$\beta$–Quartz (SiO2, $C8$): A2B_hP9_180_j_c

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Prototype : SiO2
AFLOW prototype label : A2B_hP9_180_j_c
Strukturbericht designation : $C8$
Pearson symbol : hP9
Space group number : 180
Space group symbol : $\mbox{P6}_{2}\mbox{22}$
AFLOW prototype command : aflow --proto=A2B_hP9_180_j_c
--params=
$a$,$c/a$,$x_{2}$



Hexagonal primitive vectors:

\[ \begin{array}{ccc} \mathbf{a}_1 & = & \frac12 \, a \, \mathbf{\hat{x}} - \frac{\sqrt{3}}{2} \, a \, \mathbf{\hat{y}} \\ \mathbf{a}_2 & = & \frac12 \, a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2} \, a \, \mathbf{\hat{y}} \\ \mathbf{a}_3 & = & c \, \mathbf{\hat{z}}\\ \end{array} \]

Basis vectors:

\[ \begin{array}{ccccccc} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{Atom Type} \\ \mathbf{B}_{1}& = &\frac12 \, \mathbf{a}_{1}& = &\frac14 \, a \, \mathbf{\hat{x}}- \frac{\sqrt3}4 \, a \, \mathbf{\hat{y}}& \left(3c\right) & \mbox{Si} \\ \mathbf{B}_{2}& = &\frac12 \, \mathbf{a}_{2}+ \frac23 \, \mathbf{a}_{3}& = &\frac14 \, a \, \mathbf{\hat{x}}+ \frac{\sqrt3}4 \, a \, \mathbf{\hat{y}}+ \frac23 \, c \, \mathbf{\hat{z}}& \left(3c\right) & \mbox{Si} \\ \mathbf{B}_{3}& = &\frac12 \, \mathbf{a}_{1}+ \frac12 \, \mathbf{a}_{2}+ \frac13 \, \mathbf{a}_{3}& = &\frac12 \, a \, \mathbf{\hat{x}}+ \frac13 \, c \, \mathbf{\hat{z}}& \left(3c\right) & \mbox{Si} \\ \mathbf{B}_{4}& = &x_{2} \, \mathbf{a}_{1}+ 2 x_{2} \, \mathbf{a}_{2}+ \frac12 \, \mathbf{a}_{3}& = &\frac32 \, x_{2} \, a \, \mathbf{\hat{x}}+ \frac{\sqrt3}2 \, x_{2} \, a \, \mathbf{\hat{y}}+ \frac12 \, c \, \mathbf{\hat{z}}& \left(6j\right) & \mbox{O} \\ \mathbf{B}_{5}& = &- 2 x_{2} \, \mathbf{a}_{1}- x_{2} \, \mathbf{a}_{2}+ \frac16 \, \mathbf{a}_{3}& = &- \frac32 \, x_{2} \, a \, \mathbf{\hat{x}}+ \frac{\sqrt3}2 \, x_{2} \, a \, \mathbf{\hat{y}}+ \frac16 \, c \, \mathbf{\hat{z}}& \left(6j\right) & \mbox{O} \\ \mathbf{B}_{6}& = &x_{2} \, \mathbf{a}_{1}- x_{2} \, \mathbf{a}_{2}+ \frac56 \, \mathbf{a}_{3}& = &- \sqrt3 \, x_{2} \, a \, \mathbf{\hat{y}}+ \frac56 \, c \, \mathbf{\hat{z}}& \left(6j\right) & \mbox{O} \\ \mathbf{B}_{7}& = &- x_{2} \, \mathbf{a}_{1}- 2 x_{2} \, \mathbf{a}_{2}+ \frac12 \, \mathbf{a}_{3}& = &- \frac32 \, x_{2} \, a \, \mathbf{\hat{x}}- \frac{\sqrt3}2 \, x_{2} \, a \, \mathbf{\hat{y}}+ \frac12 \, c \, \mathbf{\hat{z}}& \left(6j\right) & \mbox{O} \\ \mathbf{B}_{8}& = &2 x_{2} \, \mathbf{a}_{1}+ x_{2} \, \mathbf{a}_{2}+ \frac16 \, \mathbf{a}_{3}& = &\frac32 \, x_{2} \, a \, \mathbf{\hat{x}}- \frac{\sqrt3}2 \, x_{2} \, a \, \mathbf{\hat{y}}+ \frac16 \, c \, \mathbf{\hat{z}}& \left(6j\right) & \mbox{O} \\ \mathbf{B}_{9}& = &- x_{2} \, \mathbf{a}_{1}+ x_{2} \, \mathbf{a}_{2}+ \frac56 \, \mathbf{a}_{3}& = &\sqrt3 \, x_{2} \, a \, \mathbf{\hat{y}}+ \frac56 \, c \, \mathbf{\hat{z}}& \left(6j\right) & \mbox{O} \\ \end{array} \]

References

  • A. F. Wright and M. S. Lehmann, The Structure of Quartz at 25 and 590°C Determined by Neutron Diffraction, J. Solid State Chem. 36, 371–380 (1981), doi:10.1016/0022-4596(81)90449-7.

Geometry files


Prototype Generator

aflow --proto=A2B_hP9_180_j_c --params=

Species:

Running:

Output: