Moissanite–6H SiC ($B6$) Structure: AB_hP12_186_a2b_a2b

Picture of Structure; Click for Big Picture
Prototype : SiC
AFLOW prototype label : AB_hP12_186_a2b_a2b
Strukturbericht designation : $B6$
Pearson symbol : hP12
Space group number : 186
Space group symbol : $\mbox{P6}_{3}\mbox{mc}$
AFLOW prototype command : aflow --proto=AB_hP12_186_a2b_a2b
--params=
$a$,$c/a$,$z_{1}$,$z_{2}$,$z_{3}$,$z_{4}$,$z_{5}$,$z_{6}$


  • This is an alternate stacking (ABCACB) for tetrahedral structures. Compare this to zincblende (ABCABC), moissanite–4H (ABAC), and wurtzite (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. In the pictures here we take $z_{1} = 0$.

Hexagonal primitive vectors:

\[ \begin{array}{ccc} \mathbf{a}_1 & = & \frac12 \, a \, \mathbf{\hat{x}} - \frac{\sqrt{3}}{2} \, a \, \mathbf{\hat{y}} \\ \mathbf{a}_2 & = & \frac12 \, a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2} \, a \, \mathbf{\hat{y}} \\ \mathbf{a}_3 & = & c \, \mathbf{\hat{z}}\\ \end{array} \]

Basis vectors:

\[ \begin{array}{ccccccc} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{Atom Type} \\ \mathbf{B}_{1}& = &z_{1} \, \mathbf{a}_{3}& = &z_{1} \, c \, \mathbf{\hat{z}}& \left(2a\right) & \mbox{C I} \\ \mathbf{B}_{2}& = &\left(\frac12 + z_{1}\right) \, \mathbf{a}_{3}& = &\left(\frac12 + z_{1}\right) \, c \, \mathbf{\hat{z}}& \left(2a\right) & \mbox{C I} \\ \mathbf{B}_{3}& = &z_{2} \, \mathbf{a}_{3}& = &z_{2} \, c \, \mathbf{\hat{z}}& \left(2a\right) & \mbox{Si I} \\ \mathbf{B}_{4}& = &\left(\frac12 + z_{2}\right) \, \mathbf{a}_{3}& = &\left(\frac12 + z_{2}\right) \, c \, \mathbf{\hat{z}}& \left(2a\right) & \mbox{Si I} \\ \mathbf{B}_{5}& = &\frac13 \, \mathbf{a}_{1}+ \frac23 \, \mathbf{a}_{2}+ z_{3} \, \mathbf{a}_{3}& = &\frac12 \, a \, \mathbf{\hat{x}}+ \frac1{2\sqrt3} \, a \, \mathbf{\hat{y}}+ z_{3} \, c \, \mathbf{\hat{z}}& \left(2b\right) & \mbox{C II} \\ \mathbf{B}_{6}& = &\frac23 \, \mathbf{a}_{1}+ \frac13 \, \mathbf{a}_{2}+ \left(\frac12 + z_{3}\right) \, \mathbf{a}_{3}& = &\frac12 \, a \, \mathbf{\hat{x}}- \frac1{2\sqrt3} \, a \, \mathbf{\hat{y}}+ \left(\frac12 + z_{3}\right) \, c \, \mathbf{\hat{z}}& \left(2b\right) & \mbox{C II} \\ \mathbf{B}_{7}& = &\frac13 \, \mathbf{a}_{1}+ \frac23 \, \mathbf{a}_{2}+ z_{4} \, \mathbf{a}_{3}& = &\frac12 \, a \, \mathbf{\hat{x}}+ \frac1{2\sqrt3} \, a \, \mathbf{\hat{y}}+ z_{4} \, c \, \mathbf{\hat{z}}& \left(2b\right) & \mbox{C III} \\ \mathbf{B}_{8}& = &\frac23 \, \mathbf{a}_{1}+ \frac13 \, \mathbf{a}_{2}+ \left(\frac12 + z_{4}\right) \, \mathbf{a}_{3}& = &\frac12 \, a \, \mathbf{\hat{x}}- \frac1{2\sqrt3} \, a \, \mathbf{\hat{y}}+ \left(\frac12 + z_{4}\right) \, c \, \mathbf{\hat{z}}& \left(2b\right) & \mbox{C III} \\ \mathbf{B}_{9}& = &\frac13 \, \mathbf{a}_{1}+ \frac23 \, \mathbf{a}_{2}+ z_{5} \, \mathbf{a}_{3}& = &\frac12 \, a \, \mathbf{\hat{x}}+ \frac1{2\sqrt3} \, a \, \mathbf{\hat{y}}+ z_{5} \, c \, \mathbf{\hat{z}}& \left(2b\right) & \mbox{Si II} \\ \mathbf{B}_{10}& = &\frac23 \, \mathbf{a}_{1}+ \frac13 \, \mathbf{a}_{2}+ \left(\frac12 + z_{5}\right) \, \mathbf{a}_{3}& = &\frac12 \, a \, \mathbf{\hat{x}}- \frac1{2\sqrt3} \, a \, \mathbf{\hat{y}}+ \left(\frac12 + z_{5}\right) \, c \, \mathbf{\hat{z}}& \left(2b\right) & \mbox{Si II} \\ \mathbf{B}_{11}& = &\frac13 \, \mathbf{a}_{1}+ \frac23 \, \mathbf{a}_{2}+ z_{6} \, \mathbf{a}_{3}& = &\frac12 \, a \, \mathbf{\hat{x}}+ \frac1{2\sqrt3} \, a \, \mathbf{\hat{y}}+ z_{6} \, c \, \mathbf{\hat{z}}& \left(2b\right) & \mbox{Si III} \\ \mathbf{B}_{12}& = &\frac23 \, \mathbf{a}_{1}+ \frac13 \, \mathbf{a}_{2}+ \left(\frac12 + z_{6}\right) \, \mathbf{a}_{3}& = &\frac12 \, a \, \mathbf{\hat{x}}- \frac1{2\sqrt3} \, a \, \mathbf{\hat{y}}+ \left(\frac12 + z_{6}\right) \, c \, \mathbf{\hat{z}}& \left(2b\right) & \mbox{Si III} \\ \end{array} \]

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.

Geometry files


Prototype Generator

aflow --proto=AB_hP12_186_a2b_a2b --params=

Species:

Running:

Output: