Moissanite–15R (SiC, $B7$) Structure: AB_hR10_160_5a_5a

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Prototype : SiC
AFLOW prototype label : AB_hR10_160_5a_5a
Strukturbericht designation : $B7$
Pearson symbol : hR10
Space group number : 160
Space group symbol : $R3m$
AFLOW prototype command : aflow --proto=AB_hR10_160_5a_5a [--hex]
--params=
$a$,$c/a$,$x_{1}$,$x_{2}$,$x_{3}$,$x_{4}$,$x_{5}$,$x_{6}$,$x_{7}$,$x_{8}$,$x_{9}$,$x_{10}$


  • (Ewald, 1931) and (Thibault, 1944) both call this structure Type I $\alpha$-silicon carbide. The atomic positions are not well determined. We follow (Thibault, 1944) and assume that the (0001) planes of carbon atoms are equally spaced, and that each carbon atom has a silicon atom at a distance of $c/20$ along the $\mathbf{\hat{z}}$ axis.

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:

\[ \begin{array}{ccccccc} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{Atom Type} \\ \mathbf{B}_{1} & = & x_{1} \, \mathbf{a}_{1} + x_{1} \, \mathbf{a}_{2} + x_{1} \, \mathbf{a}_{3} & = & x_{1}c \, \mathbf{\hat{z}} & \left(1a\right) & \mbox{C I} \\ \mathbf{B}_{2} & = & x_{2} \, \mathbf{a}_{1} + x_{2} \, \mathbf{a}_{2} + x_{2} \, \mathbf{a}_{3} & = & x_{2}c \, \mathbf{\hat{z}} & \left(1a\right) & \mbox{C II} \\ \mathbf{B}_{3} & = & x_{3} \, \mathbf{a}_{1} + x_{3} \, \mathbf{a}_{2} + x_{3} \, \mathbf{a}_{3} & = & x_{3}c \, \mathbf{\hat{z}} & \left(1a\right) & \mbox{C III} \\ \mathbf{B}_{4} & = & x_{4} \, \mathbf{a}_{1} + x_{4} \, \mathbf{a}_{2} + x_{4} \, \mathbf{a}_{3} & = & x_{4}c \, \mathbf{\hat{z}} & \left(1a\right) & \mbox{C IV} \\ \mathbf{B}_{5} & = & x_{5} \, \mathbf{a}_{1} + x_{5} \, \mathbf{a}_{2} + x_{5} \, \mathbf{a}_{3} & = & x_{5}c \, \mathbf{\hat{z}} & \left(1a\right) & \mbox{C V} \\ \mathbf{B}_{6} & = & x_{6} \, \mathbf{a}_{1} + x_{6} \, \mathbf{a}_{2} + x_{6} \, \mathbf{a}_{3} & = & x_{6}c \, \mathbf{\hat{z}} & \left(1a\right) & \mbox{Si I} \\ \mathbf{B}_{7} & = & x_{7} \, \mathbf{a}_{1} + x_{7} \, \mathbf{a}_{2} + x_{7} \, \mathbf{a}_{3} & = & x_{7}c \, \mathbf{\hat{z}} & \left(1a\right) & \mbox{Si II} \\ \mathbf{B}_{8} & = & x_{8} \, \mathbf{a}_{1} + x_{8} \, \mathbf{a}_{2} + x_{8} \, \mathbf{a}_{3} & = & x_{8}c \, \mathbf{\hat{z}} & \left(1a\right) & \mbox{Si III} \\ \mathbf{B}_{9} & = & x_{9} \, \mathbf{a}_{1} + x_{9} \, \mathbf{a}_{2} + x_{9} \, \mathbf{a}_{3} & = & x_{9}c \, \mathbf{\hat{z}} & \left(1a\right) & \mbox{Si IV} \\ \mathbf{B}_{10} & = & x_{10} \, \mathbf{a}_{1} + x_{10} \, \mathbf{a}_{2} + x_{10} \, \mathbf{a}_{3} & = & x_{10}c \, \mathbf{\hat{z}} & \left(1a\right) & \mbox{Si V} \\ \end{array} \]

References

  • 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).
  • P. P. Ewald and C. Hermann, eds., Strukturbericht 1913–1928 (Akademische Verlagsgesellschaft M. B. H., Leipzig, 1931).

Found in

  • G. L. Harris, ed., Properties of Silicon Carbide (INSPEC, London, 1995).

Geometry files


Prototype Generator

aflow --proto=AB_hR10_160_5a_5a --params=

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