SiO2 Structure: A2B_hP36_177_j2lm_n

Picture of Structure; Click for Big Picture
Prototype : SiO2
AFLOW prototype label : A2B_hP36_177_j2lm_n
Strukturbericht designation : None
Pearson symbol : hP36
Space group number : 177
Space group symbol : $P622$
AFLOW prototype command : aflow --proto=A2B_hP36_177_j2lm_n
--params=
$a$,$c/a$,$x_{1}$,$x_{2}$,$x_{3}$,$x_{4}$,$x_{5}$,$y_{5}$,$z_{5}$


Hexagonal primitive vectors:

\[ \begin{array}{ccc} \mathbf{a}_1 & = & \frac12 \, a \, \mathbf{\hat{x}} - \frac{\sqrt3}2 \, a \, \mathbf{\hat{y}} \\ \mathbf{a}_2 & = & \frac12 \, a \, \mathbf{\hat{x}} + \frac{\sqrt3}2 \, a \, \mathbf{\hat{y}} \\ \mathbf{a}_3 & = & c \, \mathbf{\hat{z}} \\ \end{array} \]

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} & = & \frac{1}{2}x_{1}a \, \mathbf{\hat{x}}-\frac{\sqrt{3}}{2}x_{1}a \, \mathbf{\hat{y}} & \left(6j\right) & \mbox{O I} \\ \mathbf{B}_{2} & = & x_{1} \, \mathbf{a}_{2} & = & \frac{1}{2}x_{1}a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}x_{1}a \, \mathbf{\hat{y}} & \left(6j\right) & \mbox{O I} \\ \mathbf{B}_{3} & = & -x_{1} \, \mathbf{a}_{1}-x_{1} \, \mathbf{a}_{2} & = & -x_{1}a \, \mathbf{\hat{x}} & \left(6j\right) & \mbox{O I} \\ \mathbf{B}_{4} & = & -x_{1} \, \mathbf{a}_{1} & = & -\frac{1}{2}x_{1}a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}x_{1}a \, \mathbf{\hat{y}} & \left(6j\right) & \mbox{O I} \\ \mathbf{B}_{5} & = & -x_{1} \, \mathbf{a}_{2} & = & -\frac{1}{2}x_{1}a \, \mathbf{\hat{x}}-\frac{\sqrt{3}}{2}x_{1}a \, \mathbf{\hat{y}} & \left(6j\right) & \mbox{O I} \\ \mathbf{B}_{6} & = & x_{1} \, \mathbf{a}_{1} + x_{1} \, \mathbf{a}_{2} & = & x_{1}a \, \mathbf{\hat{x}} & \left(6j\right) & \mbox{O I} \\ \mathbf{B}_{7} & = & x_{2} \, \mathbf{a}_{1}-x_{2} \, \mathbf{a}_{2} & = & -\sqrt{3}x_{2}a \, \mathbf{\hat{y}} & \left(6l\right) & \mbox{O II} \\ \mathbf{B}_{8} & = & x_{2} \, \mathbf{a}_{1} + 2x_{2} \, \mathbf{a}_{2} & = & \frac{3}{2}x_{2}a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}x_{2}a \, \mathbf{\hat{y}} & \left(6l\right) & \mbox{O II} \\ \mathbf{B}_{9} & = & -2x_{2} \, \mathbf{a}_{1}-x_{2} \, \mathbf{a}_{2} & = & -\frac{3}{2}x_{2}a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}x_{2}a \, \mathbf{\hat{y}} & \left(6l\right) & \mbox{O II} \\ \mathbf{B}_{10} & = & -x_{2} \, \mathbf{a}_{1} + x_{2} \, \mathbf{a}_{2} & = & \sqrt{3}x_{2}a \, \mathbf{\hat{y}} & \left(6l\right) & \mbox{O II} \\ \mathbf{B}_{11} & = & -x_{2} \, \mathbf{a}_{1}-2x_{2} \, \mathbf{a}_{2} & = & -\frac{3}{2}x_{2}a \, \mathbf{\hat{x}}-\frac{\sqrt{3}}{2}x_{2}a \, \mathbf{\hat{y}} & \left(6l\right) & \mbox{O II} \\ \mathbf{B}_{12} & = & 2x_{2} \, \mathbf{a}_{1} + x_{2} \, \mathbf{a}_{2} & = & \frac{3}{2}x_{2}a \, \mathbf{\hat{x}}-\frac{\sqrt{3}}{2}x_{2}a \, \mathbf{\hat{y}} & \left(6l\right) & \mbox{O II} \\ \mathbf{B}_{13} & = & x_{3} \, \mathbf{a}_{1}-x_{3} \, \mathbf{a}_{2} & = & -\sqrt{3}x_{3}a \, \mathbf{\hat{y}} & \left(6l\right) & \mbox{O III} \\ \mathbf{B}_{14} & = & x_{3} \, \mathbf{a}_{1} + 2x_{3} \, \mathbf{a}_{2} & = & \frac{3}{2}x_{3}a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}x_{3}a \, \mathbf{\hat{y}} & \left(6l\right) & \mbox{O III} \\ \mathbf{B}_{15} & = & -2x_{3} \, \mathbf{a}_{1}-x_{3} \, \mathbf{a}_{2} & = & -\frac{3}{2}x_{3}a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}x_{3}a \, \mathbf{\hat{y}} & \left(6l\right) & \mbox{O III} \\ \mathbf{B}_{16} & = & -x_{3} \, \mathbf{a}_{1} + x_{3} \, \mathbf{a}_{2} & = & \sqrt{3}x_{3}a \, \mathbf{\hat{y}} & \left(6l\right) & \mbox{O III} \\ \mathbf{B}_{17} & = & -x_{3} \, \mathbf{a}_{1}-2x_{3} \, \mathbf{a}_{2} & = & -\frac{3}{2}x_{3}a \, \mathbf{\hat{x}}-\frac{\sqrt{3}}{2}x_{3}a \, \mathbf{\hat{y}} & \left(6l\right) & \mbox{O III} \\ \mathbf{B}_{18} & = & 2x_{3} \, \mathbf{a}_{1} + x_{3} \, \mathbf{a}_{2} & = & \frac{3}{2}x_{3}a \, \mathbf{\hat{x}}-\frac{\sqrt{3}}{2}x_{3}a \, \mathbf{\hat{y}} & \left(6l\right) & \mbox{O III} \\ \mathbf{B}_{19} & = & x_{4} \, \mathbf{a}_{1}-x_{4} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & -\sqrt{3}x_{4}a \, \mathbf{\hat{y}} + \frac{1}{2}c \, \mathbf{\hat{z}} & \left(6m\right) & \mbox{O IV} \\ \mathbf{B}_{20} & = & x_{4} \, \mathbf{a}_{1} + 2x_{4} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{3}{2}x_{4}a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}x_{4}a \, \mathbf{\hat{y}} + \frac{1}{2}c \, \mathbf{\hat{z}} & \left(6m\right) & \mbox{O IV} \\ \mathbf{B}_{21} & = & -2x_{4} \, \mathbf{a}_{1}-x_{4} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & -\frac{3}{2}x_{4}a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}x_{4}a \, \mathbf{\hat{y}} + \frac{1}{2}c \, \mathbf{\hat{z}} & \left(6m\right) & \mbox{O IV} \\ \mathbf{B}_{22} & = & -x_{4} \, \mathbf{a}_{1} + x_{4} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \sqrt{3}x_{4}a \, \mathbf{\hat{y}} + \frac{1}{2}c \, \mathbf{\hat{z}} & \left(6m\right) & \mbox{O IV} \\ \mathbf{B}_{23} & = & -x_{4} \, \mathbf{a}_{1}-2x_{4} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & -\frac{3}{2}x_{4}a \, \mathbf{\hat{x}}-\frac{\sqrt{3}}{2}x_{4}a \, \mathbf{\hat{y}} + \frac{1}{2}c \, \mathbf{\hat{z}} & \left(6m\right) & \mbox{O IV} \\ \mathbf{B}_{24} & = & 2x_{4} \, \mathbf{a}_{1} + x_{4} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{3}{2}x_{4}a \, \mathbf{\hat{x}}-\frac{\sqrt{3}}{2}x_{4}a \, \mathbf{\hat{y}} + \frac{1}{2}c \, \mathbf{\hat{z}} & \left(6m\right) & \mbox{O IV} \\ \mathbf{B}_{25} & = & x_{5} \, \mathbf{a}_{1} + y_{5} \, \mathbf{a}_{2} + z_{5} \, \mathbf{a}_{3} & = & \frac{1}{2}\left(x_{5}+y_{5}\right)a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}\left(-x_{5}+y_{5}\right)a \, \mathbf{\hat{y}} + z_{5}c \, \mathbf{\hat{z}} & \left(12n\right) & \mbox{Si} \\ \mathbf{B}_{26} & = & -y_{5} \, \mathbf{a}_{1} + \left(x_{5}-y_{5}\right) \, \mathbf{a}_{2} + z_{5} \, \mathbf{a}_{3} & = & \left(\frac{1}{2}x_{5}-y_{5}\right)a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}x_{5}a \, \mathbf{\hat{y}} + z_{5}c \, \mathbf{\hat{z}} & \left(12n\right) & \mbox{Si} \\ \mathbf{B}_{27} & = & \left(-x_{5}+y_{5}\right) \, \mathbf{a}_{1}-x_{5} \, \mathbf{a}_{2} + z_{5} \, \mathbf{a}_{3} & = & \left(-x_{5}+\frac{1}{2}y_{5}\right)a \, \mathbf{\hat{x}}-\frac{\sqrt{3}}{2}y_{5}a \, \mathbf{\hat{y}} + z_{5}c \, \mathbf{\hat{z}} & \left(12n\right) & \mbox{Si} \\ \mathbf{B}_{28} & = & -x_{5} \, \mathbf{a}_{1}-y_{5} \, \mathbf{a}_{2} + z_{5} \, \mathbf{a}_{3} & = & -\frac{1}{2}\left(x_{5}+y_{5}\right)a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}\left(x_{5}-y_{5}\right)a \, \mathbf{\hat{y}} + z_{5}c \, \mathbf{\hat{z}} & \left(12n\right) & \mbox{Si} \\ \mathbf{B}_{29} & = & y_{5} \, \mathbf{a}_{1} + \left(-x_{5}+y_{5}\right) \, \mathbf{a}_{2} + z_{5} \, \mathbf{a}_{3} & = & \left(-\frac{1}{2}x_{5}+y_{5}\right)a \, \mathbf{\hat{x}}-\frac{\sqrt{3}}{2}x_{5}a \, \mathbf{\hat{y}} + z_{5}c \, \mathbf{\hat{z}} & \left(12n\right) & \mbox{Si} \\ \mathbf{B}_{30} & = & \left(x_{5}-y_{5}\right) \, \mathbf{a}_{1} + x_{5} \, \mathbf{a}_{2} + z_{5} \, \mathbf{a}_{3} & = & \left(x_{5}-\frac{1}{2}y_{5}\right)a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}y_{5}a \, \mathbf{\hat{y}} + z_{5}c \, \mathbf{\hat{z}} & \left(12n\right) & \mbox{Si} \\ \mathbf{B}_{31} & = & y_{5} \, \mathbf{a}_{1} + x_{5} \, \mathbf{a}_{2}-z_{5} \, \mathbf{a}_{3} & = & \frac{1}{2}\left(x_{5}+y_{5}\right)a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}\left(x_{5}-y_{5}\right)a \, \mathbf{\hat{y}}-z_{5}c \, \mathbf{\hat{z}} & \left(12n\right) & \mbox{Si} \\ \mathbf{B}_{32} & = & \left(x_{5}-y_{5}\right) \, \mathbf{a}_{1}-y_{5} \, \mathbf{a}_{2}-z_{5} \, \mathbf{a}_{3} & = & \left(\frac{1}{2}x_{5}-y_{5}\right)a \, \mathbf{\hat{x}}-\frac{\sqrt{3}}{2}x_{5}a \, \mathbf{\hat{y}}-z_{5}c \, \mathbf{\hat{z}} & \left(12n\right) & \mbox{Si} \\ \mathbf{B}_{33} & = & -x_{5} \, \mathbf{a}_{1} + \left(-x_{5}+y_{5}\right) \, \mathbf{a}_{2}-z_{5} \, \mathbf{a}_{3} & = & \left(-x_{5}+\frac{1}{2}y_{5}\right)a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}y_{5}a \, \mathbf{\hat{y}}-z_{5}c \, \mathbf{\hat{z}} & \left(12n\right) & \mbox{Si} \\ \mathbf{B}_{34} & = & -y_{5} \, \mathbf{a}_{1}-x_{5} \, \mathbf{a}_{2}-z_{5} \, \mathbf{a}_{3} & = & -\frac{1}{2}\left(x_{5}+y_{5}\right)a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}\left(-x_{5}+y_{5}\right)a \, \mathbf{\hat{y}}-z_{5}c \, \mathbf{\hat{z}} & \left(12n\right) & \mbox{Si} \\ \mathbf{B}_{35} & = & \left(-x_{5}+y_{5}\right) \, \mathbf{a}_{1} + y_{5} \, \mathbf{a}_{2}-z_{5} \, \mathbf{a}_{3} & = & \left(-\frac{1}{2}x_{5}+y_{5}\right)a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}x_{5}a \, \mathbf{\hat{y}}-z_{5}c \, \mathbf{\hat{z}} & \left(12n\right) & \mbox{Si} \\ \mathbf{B}_{36} & = & x_{5} \, \mathbf{a}_{1} + \left(x_{5}-y_{5}\right) \, \mathbf{a}_{2}-z_{5} \, \mathbf{a}_{3} & = & \left(x_{5}-\frac{1}{2}y_{5}\right)a \, \mathbf{\hat{x}}-\frac{\sqrt{3}}{2}y_{5}a \, \mathbf{\hat{y}}-z_{5}c \, \mathbf{\hat{z}} & \left(12n\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 170519.

Geometry files


Prototype Generator

aflow --proto=A2B_hP36_177_j2lm_n --params=

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