$\beta$–SiO2 Structure: A2B_hP9_181_j_c

Picture of Structure; Click for Big Picture
Prototype : SiO2
AFLOW prototype label : A2B_hP9_181_j_c
Strukturbericht designation : None
Pearson symbol : hP9
Space group number : 181
Space group symbol : $P6_{4}22$
AFLOW prototype command : aflow --proto=A2B_hP9_181_j_c
--params=
$a$,$c/a$,$x_{2}$



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} & = & \frac{1}{2} \, \mathbf{a}_{1} & = & \frac{1}{4}a \, \mathbf{\hat{x}}- \frac{\sqrt{3}}{4}a \, \mathbf{\hat{y}} & \left(3c\right) & \mbox{Si} \\ \mathbf{B}_{2} & = & \frac{1}{2} \, \mathbf{a}_{2} + \frac{1}{3} \, \mathbf{a}_{3} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{4}a \, \mathbf{\hat{y}} + \frac{1}{3}c \, \mathbf{\hat{z}} & \left(3c\right) & \mbox{Si} \\ \mathbf{B}_{3} & = & \frac{1}{2} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{2} + \frac{2}{3} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + \frac{2}{3}c \, \mathbf{\hat{z}} & \left(3c\right) & \mbox{Si} \\ \mathbf{B}_{4} & = & x_{2} \, \mathbf{a}_{1} + 2x_{2} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{3}{2}x_{2}a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}x_{2}a \, \mathbf{\hat{y}} + \frac{1}{2}c \, \mathbf{\hat{z}} & \left(6j\right) & \mbox{O} \\ \mathbf{B}_{5} & = & -2x_{2} \, \mathbf{a}_{1}-x_{2} \, \mathbf{a}_{2} + \frac{5}{6} \, \mathbf{a}_{3} & = & -\frac{3}{2}x_{2}a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}x_{2}a \, \mathbf{\hat{y}} + \frac{5}{6}c \, \mathbf{\hat{z}} & \left(6j\right) & \mbox{O} \\ \mathbf{B}_{6} & = & x_{2} \, \mathbf{a}_{1}-x_{2} \, \mathbf{a}_{2} + \frac{1}{6} \, \mathbf{a}_{3} & = & -\sqrt{3}x_{2}a \, \mathbf{\hat{y}} + \frac{1}{6}c \, \mathbf{\hat{z}} & \left(6j\right) & \mbox{O} \\ \mathbf{B}_{7} & = & -x_{2} \, \mathbf{a}_{1}-2x_{2} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & -\frac{3}{2}x_{2}a \, \mathbf{\hat{x}}-\frac{\sqrt{3}}{2}x_{2}a \, \mathbf{\hat{y}} + \frac{1}{2}c \, \mathbf{\hat{z}} & \left(6j\right) & \mbox{O} \\ \mathbf{B}_{8} & = & 2x_{2} \, \mathbf{a}_{1} + x_{2} \, \mathbf{a}_{2} + \frac{5}{6} \, \mathbf{a}_{3} & = & \frac{3}{2}x_{2}a \, \mathbf{\hat{x}}-\frac{\sqrt{3}}{2}x_{2}a \, \mathbf{\hat{y}} + \frac{5}{6}c \, \mathbf{\hat{z}} & \left(6j\right) & \mbox{O} \\ \mathbf{B}_{9} & = & -x_{2} \, \mathbf{a}_{1} + x_{2} \, \mathbf{a}_{2} + \frac{1}{6} \, \mathbf{a}_{3} & = & \sqrt{3}x_{2}a \, \mathbf{\hat{y}} + \frac{1}{6}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_181_j_c --params=

Species:

Running:

Output: