Ideal $\beta$–Cristobalite (SiO2, $C9$) Structure: A2B_cF24_227_c_a

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Prototype : SiO2
AFLOW prototype label : A2B_cF24_227_c_a
Strukturbericht designation : $C9$
Pearson symbol : cF24
Space group number : 227
Space group symbol : $\mbox{Fd}\bar{3}\mbox{m}$
AFLOW prototype command : aflow --proto=A2B_cF24_227_c_a
--params=
$a$


Other compounds with this structure

  • BeF2, AlPO4

  • This is an idealized version of the high-temperature phase of $\alpha$-cristobalite. (Peacor, 1973) concludes that the oxygen atoms partially occupy the (96g) positions in the space group Fd3m. We average those positions to put the oxygen on the (16c) sites. $\beta$-cristobalite is also known as "high" cristobalite.

Face-centered Cubic primitive vectors:

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

Basis vectors:

\[ \begin{array}{ccccccc} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{Atom Type} \\ \mathbf{B}_{1} & = &\frac18 \mathbf{a}_{1}+ \frac18 \mathbf{a}_{2}+ \frac18 \mathbf{a}_{3}& = &\frac18 \, a \, \mathbf{\hat{x}}+ \frac18 \, a \, \mathbf{\hat{y}}+ \frac18 \, a \, \mathbf{\hat{z}}& \left(8a\right) & \mbox{Si} \\ \mathbf{B}_{2} & = &\frac78 \mathbf{a}_{1}+ \frac78 \mathbf{a}_{2}+ \frac78 \mathbf{a}_{3}& = &\frac78 \, a \, \mathbf{\hat{x}}+ \frac78 \, a \, \mathbf{\hat{y}}+ \frac78 \, a \, \mathbf{\hat{z}}& \left(8a\right) & \mbox{Si} \\ \mathbf{B}_{3} & = &0 \, \mathbf{a}_{1} + 0 \, \mathbf{a}_{2} + 0 \, \mathbf{a}_{3} & = &0 \mathbf{\hat{x}} + 0 \mathbf{\hat{y}} + 0 \mathbf{\hat{z}} & \left(16c\right) & \mbox{O} \\ \mathbf{B}_{4} & = &\frac12 \mathbf{a}_{3}& = &\frac14 \, a \, \mathbf{\hat{x}}+ \frac14 \, a \, \mathbf{\hat{y}}& \left(16c\right) & \mbox{O} \\ \mathbf{B}_{5} & = &\frac12 \mathbf{a}_{2}& = &\frac14 \, a \, \mathbf{\hat{x}}+ \frac14 \, a \, \mathbf{\hat{z}}& \left(16c\right) & \mbox{O} \\ \mathbf{B}_{6} & = &\frac12 \mathbf{a}_{1}& = &\frac14 \, a \, \mathbf{\hat{y}}+ \frac14 \, a \, \mathbf{\hat{z}}& \left(16c\right) & \mbox{O} \\ \end{array} \]

References

  • D. R. Peacor, High–temperature single–crystal study of the cristobalite inversion, Zeitschrift für Kristallographie 138, 274–298 (1973), doi:10.1524/zkri.1973.138.1-4.274.

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_cF24_227_c_a --params=

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