BC8 (Si) Structure: A_cI16_206_c-001
| Prototype | Si |
| AFLOW prototype label | A_cI16_206_c-001 |
| ICSD | none |
| Pearson symbol | cI16 |
| Space group number | 206 |
| Space group symbol | $Ia\overline{3}$ |
| AFLOW prototype command |
aflow --proto=A_cI16_206_c-001
--params=$a, \allowbreak x_{1}$ |
- This is a tetragonally bonded structure which packs more efficiently than diamond. See (Crain, 1995) and references therein. The reference compound chosen here, found in (Wentorf, 1963), is stable in the range 11-16 GPa.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&- \frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}- \frac{1}{2}a \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $2 x_{1} \, \mathbf{a}_{1}+2 x_{1} \, \mathbf{a}_{2}+2 x_{1} \, \mathbf{a}_{3}$ | = | $a x_{1} \,\mathbf{\hat{x}}+a x_{1} \,\mathbf{\hat{y}}+a x_{1} \,\mathbf{\hat{z}}$ | (16c) | Si I |
| $\mathbf{B_{2}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}- \left(2 x_{1} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{1} \,\mathbf{\hat{x}}- a \left(x_{1} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+a x_{1} \,\mathbf{\hat{z}}$ | (16c) | Si I |
| $\mathbf{B_{3}}$ | = | $- \left(2 x_{1} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- a \left(x_{1} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a x_{1} \,\mathbf{\hat{y}}- a x_{1} \,\mathbf{\hat{z}}$ | (16c) | Si I |
| $\mathbf{B_{4}}$ | = | $- \left(2 x_{1} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}$ | = | $a x_{1} \,\mathbf{\hat{x}}- a x_{1} \,\mathbf{\hat{y}}- a \left(x_{1} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (16c) | Si I |
| $\mathbf{B_{5}}$ | = | $- 2 x_{1} \, \mathbf{a}_{1}- 2 x_{1} \, \mathbf{a}_{2}- 2 x_{1} \, \mathbf{a}_{3}$ | = | $- a x_{1} \,\mathbf{\hat{x}}- a x_{1} \,\mathbf{\hat{y}}- a x_{1} \,\mathbf{\hat{z}}$ | (16c) | Si I |
| $\mathbf{B_{6}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\left(2 x_{1} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{1} \,\mathbf{\hat{x}}+a \left(x_{1} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- a x_{1} \,\mathbf{\hat{z}}$ | (16c) | Si I |
| $\mathbf{B_{7}}$ | = | $\left(2 x_{1} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $a \left(x_{1} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a x_{1} \,\mathbf{\hat{y}}+a x_{1} \,\mathbf{\hat{z}}$ | (16c) | Si I |
| $\mathbf{B_{8}}$ | = | $\left(2 x_{1} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}$ | = | $- a x_{1} \,\mathbf{\hat{x}}+a x_{1} \,\mathbf{\hat{y}}+a \left(x_{1} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (16c) | Si I |
References
- J. R. H. Wentorf and J. S. Kasper, Two New Forms of Silicon, Science 139, 338–339 (1963), doi:10.1126/science.139.3552.338.b.
- J. Crain, S. J. Clark, G. J. Ackland, M. C. Payne, V. Milman, P. D. Hatton, and B. J. Reid, Theoretical study of high-density phases of covalent semiconductors. I. {\em Ab initio} treatment, Phys. Rev. B 49, 5329–5340 (1994), doi:10.1103/PhysRevB.49.5329.
Prototype Generator
aflow --proto=A_cI16_206_c --params=$a,x_{1}$