P$_{2}$I$_{4}$ Structure: A2B_aP6_2_2i_i-001
| Prototype | I$_{4}$P$_{2}$ |
| AFLOW prototype label | A2B_aP6_2_2i_i-001 |
| ICSD | 36293 |
| Pearson symbol | aP6 |
| Space group number | 2 |
| Space group symbol | $P\overline{1}$ |
| AFLOW prototype command |
aflow --proto=A2B_aP6_2_2i_i-001
--params=$a, \allowbreak b/a, \allowbreak c/a, \allowbreak \alpha, \allowbreak \beta, \allowbreak \gamma, \allowbreak x_{1}, \allowbreak y_{1}, \allowbreak z_{1}, \allowbreak x_{2}, \allowbreak y_{2}, \allowbreak z_{2}, \allowbreak x_{3}, \allowbreak y_{3}, \allowbreak z_{3}$ |
- The ICSD entry for this structure has a much different value for $\beta$ than what appears in the published work. At the present time we do not have a resolution to this problem
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&a \,\mathbf{\hat{x}}\\\mathbf{a_{2}}&=&b \cos{\gamma} \,\mathbf{\hat{x}}+b \sin{\gamma} \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c_{x} \,\mathbf{\hat{x}}+c_{y} \,\mathbf{\hat{y}}+c_{z} \,\mathbf{\hat{z}}\\c_{x} & = & c \cos{\beta} \\ c_{y} & = & c (\cos{\alpha} - \cos{\beta}\cos{\gamma}) / {\sin{\gamma}} \\ c_{z} & = & \sqrt{c^2 - c_{x}^2- c_{y}^2}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $x_{1} \, \mathbf{a}_{1}+y_{1} \, \mathbf{a}_{2}+z_{1} \, \mathbf{a}_{3}$ | = | $\left(a x_{1} + b y_{1} \cos{\gamma} + c_{x} z_{1}\right) \,\mathbf{\hat{x}}+\left(b y_{1} \sin{\gamma} + c_{y} z_{1}\right) \,\mathbf{\hat{y}}+c_{z} z_{1} \,\mathbf{\hat{z}}$ | (2i) | I I |
| $\mathbf{B_{2}}$ | = | $- x_{1} \, \mathbf{a}_{1}- y_{1} \, \mathbf{a}_{2}- z_{1} \, \mathbf{a}_{3}$ | = | $- \left(a x_{1} + b y_{1} \cos{\gamma} + c_{x} z_{1}\right) \,\mathbf{\hat{x}}- \left(b y_{1} \sin{\gamma} + c_{y} z_{1}\right) \,\mathbf{\hat{y}}- c_{z} z_{1} \,\mathbf{\hat{z}}$ | (2i) | I I |
| $\mathbf{B_{3}}$ | = | $x_{2} \, \mathbf{a}_{1}+y_{2} \, \mathbf{a}_{2}+z_{2} \, \mathbf{a}_{3}$ | = | $\left(a x_{2} + b y_{2} \cos{\gamma} + c_{x} z_{2}\right) \,\mathbf{\hat{x}}+\left(b y_{2} \sin{\gamma} + c_{y} z_{2}\right) \,\mathbf{\hat{y}}+c_{z} z_{2} \,\mathbf{\hat{z}}$ | (2i) | I II |
| $\mathbf{B_{4}}$ | = | $- x_{2} \, \mathbf{a}_{1}- y_{2} \, \mathbf{a}_{2}- z_{2} \, \mathbf{a}_{3}$ | = | $- \left(a x_{2} + b y_{2} \cos{\gamma} + c_{x} z_{2}\right) \,\mathbf{\hat{x}}- \left(b y_{2} \sin{\gamma} + c_{y} z_{2}\right) \,\mathbf{\hat{y}}- c_{z} z_{2} \,\mathbf{\hat{z}}$ | (2i) | I II |
| $\mathbf{B_{5}}$ | = | $x_{3} \, \mathbf{a}_{1}+y_{3} \, \mathbf{a}_{2}+z_{3} \, \mathbf{a}_{3}$ | = | $\left(a x_{3} + b y_{3} \cos{\gamma} + c_{x} z_{3}\right) \,\mathbf{\hat{x}}+\left(b y_{3} \sin{\gamma} + c_{y} z_{3}\right) \,\mathbf{\hat{y}}+c_{z} z_{3} \,\mathbf{\hat{z}}$ | (2i) | P I |
| $\mathbf{B_{6}}$ | = | $- x_{3} \, \mathbf{a}_{1}- y_{3} \, \mathbf{a}_{2}- z_{3} \, \mathbf{a}_{3}$ | = | $- \left(a x_{3} + b y_{3} \cos{\gamma} + c_{x} z_{3}\right) \,\mathbf{\hat{x}}- \left(b y_{3} \sin{\gamma} + c_{y} z_{3}\right) \,\mathbf{\hat{y}}- c_{z} z_{3} \,\mathbf{\hat{z}}$ | (2i) | P I |
References
- Y. C. Leung and J. Waser, The Crystal Structure of Phosphorus Diiodide, P$_2$I$_4$, J. Phys. Chem. 60, 539–543 (1956), doi:10.1021/j150539a007.
Prototype Generator
aflow --proto=A2B_aP6_2_2i_i --params=$a,b/a,c/a,\alpha,\beta,\gamma,x_{1},y_{1},z_{1},x_{2},y_{2},z_{2},x_{3},y_{3},z_{3}$