$\alpha$–As ($A7$) Structure: A_hR2_166_c

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Prototype : $\alpha$–As
AFLOW prototype label : A_hR2_166_c
Strukturbericht designation : $A7$
Pearson symbol : hR2
Space group number : 166
Space group symbol : $\mbox{R}\bar{3}\mbox{m}$
AFLOW prototype command : aflow --proto=A_hR2_166_c [--hex]
--params=
$a$,$c/a$,$x_{1}$


Other elements with this structure

  • Sb, Bi

  • When $c/a = \sqrt6$ and $z_1 = 1/8$ this becomes the diamond (A4) structure. Note that $\alpha$–As (A_hR2_166_c, $\alpha$–As), rhombohedral graphite (A_hR2_166_c, C), and $\beta$–O (A_hR2_166_c, $\beta$–O) have the same AFLOW prototype label. They are generated by the same symmetry operations with different sets of parameters (––params) specified in their corresponding CIF files. 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:

\[ \begin{array}{ccccccc} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{Atom Type} \\ \mathbf{B}_{1} & =&x_{1} \, \mathbf{a}_{1}+ x_{1} \, \mathbf{a}_{2}+ x_{1} \, \mathbf{a}_{3}& =&x_{1} \, c \, \mathbf{\hat{z}}& \left(2c\right) & \mbox{As} \\ \mathbf{B}_{2} & =&- x_{1} \, \mathbf{a}_{1}- x_{1} \, \mathbf{a}_{2}- x_{1} \, \mathbf{a}_{3}& =&- x_{1} \, c \, \mathbf{\hat{z}}& \left(2c\right) & \mbox{As} \\ \end{array} \]

References

  • D. Schiferl and C. S. Barrett, The crystal structure of arsenic at 4.2, 78 and 299°K, J. Appl. Crystallogr. 2, 30–36 (1969), doi:10.1107/S0021889869006443.
  • R. J. Meier and R. B. Helmholdt, Neutron–diffraction study of alpha– and beta–oxygen, Phys. Rev. B 29, 1387–1393 (1984), doi:10.1103/PhysRevB.29.1387.

Found in

  • R. T. Downs and M. Hall–Wallace, The American Mineralogist Crystal Structure Database, Am. Mineral. 88, 247–250 (2003).

Geometry files


Prototype Generator

aflow --proto=A_hR2_166_c --params=

Species:

Running:

Output: