. Chen, Crystal Structure of KBe2BO3F2, Zeitschrift für Kristallographie – Crystalline Materials 210, 93–95 (1995), doi:10.1524/zkri.1995.210.2.93.