SiO2 (P2) Structure: A2B_mP12_3_bc3e_2e

Picture of Structure; Click for Big Picture
Prototype : SiO2
AFLOW prototype label : A2B_mP12_3_bc3e_2e
Strukturbericht designation : None
Pearson symbol : mP12
Space group number : 3
Space group symbol : $\mbox{P2}$
AFLOW prototype command : aflow --proto=A2B_mP12_3_bc3e_2e
--params=
$a$,$b/a$,$c/a$,$\beta$,$y_{1}$,$y_{2}$,$x_{3}$,$y_{3}$,$z_{3}$,$x_{4}$,$y_{4}$,$z_{4}$,$x_{5}$,$y_{5}$,$z_{5}$,$x_{6}$,$y_{6}$,$z_{6}$,$x_{7}$,$y_{7}$,$z_{7}$


  • This structure is the result of simulations of SiO2 structures from a potential fitted to the H6Si2O7 molecule. As such, we do not believe it has been seen in nature. It does, however, describe a structure in space group P2 (#3).

Simple Monoclinic primitive vectors:

\[ \begin{array}{ccc} \mathbf{a}_1 & = & a \, \mathbf{\hat{x}} \\ \mathbf{a}_2 & = & b \, \mathbf{\hat{y}} \\ \mathbf{a}_3 & = & c \cos\beta \, \mathbf{\hat{x}} + c \sin\beta \, \mathbf{\hat{z}} \end{array} \]

Basis vectors:

\[ \begin{array}{ccccccc} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{Atom Type} \\ \mathbf{B}_{1} & =& y_{1} \, \mathbf{a}_{2} + \frac12 \, \mathbf{a}_{3}& =& \frac12 \, c \, \cos\beta \, \mathbf{\hat{x}}+ y_{1} b \, \mathbf{\hat{y}}+ \frac12 \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(1b\right) & \mbox{O I} \\ \mathbf{B}_{2} & =& \frac12 \, \mathbf{a}_{1} + y_{2} \, \mathbf{a}_{2}& =& \frac12 \, a \, \mathbf{\hat{x}}+ y_{2} b \, \mathbf{\hat{y}}& \left(1c\right) & \mbox{O II} \\ \mathbf{B}_{3} & =& x_{3} \, \mathbf{a}_{1} + y_{3} \, \mathbf{a}_{2} + z_{3} \, \mathbf{a}_{3}& =& \left(x_{3} \, a + z_{3} \, c \, \cos\beta\right) \, \mathbf{\hat{x}}+ y_{3} \, b \, \mathbf{\hat{y}}+ z_{3} \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(2e\right) & \mbox{O III} \\ \mathbf{B}_{4} & =& - x_{3} \, \mathbf{a}_{1} + y_{3} \, \mathbf{a}_{2} - z_{3} \, \mathbf{a}_{3}& =& - \left(x_{3} \, a + z_{3} \, c \, \cos\beta\right) \, \mathbf{\hat{x}}+ y_{3} \, b \, \mathbf{\hat{y}}- z_{3} \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(2e\right) & \mbox{O III} \\ \mathbf{B}_{5} & =& x_{4} \, \mathbf{a}_{1} + y_{4} \, \mathbf{a}_{2} + z_{4} \, \mathbf{a}_{3}& =& \left(x_{4} \, a + z_{4} \, c \, \cos\beta\right) \, \mathbf{\hat{x}}+ y_{4} \, b \, \mathbf{\hat{y}}+ z_{4} \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(2e\right) & \mbox{O IV} \\ \mathbf{B}_{6} & =& - x_{4} \, \mathbf{a}_{1} + y_{4} \, \mathbf{a}_{2} - z_{4} \, \mathbf{a}_{3}& =& - \left(x_{4} \, a + z_{4} \, c \, \cos\beta\right) \, \mathbf{\hat{x}}+ y_{4} \, b \, \mathbf{\hat{y}}- z_{4} \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(2e\right) & \mbox{O IV} \\ \mathbf{B}_{7} & =& x_{5} \, \mathbf{a}_{1} + y_{5} \, \mathbf{a}_{2} + z_{5} \, \mathbf{a}_{3}& =& \left(x_{5} \, a + z_{5} \, c \, \cos\beta\right) \, \mathbf{\hat{x}}+ y_{5} \, b \, \mathbf{\hat{y}}+ z_{5} \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(2e\right) & \mbox{O V} \\ \mathbf{B}_{8} & =& - x_{5} \, \mathbf{a}_{1} + y_{5} \, \mathbf{a}_{2} - z_{5} \, \mathbf{a}_{3}& =& - \left(x_{5} \, a + z_{5} \, c \, \cos\beta\right) \, \mathbf{\hat{x}}+ y_{5} \, b \, \mathbf{\hat{y}}- z_{5} \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(2e\right) & \mbox{O V} \\ \mathbf{B}_{9} & =& x_{6} \, \mathbf{a}_{1} + y_{6} \, \mathbf{a}_{2} + z_{6} \, \mathbf{a}_{3}& =& \left(x_{6} \, a + z_{6} \, c \, \cos\beta\right) \, \mathbf{\hat{x}}+ y_{6} \, b \, \mathbf{\hat{y}}+ z_{6} \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(2e\right) & \mbox{Si I} \\ \mathbf{B}_{10} & =& - x_{6} \, \mathbf{a}_{1} + y_{6} \, \mathbf{a}_{2} - z_{6} \, \mathbf{a}_{3}& =& - \left(x_{6} \, a + z_{6} \, c \, \cos\beta\right) \, \mathbf{\hat{x}}+ y_{6} \, b \, \mathbf{\hat{y}}- z_{6} \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(2e\right) & \mbox{Si I} \\ \mathbf{B}_{11} & =& x_{7} \, \mathbf{a}_{1} + y_{7} \, \mathbf{a}_{2} + z_{7} \, \mathbf{a}_{3}& =& \left(x_{7} \, a + z_{7} \, c \, \cos\beta\right) \, \mathbf{\hat{x}}+ y_{7} \, b \, \mathbf{\hat{y}}+ z_{7} \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(2e\right) & \mbox{Si II} \\ \mathbf{B}_{12} & =& - x_{7} \, \mathbf{a}_{1} + y_{7} \, \mathbf{a}_{2} - z_{7} \, \mathbf{a}_{3}& =& - \left(x_{7} \, a + z_{7} \, c \, \cos\beta\right) \, \mathbf{\hat{x}}+ y_{7} \, b \, \mathbf{\hat{y}}- z_{7} \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(2e\right) & \mbox{Si II} \\ \end{array} \]

References

  • M. B. Boisen, Jr., G. V. Gibbs, and M. S. T. Bukowinski, Framework silica structures generated using simulated annealing with a potential energy function based on an H6Si2O7 molecule, Phys. Chem. Miner. 21, 269–284 (1994), doi:10.1007/BF00202091.

Geometry files


Prototype Generator

aflow --proto=A2B_mP12_3_bc3e_2e --params=

Species:

Running:

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