Cuprite (Cu$_{2}$O, $C3$) Structure: A2B_cP6_224_b_a-001
| Prototype | Cu$_{2}$O |
| AFLOW prototype label | A2B_cP6_224_b_a-001 |
| Strukturbericht designation | $C3$ |
| Mineral name | cuprite |
| ICSD | 52043 |
| Pearson symbol | cP6 |
| Space group number | 224 |
| Space group symbol | $Pn\overline{3}m$ |
| AFLOW prototype command |
aflow --proto=A2B_cP6_224_b_a-001
--params=$a$ |
Other compounds with this structure
Ag$_{2}$O, Pb$_{2}$O
- (Restori, 1986) gives the equilibrium lattice constant of Cu$_{2}$O as $a$=4.627Å, but gives nearest-neighbor distances which yield a lattice constant of 4.267Å. Since this value agrees with other sources, including those in (Downs, 2003), we use it. The ICSD entry uses 4.2685Å.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&a \,\mathbf{\hat{x}}\\\mathbf{a_{2}}&=&a \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&a \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (2a) | O I |
| $\mathbf{B_{2}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{3}{4}a \,\mathbf{\hat{x}}+\frac{3}{4}a \,\mathbf{\hat{y}}+\frac{3}{4}a \,\mathbf{\hat{z}}$ | (2a) | O I |
| $\mathbf{B_{3}}$ | = | $0$ | = | $0$ | (4b) | Cu I |
| $\mathbf{B_{4}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}$ | (4b) | Cu I |
| $\mathbf{B_{5}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{z}}$ | (4b) | Cu I |
| $\mathbf{B_{6}}$ | = | $\frac{1}{2} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}$ | (4b) | Cu I |
References
- R. Restori and D. Schwarzenbach, Charge Density in Cuprite, Cu$_2$O, Acta Crystallogr. Sect. B 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 Al$_2$O$_3$ and Cu$_2$O, Acta Crystallogr. Sect. A 46, 271–284 (1990), doi:10.1107/S0108767389012596.
Prototype Generator
aflow --proto=A2B_cP6_224_b_a --params=$a$