Cuprite (Cu2O, $C3$) Structure: A2B_cP6_224_b_a

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Prototype : Cu2O
AFLOW prototype label : A2B_cP6_224_b_a
Strukturbericht designation : $C3$
Pearson symbol : cP6
Space group number : 224
Space group symbol : $\mbox{Pn}\bar{3}\mbox{m}$
AFLOW prototype command : aflow --proto=A2B_cP6_224_b_a
--params=
$a$


  • (Restori, 1986) gives the equilibrium lattice constant of Cu2O as $a=4.627\AA$, but gives nearest-neighbor distances which yield a lattice constant of $4.267\AA$. Since this value agrees with other sources, including those in (Downs, 2003), we use it.

Simple Cubic primitive vectors:

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

Basis vectors:

\[ \begin{array}{ccccccc} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{Atom Type} \\ \mathbf{B}_{1} & = &\frac14 \, \mathbf{a}_{1}+ \frac14 \, \mathbf{a}_{2}+ \frac14 \, \mathbf{a}_{3}& = &\frac14 \, a \, \mathbf{\hat{x}}+ \frac14 \, a \, \mathbf{\hat{y}}+ \frac14 \, a \, \mathbf{\hat{z}}& \left(2a\right) & \mbox{O} \\ \mathbf{B}_{2} & = &\frac34 \, \mathbf{a}_{1}+ \frac34 \, \mathbf{a}_{2}+ \frac34 \, \mathbf{a}_{3}& = &\frac34 \, a \, \mathbf{\hat{x}}+ \frac34 \, a \, \mathbf{\hat{y}}+ \frac34 \, a \, \mathbf{\hat{z}}& \left(2a\right) & \mbox{O} \\ \mathbf{B}_{3} & = &0 \, \mathbf{a}_{1} + 0 \, \mathbf{a}_{2} + 0 \, \mathbf{a}_{3} & = &0 \mathbf{\hat{x}} + 0 \mathbf{\hat{y}} + 0 \mathbf{\hat{z}} & \left(4b\right) & \mbox{Cu} \\ \mathbf{B}_{4} & = &\frac12 \, \mathbf{a}_{1}+ \frac12 \, \mathbf{a}_{2}& = &\frac12 \, a \, \mathbf{\hat{x}}+ \frac12 \, a \, \mathbf{\hat{y}}& \left(4b\right) & \mbox{Cu} \\ \mathbf{B}_{5} & = &\frac12 \, \mathbf{a}_{1}+ \frac12 \, \mathbf{a}_{3}& = &\frac12 \, a \, \mathbf{\hat{x}}+ \frac12 \, a \, \mathbf{\hat{z}}& \left(4b\right) & \mbox{Cu} \\ \mathbf{B}_{6} & = &\frac12 \, \mathbf{a}_{2}+ \frac12 \, \mathbf{a}_{3}& = &\frac12 \, a \, \mathbf{\hat{y}}+ \frac12 \, a \, \mathbf{\hat{z}}& \left(4b\right) & \mbox{Cu} \\ \end{array} \]

References

  • R. Restori and D. Schwarzenbach, Charge Density in Cuprite, Cu2O, Acta Crystallogr. Sect. B Struct. Sci. 42, 201–208 (1986), doi:10.1107/S0108768186098336.
  • R. T. Downs and M. Hall–Wallace, The American Mineralogist Crystal Structure Database, Am. Mineral. 88, 247–250 (2003).

Found in

  • A. Kirfel and K. Eichhorn, Accurate structure analysis with synchrotron radiation. The electron density in Al2O3 and Cu2O, Acta Crystallogr. Sect. A 46, 271–284 (1990), doi:10.1107/S0108767389012596.

Geometry files


Prototype Generator

aflow --proto=A2B_cP6_224_b_a --params=

Species:

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Output: