Moissanite 9R Crystal Structure: AB_hR6_160_3a_3a

Picture of Structure; Click for Big Picture
Prototype : CSi
AFLOW prototype label : AB_hR6_160_3a_3a
Strukturbericht designation : None
Pearson symbol : hR6
Space group number : 160
Space group symbol : $\mbox{R3m}$
AFLOW prototype command : aflow --proto=AB_hR6_160_3a_3a [--hex]
--params=
$a$,$c/a$,$x_{1}$,$x_{2}$,$x_{3}$,$x_{4}$,$x_{5}$,$x_{6}$


  • We will loosely use the name moissanite to describe any tetrahedrally bonded silicon carbide compound that does not have another name. The labels 4H, 6H, 9R, etc., refer to the repeat stacking distance in the hexagonal unit cell, while H and R refer to the primitive hexagonal and rhombohedral lattices, respectively. The label C refers to a cubic unit cell, which is a special case of R. Note that 2, 3, 6, 9, etc., refers to the number of C–Si dimers that are stacked. Moissanite 9R is a hypothetical alternate stacking (ABCBCACAB) for tetrahedral structures. Compare this to wurtzite (ABABAB, 2H), zincblende (ABCABC, 3C), moissanite 4H (ABAC) and moissanite 6H (ABCACB). Hexagonal settings of this structure can be obtained with the option ––hex.

Rhombohedral primitive vectors:

\[ \begin{array}{ccc} \mathbf{a}_1 & = & ~ \frac12 \, a \, \mathbf{\hat{x}} - \frac{1}{2\sqrt{3}} \, a \, \mathbf{\hat{y}} + \frac13 \, c \, \mathbf{\hat{z}} \\ \mathbf{a}_2 & = & \frac{1}{\sqrt{3}} \, a \, \mathbf{\hat{y}} + \frac13 \, c \, \mathbf{\hat{z}} \\ \mathbf{a}_3 & = & - \frac12 \, a \, \mathbf{\hat{x}} - \frac{1}{2\sqrt{3}} \, a \, \mathbf{\hat{y}} + \frac13 \, c \, \mathbf{\hat{z}} \\ \end{array} \]

Basis vectors:

\[ \begin{array}{ccccccc} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{Atom Type} \\ \mathbf{B}_{1} & =& x_{1} \, \mathbf{a}_{1} + x_{1} \, \mathbf{a}_{2} + x_{1} \, \mathbf{a}_{3}& =& x_{1} \, c \, \mathbf{\hat{z}}& \left(1a\right) & \mbox{C I} \\ \mathbf{B}_{2} & =& x_{2} \, \mathbf{a}_{1} + x_{2} \, \mathbf{a}_{2} + x_{2} \, \mathbf{a}_{3}& =& x_{2} \, c \, \mathbf{\hat{z}}& \left(1a\right) & \mbox{C II} \\ \mathbf{B}_{3} & =& x_{3} \, \mathbf{a}_{1} + x_{3} \, \mathbf{a}_{2} + x_{3} \, \mathbf{a}_{3}& =& x_{3} \, c \, \mathbf{\hat{z}}& \left(1a\right) & \mbox{C III} \\ \mathbf{B}_{4} & =& x_{4} \, \mathbf{a}_{1} + x_{4} \, \mathbf{a}_{2} + x_{4} \, \mathbf{a}_{3}& =& x_{4} \, c \, \mathbf{\hat{z}}& \left(1a\right) & \mbox{Si I} \\ \mathbf{B}_{5} & =& x_{5} \, \mathbf{a}_{1} + x_{5} \, \mathbf{a}_{2} + x_{5} \, \mathbf{a}_{3}& =& x_{5} \, c \, \mathbf{\hat{z}}& \left(1a\right) & \mbox{Si II} \\ \mathbf{B}_{6} & =& x_{6} \, \mathbf{a}_{1} + x_{6} \, \mathbf{a}_{2} + x_{6} \, \mathbf{a}_{3}& =& x_{6} \, c \, \mathbf{\hat{z}}& \left(1a\right) & \mbox{Si III} \\ \end{array} \]

References

Geometry files


Prototype Generator

aflow --proto=AB_hR6_160_3a_3a --params=

Species:

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Output: