CaCu$_{3}$Mn$_{4}$O$_{12}$ Structure: AB3C4D12_cI40_204_a_b_c_g-001
| Prototype | CaCu$_{3}$Mn$_{4}$O$_{12}$ |
| AFLOW prototype label | AB3C4D12_cI40_204_a_b_c_g-001 |
| ICSD | 15757 |
| Pearson symbol | cI40 |
| Space group number | 204 |
| Space group symbol | $Im\overline{3}$ |
| AFLOW prototype command |
aflow --proto=AB3C4D12_cI40_204_a_b_c_g-001
--params=$a, \allowbreak y_{4}, \allowbreak z_{4}$ |
Other compounds with this structure
CaCu$_{3}$Co$_{4}$O$_{12}$, CaCu$_{3}$Cr$_{4}$O$_{12}$, CaCu$_{3}$Fe$_{4}$O$_{12}$, CaCu$_{3}$Ge$_{4}$O$_{12}$, CaCu$_{3}$Ir$_{4}$O$_{12}$, CaCu$_{3}$Pt$_{4}$O$_{12}$, CaCu$_{3}$Rh$_{4}$O$_{12}$, CaCu$_{3}$Ru$_{4}$O$_{12}$, CaCu$_{3}$Sn$_{4}$O$_{12}$, CaCu$_{3}$Ti$_{4}$O$_{12}$, CaCu$_{3}$V$_{4}$O$_{12}$, CaCu$_{3}$Zn$_{4}$O$_{12}$, LaCu$_{3}$Ir$_{4}$O$_{12}$, LaCu$_{3}$Mn$_{4}$O$_{12}$, LaCu$_{3}$Ru$_{4}$O$_{12}$, NaCu$_{3}$Ir$_{4}$O$_{12}$, NaCu$_{3}$Ru$_{4}$O$_{12}$, SrCu$_{3}$Fe$_{4}$O$_{12}$
- This is the quaternary form of the double perovskite NaMn$_{7}$O$_{12}$.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&- \frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}- \frac{1}{2}a \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $0$ | = | $0$ | (2a) | Ca I |
| $\mathbf{B_{2}}$ | = | $\frac{1}{2} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}$ | (6b) | Cu I |
| $\mathbf{B_{3}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{y}}$ | (6b) | Cu I |
| $\mathbf{B_{4}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}$ | = | $\frac{1}{2}a \,\mathbf{\hat{z}}$ | (6b) | Cu I |
| $\mathbf{B_{5}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (8c) | Mn I |
| $\mathbf{B_{6}}$ | = | $\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}- \frac{1}{4}a \,\mathbf{\hat{z}}$ | (8c) | Mn I |
| $\mathbf{B_{7}}$ | = | $\frac{1}{2} \, \mathbf{a}_{2}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}- \frac{1}{4}a \,\mathbf{\hat{y}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (8c) | Mn I |
| $\mathbf{B_{8}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}$ | = | $- \frac{1}{4}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (8c) | Mn I |
| $\mathbf{B_{9}}$ | = | $\left(y_{4} + z_{4}\right) \, \mathbf{a}_{1}+z_{4} \, \mathbf{a}_{2}+y_{4} \, \mathbf{a}_{3}$ | = | $a y_{4} \,\mathbf{\hat{y}}+a z_{4} \,\mathbf{\hat{z}}$ | (24g) | O I |
| $\mathbf{B_{10}}$ | = | $- \left(y_{4} - z_{4}\right) \, \mathbf{a}_{1}+z_{4} \, \mathbf{a}_{2}- y_{4} \, \mathbf{a}_{3}$ | = | $- a y_{4} \,\mathbf{\hat{y}}+a z_{4} \,\mathbf{\hat{z}}$ | (24g) | O I |
| $\mathbf{B_{11}}$ | = | $\left(y_{4} - z_{4}\right) \, \mathbf{a}_{1}- z_{4} \, \mathbf{a}_{2}+y_{4} \, \mathbf{a}_{3}$ | = | $a y_{4} \,\mathbf{\hat{y}}- a z_{4} \,\mathbf{\hat{z}}$ | (24g) | O I |
| $\mathbf{B_{12}}$ | = | $- \left(y_{4} + z_{4}\right) \, \mathbf{a}_{1}- z_{4} \, \mathbf{a}_{2}- y_{4} \, \mathbf{a}_{3}$ | = | $- a y_{4} \,\mathbf{\hat{y}}- a z_{4} \,\mathbf{\hat{z}}$ | (24g) | O I |
| $\mathbf{B_{13}}$ | = | $y_{4} \, \mathbf{a}_{1}+\left(y_{4} + z_{4}\right) \, \mathbf{a}_{2}+z_{4} \, \mathbf{a}_{3}$ | = | $a z_{4} \,\mathbf{\hat{x}}+a y_{4} \,\mathbf{\hat{z}}$ | (24g) | O I |
| $\mathbf{B_{14}}$ | = | $- y_{4} \, \mathbf{a}_{1}- \left(y_{4} - z_{4}\right) \, \mathbf{a}_{2}+z_{4} \, \mathbf{a}_{3}$ | = | $a z_{4} \,\mathbf{\hat{x}}- a y_{4} \,\mathbf{\hat{z}}$ | (24g) | O I |
| $\mathbf{B_{15}}$ | = | $y_{4} \, \mathbf{a}_{1}+\left(y_{4} - z_{4}\right) \, \mathbf{a}_{2}- z_{4} \, \mathbf{a}_{3}$ | = | $- a z_{4} \,\mathbf{\hat{x}}+a y_{4} \,\mathbf{\hat{z}}$ | (24g) | O I |
| $\mathbf{B_{16}}$ | = | $- y_{4} \, \mathbf{a}_{1}- \left(y_{4} + z_{4}\right) \, \mathbf{a}_{2}- z_{4} \, \mathbf{a}_{3}$ | = | $- a z_{4} \,\mathbf{\hat{x}}- a y_{4} \,\mathbf{\hat{z}}$ | (24g) | O I |
| $\mathbf{B_{17}}$ | = | $z_{4} \, \mathbf{a}_{1}+y_{4} \, \mathbf{a}_{2}+\left(y_{4} + z_{4}\right) \, \mathbf{a}_{3}$ | = | $a y_{4} \,\mathbf{\hat{x}}+a z_{4} \,\mathbf{\hat{y}}$ | (24g) | O I |
| $\mathbf{B_{18}}$ | = | $z_{4} \, \mathbf{a}_{1}- y_{4} \, \mathbf{a}_{2}- \left(y_{4} - z_{4}\right) \, \mathbf{a}_{3}$ | = | $- a y_{4} \,\mathbf{\hat{x}}+a z_{4} \,\mathbf{\hat{y}}$ | (24g) | O I |
| $\mathbf{B_{19}}$ | = | $- z_{4} \, \mathbf{a}_{1}+y_{4} \, \mathbf{a}_{2}+\left(y_{4} - z_{4}\right) \, \mathbf{a}_{3}$ | = | $a y_{4} \,\mathbf{\hat{x}}- a z_{4} \,\mathbf{\hat{y}}$ | (24g) | O I |
| $\mathbf{B_{20}}$ | = | $- z_{4} \, \mathbf{a}_{1}- y_{4} \, \mathbf{a}_{2}- \left(y_{4} + z_{4}\right) \, \mathbf{a}_{3}$ | = | $- a y_{4} \,\mathbf{\hat{x}}- a z_{4} \,\mathbf{\hat{y}}$ | (24g) | O I |
References
- J. Chenavas, J. C. Joubert, and M. M. B. Bochu, The synthesis and crystal structure of CaCu$_{3}$Mn$_{4}$O$_{12}$: A new ferromagnetic-perovskite-like compound, J. Solid State Chem. 14, 25–32 (1975), doi:10.1016/0022-4596(75)90358-8.
Prototype Generator
aflow --proto=AB3C4D12_cI40_204_a_b_c_g --params=$a,y_{4},z_{4}$