AsTi ($B_{i}$) Structure: AB_hP8_194_ad_f

Picture of Structure; Click for Big Picture
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.

Geometry files


Prototype Generator

aflow --proto=AB_hP8_194_ad_f --params=

Species:

Running:

Output: