Bi2Te3 ($C33$) Structure: A2B3_hR5_166_c_ac

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Prototype : Bi2Te3
AFLOW prototype label : A2B3_hR5_166_c_ac
Strukturbericht designation : $C33$
Pearson symbol : hR5
Space group number : 166
Space group symbol : $\mbox{R}\bar{3}\mbox{m}$
AFLOW prototype command : aflow --proto=A2B3_hR5_166_c_ac [--hex]
--params=
$a$,$c/a$,$x_{2}$,$x_{3}$


Other compounds with this structure

  • Be2Te2S, Sb2Te3, Bi2Te2Se, Bi2Te3, and Bi2Se3

  • (Gottfried, 1937) assigns Bi2Te2S as the prototype for Strukturbericht symbol, but (Lange, 1939) shows that this is isostructural with Bi2Te3, the sulfur atom being replaced by a tellurium atom. We will therefore retain our original designation. 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:

\[ \begin{array}{ccccccc} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{Atom Type} \\ \mathbf{B}_{1} & =&0 \, \mathbf{a}_{1} + 0 \, \mathbf{a}_{2} + 0 \, \mathbf{a}_{3} & =&0 \mathbf{\hat{x}} + 0 \mathbf{\hat{y}} + 0 \mathbf{\hat{z}} & \left(1a\right) & \mbox{Te I} \\ \mathbf{B}_{2} & =&x_{2} \, \mathbf{a}_{1}+ x_{2} \, \mathbf{a}_{2}+ x_{2} \, \mathbf{a}_{3}& =&x_{2} \, c \, \mathbf{\hat{z}}& \left(2c\right) & \mbox{Bi} \\ \mathbf{B}_{3} & =&- x_{2} \, \mathbf{a}_{1}- x_{2} \, \mathbf{a}_{2}- x_{2} \, \mathbf{a}_{3}& =&- x_{2} \, c \, \mathbf{\hat{z}}& \left(2c\right) & \mbox{Bi} \\ \mathbf{B}_{4} & =&x_{3} \, \mathbf{a}_{1}+ x_{3} \, \mathbf{a}_{2}+ x_{3} \, \mathbf{a}_{3}& =&x_{3} \, c \, \mathbf{\hat{z}}& \left(2c\right) & \mbox{Te II} \\ \mathbf{B}_{5} & =&- x_{3} \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}- x_{3} \, \mathbf{a}_{3}& =&- x_{3} \, c \, \mathbf{\hat{z}}& \left(2c\right) & \mbox{Te II} \\ \end{array} \]

References

  • C. Gottfried and F. Schossberger, eds., Strukturbericht Band III 1933-1935, (Akademische Verlagsgesellschaft M. B. H., Leipzig, 1937).
  • P. W. Lange, Ein Vergleich zwischen Bi2Te3 und Bi2Te2S, Naturwissenschaften 27, 133–134 (1939), doi:10.1007/BF01490284.

Geometry files


Prototype Generator

aflow --proto=A2B3_hR5_166_c_ac --params=

Species:

Running:

Output: