CdI$_{2}$ (Polytype 6H$_{1}$) Structure: AB2_hP9_156_2ab_a2b3c-001
| Prototype | CdI$_{2}$ |
| AFLOW prototype label | AB2_hP9_156_2ab_a2b3c-001 |
| ICSD | none |
| Pearson symbol | hP9 |
| Space group number | 156 |
| Space group symbol | $P3m1$ |
| AFLOW prototype command |
aflow --proto=AB2_hP9_156_2ab_a2b3c-001
--params=$a, \allowbreak c/a, \allowbreak z_{1}, \allowbreak z_{2}, \allowbreak z_{3}, \allowbreak z_{4}, \allowbreak z_{5}, \allowbreak z_{6}, \allowbreak z_{7}, \allowbreak z_{8}, \allowbreak z_{9}$ |
Other compounds with this structure
PdTe$_{2}$, PtTe$_{2}$, SnS$_{2}$ (berndtite)
- This is the $6H_{(a)}$ structure described by (Mitchell, 1956). He did not list the atomic positions, so the atoms are assumed to be evenly placed along the $z$-axis.
- This is an alternative stacking for CdI$_{2}$, which is usually found in the 2H $\omega$ ($C6$) phase.
- The $C27$ structure was also proposed as a structure of CdI$_{2}$, but this is now depreciated.
- (Mitchell, 1956) lists other possible stackings for CdI$_{2}$.
- Space group $P3m1$ #156 allows an arbitary choice for the origin of the $z$-axis. We exploit this to place the first iodine atom at the origin.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \,\mathbf{\hat{y}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $z_{1} \, \mathbf{a}_{3}$ | = | $c z_{1} \,\mathbf{\hat{z}}$ | (1a) | Cd I |
| $\mathbf{B_{2}}$ | = | $z_{2} \, \mathbf{a}_{3}$ | = | $c z_{2} \,\mathbf{\hat{z}}$ | (1a) | Cd II |
| $\mathbf{B_{3}}$ | = | $z_{3} \, \mathbf{a}_{3}$ | = | $c z_{3} \,\mathbf{\hat{z}}$ | (1a) | I I |
| $\mathbf{B_{4}}$ | = | $\frac{1}{3} \, \mathbf{a}_{1}+\frac{2}{3} \, \mathbf{a}_{2}+z_{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+c z_{4} \,\mathbf{\hat{z}}$ | (1b) | Cd III |
| $\mathbf{B_{5}}$ | = | $\frac{1}{3} \, \mathbf{a}_{1}+\frac{2}{3} \, \mathbf{a}_{2}+z_{5} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+c z_{5} \,\mathbf{\hat{z}}$ | (1b) | I II |
| $\mathbf{B_{6}}$ | = | $\frac{1}{3} \, \mathbf{a}_{1}+\frac{2}{3} \, \mathbf{a}_{2}+z_{6} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+c z_{6} \,\mathbf{\hat{z}}$ | (1b) | I III |
| $\mathbf{B_{7}}$ | = | $\frac{2}{3} \, \mathbf{a}_{1}+\frac{1}{3} \, \mathbf{a}_{2}+z_{7} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+c z_{7} \,\mathbf{\hat{z}}$ | (1c) | I IV |
| $\mathbf{B_{8}}$ | = | $\frac{2}{3} \, \mathbf{a}_{1}+\frac{1}{3} \, \mathbf{a}_{2}+z_{8} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+c z_{8} \,\mathbf{\hat{z}}$ | (1c) | I V |
| $\mathbf{B_{9}}$ | = | $\frac{2}{3} \, \mathbf{a}_{1}+\frac{1}{3} \, \mathbf{a}_{2}+z_{9} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+c z_{9} \,\mathbf{\hat{z}}$ | (1c) | I VI |
References
- R. S. Mitchell, Polytypism of Cadmium Iodide and its Relationship to Screw Dislocations: I. Cadmium Iodide Polytypes, Z. Kristallogr. 108, 296–315 (1956), doi:10.1524/zkri.1956.108.3-4.296.
Found in
- P. Villars and K. Cenzual, CdI2 Crystal Structure: Datasheet from
PAULING FILE Multinaries Edition – 2022
(2022). SpringerMaterials (https://materials.springer.com/isp/crystallographic/docs/sd_1012215).
Prototype Generator
aflow --proto=AB2_hP9_156_2ab_a2b3c --params=$a,c/a,z_{1},z_{2},z_{3},z_{4},z_{5},z_{6},z_{7},z_{8},z_{9}$