AlF$_{3}$ ($D0_{14}$) Structure: AB3_hR8_155_c_de-001
| Prototype | AlF$_{3}$ |
| AFLOW prototype label | AB3_hR8_155_c_de-001 |
| Strukturbericht designation | $D0_{14}$ |
| ICSD | 30274 |
| Pearson symbol | hR8 |
| Space group number | 155 |
| Space group symbol | $R32$ |
| AFLOW prototype command |
aflow --proto=AB3_hR8_155_c_de-001
--params=$a, \allowbreak c/a, \allowbreak x_{1}, \allowbreak y_{2}, \allowbreak y_{3}$ |
Other compounds with this structure
FeF$_{3}$
- 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 | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $x_{1} \, \mathbf{a}_{1}+x_{1} \, \mathbf{a}_{2}+x_{1} \, \mathbf{a}_{3}$ | = | $c x_{1} \,\mathbf{\hat{z}}$ | (2c) | Al I |
| $\mathbf{B_{2}}$ | = | $- x_{1} \, \mathbf{a}_{1}- x_{1} \, \mathbf{a}_{2}- x_{1} \, \mathbf{a}_{3}$ | = | $- c x_{1} \,\mathbf{\hat{z}}$ | (2c) | Al I |
| $\mathbf{B_{3}}$ | = | $y_{2} \, \mathbf{a}_{2}- y_{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a y_{2} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a y_{2} \,\mathbf{\hat{y}}$ | (3d) | F I |
| $\mathbf{B_{4}}$ | = | $- y_{2} \, \mathbf{a}_{1}+y_{2} \, \mathbf{a}_{3}$ | = | $- a y_{2} \,\mathbf{\hat{x}}$ | (3d) | F I |
| $\mathbf{B_{5}}$ | = | $y_{2} \, \mathbf{a}_{1}- y_{2} \, \mathbf{a}_{2}$ | = | $\frac{1}{2}a y_{2} \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a y_{2} \,\mathbf{\hat{y}}$ | (3d) | F I |
| $\mathbf{B_{6}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+y_{3} \, \mathbf{a}_{2}- y_{3} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \left(2 y_{3} + 1\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{12}a \left(6 y_{3} - 1\right) \,\mathbf{\hat{y}}+\frac{1}{6}c \,\mathbf{\hat{z}}$ | (3e) | F II |
| $\mathbf{B_{7}}$ | = | $- y_{3} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+y_{3} \, \mathbf{a}_{3}$ | = | $- a y_{3} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+\frac{1}{6}c \,\mathbf{\hat{z}}$ | (3e) | F II |
| $\mathbf{B_{8}}$ | = | $y_{3} \, \mathbf{a}_{1}- y_{3} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \left(2 y_{3} - 1\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{12}a \left(6 y_{3} + 1\right) \,\mathbf{\hat{y}}+\frac{1}{6}c \,\mathbf{\hat{z}}$ | (3e) | F II |
References
- J. A. A. Ketelaar, Die Kristallstruktur der Aluminiumhalogenide: I. Die Kristallstruktur von AlF$_3$, Z. Kristallogr. 85, 119–131 (1933), doi:10.1524/zkri.1933.85.1.119.
- R. Hoppe and D. Kissel, Zur kenntnis von AlF$_3$ und InF$_3$ [1], J. Flourine Chem. 24, 324–340 (1984), doi:10.1016/S0022-1139(00)81321-4.
Found in
- R. T. Downs and M. Hall-Wallace, The American Mineralogist Crystal Structure Database, Am. Mineral. 88, 247–250 (2003).
Prototype Generator
aflow --proto=AB3_hR8_155_c_de --params=$a,c/a,x_{1},y_{2},y_{3}$