Downeyite (SeO2, $C47$) Structure: A2B_tP24_135_gh_h

Picture of Structure; Click for Big Picture
Prototype : SeO2
AFLOW prototype label : A2B_tP24_135_gh_h
Strukturbericht designation : $C47$
Pearson symbol : tP24
Space group number : 135
Space group symbol : $P4_{2}/mbc$
AFLOW prototype command : aflow --proto=A2B_tP24_135_gh_h
--params=
$a$,$c/a$,$x_{1}$,$x_{2}$,$y_{2}$,$x_{3}$,$y_{3}$


  • Data for this structure was taken at 139 K.

Simple Tetragonal primitive vectors:

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

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} + \left(\frac{1}{2} +x_{1}\right) \, \mathbf{a}_{2} + \frac{1}{4} \, \mathbf{a}_{3} & = & x_{1}a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +x_{1}\right)a \, \mathbf{\hat{y}} + \frac{1}{4}c \, \mathbf{\hat{z}} & \left(8g\right) & \mbox{O I} \\ \mathbf{B}_{2} & = & -x_{1} \, \mathbf{a}_{1} + \left(\frac{1}{2} - x_{1}\right) \, \mathbf{a}_{2} + \frac{1}{4} \, \mathbf{a}_{3} & = & -x_{1}a \, \mathbf{\hat{x}} + \left(\frac{1}{2} - x_{1}\right)a \, \mathbf{\hat{y}} + \frac{1}{4}c \, \mathbf{\hat{z}} & \left(8g\right) & \mbox{O I} \\ \mathbf{B}_{3} & = & \left(\frac{1}{2} - x_{1}\right) \, \mathbf{a}_{1} + x_{1} \, \mathbf{a}_{2} + \frac{3}{4} \, \mathbf{a}_{3} & = & \left(\frac{1}{2} - x_{1}\right)a \, \mathbf{\hat{x}} + x_{1}a \, \mathbf{\hat{y}} + \frac{3}{4}c \, \mathbf{\hat{z}} & \left(8g\right) & \mbox{O I} \\ \mathbf{B}_{4} & = & \left(\frac{1}{2} +x_{1}\right) \, \mathbf{a}_{1}-x_{1} \, \mathbf{a}_{2} + \frac{3}{4} \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +x_{1}\right)a \, \mathbf{\hat{x}}-x_{1}a \, \mathbf{\hat{y}} + \frac{3}{4}c \, \mathbf{\hat{z}} & \left(8g\right) & \mbox{O I} \\ \mathbf{B}_{5} & = & -x_{1} \, \mathbf{a}_{1} + \left(\frac{1}{2} - x_{1}\right) \, \mathbf{a}_{2} + \frac{3}{4} \, \mathbf{a}_{3} & = & -x_{1}a \, \mathbf{\hat{x}} + \left(\frac{1}{2} - x_{1}\right)a \, \mathbf{\hat{y}} + \frac{3}{4}c \, \mathbf{\hat{z}} & \left(8g\right) & \mbox{O I} \\ \mathbf{B}_{6} & = & x_{1} \, \mathbf{a}_{1} + \left(\frac{1}{2} +x_{1}\right) \, \mathbf{a}_{2} + \frac{3}{4} \, \mathbf{a}_{3} & = & x_{1}a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +x_{1}\right)a \, \mathbf{\hat{y}} + \frac{3}{4}c \, \mathbf{\hat{z}} & \left(8g\right) & \mbox{O I} \\ \mathbf{B}_{7} & = & \left(\frac{1}{2} +x_{1}\right) \, \mathbf{a}_{1}-x_{1} \, \mathbf{a}_{2} + \frac{1}{4} \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +x_{1}\right)a \, \mathbf{\hat{x}}-x_{1}a \, \mathbf{\hat{y}} + \frac{1}{4}c \, \mathbf{\hat{z}} & \left(8g\right) & \mbox{O I} \\ \mathbf{B}_{8} & = & \left(\frac{1}{2} - x_{1}\right) \, \mathbf{a}_{1} + x_{1} \, \mathbf{a}_{2} + \frac{1}{4} \, \mathbf{a}_{3} & = & \left(\frac{1}{2} - x_{1}\right)a \, \mathbf{\hat{x}} + x_{1}a \, \mathbf{\hat{y}} + \frac{1}{4}c \, \mathbf{\hat{z}} & \left(8g\right) & \mbox{O I} \\ \mathbf{B}_{9} & = & x_{2} \, \mathbf{a}_{1} + y_{2} \, \mathbf{a}_{2} & = & x_{2}a \, \mathbf{\hat{x}} + y_{2}a \, \mathbf{\hat{y}} & \left(8h\right) & \mbox{O II} \\ \mathbf{B}_{10} & = & -x_{2} \, \mathbf{a}_{1}-y_{2} \, \mathbf{a}_{2} & = & -x_{2}a \, \mathbf{\hat{x}}-y_{2}a \, \mathbf{\hat{y}} & \left(8h\right) & \mbox{O II} \\ \mathbf{B}_{11} & = & -y_{2} \, \mathbf{a}_{1} + x_{2} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & -y_{2}a \, \mathbf{\hat{x}} + x_{2}a \, \mathbf{\hat{y}} + \frac{1}{2}c \, \mathbf{\hat{z}} & \left(8h\right) & \mbox{O II} \\ \mathbf{B}_{12} & = & y_{2} \, \mathbf{a}_{1}-x_{2} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & y_{2}a \, \mathbf{\hat{x}}-x_{2}a \, \mathbf{\hat{y}} + \frac{1}{2}c \, \mathbf{\hat{z}} & \left(8h\right) & \mbox{O II} \\ \mathbf{B}_{13} & = & \left(\frac{1}{2} - x_{2}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +y_{2}\right) \, \mathbf{a}_{2} & = & \left(\frac{1}{2} - x_{2}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +y_{2}\right)a \, \mathbf{\hat{y}} & \left(8h\right) & \mbox{O II} \\ \mathbf{B}_{14} & = & \left(\frac{1}{2} +x_{2}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - y_{2}\right) \, \mathbf{a}_{2} & = & \left(\frac{1}{2} +x_{2}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2} - y_{2}\right)a \, \mathbf{\hat{y}} & \left(8h\right) & \mbox{O II} \\ \mathbf{B}_{15} & = & \left(\frac{1}{2} +y_{2}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +x_{2}\right) \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +y_{2}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +x_{2}\right)a \, \mathbf{\hat{y}} + \frac{1}{2}c \, \mathbf{\hat{z}} & \left(8h\right) & \mbox{O II} \\ \mathbf{B}_{16} & = & \left(\frac{1}{2} - y_{2}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - x_{2}\right) \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \left(\frac{1}{2} - y_{2}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2} - x_{2}\right)a \, \mathbf{\hat{y}} + \frac{1}{2}c \, \mathbf{\hat{z}} & \left(8h\right) & \mbox{O II} \\ \mathbf{B}_{17} & = & x_{3} \, \mathbf{a}_{1} + y_{3} \, \mathbf{a}_{2} & = & x_{3}a \, \mathbf{\hat{x}} + y_{3}a \, \mathbf{\hat{y}} & \left(8h\right) & \mbox{Se} \\ \mathbf{B}_{18} & = & -x_{3} \, \mathbf{a}_{1}-y_{3} \, \mathbf{a}_{2} & = & -x_{3}a \, \mathbf{\hat{x}}-y_{3}a \, \mathbf{\hat{y}} & \left(8h\right) & \mbox{Se} \\ \mathbf{B}_{19} & = & -y_{3} \, \mathbf{a}_{1} + x_{3} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & -y_{3}a \, \mathbf{\hat{x}} + x_{3}a \, \mathbf{\hat{y}} + \frac{1}{2}c \, \mathbf{\hat{z}} & \left(8h\right) & \mbox{Se} \\ \mathbf{B}_{20} & = & y_{3} \, \mathbf{a}_{1}-x_{3} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & y_{3}a \, \mathbf{\hat{x}}-x_{3}a \, \mathbf{\hat{y}} + \frac{1}{2}c \, \mathbf{\hat{z}} & \left(8h\right) & \mbox{Se} \\ \mathbf{B}_{21} & = & \left(\frac{1}{2} - x_{3}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +y_{3}\right) \, \mathbf{a}_{2} & = & \left(\frac{1}{2} - x_{3}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +y_{3}\right)a \, \mathbf{\hat{y}} & \left(8h\right) & \mbox{Se} \\ \mathbf{B}_{22} & = & \left(\frac{1}{2} +x_{3}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - y_{3}\right) \, \mathbf{a}_{2} & = & \left(\frac{1}{2} +x_{3}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2} - y_{3}\right)a \, \mathbf{\hat{y}} & \left(8h\right) & \mbox{Se} \\ \mathbf{B}_{23} & = & \left(\frac{1}{2} +y_{3}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +x_{3}\right) \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +y_{3}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +x_{3}\right)a \, \mathbf{\hat{y}} + \frac{1}{2}c \, \mathbf{\hat{z}} & \left(8h\right) & \mbox{Se} \\ \mathbf{B}_{24} & = & \left(\frac{1}{2} - y_{3}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - x_{3}\right) \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \left(\frac{1}{2} - y_{3}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2} - x_{3}\right)a \, \mathbf{\hat{y}} + \frac{1}{2}c \, \mathbf{\hat{z}} & \left(8h\right) & \mbox{Se} \\ \end{array} \]

References

  • K. Ståhl, J. P. Legros, and J. Galy, The crystal structure of SeO2 at 139 and 286 K, Zeitschrift für Kristallographie – Crystalline Materials 202, 99–107 (1992), doi:10.1524/zkri.1992.202.14.99.

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_tP24_135_gh_h --params=

Species:

Running:

Output: