Black Phosphorus ($A17$) Structure: A_oC8_64_f-002
| Prototype | P |
| AFLOW prototype label | A_oC8_64_f-002 |
| Strukturbericht designation | $A17$ |
| ICSD | 23836 |
| Pearson symbol | oC8 |
| Space group number | 64 |
| Space group symbol | $Cmce$ |
| AFLOW prototype command |
aflow --proto=A_oC8_64_f-002
--params=$a, \allowbreak b/a, \allowbreak c/a, \allowbreak y_{1}, \allowbreak z_{1}$ |
- Phosphorus is found in at least three forms:
- Black phosphorus, Strukturbericht $A17$, (this structure)
- Monoclinic Hittorf's phosphorus, and
- Low temperature triclinic
white
phosphorus, stable below 197K.
- $\alpha$-gallium ($A11$), molecular iodine ($A14$), and black phosphorous ($A17$) all share the same AFLOW label, A_oC8_64_f. The structures are generated by the same symmetry operations with different sets of parameters (
--params) specified in their corresponding CIF files.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{1}{2}b \,\mathbf{\hat{y}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}b \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $- y_{1} \, \mathbf{a}_{1}+y_{1} \, \mathbf{a}_{2}+z_{1} \, \mathbf{a}_{3}$ | = | $b y_{1} \,\mathbf{\hat{y}}+c z_{1} \,\mathbf{\hat{z}}$ | (8f) | P I |
| $\mathbf{B_{2}}$ | = | $\left(y_{1} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{1} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(z_{1} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- b y_{1} \,\mathbf{\hat{y}}+c \left(z_{1} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8f) | P I |
| $\mathbf{B_{3}}$ | = | $- \left(y_{1} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{1} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{1} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+b y_{1} \,\mathbf{\hat{y}}- c \left(z_{1} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8f) | P I |
| $\mathbf{B_{4}}$ | = | $y_{1} \, \mathbf{a}_{1}- y_{1} \, \mathbf{a}_{2}- z_{1} \, \mathbf{a}_{3}$ | = | $- b y_{1} \,\mathbf{\hat{y}}- c z_{1} \,\mathbf{\hat{z}}$ | (8f) | P I |
References
- A. Brown and S. Rundqvist, Refinement of the crystal structure of black phosphorus, Acta Cryst. 19, 684–685 (1965), doi:10.1107/S0365110X65004140.
Prototype Generator
aflow --proto=A_oC8_64_f --params=$a,b/a,c/a,y_{1},z_{1}$