Co9S8 ($D8_{9}$) Structure : A9B8_cF68_225_af_ce

Picture of Structure; Click for Big Picture
Prototype : Co9S8
AFLOW prototype label : A9B8_cF68_225_af_ce
Strukturbericht designation : $D8_{9}$
Pearson symbol : cF68
Space group number : 225
Space group symbol : $Fm\bar{3}m$
AFLOW prototype command : aflow --proto=A9B8_cF68_225_af_ce
--params=
$a$,$x_{3}$,$x_{4}$


Other compounds with this structure

  • (Fe,Ni)9S8 (pentlandite)

  • (Geller,1962) placed the first Co atom at the ($4b$) Wyckoff position. We have shifted this to the origin, the ($4a$) Wyckoff position.

Face-centered Cubic primitive vectors:

\[ \begin{array}{ccc} \mathbf{a}_1 & = & \frac12 \, a \, \mathbf{\hat{y}} + \frac12 \, a \, \mathbf{\hat{z}} \\ \mathbf{a}_2 & = & \frac12 \, a \, \mathbf{\hat{x}} + \frac12 \, a \, \mathbf{\hat{z}} \\ \mathbf{a}_3 & = & \frac12 \, a \, \mathbf{\hat{x}} + \frac12 \, a \, \mathbf{\hat{y}} \\ \end{array} \]

Basis vectors:

\[ \begin{array}{ccccccc} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{Atom Type} \\ \mathbf{B}_{1} & = & 0 \, \mathbf{a}_{1} + 0 \, \mathbf{a}_{2} + 0 \, \mathbf{a}_{3} & = & 0 \, \mathbf{\hat{x}} + 0 \, \mathbf{\hat{y}} + 0 \, \mathbf{\hat{z}} & \left(4a\right) & \mbox{Co I} \\ \mathbf{B}_{2} & = & \frac{1}{4} \, \mathbf{a}_{1} + \frac{1}{4} \, \mathbf{a}_{2} + \frac{1}{4} \, \mathbf{a}_{3} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + \frac{1}{4}a \, \mathbf{\hat{y}} + \frac{1}{4}a \, \mathbf{\hat{z}} & \left(8c\right) & \mbox{S I} \\ \mathbf{B}_{3} & = & \frac{3}{4} \, \mathbf{a}_{1} + \frac{3}{4} \, \mathbf{a}_{2} + \frac{3}{4} \, \mathbf{a}_{3} & = & \frac{3}{4}a \, \mathbf{\hat{x}} + \frac{3}{4}a \, \mathbf{\hat{y}} + \frac{3}{4}a \, \mathbf{\hat{z}} & \left(8c\right) & \mbox{S I} \\ \mathbf{B}_{4} & = & -x_{3} \, \mathbf{a}_{1} + x_{3} \, \mathbf{a}_{2} + x_{3} \, \mathbf{a}_{3} & = & x_{3}a \, \mathbf{\hat{x}} & \left(24e\right) & \mbox{S II} \\ \mathbf{B}_{5} & = & x_{3} \, \mathbf{a}_{1}-x_{3} \, \mathbf{a}_{2}-x_{3} \, \mathbf{a}_{3} & = & -x_{3}a \, \mathbf{\hat{x}} & \left(24e\right) & \mbox{S II} \\ \mathbf{B}_{6} & = & x_{3} \, \mathbf{a}_{1}-x_{3} \, \mathbf{a}_{2} + x_{3} \, \mathbf{a}_{3} & = & x_{3}a \, \mathbf{\hat{y}} & \left(24e\right) & \mbox{S II} \\ \mathbf{B}_{7} & = & -x_{3} \, \mathbf{a}_{1} + x_{3} \, \mathbf{a}_{2}-x_{3} \, \mathbf{a}_{3} & = & -x_{3}a \, \mathbf{\hat{y}} & \left(24e\right) & \mbox{S II} \\ \mathbf{B}_{8} & = & x_{3} \, \mathbf{a}_{1} + x_{3} \, \mathbf{a}_{2}-x_{3} \, \mathbf{a}_{3} & = & x_{3}a \, \mathbf{\hat{z}} & \left(24e\right) & \mbox{S II} \\ \mathbf{B}_{9} & = & -x_{3} \, \mathbf{a}_{1}-x_{3} \, \mathbf{a}_{2} + x_{3} \, \mathbf{a}_{3} & = & -x_{3}a \, \mathbf{\hat{z}} & \left(24e\right) & \mbox{S II} \\ \mathbf{B}_{10} & = & x_{4} \, \mathbf{a}_{1} + x_{4} \, \mathbf{a}_{2} + x_{4} \, \mathbf{a}_{3} & = & x_{4}a \, \mathbf{\hat{x}} + x_{4}a \, \mathbf{\hat{y}} + x_{4}a \, \mathbf{\hat{z}} & \left(32f\right) & \mbox{Co II} \\ \mathbf{B}_{11} & = & x_{4} \, \mathbf{a}_{1} + x_{4} \, \mathbf{a}_{2}-3x_{4} \, \mathbf{a}_{3} & = & -x_{4}a \, \mathbf{\hat{x}}-x_{4}a \, \mathbf{\hat{y}} + x_{4}a \, \mathbf{\hat{z}} & \left(32f\right) & \mbox{Co II} \\ \mathbf{B}_{12} & = & x_{4} \, \mathbf{a}_{1}-3x_{4} \, \mathbf{a}_{2} + x_{4} \, \mathbf{a}_{3} & = & -x_{4}a \, \mathbf{\hat{x}} + x_{4}a \, \mathbf{\hat{y}}-x_{4}a \, \mathbf{\hat{z}} & \left(32f\right) & \mbox{Co II} \\ \mathbf{B}_{13} & = & -3x_{4} \, \mathbf{a}_{1} + x_{4} \, \mathbf{a}_{2} + x_{4} \, \mathbf{a}_{3} & = & x_{4}a \, \mathbf{\hat{x}}-x_{4}a \, \mathbf{\hat{y}}-x_{4}a \, \mathbf{\hat{z}} & \left(32f\right) & \mbox{Co II} \\ \mathbf{B}_{14} & = & -x_{4} \, \mathbf{a}_{1}-x_{4} \, \mathbf{a}_{2} + 3x_{4} \, \mathbf{a}_{3} & = & x_{4}a \, \mathbf{\hat{x}} + x_{4}a \, \mathbf{\hat{y}}-x_{4}a \, \mathbf{\hat{z}} & \left(32f\right) & \mbox{Co II} \\ \mathbf{B}_{15} & = & -x_{4} \, \mathbf{a}_{1}-x_{4} \, \mathbf{a}_{2}-x_{4} \, \mathbf{a}_{3} & = & -x_{4}a \, \mathbf{\hat{x}}-x_{4}a \, \mathbf{\hat{y}}-x_{4}a \, \mathbf{\hat{z}} & \left(32f\right) & \mbox{Co II} \\ \mathbf{B}_{16} & = & -x_{4} \, \mathbf{a}_{1} + 3x_{4} \, \mathbf{a}_{2}-x_{4} \, \mathbf{a}_{3} & = & x_{4}a \, \mathbf{\hat{x}}-x_{4}a \, \mathbf{\hat{y}} + x_{4}a \, \mathbf{\hat{z}} & \left(32f\right) & \mbox{Co II} \\ \mathbf{B}_{17} & = & 3x_{4} \, \mathbf{a}_{1}-x_{4} \, \mathbf{a}_{2}-x_{4} \, \mathbf{a}_{3} & = & -x_{4}a \, \mathbf{\hat{x}} + x_{4}a \, \mathbf{\hat{y}} + x_{4}a \, \mathbf{\hat{z}} & \left(32f\right) & \mbox{Co II} \\ \end{array} \]

References

Geometry files


Prototype Generator

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