$C27$ (CdI2) (questionable) Structure : AB2_hP6_186_b_ab
| Prototype | : | CdI2 |
| AFLOW prototype label | : | AB2_hP6_186_b_ab |
| Strukturbericht designation | : | $C27$ |
| Pearson symbol | : | hP6 |
| Space group number | : | 186 |
| Space group symbol | : | $P6_{3}mc$ |
| AFLOW prototype command | : | aflow --proto=AB2_hP6_186_b_ab --params=$a$,$c/a$,$z_{1}$,$z_{2}$,$z_{3}$ |
- This is a modification of the $C6$ ($\omega$ phase) CdI$_2$ structure proposed by (Hassel, 1933) to explain extra lines found in the x–ray spectra. This structure was never accepted by most researchers and does not appear in modern lists of Strukturbericht symbols, although (Parthé, 1993) lists it as a stacking varient of CdI2. We include it here as part of the historical record.
- Hassel originally placed a Cd atom at the origin, however both (Gottfried, 1937) and FINDSYM shift the origin as shown.
Hexagonal primitive vectors:
\[ \begin{array}{ccc} \mathbf{a}_1 & = & \frac12 \, a \, \mathbf{\hat{x}} - \frac{\sqrt3}2 \, a \, \mathbf{\hat{y}} \\ \mathbf{a}_2 & = & \frac12 \, a \, \mathbf{\hat{x}} + \frac{\sqrt3}2 \, a \, \mathbf{\hat{y}} \\ \mathbf{a}_3 & = & c \, \mathbf{\hat{z}} \\ \end{array} \]
Basis vectors:
\[ \begin{array}{ccccccc} & & \text{Lattice Coordinates} & & \text{Cartesian Coordinates} &\text{Wyckoff Position} & \text{Atom Type} \\ \mathbf{B}_{1} & = & z_{1} \, \mathbf{a}_{3} & = & z_{1}c \, \mathbf{\hat{z}} & \left(2a\right) & \text{I I} \\ \mathbf{B}_{2} & = & \left(\frac{1}{2} +z_{1}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +z_{1}\right)c \, \mathbf{\hat{z}} & \left(2a\right) & \text{I I} \\ \mathbf{B}_{3} & = & \frac{1}{3} \, \mathbf{a}_{1} + \frac{2}{3} \, \mathbf{a}_{2} + z_{2} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + \frac{1}{2\sqrt{3}}a \, \mathbf{\hat{y}} + z_{2}c \, \mathbf{\hat{z}} & \left(2b\right) & \text{Cd} \\ \mathbf{B}_{4} & = & \frac{2}{3} \, \mathbf{a}_{1} + \frac{1}{3} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{2}\right) \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}}- \frac{1}{2\sqrt{3}}a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{2}\right)c \, \mathbf{\hat{z}} & \left(2b\right) & \text{Cd} \\ \mathbf{B}_{5} & = & \frac{1}{3} \, \mathbf{a}_{1} + \frac{2}{3} \, \mathbf{a}_{2} + z_{3} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + \frac{1}{2\sqrt{3}}a \, \mathbf{\hat{y}} + z_{3}c \, \mathbf{\hat{z}} & \left(2b\right) & \text{I II} \\ \mathbf{B}_{6} & = & \frac{2}{3} \, \mathbf{a}_{1} + \frac{1}{3} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{3}\right) \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}}- \frac{1}{2\sqrt{3}}a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{3}\right)c \, \mathbf{\hat{z}} & \left(2b\right) & \text{I II} \\ \end{array} \]References
- O. Hassel, Zur Kristallstruktur des Cadmiumjodids CdJ2, Z. Physik. Chem. 22B, 333–334 (1933), doi:10.1515/zpch-1933-2228.
- E. Parthé, L. Gelato, B. Chabot, M. Penso, K. Cenzual, and R. Gladyshevskii, in Standardized Data and Crystal Chemical Characterization of Inorganic Structure Types (Springer–Verlag, Berlin, Heidelberg, 1993), Gmelin Handbook of Inorganic and Organometallic Chemistry, vol. 2, chap. Crystal Chemical Characterization of Inorganic Structure Types, 8 edn., doi:10.1007/978-3-662-02909-1_3.
Found in
- C. Gottfried and F. Schossberger, eds., Strukturbericht Band III 1933–1935 (Akademische Verlagsgesellschaft M. B. H., Leipzig, 1937).