SnP$_{3}$ Structure: A3B_hR8_166_h_c-001
| Prototype | P$_{3}$Sn |
| AFLOW prototype label | A3B_hR8_166_h_c-001 |
| ICSD | 16293 |
| Pearson symbol | hR8 |
| Space group number | 166 |
| Space group symbol | $R\overline{3}m$ |
| AFLOW prototype command |
aflow --proto=A3B_hR8_166_h_c-001
--params=$a, \allowbreak c/a, \allowbreak x_{1}, \allowbreak x_{2}, \allowbreak z_{2}$ |
Other compounds with this structure
GeP$_{3}$
- 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 | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $x_{1} \, \mathbf{a}_{1}+x_{1} \, \mathbf{a}_{2}+x_{1} \, \mathbf{a}_{3}$ | = | $c x_{1} \,\mathbf{\hat{z}}$ | (2c) | Sn 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) | Sn I |
| $\mathbf{B_{3}}$ | = | $x_{2} \, \mathbf{a}_{1}+x_{2} \, \mathbf{a}_{2}+z_{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{2} - z_{2}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(x_{2} - z_{2}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(2 x_{2} + z_{2}\right) \,\mathbf{\hat{z}}$ | (6h) | P I |
| $\mathbf{B_{4}}$ | = | $z_{2} \, \mathbf{a}_{1}+x_{2} \, \mathbf{a}_{2}+x_{2} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{2} - z_{2}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(x_{2} - z_{2}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(2 x_{2} + z_{2}\right) \,\mathbf{\hat{z}}$ | (6h) | P I |
| $\mathbf{B_{5}}$ | = | $x_{2} \, \mathbf{a}_{1}+z_{2} \, \mathbf{a}_{2}+x_{2} \, \mathbf{a}_{3}$ | = | $- \frac{1}{\sqrt{3}}a \left(x_{2} - z_{2}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(2 x_{2} + z_{2}\right) \,\mathbf{\hat{z}}$ | (6h) | P I |
| $\mathbf{B_{6}}$ | = | $- z_{2} \, \mathbf{a}_{1}- x_{2} \, \mathbf{a}_{2}- x_{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{2} - z_{2}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(x_{2} - z_{2}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(2 x_{2} + z_{2}\right) \,\mathbf{\hat{z}}$ | (6h) | P I |
| $\mathbf{B_{7}}$ | = | $- x_{2} \, \mathbf{a}_{1}- x_{2} \, \mathbf{a}_{2}- z_{2} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{2} - z_{2}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(x_{2} - z_{2}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(2 x_{2} + z_{2}\right) \,\mathbf{\hat{z}}$ | (6h) | P I |
| $\mathbf{B_{8}}$ | = | $- x_{2} \, \mathbf{a}_{1}- z_{2} \, \mathbf{a}_{2}- x_{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{\sqrt{3}}a \left(x_{2} - z_{2}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(2 x_{2} + z_{2}\right) \,\mathbf{\hat{z}}$ | (6h) | P I |
References
- J. Gullman and O. Olofsson, The crystal structure of SnP$_{3}$ and a note on the crystal structure of GeP$_{3}$, J. Solid State Chem. 5, 441–445 (1972), doi:10.1016/0022-4596(72)90091-6.
Prototype Generator
aflow --proto=A3B_hR8_166_h_c --params=$a,c/a,x_{1},x_{2},z_{2}$