BC8 (Si) Structure: A_cI16_206_c

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Prototype : Si
AFLOW prototype label : A_cI16_206_c
Strukturbericht designation : None
Pearson symbol : cI16
Space group number : 206
Space group symbol : $\mbox{Ia}\bar{3}$
AFLOW prototype command : aflow --proto=A_cI16_206_c
--params=
$a$,$x_{1}$


  • This is a tetragonally bonded structure which packs more efficiently than diamond. See (Crain, 1995) and references therein. The reference compound chosen here, found in (Wentorf, 1963), is stable in the range 11-16 GPa.

Body-centered Cubic primitive vectors:

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

Basis vectors:

\[ \begin{array}{ccccccc} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{Atom Type} \\ \mathbf{B}_{1} & = &2 x_{1} \, \mathbf{a}_{1}+ 2 x_{1} \, \mathbf{a}_{2}+ 2 x_{1} \, \mathbf{a}_{3}& = &x_{1} \, \, a \, \mathbf{\hat{x}}+ x_{1} \, \, a \, \mathbf{\hat{y}}+ x_{1} \, \, a \, \mathbf{\hat{z}}& \left(16c\right) & \mbox{Si} \\ \mathbf{B}_{2} & = &\frac12 \, \mathbf{a}_{1}+ \left(\frac12 - 2 x_{1}\right) \, \mathbf{a}_{3}& = &- x_{1} \, \, a \, \mathbf{\hat{x}}+ \left(\frac12 - x_{1}\right) \, \, a \, \mathbf{\hat{y}}+ x_{1} \, \, a \, \mathbf{\hat{z}}& \left(16c\right) & \mbox{Si} \\ \mathbf{B}_{3} & = &\left(\frac12 - 2 x_{1}\right) \, \mathbf{a}_{2}+ \frac12 \, \mathbf{a}_{3}& = &\left(\frac12 - x_{1}\right) \, \, a \, \mathbf{\hat{x}}+ x_{1} \, \, a \, \mathbf{\hat{y}}- x_{1} \, \, a \, \mathbf{\hat{z}}& \left(16c\right) & \mbox{Si} \\ \mathbf{B}_{4} & = &\left(\frac12 - 2 x_{1}\right) \, \mathbf{a}_{1}+ \frac12 \, \mathbf{a}_{2}& = &x_{1} \, \, a \, \mathbf{\hat{x}}- x_{1} \, \, a \, \mathbf{\hat{y}}+ \left(\frac12 - x_{1}\right) \, \, a \, \mathbf{\hat{z}}& \left(16c\right) & \mbox{Si} \\ \mathbf{B}_{5} & = &- 2 x_{1} \, \mathbf{a}_{1}- 2 x_{1} \, \mathbf{a}_{2}- 2 x_{1} \, \mathbf{a}_{3}& = &- x_{1} \, \, a \, \mathbf{\hat{x}}- x_{1} \, \, a \, \mathbf{\hat{y}}- x_{1} \, \, a \, \mathbf{\hat{z}}& \left(16c\right) & \mbox{Si} \\ \mathbf{B}_{6} & = &\frac12 \, \mathbf{a}_{1}+ \left(\frac12 + 2 x_{1}\right) \, \mathbf{a}_{3}& = &x_{1} \, \, a \, \mathbf{\hat{x}}+ \left(\frac12 + x_{1}\right) \, \, a \, \mathbf{\hat{y}}- x_{1} \, \, a \, \mathbf{\hat{z}}& \left(16c\right) & \mbox{Si} \\ \mathbf{B}_{7} & = &\left(\frac12 + 2 x_{1}\right) \, \mathbf{a}_{2}+ \frac12 \, \mathbf{a}_{3}& = &\left(\frac12 + x_{1}\right) \, \, a \, \mathbf{\hat{x}}- x_{1} \, \, a \, \mathbf{\hat{y}}+ x_{1} \, \, a \, \mathbf{\hat{z}}& \left(16c\right) & \mbox{Si} \\ \mathbf{B}_{8} & = &\left(\frac12 + 2 x_{1}\right) \, \mathbf{a}_{1}+ \frac12 \, \mathbf{a}_{2}& = &- x_{1} \, \, a \, \mathbf{\hat{x}}+ x_{1} \, \, a \, \mathbf{\hat{y}}+ \left(\frac12 + x_{1}\right) \, \, a \, \mathbf{\hat{z}}& \left(16c\right) & \mbox{Si} \\ \end{array} \]

References

  • J. Crain, G. J. Ackland, and S. J. Clark, Exotic structures of tetrahedral semiconductors, Rep. Prog. Phys. 58, 705–754 (1995), doi:10.1088/0034-4885/58/7/001.

Geometry files


Prototype Generator

aflow --proto=A_cI16_206_c --params=

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