Rhombohedral Graphite Structure: A_hR2_166_c-002
| Prototype | C |
| AFLOW prototype label | A_hR2_166_c-002 |
| ICSD | 31829 |
| Pearson symbol | hR2 |
| Space group number | 166 |
| Space group symbol | $R\overline{3}m$ |
| AFLOW prototype command |
aflow --proto=A_hR2_166_c-002
--params=$a, \allowbreak c/a, \allowbreak x_{1}$ |
Other compounds with this structure
Bi, P, Sb
- Graphite also comes in a hexagonal form, which may be either flat (A9) or buckled. When $x_{1}=1/6$ the graphite sheets are flat, however this does not produce a change in symmetry as it does in the hexagonal graphite structures.
- All of the elements listed in the
Other compounds
list have experimental entries in the ICSD. - $\alpha$–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) | C 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) | C I |
References
- H. Lipson and A. R. Stokes, The structure of graphite, Proc. Roy. Soc. A 181, 101–105 (1942), doi:10.1098/rspa.1942.0063.
Found in
- J. Donohue, The Structures of the Elements (Robert E. Krieger Publishing Company, New York, 1974).
Prototype Generator
aflow --proto=A_hR2_166_c --params=$a,c/a,x_{1}$