BiI3 ($D0_{5}$) Structure: AB3_hR8_148_c_f

Picture of Structure; Click for Big Picture
Prototype : BiI3
AFLOW prototype label : AB3_hR8_148_c_f
Strukturbericht designation : $D0_{5}$
Pearson symbol : hR8
Space group number : 148
Space group symbol : $\mbox{R}\bar{3}$
AFLOW prototype command : aflow --proto=AB3_hR8_148_c_f [--hex]
--params=
$a$,$c/a$,$x_{1}$,$x_{2}$,$y_{2}$,$z_{2}$


Other compounds with this structure

  • SbI3, AsI3, FeCl3, CrBr3

  • Hexagonal settings of this structure can be obtained with the option ––hex.

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} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{Atom Type} \\ \mathbf{B}_{1} & = &x_{1} \, \mathbf{a}_{1}+ x_{1} \, \mathbf{a}_{2}+ x_{1} \, \mathbf{a}_{3}& =&x_{1} \, c \, \mathbf{\hat{z}}& \left(2c\right) & \mbox{Bi} \\ \mathbf{B}_{2} & = &- x_{1} \, \mathbf{a}_{1}- x_{1} \, \mathbf{a}_{2}- x_{1} \, \mathbf{a}_{3}& =&- x_{1} \, c \, \mathbf{\hat{z}}& \left(2c\right) & \mbox{Bi} \\ \mathbf{B}_{3} & =&x_{2} \, \mathbf{a}_{1}+ y_{2} \, \mathbf{a}_{2}+ z_{2} \, \mathbf{a}_{3}& =&\frac12 \, \left(x_{2} - z_{2}\right) \, a \, \mathbf{\hat{x}}+ \frac{1}{2\sqrt{3}} \, \left(2 y_{2} - z_{2} - x_{2}\right) \, a \, \mathbf{\hat{y}}+ \frac13 \, \left(x_{2} + y_{2} + z_{2}\right) \, c \, \mathbf{\hat{z}}& \left(6f\right) & \mbox{I} \\ \mathbf{B}_{4} & =&z_{2} \, \mathbf{a}_{1}+ x_{2} \, \mathbf{a}_{2}+ y_{2} \, \mathbf{a}_{3}& =&\frac12 \, \left(z_{2} - y_{2}\right) \, a \, \mathbf{\hat{x}}+ \frac{1}{2\sqrt{3}} \, \left(2 x_{2} - y_{2} - z_{2}\right) \, a \, \mathbf{\hat{y}}+ \frac13 \, \left(x_{2} + y_{2} + z_{2}\right) \, c \, \mathbf{\hat{z}}& \left(6f\right) & \mbox{I} \\ \mathbf{B}_{5} & =&y_{2} \, \mathbf{a}_{1}+ z_{2} \, \mathbf{a}_{2}+ x_{2} \, \mathbf{a}_{3}& =&\frac12 \, \left(y_{2} - x_{2}\right) \, a \, \mathbf{\hat{x}}+ \frac{1}{2\sqrt{3}} \, \left(2 z_{2} - x_{2} - y_{2}\right) \, a \, \mathbf{\hat{y}}+ \frac13 \, \left(x_{2} + y_{2} + z_{2}\right) \, c \, \mathbf{\hat{z}}& \left(6f\right) & \mbox{I} \\ \mathbf{B}_{6} & =&- x_{2} \, \mathbf{a}_{1}- y_{2} \, \mathbf{a}_{2}- z_{2} \, \mathbf{a}_{3}& =&\frac12 \, \left(z_{2} - x_{2}\right) \, a \, \mathbf{\hat{x}}+ \frac{1}{2\sqrt{3}} \, \left(z_{2} + x_{2} - 2 y_{2}\right) \, a \, \mathbf{\hat{y}}- \frac13 \, \left(x_{2} + y_{2} + z_{2}\right) \, c \, \mathbf{\hat{z}}& \left(6f\right) & \mbox{I} \\ \mathbf{B}_{7} & =&- z_{2} \, \mathbf{a}_{1}- x_{2} \, \mathbf{a}_{2}- y_{2} \, \mathbf{a}_{3}& =&\frac12 \, \left(y_{2} - z_{2}\right) \, a \, \mathbf{\hat{x}}+ \frac{1}{2\sqrt{3}} \, \left(y_{2} + z_{2} - 2 x_{2}\right) \, a \, \mathbf{\hat{y}}- \frac13 \, \left(x_{2} + y_{2} + z_{2}\right) \, c \, \mathbf{\hat{z}}& \left(6f\right) & \mbox{I} \\ \mathbf{B}_{8} & =&- y_{2} \, \mathbf{a}_{1}- z_{2} \, \mathbf{a}_{2}- x_{2} \, \mathbf{a}_{3}& =&\frac12 \, \left(x_{2} - y_{2}\right) \, a \, \mathbf{\hat{x}}+ \frac{1}{2\sqrt{3}} \, \left(x_{2} + y_{2} - 2 z_{2}\right) \, a \, \mathbf{\hat{y}}- \frac13 \, \left(x_{2} + y_{2} + z_{2}\right) \, c \, \mathbf{\hat{z}}& \left(6f\right) & \mbox{I} \\ \end{array} \]

References

  • H. Braekken, Die Kristallstruktur der Trijodide von Arsen, Antimon und Wismut, Zeitschrift für Kristallographie – Crystalline Materials 74, 67–72 (1930), doi:10.1524/zkri.1930.74.1.67.

Found in

  • C. Hermann, O. Lohrmann, and H. Philipp, Strukturbericht Band II, 1928–1932 (Akademsiche Verlagsgesellschaft M. B. H., Leipzig, 1937)., pp. 25-27.

Geometry files


Prototype Generator

aflow --proto=AB3_hR8_148_c_f --params=

Species:

Running:

Output: