α-As ($A7$) Structure: A_hR2_166_c-001
| Prototype | As |
| AFLOW prototype label | A_hR2_166_c-001 |
| Strukturbericht designation | $A7$ |
| ICSD | 16517 |
| CCDC | 1597091 |
| Pearson symbol | hR2 |
| Space group number | 166 |
| Space group symbol | $R\overline{3}m$ |
| AFLOW prototype command |
aflow --proto=A_hR2_166_c-001
--params=$a, \allowbreak c/a, \allowbreak x_{1}$ |
Other compounds with this structure
Bi, Sb
- We use the data from (Schiferl, 1969) taken at 78K.
- When $c/a = \sqrt{6}$ and $z_{1} = 1/8$ this becomes the diamond ($A4$) structure.
- Note that $\alpha$–As ($A7$), rhombohedral graphite (A_hR2_166_c), and $\beta$–O have the same AFLOW prototype label, A_hR2_166_c. They are generated by the same symmetry operations with different sets of parameters (
--params) specified in their corresponding CIF files. Hexagonal settings of rhombohedral structures can be obtained with the option--hex.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+\frac{1}{3}c \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{\sqrt{3}}a \,\mathbf{\hat{y}}+\frac{1}{3}c \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&- \frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+\frac{1}{3}c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $x_{1} \, \mathbf{a}_{1}+x_{1} \, \mathbf{a}_{2}+x_{1} \, \mathbf{a}_{3}$ | = | $c x_{1} \,\mathbf{\hat{z}}$ | (2c) | As I |
| $\mathbf{B_{2}}$ | = | $- x_{1} \, \mathbf{a}_{1}- x_{1} \, \mathbf{a}_{2}- x_{1} \, \mathbf{a}_{3}$ | = | $- c x_{1} \,\mathbf{\hat{z}}$ | (2c) | As I |
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.
Found in
- R. T. Downs and M. Hall-Wallace, The American Mineralogist Crystal Structure Database, Am. Mineral. 88, 247–250 (2003).
First cited in
- M. J. Mehl, D. Hicks, C. Toher, O. Levy, R. M. Hanson, G. L. W. Hart, and S. Curtarolo, The AFLOW Library of Crystallographic Prototypes: Part 1, Comp. Mat. Sci. 136, S1-S828 (2017). (doi=10.1016/j.commatsci.2017.01.017)
Geometry files
Prototype Generator
aflow --proto=A_hR2_166_c --params=$a,c/a,x_{1}$