SiO2 Structure: A2B_cI72_211_hi_i

Picture of Structure; Click for Big Picture
Prototype : SiO2
AFLOW prototype label : A2B_cI72_211_hi_i
Strukturbericht designation : None
Pearson symbol : cI72
Space group number : 211
Space group symbol : $I432$
AFLOW prototype command : aflow --proto=A2B_cI72_211_hi_i
--params=
$a$,$y_{1}$,$y_{2}$,$y_{3}$


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} & = & 2y_{1} \, \mathbf{a}_{1} + y_{1} \, \mathbf{a}_{2} + y_{1} \, \mathbf{a}_{3} & = & y_{1}a \, \mathbf{\hat{y}} + y_{1}a \, \mathbf{\hat{z}} & \left(24h\right) & \mbox{O I} \\ \mathbf{B}_{2} & = & y_{1} \, \mathbf{a}_{2}-y_{1} \, \mathbf{a}_{3} & = & -y_{1}a \, \mathbf{\hat{y}} + y_{1}a \, \mathbf{\hat{z}} & \left(24h\right) & \mbox{O I} \\ \mathbf{B}_{3} & = & -y_{1} \, \mathbf{a}_{2} + y_{1} \, \mathbf{a}_{3} & = & y_{1}a \, \mathbf{\hat{y}}-y_{1}a \, \mathbf{\hat{z}} & \left(24h\right) & \mbox{O I} \\ \mathbf{B}_{4} & = & -2y_{1} \, \mathbf{a}_{1}-y_{1} \, \mathbf{a}_{2}-y_{1} \, \mathbf{a}_{3} & = & -y_{1}a \, \mathbf{\hat{y}}-y_{1}a \, \mathbf{\hat{z}} & \left(24h\right) & \mbox{O I} \\ \mathbf{B}_{5} & = & y_{1} \, \mathbf{a}_{1} + 2y_{1} \, \mathbf{a}_{2} + y_{1} \, \mathbf{a}_{3} & = & y_{1}a \, \mathbf{\hat{x}} + y_{1}a \, \mathbf{\hat{z}} & \left(24h\right) & \mbox{O I} \\ \mathbf{B}_{6} & = & -y_{1} \, \mathbf{a}_{1} + y_{1} \, \mathbf{a}_{3} & = & y_{1}a \, \mathbf{\hat{x}}-y_{1}a \, \mathbf{\hat{z}} & \left(24h\right) & \mbox{O I} \\ \mathbf{B}_{7} & = & y_{1} \, \mathbf{a}_{1}-y_{1} \, \mathbf{a}_{3} & = & -y_{1}a \, \mathbf{\hat{x}} + y_{1}a \, \mathbf{\hat{z}} & \left(24h\right) & \mbox{O I} \\ \mathbf{B}_{8} & = & -y_{1} \, \mathbf{a}_{1}-2y_{1} \, \mathbf{a}_{2}-y_{1} \, \mathbf{a}_{3} & = & -y_{1}a \, \mathbf{\hat{x}}-y_{1}a \, \mathbf{\hat{z}} & \left(24h\right) & \mbox{O I} \\ \mathbf{B}_{9} & = & y_{1} \, \mathbf{a}_{1} + y_{1} \, \mathbf{a}_{2} + 2y_{1} \, \mathbf{a}_{3} & = & y_{1}a \, \mathbf{\hat{x}} + y_{1}a \, \mathbf{\hat{y}} & \left(24h\right) & \mbox{O I} \\ \mathbf{B}_{10} & = & y_{1} \, \mathbf{a}_{1}-y_{1} \, \mathbf{a}_{2} & = & -y_{1}a \, \mathbf{\hat{x}} + y_{1}a \, \mathbf{\hat{y}} & \left(24h\right) & \mbox{O I} \\ \mathbf{B}_{11} & = & -y_{1} \, \mathbf{a}_{1} + y_{1} \, \mathbf{a}_{2} & = & y_{1}a \, \mathbf{\hat{x}}-y_{1}a \, \mathbf{\hat{y}} & \left(24h\right) & \mbox{O I} \\ \mathbf{B}_{12} & = & -y_{1} \, \mathbf{a}_{1}-y_{1} \, \mathbf{a}_{2}-2y_{1} \, \mathbf{a}_{3} & = & -y_{1}a \, \mathbf{\hat{x}}-y_{1}a \, \mathbf{\hat{y}} & \left(24h\right) & \mbox{O I} \\ \mathbf{B}_{13} & = & \frac{1}{2} \, \mathbf{a}_{1} + \left(\frac{3}{4} - y_{2}\right) \, \mathbf{a}_{2} + \left(\frac{1}{4} +y_{2}\right) \, \mathbf{a}_{3} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + y_{2}a \, \mathbf{\hat{y}} + \left(\frac{1}{2} - y_{2}\right)a \, \mathbf{\hat{z}} & \left(24i\right) & \mbox{O II} \\ \mathbf{B}_{14} & = & \left(\frac{1}{2} - 2y_{2}\right) \, \mathbf{a}_{1} + \left(\frac{1}{4} - y_{2}\right) \, \mathbf{a}_{2} + \left(\frac{3}{4} - y_{2}\right) \, \mathbf{a}_{3} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + \left(\frac{1}{2} - y_{2}\right)a \, \mathbf{\hat{y}}-y_{2}a \, \mathbf{\hat{z}} & \left(24i\right) & \mbox{O II} \\ \mathbf{B}_{15} & = & \left(\frac{1}{2} +2y_{2}\right) \, \mathbf{a}_{1} + \left(\frac{1}{4} +y_{2}\right) \, \mathbf{a}_{2} + \left(\frac{3}{4} +y_{2}\right) \, \mathbf{a}_{3} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +y_{2}\right)a \, \mathbf{\hat{y}} + y_{2}a \, \mathbf{\hat{z}} & \left(24i\right) & \mbox{O II} \\ \mathbf{B}_{16} & = & \frac{1}{2} \, \mathbf{a}_{1} + \left(\frac{3}{4} +y_{2}\right) \, \mathbf{a}_{2} + \left(\frac{1}{4} - y_{2}\right) \, \mathbf{a}_{3} & = & \frac{1}{4}a \, \mathbf{\hat{x}}-y_{2}a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +y_{2}\right)a \, \mathbf{\hat{z}} & \left(24i\right) & \mbox{O II} \\ \mathbf{B}_{17} & = & \left(\frac{1}{4} +y_{2}\right) \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{2} + \left(\frac{3}{4} - y_{2}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} - y_{2}\right)a \, \mathbf{\hat{x}} + \frac{1}{4}a \, \mathbf{\hat{y}} + y_{2}a \, \mathbf{\hat{z}} & \left(24i\right) & \mbox{O II} \\ \mathbf{B}_{18} & = & \left(\frac{3}{4} - y_{2}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - 2y_{2}\right) \, \mathbf{a}_{2} + \left(\frac{1}{4} - y_{2}\right) \, \mathbf{a}_{3} & = & -y_{2}a \, \mathbf{\hat{x}} + \frac{1}{4}a \, \mathbf{\hat{y}} + \left(\frac{1}{2} - y_{2}\right)a \, \mathbf{\hat{z}} & \left(24i\right) & \mbox{O II} \\ \mathbf{B}_{19} & = & \left(\frac{3}{4} +y_{2}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +2y_{2}\right) \, \mathbf{a}_{2} + \left(\frac{1}{4} +y_{2}\right) \, \mathbf{a}_{3} & = & y_{2}a \, \mathbf{\hat{x}} + \frac{1}{4}a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +y_{2}\right)a \, \mathbf{\hat{z}} & \left(24i\right) & \mbox{O II} \\ \mathbf{B}_{20} & = & \left(\frac{1}{4} - y_{2}\right) \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{2} + \left(\frac{3}{4} +y_{2}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +y_{2}\right)a \, \mathbf{\hat{x}} + \frac{1}{4}a \, \mathbf{\hat{y}}-y_{2}a \, \mathbf{\hat{z}} & \left(24i\right) & \mbox{O II} \\ \mathbf{B}_{21} & = & \left(\frac{3}{4} - y_{2}\right) \, \mathbf{a}_{1} + \left(\frac{1}{4} +y_{2}\right) \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & y_{2}a \, \mathbf{\hat{x}} + \left(\frac{1}{2} - y_{2}\right)a \, \mathbf{\hat{y}} + \frac{1}{4}a \, \mathbf{\hat{z}} & \left(24i\right) & \mbox{O II} \\ \mathbf{B}_{22} & = & \left(\frac{1}{4} - y_{2}\right) \, \mathbf{a}_{1} + \left(\frac{3}{4} - y_{2}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - 2y_{2}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} - y_{2}\right)a \, \mathbf{\hat{x}}-y_{2}a \, \mathbf{\hat{y}} + \frac{1}{4}a \, \mathbf{\hat{z}} & \left(24i\right) & \mbox{O II} \\ \mathbf{B}_{23} & = & \left(\frac{1}{4} +y_{2}\right) \, \mathbf{a}_{1} + \left(\frac{3}{4} +y_{2}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +2y_{2}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +y_{2}\right)a \, \mathbf{\hat{x}} + y_{2}a \, \mathbf{\hat{y}} + \frac{1}{4}a \, \mathbf{\hat{z}} & \left(24i\right) & \mbox{O II} \\ \mathbf{B}_{24} & = & \left(\frac{3}{4} +y_{2}\right) \, \mathbf{a}_{1} + \left(\frac{1}{4} - y_{2}\right) \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & -y_{2}a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +y_{2}\right)a \, \mathbf{\hat{y}} + \frac{1}{4}a \, \mathbf{\hat{z}} & \left(24i\right) & \mbox{O II} \\ \mathbf{B}_{25} & = & \frac{1}{2} \, \mathbf{a}_{1} + \left(\frac{3}{4} - y_{3}\right) \, \mathbf{a}_{2} + \left(\frac{1}{4} +y_{3}\right) \, \mathbf{a}_{3} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + y_{3}a \, \mathbf{\hat{y}} + \left(\frac{1}{2} - y_{3}\right)a \, \mathbf{\hat{z}} & \left(24i\right) & \mbox{Si} \\ \mathbf{B}_{26} & = & \left(\frac{1}{2} - 2y_{3}\right) \, \mathbf{a}_{1} + \left(\frac{1}{4} - y_{3}\right) \, \mathbf{a}_{2} + \left(\frac{3}{4} - y_{3}\right) \, \mathbf{a}_{3} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + \left(\frac{1}{2} - y_{3}\right)a \, \mathbf{\hat{y}}-y_{3}a \, \mathbf{\hat{z}} & \left(24i\right) & \mbox{Si} \\ \mathbf{B}_{27} & = & \left(\frac{1}{2} +2y_{3}\right) \, \mathbf{a}_{1} + \left(\frac{1}{4} +y_{3}\right) \, \mathbf{a}_{2} + \left(\frac{3}{4} +y_{3}\right) \, \mathbf{a}_{3} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +y_{3}\right)a \, \mathbf{\hat{y}} + y_{3}a \, \mathbf{\hat{z}} & \left(24i\right) & \mbox{Si} \\ \mathbf{B}_{28} & = & \frac{1}{2} \, \mathbf{a}_{1} + \left(\frac{3}{4} +y_{3}\right) \, \mathbf{a}_{2} + \left(\frac{1}{4} - y_{3}\right) \, \mathbf{a}_{3} & = & \frac{1}{4}a \, \mathbf{\hat{x}}-y_{3}a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +y_{3}\right)a \, \mathbf{\hat{z}} & \left(24i\right) & \mbox{Si} \\ \mathbf{B}_{29} & = & \left(\frac{1}{4} +y_{3}\right) \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{2} + \left(\frac{3}{4} - y_{3}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} - y_{3}\right)a \, \mathbf{\hat{x}} + \frac{1}{4}a \, \mathbf{\hat{y}} + y_{3}a \, \mathbf{\hat{z}} & \left(24i\right) & \mbox{Si} \\ \mathbf{B}_{30} & = & \left(\frac{3}{4} - y_{3}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - 2y_{3}\right) \, \mathbf{a}_{2} + \left(\frac{1}{4} - y_{3}\right) \, \mathbf{a}_{3} & = & -y_{3}a \, \mathbf{\hat{x}} + \frac{1}{4}a \, \mathbf{\hat{y}} + \left(\frac{1}{2} - y_{3}\right)a \, \mathbf{\hat{z}} & \left(24i\right) & \mbox{Si} \\ \mathbf{B}_{31} & = & \left(\frac{3}{4} +y_{3}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +2y_{3}\right) \, \mathbf{a}_{2} + \left(\frac{1}{4} +y_{3}\right) \, \mathbf{a}_{3} & = & y_{3}a \, \mathbf{\hat{x}} + \frac{1}{4}a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +y_{3}\right)a \, \mathbf{\hat{z}} & \left(24i\right) & \mbox{Si} \\ \mathbf{B}_{32} & = & \left(\frac{1}{4} - y_{3}\right) \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{2} + \left(\frac{3}{4} +y_{3}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +y_{3}\right)a \, \mathbf{\hat{x}} + \frac{1}{4}a \, \mathbf{\hat{y}}-y_{3}a \, \mathbf{\hat{z}} & \left(24i\right) & \mbox{Si} \\ \mathbf{B}_{33} & = & \left(\frac{3}{4} - y_{3}\right) \, \mathbf{a}_{1} + \left(\frac{1}{4} +y_{3}\right) \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & y_{3}a \, \mathbf{\hat{x}} + \left(\frac{1}{2} - y_{3}\right)a \, \mathbf{\hat{y}} + \frac{1}{4}a \, \mathbf{\hat{z}} & \left(24i\right) & \mbox{Si} \\ \mathbf{B}_{34} & = & \left(\frac{1}{4} - y_{3}\right) \, \mathbf{a}_{1} + \left(\frac{3}{4} - y_{3}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - 2y_{3}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} - y_{3}\right)a \, \mathbf{\hat{x}}-y_{3}a \, \mathbf{\hat{y}} + \frac{1}{4}a \, \mathbf{\hat{z}} & \left(24i\right) & \mbox{Si} \\ \mathbf{B}_{35} & = & \left(\frac{1}{4} +y_{3}\right) \, \mathbf{a}_{1} + \left(\frac{3}{4} +y_{3}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +2y_{3}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +y_{3}\right)a \, \mathbf{\hat{x}} + y_{3}a \, \mathbf{\hat{y}} + \frac{1}{4}a \, \mathbf{\hat{z}} & \left(24i\right) & \mbox{Si} \\ \mathbf{B}_{36} & = & \left(\frac{3}{4} +y_{3}\right) \, \mathbf{a}_{1} + \left(\frac{1}{4} - y_{3}\right) \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & -y_{3}a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +y_{3}\right)a \, \mathbf{\hat{y}} + \frac{1}{4}a \, \mathbf{\hat{z}} & \left(24i\right) & \mbox{Si} \\ \end{array} \]

References

  • M. D. Foster, O. Delgado Friedrichs, R. G. Bell, F. A. Almeida Paz, and J. Klinowski, Chemical Evaluation of Hypothetical Uninodal Zeolites, J. Am. Chem. Soc. 126, 9769–9775 (2004), doi:10.1021/ja037334j.

Found in

  • ICSD, Inorganic Crystal Structure Database. ID 170506.

Geometry files


Prototype Generator

aflow --proto=A2B_cI72_211_hi_i --params=

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