Moissanite-6H SiC ($B6$) Structure: AB_hP12_186_a2b_a2b-001
| Prototype | SiC |
| AFLOW prototype label | AB_hP12_186_a2b_a2b-001 |
| Strukturbericht designation | $B6$ |
| Mineral name | moissanite |
| ICSD | 156190 |
| Pearson symbol | hP12 |
| Space group number | 186 |
| Space group symbol | $P6_3mc$ |
| AFLOW prototype command |
aflow --proto=AB_hP12_186_a2b_a2b-001
--params=$a, \allowbreak c/a, \allowbreak z_{1}, \allowbreak z_{2}, \allowbreak z_{3}, \allowbreak z_{4}, \allowbreak z_{5}, \allowbreak z_{6}$ |
- This is an alternate stacking (ABCACB) for tetrahedral structures. Compare this to zincblende ($B3$, ABCABC), moissanite-4H ($B5$, ABAC), and wurtzite ($B4$, ABABAB).
- The 6H refers to the fact that there are 6 CSi dimers in a hexagonal unit cell. Zincblende is denoted 3C, and wurtzite is 2H.
- Without loss of generality, we can take any of the $z_{i}$ to be zero. Here we take $z_{2} = 0$ for the silicon (2a) site.
- The ICSD entry is from the later work of (Capitani, 2007).
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \,\mathbf{\hat{y}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $z_{1} \, \mathbf{a}_{3}$ | = | $c z_{1} \,\mathbf{\hat{z}}$ | (2a) | C I |
| $\mathbf{B_{2}}$ | = | $\left(z_{1} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $c \left(z_{1} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (2a) | C I |
| $\mathbf{B_{3}}$ | = | $z_{2} \, \mathbf{a}_{3}$ | = | $c z_{2} \,\mathbf{\hat{z}}$ | (2a) | Si I |
| $\mathbf{B_{4}}$ | = | $\left(z_{2} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $c \left(z_{2} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (2a) | Si I |
| $\mathbf{B_{5}}$ | = | $\frac{1}{3} \, \mathbf{a}_{1}+\frac{2}{3} \, \mathbf{a}_{2}+z_{3} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+c z_{3} \,\mathbf{\hat{z}}$ | (2b) | C II |
| $\mathbf{B_{6}}$ | = | $\frac{2}{3} \, \mathbf{a}_{1}+\frac{1}{3} \, \mathbf{a}_{2}+\left(z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+c \left(z_{3} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (2b) | C II |
| $\mathbf{B_{7}}$ | = | $\frac{1}{3} \, \mathbf{a}_{1}+\frac{2}{3} \, \mathbf{a}_{2}+z_{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+c z_{4} \,\mathbf{\hat{z}}$ | (2b) | C III |
| $\mathbf{B_{8}}$ | = | $\frac{2}{3} \, \mathbf{a}_{1}+\frac{1}{3} \, \mathbf{a}_{2}+\left(z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+c \left(z_{4} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (2b) | C III |
| $\mathbf{B_{9}}$ | = | $\frac{1}{3} \, \mathbf{a}_{1}+\frac{2}{3} \, \mathbf{a}_{2}+z_{5} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+c z_{5} \,\mathbf{\hat{z}}$ | (2b) | Si II |
| $\mathbf{B_{10}}$ | = | $\frac{2}{3} \, \mathbf{a}_{1}+\frac{1}{3} \, \mathbf{a}_{2}+\left(z_{5} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+c \left(z_{5} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (2b) | Si II |
| $\mathbf{B_{11}}$ | = | $\frac{1}{3} \, \mathbf{a}_{1}+\frac{2}{3} \, \mathbf{a}_{2}+z_{6} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+c z_{6} \,\mathbf{\hat{z}}$ | (2b) | Si III |
| $\mathbf{B_{12}}$ | = | $\frac{2}{3} \, \mathbf{a}_{1}+\frac{1}{3} \, \mathbf{a}_{2}+\left(z_{6} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+c \left(z_{6} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (2b) | Si III |
References
- A. Bauer, P. Reischauer, J. Kräusslich, N. Schell, W. Matz, and K. Goetz, Structure refinement of the silicon carbide polytypes 4H and 6H: unambiguous determination of the refinement parameters, Acta Crystallogr. Sect. A 57, 60–67 (2001), doi:10.1107/S0108767300012915.
- N. W. Thibault, Morphological and Structural Crystallography and Optical Properties of Silicon Carbide (SiC) Part II: Structural Crystallography and Optical Properties, Am. Mineral. 29, 327–362 (1944).
- G. C. Capitani, S. D. Pierro, and G. Tempesta, The 6H-SiC structure model: Further refinement from SCXRD data from a terrestrial moissanite, Am. Mineral. 92, 403–407 (2007).
Prototype Generator
aflow --proto=AB_hP12_186_a2b_a2b --params=$a,c/a,z_{1},z_{2},z_{3},z_{4},z_{5},z_{6}$