Si46 Clathrate Structure: A_cP46_223_dik

Picture of Structure; Click for Big Picture
Prototype : Si
AFLOW prototype label : A_cP46_223_dik
Strukturbericht designation : None
Pearson symbol : cP46
Space group number : 223
Space group symbol : $\mbox{Pm}\bar{3}\mbox{n}$
AFLOW prototype command : aflow --proto=A_cP46_223_dik
--params=
$a$,$x_{2}$,$y_{3}$,$z_{3}$


Other compounds with this structure

  • beta–W, Nb3Al, CdV3, Cr3O, Ti3Sb, Ti3Au, many more

  • Silicon clathrates are open structures of pentagonal dodecahedra connected so that all of the silicon atoms have sp$^{3}$ bonding. In nature these structures are stabilized by alkali impurity atoms. This structure and the Si34 structure are proposed pure silicon clathrate structures. For more information about these structures and their possible stability, see (Adams, 1994). Note that this is a theoretical description of a possible silicon clathrate crystal.

Simple Cubic primitive vectors:

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

Basis vectors:

\[ \begin{array}{ccccccc} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{Atom Type} \\ \mathbf{B}_{1} & = &\frac14 \, \mathbf{a}_{1}+ \frac12 \, \mathbf{a}_{2}& = &\frac14 \, a \, \mathbf{\hat{x}}+ \frac12 \, a \, \mathbf{\hat{y}}& \left(6d\right) & \mbox{Si I} \\ \mathbf{B}_{2} & = &\frac34 \, \mathbf{a}_{1}+ \frac12 \, \mathbf{a}_{2}& = &\frac34 \, a \, \mathbf{\hat{x}}+ \frac12 \, a \, \mathbf{\hat{y}}& \left(6d\right) & \mbox{Si I} \\ \mathbf{B}_{3} & = &\frac14 \, \mathbf{a}_{2}+ \frac12 \, \mathbf{a}_{3}& = &\frac14 \, a \, \mathbf{\hat{y}}+ \frac12 \, a \, \mathbf{\hat{z}}& \left(6d\right) & \mbox{Si I} \\ \mathbf{B}_{4} & = &\frac34 \, \mathbf{a}_{2}+ \frac12 \, \mathbf{a}_{3}& = &\frac34 \, a \, \mathbf{\hat{y}}+ \frac12 \, a \, \mathbf{\hat{z}}& \left(6d\right) & \mbox{Si I} \\ \mathbf{B}_{5} & = &\frac12 \, \mathbf{a}_{1}+ \frac14 \, \mathbf{a}_{3}& = &\frac12 \, a \, \mathbf{\hat{x}}+ \frac14 \, a \, \mathbf{\hat{z}}& \left(6d\right) & \mbox{Si I} \\ \mathbf{B}_{6} & = &\frac12 \, \mathbf{a}_{1}+ \frac34 \, \mathbf{a}_{3}& = &\frac12 \, a \, \mathbf{\hat{x}}+ \frac34 \, a \, \mathbf{\hat{z}}& \left(6d\right) & \mbox{Si I} \\ \mathbf{B}_{7} & = &x_{2} \, \mathbf{a}_{1}+ x_{2} \, \mathbf{a}_{2}+ x_{2} \, \mathbf{a}_{3}& = &x_{2} \, a \, \mathbf{\hat{x}}+ x_{2} \, a \, \mathbf{\hat{y}}+ x_{2} \, a \, \mathbf{\hat{z}}& \left(16i\right) & \mbox{Si II} \\ \mathbf{B}_{8} & = &- x_{2} \, \mathbf{a}_{1}- x_{2} \, \mathbf{a}_{2}+ x_{2} \, \mathbf{a}_{3}& = &- x_{2} \, a \, \mathbf{\hat{x}}- x_{2} \, a \, \mathbf{\hat{y}}+ x_{2} \, a \, \mathbf{\hat{z}}& \left(16i\right) & \mbox{Si II} \\ \mathbf{B}_{9} & = &- x_{2} \, \mathbf{a}_{1}+ x_{2} \, \mathbf{a}_{2}- x_{2} \, \mathbf{a}_{3}& = &- x_{2} \, a \, \mathbf{\hat{x}}+ x_{2} \, a \, \mathbf{\hat{y}}- x_{2} \, a \, \mathbf{\hat{z}}& \left(16i\right) & \mbox{Si II} \\ \mathbf{B}_{10} & = &x_{2} \, \mathbf{a}_{1}- x_{2} \, \mathbf{a}_{2}- x_{2} \, \mathbf{a}_{3}& = &x_{2} \, a \, \mathbf{\hat{x}}- x_{2} \, a \, \mathbf{\hat{y}}- x_{2} \, a \, \mathbf{\hat{z}}& \left(16i\right) & \mbox{Si II} \\ \mathbf{B}_{11} & = &\left(\frac12 + x_{2}\right) \, \mathbf{a}_{1}+ \left(\frac12 + x_{2}\right) \, \mathbf{a}_{2}+ \left(\frac12 - x_{2}\right) \, \mathbf{a}_{3}& = &\left(\frac12 + x_{2}\right) \, a \, \mathbf{\hat{x}}+ \left(\frac12 + x_{2}\right) \, a \, \mathbf{\hat{y}}+ \left(\frac12 - x_{2}\right) \, a \, \mathbf{\hat{z}}& \left(16i\right) & \mbox{Si II} \\ \mathbf{B}_{12} & = &\left(\frac12 - x_{2}\right) \, \mathbf{a}_{1}+ \left(\frac12 - x_{2}\right) \, \mathbf{a}_{2}+ \left(\frac12 - x_{2}\right) \, \mathbf{a}_{3}& = &\left(\frac12 - x_{2}\right) \, a \, \mathbf{\hat{x}}+ \left(\frac12 - x_{2}\right) \, a \, \mathbf{\hat{y}}+ \left(\frac12 - x_{2}\right) \, a \, \mathbf{\hat{z}}& \left(16i\right) & \mbox{Si II} \\ \mathbf{B}_{13} & = &\left(\frac12 + x_{2}\right) \, \mathbf{a}_{1}+ \left(\frac12 - x_{2}\right) \, \mathbf{a}_{2}+ \left(\frac12 + x_{2}\right) \, \mathbf{a}_{3}& = &\left(\frac12 + x_{2}\right) \, a \, \mathbf{\hat{x}}+ \left(\frac12 - x_{2}\right) \, a \, \mathbf{\hat{y}}+ \left(\frac12 + x_{2}\right) \, a \, \mathbf{\hat{z}}& \left(16i\right) & \mbox{Si II} \\ \mathbf{B}_{14} & = &\left(\frac12 - x_{2}\right) \, \mathbf{a}_{1}+ \left(\frac12 + x_{2}\right) \, \mathbf{a}_{2}+ \left(\frac12 + x_{2}\right) \, \mathbf{a}_{3}& = &\left(\frac12 - x_{2}\right) \, a \, \mathbf{\hat{x}}+ \left(\frac12 + x_{2}\right) \, a \, \mathbf{\hat{y}}+ \left(\frac12 + x_{2}\right) \, a \, \mathbf{\hat{z}}& \left(16i\right) & \mbox{Si II} \\ \mathbf{B}_{15} & = &- x_{2} \, \mathbf{a}_{1}- x_{2} \, \mathbf{a}_{2}- x_{2} \, \mathbf{a}_{3}& = &- x_{2} \, a \, \mathbf{\hat{x}}- x_{2} \, a \, \mathbf{\hat{y}}- x_{2} \, a \, \mathbf{\hat{z}}& \left(16i\right) & \mbox{Si II} \\ \mathbf{B}_{16} & = &x_{2} \, \mathbf{a}_{1}+ x_{2} \, \mathbf{a}_{2}- x_{2} \, \mathbf{a}_{3}& = &x_{2} \, a \, \mathbf{\hat{x}}+ x_{2} \, a \, \mathbf{\hat{y}}- x_{2} \, a \, \mathbf{\hat{z}}& \left(16i\right) & \mbox{Si II} \\ \mathbf{B}_{17} & = &x_{2} \, \mathbf{a}_{1}- x_{2} \, \mathbf{a}_{2}+ x_{2} \, \mathbf{a}_{3}& = &x_{2} \, a \, \mathbf{\hat{x}}- x_{2} \, a \, \mathbf{\hat{y}}+ x_{2} \, a \, \mathbf{\hat{z}}& \left(16i\right) & \mbox{Si II} \\ \mathbf{B}_{18} & = &- x_{2} \, \mathbf{a}_{1}+ x_{2} \, \mathbf{a}_{2}+ x_{2} \, \mathbf{a}_{3}& = &- x_{2} \, a \, \mathbf{\hat{x}}+ x_{2} \, a \, \mathbf{\hat{y}}+ x_{2} \, a \, \mathbf{\hat{z}}& \left(16i\right) & \mbox{Si II} \\ \mathbf{B}_{19} & = &\left(\frac12 - x_{2}\right) \, \mathbf{a}_{1}+ \left(\frac12 - x_{2}\right) \, \mathbf{a}_{2}+ \left(\frac12 + x_{2}\right) \, \mathbf{a}_{3}& = &\left(\frac12 - x_{2}\right) \, a \, \mathbf{\hat{x}}+ \left(\frac12 - x_{2}\right) \, a \, \mathbf{\hat{y}}+ \left(\frac12 + x_{2}\right) \, a \, \mathbf{\hat{z}}& \left(16i\right) & \mbox{Si II} \\ \mathbf{B}_{20} & = &\left(\frac12 + x_{2}\right) \, \mathbf{a}_{1}+ \left(\frac12 + x_{2}\right) \, \mathbf{a}_{2}+ \left(\frac12 + x_{2}\right) \, \mathbf{a}_{3}& = &\left(\frac12 + x_{2}\right) \, a \, \mathbf{\hat{x}}+ \left(\frac12 + x_{2}\right) \, a \, \mathbf{\hat{y}}+ \left(\frac12 + x_{2}\right) \, a \, \mathbf{\hat{z}}& \left(16i\right) & \mbox{Si II} \\ \mathbf{B}_{21} & = &\left(\frac12 - x_{2}\right) \, \mathbf{a}_{1}+ \left(\frac12 + x_{2}\right) \, \mathbf{a}_{2}+ \left(\frac12 - x_{2}\right) \, \mathbf{a}_{3}& = &\left(\frac12 - x_{2}\right) \, a \, \mathbf{\hat{x}}+ \left(\frac12 + x_{2}\right) \, a \, \mathbf{\hat{y}}+ \left(\frac12 - x_{2}\right) \, a \, \mathbf{\hat{z}}& \left(16i\right) & \mbox{Si II} \\ \mathbf{B}_{22} & = &\left(\frac12 + x_{2}\right) \, \mathbf{a}_{1}+ \left(\frac12 - x_{2}\right) \, \mathbf{a}_{2}+ \left(\frac12 - x_{2}\right) \, \mathbf{a}_{3}& = &\left(\frac12 + x_{2}\right) \, a \, \mathbf{\hat{x}}+ \left(\frac12 - x_{2}\right) \, a \, \mathbf{\hat{y}}+ \left(\frac12 - x_{2}\right) \, a \, \mathbf{\hat{z}}& \left(16i\right) & \mbox{Si II} \\ \mathbf{B}_{23} & = &y_{3} \, \mathbf{a}_{2}+ z_{3} \, \mathbf{a}_{3}& = &y_{3} \, a \, \mathbf{\hat{y}}+ z_{3} \, a \, \mathbf{\hat{z}}& \left(24k\right) & \mbox{Si III} \\ \mathbf{B}_{24} & = &- y_{3} \, \mathbf{a}_{2}+ z_{3} \, \mathbf{a}_{3}& = &- y_{3} \, a \, \mathbf{\hat{y}}+ z_{3} \, a \, \mathbf{\hat{z}}& \left(24k\right) & \mbox{Si III} \\ \mathbf{B}_{25} & = &y_{3} \, \mathbf{a}_{2}- z_{3} \, \mathbf{a}_{3}& = &y_{3} \, a \, \mathbf{\hat{y}}- z_{3} \, a \, \mathbf{\hat{z}}& \left(24k\right) & \mbox{Si III} \\ \mathbf{B}_{26} & = &- y_{3} \, \mathbf{a}_{2}- z_{3} \, \mathbf{a}_{3}& = &- y_{3} \, a \, \mathbf{\hat{y}}- z_{3} \, a \, \mathbf{\hat{z}}& \left(24k\right) & \mbox{Si III} \\ \mathbf{B}_{27} & = &z_{3} \, \mathbf{a}_{1}+ y_{3} \, \mathbf{a}_{3}& = &z_{3} \, a \, \mathbf{\hat{x}}+ y_{3} \, a \, \mathbf{\hat{z}}& \left(24k\right) & \mbox{Si III} \\ \mathbf{B}_{28} & = &- z_{3} \, \mathbf{a}_{1}+ y_{3} \, \mathbf{a}_{3}& = &- z_{3} \, a \, \mathbf{\hat{x}}+ y_{3} \, a \, \mathbf{\hat{z}}& \left(24k\right) & \mbox{Si III} \\ \mathbf{B}_{29} & = &z_{3} \, \mathbf{a}_{1}- y_{3} \, \mathbf{a}_{3}& = &z_{3} \, a \, \mathbf{\hat{x}}- y_{3} \, a \, \mathbf{\hat{z}}& \left(24k\right) & \mbox{Si III} \\ \mathbf{B}_{30} & = &- z_{3} \, \mathbf{a}_{1}- y_{3} \, \mathbf{a}_{3}& = &- z_{3} \, a \, \mathbf{\hat{x}}- y_{3} \, a \, \mathbf{\hat{z}}& \left(24k\right) & \mbox{Si III} \\ \mathbf{B}_{31} & = &y_{3} \, \mathbf{a}_{1}+ z_{3} \, \mathbf{a}_{2}& = &y_{3} \, a \, \mathbf{\hat{x}}+ z_{3} \, a \, \mathbf{\hat{y}}& \left(24k\right) & \mbox{Si III} \\ \mathbf{B}_{32} & = &- y_{3} \, \mathbf{a}_{1}+ z_{3} \, \mathbf{a}_{2}& = &- y_{3} \, a \, \mathbf{\hat{x}}+ z_{3} \, a \, \mathbf{\hat{y}}& \left(24k\right) & \mbox{Si III} \\ \mathbf{B}_{33} & = &y_{3} \, \mathbf{a}_{1}- z_{3} \, \mathbf{a}_{2}& = &y_{3} \, a \, \mathbf{\hat{x}}- z_{3} \, a \, \mathbf{\hat{y}}& \left(24k\right) & \mbox{Si III} \\ \mathbf{B}_{34} & = &- y_{3} \, \mathbf{a}_{1}- z_{3} \, \mathbf{a}_{2}& = &- y_{3} \, a \, \mathbf{\hat{x}}- z_{3} \, a \, \mathbf{\hat{y}}& \left(24k\right) & \mbox{Si III} \\ \mathbf{B}_{35} & = &\left(\frac12 + y_{3}\right) \, \mathbf{a}_{1}+ \frac12 \, \mathbf{a}_{2}+ \left(\frac12 - z_{3}\right) \, \mathbf{a}_{3}& = &\left(\frac12 + y_{3}\right) \, a \, \mathbf{\hat{x}}+ \frac12 \, a \, \mathbf{\hat{y}}+ \left(\frac12 - z_{3}\right) \, a \, \mathbf{\hat{z}}& \left(24k\right) & \mbox{Si III} \\ \mathbf{B}_{36} & = &\left(\frac12 - y_{3}\right) \, \mathbf{a}_{1}+ \frac12 \, \mathbf{a}_{2}+ \left(\frac12 - z_{3}\right) \, \mathbf{a}_{3}& = &\left(\frac12 - y_{3}\right) \, a \, \mathbf{\hat{x}}+ \frac12 \, a \, \mathbf{\hat{y}}+ \left(\frac12 - z_{3}\right) \, a \, \mathbf{\hat{z}}& \left(24k\right) & \mbox{Si III} \\ \mathbf{B}_{37} & = &\left(\frac12 + y_{3}\right) \, \mathbf{a}_{1}+ \frac12 \, \mathbf{a}_{2}+ \left(\frac12 + z_{3}\right) \, \mathbf{a}_{3}& = &\left(\frac12 + y_{3}\right) \, a \, \mathbf{\hat{x}}+ \frac12 \, a \, \mathbf{\hat{y}}+ \left(\frac12 + z_{3}\right) \, a \, \mathbf{\hat{z}}& \left(24k\right) & \mbox{Si III} \\ \mathbf{B}_{38} & = &\left(\frac12 - y_{3}\right) \, \mathbf{a}_{1}+ \frac12 \, \mathbf{a}_{2}+ \left(\frac12 + z_{3}\right) \, \mathbf{a}_{3}& = &\left(\frac12 - y_{3}\right) \, a \, \mathbf{\hat{x}}+ \frac12 \, a \, \mathbf{\hat{y}}+ \left(\frac12 + z_{3}\right) \, a \, \mathbf{\hat{z}}& \left(24k\right) & \mbox{Si III} \\ \mathbf{B}_{39} & = &\frac12 \, \mathbf{a}_{1}+ \left(\frac12 + z_{3}\right) \, \mathbf{a}_{2}+ \left(\frac12 - y_{3}\right) \, \mathbf{a}_{3}& = &\frac12 \, a \, \mathbf{\hat{x}}+ \left(\frac12 + z_{3}\right) \, a \, \mathbf{\hat{y}}+ \left(\frac12 - y_{3}\right) \, a \, \mathbf{\hat{z}}& \left(24k\right) & \mbox{Si III} \\ \mathbf{B}_{40} & = &\frac12 \, \mathbf{a}_{1}+ \left(\frac12 + z_{3}\right) \, \mathbf{a}_{2}+ \left(\frac12 + y_{3}\right) \, \mathbf{a}_{3}& = &\frac12 \, a \, \mathbf{\hat{x}}+ \left(\frac12 + z_{3}\right) \, a \, \mathbf{\hat{y}}+ \left(\frac12 + y_{3}\right) \, a \, \mathbf{\hat{z}}& \left(24k\right) & \mbox{Si III} \\ \mathbf{B}_{41} & = &\frac12 \, \mathbf{a}_{1}+ \left(\frac12 - z_{3}\right) \, \mathbf{a}_{2}+ \left(\frac12 - y_{3}\right) \, \mathbf{a}_{3}& = &\frac12 \, a \, \mathbf{\hat{x}}+ \left(\frac12 - z_{3}\right) \, a \, \mathbf{\hat{y}}+ \left(\frac12 - y_{3}\right) \, a \, \mathbf{\hat{z}}& \left(24k\right) & \mbox{Si III} \\ \mathbf{B}_{42} & = &\frac12 \, \mathbf{a}_{1}+ \left(\frac12 - z_{3}\right) \, \mathbf{a}_{2}+ \left(\frac12 + y_{3}\right) \, \mathbf{a}_{3}& = &\frac12 \, a \, \mathbf{\hat{x}}+ \left(\frac12 - z_{3}\right) \, a \, \mathbf{\hat{y}}+ \left(\frac12 + y_{3}\right) \, a \, \mathbf{\hat{z}}& \left(24k\right) & \mbox{Si III} \\ \mathbf{B}_{43} & = &\left(\frac12 + z_{3}\right) \, \mathbf{a}_{1}+ \left(\frac12 - y_{3}\right) \, \mathbf{a}_{2}+ \frac12 \, \mathbf{a}_{3}& = &\left(\frac12 + z_{3}\right) \, a \, \mathbf{\hat{x}}+ \left(\frac12 - y_{3}\right) \, a \, \mathbf{\hat{y}}+ \frac12 \, a \, \mathbf{\hat{z}}& \left(24k\right) & \mbox{Si III} \\ \mathbf{B}_{44} & = &\left(\frac12 + z_{3}\right) \, \mathbf{a}_{1}+ \left(\frac12 + y_{3}\right) \, \mathbf{a}_{2}+ \frac12 \, \mathbf{a}_{3}& = &\left(\frac12 + z_{3}\right) \, a \, \mathbf{\hat{x}}+ \left(\frac12 + y_{3}\right) \, a \, \mathbf{\hat{y}}+ \frac12 \, a \, \mathbf{\hat{z}}& \left(24k\right) & \mbox{Si III} \\ \mathbf{B}_{45} & = &\left(\frac12 - z_{3}\right) \, \mathbf{a}_{1}+ \left(\frac12 - y_{3}\right) \, \mathbf{a}_{2}+ \frac12 \, \mathbf{a}_{3}& = &\left(\frac12 - z_{3}\right) \, a \, \mathbf{\hat{x}}+ \left(\frac12 - y_{3}\right) \, a \, \mathbf{\hat{y}}+ \frac12 \, a \, \mathbf{\hat{z}}& \left(24k\right) & \mbox{Si III} \\ \mathbf{B}_{46} & = &\left(\frac12 - z_{3}\right) \, \mathbf{a}_{1}+ \left(\frac12 + y_{3}\right) \, \mathbf{a}_{2}+ \frac12 \, \mathbf{a}_{3}& = &\left(\frac12 - z_{3}\right) \, a \, \mathbf{\hat{x}}+ \left(\frac12 + y_{3}\right) \, a \, \mathbf{\hat{y}}+ \frac12 \, a \, \mathbf{\hat{z}}& \left(24k\right) & \mbox{Si III} \\ \end{array} \]

References

  • G. B. Adams, M. O'Keeffe, A. A. Demkov, O. F. Sankey, and Y.–M. Huang, Wide–band–gap Si in open fourfold–coordinated clathrate structures, Phys. Rev. B 49, 8048–8053 (1994), doi:10.1103/PhysRevB.49.8048.

Geometry files


Prototype Generator

aflow --proto=A_cP46_223_dik --params=

Species:

Running:

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