AsTi (Bi) Structure: AB_hP8_194_ad_f
| Prototype | : | AsTi |
| AFLOW prototype label | : | AB_hP8_194_ad_f |
| Strukturbericht designation | : | $B_{i}$ |
| Pearson symbol | : | hP8 |
| Space group number | : | 194 |
| Space group symbol | : | $\mbox{P6}_{3}\mbox{/mmc}$ |
| AFLOW prototype command | : | aflow --proto=AB_hP8_194_ad_f --params=$a,c/a,z_{3}$ |
Other compounds with this structure
- CMo, CSTi2, CSZr2, PTi, PZr
Hexagonal primitive vectors:
\[
\begin{array}{ccc}
\mathbf{a}_1 & = & \frac12 \, a \, \mathbf{\hat{x}} - \frac{\sqrt3}2 \, a \, \mathbf{\hat{y}} \\
\mathbf{a}_2 & = & \frac12 \, a \, \mathbf{\hat{x}} + \frac{\sqrt3}2 \, a \, \mathbf{\hat{y}} \\
\mathbf{a}_3 & = & c \, \mathbf{\hat{z}}\\
\end{array}
\]
Basis vectors:
\[ \begin{array}{ccccccc} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{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(2a\right) & \mbox{As I} \\ \mathbf{B}_{2}& = &\frac12 \, \mathbf{a}_{3}& = &\frac12 \, c \, \mathbf{\hat{z}}& \left(2a\right) & \mbox{As I} \\ \mathbf{B}_{3}& = &\frac13 \, \mathbf{a}_{1}+ \frac23 \, \mathbf{a}_{2}+ \frac34 \, \mathbf{a}_{3}& = &\frac12 \, a \, \mathbf{\hat{x}}+ \frac{1}{2\sqrt{3}} \, a \, \mathbf{\hat{y}}+ \frac34 \, c \, \mathbf{\hat{z}}& \left(2d\right) & \mbox{As II} \\ \mathbf{B}_{4}& = &\frac23 \, \mathbf{a}_{1}+ \frac13 \, \mathbf{a}_{2}+ \frac14 \, \mathbf{a}_{3}& = &\frac12 \, a \, \mathbf{\hat{x}}- \frac{1}{2\sqrt{3}} \, a \, \mathbf{\hat{y}}+ \frac14 \, c \, \mathbf{\hat{z}}& \left(2d\right) & \mbox{As II} \\ \mathbf{B}_{5}& = &\frac13 \, \mathbf{a}_{1}+ \frac23 \, \mathbf{a}_{2}+ z_{3} \, \mathbf{a}_{3}& = &\frac12 \, a \, \mathbf{\hat{x}}+\frac{1}{2\sqrt{3}} \, a \, \mathbf{\hat{y}}+ z_{3} \, c \, \mathbf{\hat{z}}& \left(4f\right) & \mbox{Ti} \\ \mathbf{B}_{6}& = &\frac23 \, \mathbf{a}_{1}+ \frac13 \, \mathbf{a}_{2}+ \left(\frac12 + z_{3}\right) \, \mathbf{a}_{3}& = &\frac12 \, a \, \mathbf{\hat{x}}- \frac{1}{2\sqrt{3}} \, a \, \mathbf{\hat{y}}+ \left(\frac12 + z_{3}\right) \, c \, \mathbf{\hat{z}}& \left(4f\right) & \mbox{Ti} \\ \mathbf{B}_{7}& = &\frac23 \, \mathbf{a}_{1}+ \frac13 \, \mathbf{a}_{2}- z_{3} \, \mathbf{a}_{3}& = &\frac12 \, a \, \mathbf{\hat{x}}- \frac{1}{2\sqrt{3}} \, a \, \mathbf{\hat{y}}- z_{3} \, c \, \mathbf{\hat{z}}& \left(4f\right) & \mbox{Ti} \\ \mathbf{B}_{8}& = &\frac13 \, \mathbf{a}_{1}+ \frac23 \, \mathbf{a}_{2}+ \left(\frac12 - z_{3}\right) \, \mathbf{a}_{3}& = &\frac12 \, a \, \mathbf{\hat{x}}+ \frac{1}{2\sqrt{3}} \, a \, \mathbf{\hat{y}}+ \left(\frac12 - z_{3}\right) \, c \, \mathbf{\hat{z}}& \left(4f\right) & \mbox{Ti} \\ \end{array} \]References
- K. Bachmayer, H. Nowotny, and A. Kohl, Die Struktur von TiAs, Monatsh. Chem. Verw. Tl. 86, 39–43 (1955), doi:10.1007/BF00899271.
Found in
- R. W. G. Wyckoff, Crystal Structures Vol. 1 (Wiley, 1963), 2nd edn., pp. 146-149.