S$_{6}$ (ρ-S) Sulfur Structure: A_hR6_148_f-001
| Prototype | S |
| AFLOW prototype label | A_hR6_148_f-001 |
| ICSD | 27495 |
| Pearson symbol | hR6 |
| Space group number | 148 |
| Space group symbol | $R\overline{3}$ |
| AFLOW prototype command |
aflow --proto=A_hR6_148_f-001
--params=$a, \allowbreak c/a, \allowbreak x_{1}, \allowbreak y_{1}, \allowbreak z_{1}$ |
- We follow the notation of (Donohue, 1961) and (Donhoue, 1974) and call this S$_{6}$ sulfur. Alternative names are: rhombohedral sulfur, trigonal sulfur, Engel's sulfur, Aten's sulfur, $\epsilon$-sulfur, and $\rho$-sulfur. (Donohue, 1974)
- Hexagonal settings of this structure 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 | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $x_{1} \, \mathbf{a}_{1}+y_{1} \, \mathbf{a}_{2}+z_{1} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{1} - z_{1}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(x_{1} - 2 y_{1} + z_{1}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(x_{1} + y_{1} + z_{1}\right) \,\mathbf{\hat{z}}$ | (6f) | S I |
| $\mathbf{B_{2}}$ | = | $z_{1} \, \mathbf{a}_{1}+x_{1} \, \mathbf{a}_{2}+y_{1} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(y_{1} - z_{1}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(2 x_{1} - y_{1} - z_{1}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(x_{1} + y_{1} + z_{1}\right) \,\mathbf{\hat{z}}$ | (6f) | S I |
| $\mathbf{B_{3}}$ | = | $y_{1} \, \mathbf{a}_{1}+z_{1} \, \mathbf{a}_{2}+x_{1} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{1} - y_{1}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(x_{1} + y_{1} - 2 z_{1}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(x_{1} + y_{1} + z_{1}\right) \,\mathbf{\hat{z}}$ | (6f) | S I |
| $\mathbf{B_{4}}$ | = | $- x_{1} \, \mathbf{a}_{1}- y_{1} \, \mathbf{a}_{2}- z_{1} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{1} - z_{1}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(x_{1} - 2 y_{1} + z_{1}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(x_{1} + y_{1} + z_{1}\right) \,\mathbf{\hat{z}}$ | (6f) | S I |
| $\mathbf{B_{5}}$ | = | $- z_{1} \, \mathbf{a}_{1}- x_{1} \, \mathbf{a}_{2}- y_{1} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(y_{1} - z_{1}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(2 x_{1} - y_{1} - z_{1}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(x_{1} + y_{1} + z_{1}\right) \,\mathbf{\hat{z}}$ | (6f) | S I |
| $\mathbf{B_{6}}$ | = | $- y_{1} \, \mathbf{a}_{1}- z_{1} \, \mathbf{a}_{2}- x_{1} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{1} - y_{1}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(x_{1} + y_{1} - 2 z_{1}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(x_{1} + y_{1} + z_{1}\right) \,\mathbf{\hat{z}}$ | (6f) | S I |
References
- J. Donohue, A. Caron, and E. Goldish, The Crystal and Molecular Structure of S$_{6}$ (Sulfur-6), J. Am. Chem. Soc. 83, 3748–3751 (1961), doi:10.1021/ja01479a003.
Found in
- J. Donohue, The Structures of the Elements (Robert E. Krieger Publishing Company, New York, 1974).
Prototype Generator
aflow --proto=A_hR6_148_f --params=$a,c/a,x_{1},y_{1},z_{1}$