$\beta$–BeO Structure: AB_tP8_136_g_f

Picture of Structure; Click for Big Picture
Prototype : $\beta$–BeO
AFLOW prototype label : AB_tP8_136_g_f
Strukturbericht designation : None
Pearson symbol : tP8
Space group number : 136
Space group symbol : $\mbox{P4}_{2}\mbox{/mnm}$
AFLOW prototype command : aflow --proto=AB_tP8_136_g_f
--params=
$a$,$c/a$,$x_{1}$,$x_{2}$


Other compounds with this structure

  • ZnO

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}+ x_{1} \, \mathbf{a}_{2}& =&x_{1} \, a \, \mathbf{\hat{x}}+ x_{1} \, a \, \mathbf{\hat{y}}& \left(4f\right) & \mbox{O} \\ \mathbf{B}_{2} & =&- x_{1} \, \mathbf{a}_{1}- x_{1} \, \mathbf{a}_{2}& =&- x_{1} \, a \, \mathbf{\hat{x}}- x_{1} \, a \, \mathbf{\hat{y}}& \left(4f\right) & \mbox{O} \\ \mathbf{B}_{3} & =&\left(\frac12 - x_{1}\right) \, \mathbf{a}_{1}+ \left(\frac12 + x_{1}\right) \, \mathbf{a}_{2}+ \frac12 \, \mathbf{a}_{3}& =&\left(\frac12 - x_{1}\right) \, a \, \mathbf{\hat{x}}+ \left(\frac12 + x_{1}\right) \, a \, \mathbf{\hat{y}}+ \frac12 \, c \, \mathbf{\hat{z}}& \left(4f\right) & \mbox{O} \\ \mathbf{B}_{4} & =&\left(\frac12 + x_{1}\right) \, \mathbf{a}_{1}+ \left(\frac12 - x_{1}\right) \, \mathbf{a}_{2}+ \frac12 \, \mathbf{a}_{3}& =&\left(\frac12 + x_{1}\right) \, a \, \mathbf{\hat{x}}+ \left(\frac12 - x_{1}\right) \, a \, \mathbf{\hat{y}}+ \frac12 \, c \, \mathbf{\hat{z}}& \left(4f\right) & \mbox{O} \\ \mathbf{B}_{5} & =&x_{2} \, \mathbf{a}_{1}- x_{2} \, \mathbf{a}_{2}& =&x_{2} \, a \, \mathbf{\hat{x}}- x_{2} \, a \, \mathbf{\hat{y}}& \left(4g\right) & \mbox{Be} \\ \mathbf{B}_{6} & =&- x_{2} \, \mathbf{a}_{1}+ x_{2} \, \mathbf{a}_{2}& =&- x_{2} \, a \, \mathbf{\hat{x}}+ x_{2} \, a \, \mathbf{\hat{y}}& \left(4g\right) & \mbox{Be} \\ \mathbf{B}_{7} & =&\left(\frac12 + x_{2}\right) \, \mathbf{a}_{1}+ \left(\frac12 + x_{2}\right) \, \mathbf{a}_{2}+ \frac12 \, \mathbf{a}_{3}& =&\left(\frac12 + x_{2}\right) \, a \, \mathbf{\hat{x}}+ \left(\frac12 + x_{2}\right) \, a \, \mathbf{\hat{y}}+ \frac12 \, c \, \mathbf{\hat{z}}& \left(4g\right) & \mbox{Be} \\ \mathbf{B}_{8} & =&\left(\frac12 - x_{2}\right) \, \mathbf{a}_{1}+ \left(\frac12 - x_{2}\right) \, \mathbf{a}_{2}+ \frac12 \, \mathbf{a}_{3}& =&\left(\frac12 - x_{2}\right) \, a \, \mathbf{\hat{x}}+ \left(\frac12 - x_{2}\right) \, a \, \mathbf{\hat{y}}+ \frac12 \, c \, \mathbf{\hat{z}}& \left(4g\right) & \mbox{Be} \\ \end{array} \]

References

  • D. K. Smith, C. F. Cline, and S. B. Austerman, The Crystal Structure of beta–Beryllia, Acta Cryst. 18, 393–397 (1965), doi:10.1107/S0365110X65000877.

Geometry files


Prototype Generator

aflow --proto=AB_tP8_136_g_f --params=

Species:

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Output: