$\alpha$–Quartz (low Quartz) Structure: A2B_hP9_152_c_a

Picture of Structure; Click for Big Picture
Prototype : SiO2
AFLOW prototype label : A2B_hP9_152_c_a
Strukturbericht designation : None
Pearson symbol : hP9
Space group number : 152
Space group symbol : $\mbox{P3}_{1}\mbox{21}$
AFLOW prototype command : aflow --proto=A2B_hP9_152_c_a
--params=
$a$,$c/a$,$x_{1}$,$x_{2}$,$y_{2}$,$z_{2}$


  • When $x_{1}=1/2$, $y_{2}=2x_{2}$, and $z_{2}=1/2$, this tranforms into the high quartz (C8) structure. This structure is sometimes given using the enantiomorphic space groups P3221 (#154).

Trigonal 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} & =& x_{1} \, \mathbf{a}_{1} + \frac13 \, \mathbf{a}_{3}& =& \frac12 \, x_{1} \, a \, \mathbf{\hat{x}} - \frac{\sqrt3}2 \, x_{1} \, a \, \mathbf{\hat{y}} +\frac13 \, c \, \mathbf{\hat{z}}& \left(3a\right) & \mbox{Si} \\ \mathbf{B}_{2} & =& x_{1} \, \mathbf{a}_{2} + \frac23 \, \mathbf{a}_{3}& =& \frac12 \, x_{1} \, a \, \mathbf{\hat{x}} + \frac{\sqrt3}2 \, x_{1} \, a \, \mathbf{\hat{y}} +\frac23 \, c \, \mathbf{\hat{z}}& \left(3a\right) & \mbox{Si} \\ \mathbf{B}_{3} & =& - x_{1} \, \mathbf{a}_{1} - x_{1} \, \mathbf{a}_{2}& =& - x_{1} \, a \, \mathbf{\hat{x}}& \left(3a\right) & \mbox{Si} \\ \mathbf{B}_{4} & =&x_{2} \, \mathbf{a}_{1}+ y_{2} \, \mathbf{a}_{2}+ z_{2} \, \mathbf{a}_{3}& =&\frac12 \left(x_{2} + y_{2}\right) \, a \, \mathbf{\hat{x}}+ \frac{\sqrt3}2 \left(y_{2} -x_{2}\right) \, a \, \mathbf{\hat{y}}+ z_{2} \, c \, \mathbf{\hat{z}}& \left(6c\right) & \mbox{O} \\ \mathbf{B}_{5} & =&- y_{2} \, \mathbf{a}_{1}+ \left(x_{2} - y_{2}\right) \, \mathbf{a}_{2}+ \left(\frac13 + z_{2}\right) \, \mathbf{a}_{3}& =&\frac12 \left(x_{2} - 2 y_{2}\right) \, a \, \mathbf{\hat{x}}+ \frac{\sqrt3}2 x_{2} \, a \, \mathbf{\hat{y}}+ \left(\frac13 + z_{2}\right) \, c \, \mathbf{\hat{z}}& \left(6c\right) & \mbox{O} \\ \mathbf{B}_{6} & =&\left(y_{2} - x_{2}\right) \, \mathbf{a}_{1}- x_{2} \, \mathbf{a}_{2}+ \left(\frac23 + z_{2}\right) \, \mathbf{a}_{3}& =&\frac12 \left(y_{2} - 2 x_{2}\right) \, a \, \mathbf{\hat{x}}- \frac{\sqrt3}2 y_{2} \, a \, \mathbf{\hat{y}}+ \left(\frac23 + z_{2}\right) \, c \, \mathbf{\hat{z}}& \left(6c\right) & \mbox{O} \\ \mathbf{B}_{7} & =&y_{2} \, \mathbf{a}_{1}+ x_{2} \, \mathbf{a}_{2}- z_{2} \, \mathbf{a}_{3}& =&\frac12 \left(x_{2} + y_{2}\right) \, a \, \mathbf{\hat{x}}+ \frac{\sqrt3}2 \left(x_{2} - y_{2}\right) \, a \, \mathbf{\hat{y}}- z_{2} \, c \, \mathbf{\hat{z}}& \left(6c\right) & \mbox{O} \\ \mathbf{B}_{8} & =&\left(x_{2} - y_{2}\right) \, \mathbf{a}_{1}- y_{2} \, \mathbf{a}_{2}+ \left(\frac23 - z_{2}\right) \, \mathbf{a}_{3}& =&\frac12 \left(x_{2} - 2 y_{2}\right) \, a \, \mathbf{\hat{x}}- \frac{\sqrt3}2 x_{2} \, a \, \mathbf{\hat{y}}+ \left(\frac23 - z_{2}\right) \, c \, \mathbf{\hat{z}}& \left(6c\right) & \mbox{O} \\ \mathbf{B}_{9} & =&- x_{2} \, \mathbf{a}_{1}+ \left(y_{2} - x_{2}\right) \, \mathbf{a}_{2}+ \left(\frac13 - z_{2}\right) \, \mathbf{a}_{3}& =&\frac12 \left(y_{2} - 2 x_{2}\right) \, a \, \mathbf{\hat{x}}+ \frac{\sqrt3}2 y_{2} \, a \, \mathbf{\hat{y}}+ \left(\frac13 - z_{2}\right) \, c \, \mathbf{\hat{z}}& \left(6c\right) & \mbox{O} \\ \end{array} \]

References

  • R. M. Hazen, L. W. Finger, R. J. Hemley, and H. K. Mao, High–pressure crystal chemistry and amorphization of alpha–quartz, Solid State Commun. 72, 507–511 (1989), doi:10.1016/0038-1098(89)90607-8.

Found in

  • R. T. Downs and M. Hall–Wallace, The American Mineralogist Crystal Structure Database, Am. Mineral. 88, 247–250 (2003).

Geometry files


Prototype Generator

aflow --proto=A2B_hP9_152_c_a --params=

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