Al$_{2}$Mo$_{3}$C Structure: A2BC3_cP24_213_c_a_d-001
| Prototype | Al$_{2}$CMo$_{3}$ |
| AFLOW prototype label | A2BC3_cP24_213_c_a_d-001 |
| ICSD | 42917 |
| Pearson symbol | cP24 |
| Space group number | 213 |
| Space group symbol | $P4_132$ |
| AFLOW prototype command |
aflow --proto=A2BC3_cP24_213_c_a_d-001
--params=$a, \allowbreak x_{2}, \allowbreak y_{3}$ |
Other compounds with this structure
Ag$_{2}$Pd$_{3}$Sn, Al$_{2}$Nb$_{3}$C, Al$_{2}$Nb$_{3}$N, Al$_{2}$Ta$_{3}$C, Cr$_{2}$Re$_{3}$B, Li$_{2}$Pd$_{3}$B, Li$_{2}$Pt$_{3}$B, Mn$_{2}$Rh$_{3}$P, Ni$_{2}$W$_{3}$N, Re$_{2}$W$_{3}$C, Rh$_{2}$Mo$_{3}$N, (Fe$_{2-x}$Rh$_{x}$)Mo$_{3}$N
- This is a
filled
$\beta$–Mn (A13) structure, with the aluminum and molybdenum atoms almost exactly on the sites of the manganese atoms in A13. - This structure may also be found in the enantiomorphic space group $P4_{3}32$ #212.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&a \,\mathbf{\hat{x}}\\\mathbf{a_{2}}&=&a \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&a \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $\frac{3}{8} \, \mathbf{a}_{1}+\frac{3}{8} \, \mathbf{a}_{2}+\frac{3}{8} \, \mathbf{a}_{3}$ | = | $\frac{3}{8}a \,\mathbf{\hat{x}}+\frac{3}{8}a \,\mathbf{\hat{y}}+\frac{3}{8}a \,\mathbf{\hat{z}}$ | (4a) | C I |
| $\mathbf{B_{2}}$ | = | $\frac{1}{8} \, \mathbf{a}_{1}+\frac{5}{8} \, \mathbf{a}_{2}+\frac{7}{8} \, \mathbf{a}_{3}$ | = | $\frac{1}{8}a \,\mathbf{\hat{x}}+\frac{5}{8}a \,\mathbf{\hat{y}}+\frac{7}{8}a \,\mathbf{\hat{z}}$ | (4a) | C I |
| $\mathbf{B_{3}}$ | = | $\frac{5}{8} \, \mathbf{a}_{1}+\frac{7}{8} \, \mathbf{a}_{2}+\frac{1}{8} \, \mathbf{a}_{3}$ | = | $\frac{5}{8}a \,\mathbf{\hat{x}}+\frac{7}{8}a \,\mathbf{\hat{y}}+\frac{1}{8}a \,\mathbf{\hat{z}}$ | (4a) | C I |
| $\mathbf{B_{4}}$ | = | $\frac{7}{8} \, \mathbf{a}_{1}+\frac{1}{8} \, \mathbf{a}_{2}+\frac{5}{8} \, \mathbf{a}_{3}$ | = | $\frac{7}{8}a \,\mathbf{\hat{x}}+\frac{1}{8}a \,\mathbf{\hat{y}}+\frac{5}{8}a \,\mathbf{\hat{z}}$ | (4a) | C I |
| $\mathbf{B_{5}}$ | = | $x_{2} \, \mathbf{a}_{1}+x_{2} \, \mathbf{a}_{2}+x_{2} \, \mathbf{a}_{3}$ | = | $a x_{2} \,\mathbf{\hat{x}}+a x_{2} \,\mathbf{\hat{y}}+a x_{2} \,\mathbf{\hat{z}}$ | (8c) | Al I |
| $\mathbf{B_{6}}$ | = | $- \left(x_{2} - \frac{1}{2}\right) \, \mathbf{a}_{1}- x_{2} \, \mathbf{a}_{2}+\left(x_{2} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{2} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a x_{2} \,\mathbf{\hat{y}}+a \left(x_{2} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8c) | Al I |
| $\mathbf{B_{7}}$ | = | $- x_{2} \, \mathbf{a}_{1}+\left(x_{2} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{2} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{2} \,\mathbf{\hat{x}}+a \left(x_{2} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(x_{2} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8c) | Al I |
| $\mathbf{B_{8}}$ | = | $\left(x_{2} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{2} - \frac{1}{2}\right) \, \mathbf{a}_{2}- x_{2} \, \mathbf{a}_{3}$ | = | $a \left(x_{2} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(x_{2} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- a x_{2} \,\mathbf{\hat{z}}$ | (8c) | Al I |
| $\mathbf{B_{9}}$ | = | $\left(x_{2} + \frac{3}{4}\right) \, \mathbf{a}_{1}+\left(x_{2} + \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(x_{2} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{2} + \frac{3}{4}\right) \,\mathbf{\hat{x}}+a \left(x_{2} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(x_{2} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (8c) | Al I |
| $\mathbf{B_{10}}$ | = | $- \left(x_{2} - \frac{3}{4}\right) \, \mathbf{a}_{1}- \left(x_{2} - \frac{3}{4}\right) \, \mathbf{a}_{2}- \left(x_{2} - \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{2} - \frac{3}{4}\right) \,\mathbf{\hat{x}}- a \left(x_{2} - \frac{3}{4}\right) \,\mathbf{\hat{y}}- a \left(x_{2} - \frac{3}{4}\right) \,\mathbf{\hat{z}}$ | (8c) | Al I |
| $\mathbf{B_{11}}$ | = | $\left(x_{2} + \frac{1}{4}\right) \, \mathbf{a}_{1}- \left(x_{2} - \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(x_{2} + \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{2} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(x_{2} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(x_{2} + \frac{3}{4}\right) \,\mathbf{\hat{z}}$ | (8c) | Al I |
| $\mathbf{B_{12}}$ | = | $- \left(x_{2} - \frac{1}{4}\right) \, \mathbf{a}_{1}+\left(x_{2} + \frac{3}{4}\right) \, \mathbf{a}_{2}+\left(x_{2} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{2} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(x_{2} + \frac{3}{4}\right) \,\mathbf{\hat{y}}+a \left(x_{2} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (8c) | Al I |
| $\mathbf{B_{13}}$ | = | $\frac{1}{8} \, \mathbf{a}_{1}+y_{3} \, \mathbf{a}_{2}+\left(y_{3} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{8}a \,\mathbf{\hat{x}}+a y_{3} \,\mathbf{\hat{y}}+a \left(y_{3} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (12d) | Mo I |
| $\mathbf{B_{14}}$ | = | $\frac{3}{8} \, \mathbf{a}_{1}- y_{3} \, \mathbf{a}_{2}+\left(y_{3} + \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $\frac{3}{8}a \,\mathbf{\hat{x}}- a y_{3} \,\mathbf{\hat{y}}+a \left(y_{3} + \frac{3}{4}\right) \,\mathbf{\hat{z}}$ | (12d) | Mo I |
| $\mathbf{B_{15}}$ | = | $\frac{7}{8} \, \mathbf{a}_{1}+\left(y_{3} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(y_{3} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $\frac{7}{8}a \,\mathbf{\hat{x}}+a \left(y_{3} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(y_{3} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (12d) | Mo I |
| $\mathbf{B_{16}}$ | = | $\frac{5}{8} \, \mathbf{a}_{1}- \left(y_{3} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(y_{3} - \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $\frac{5}{8}a \,\mathbf{\hat{x}}- a \left(y_{3} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(y_{3} - \frac{3}{4}\right) \,\mathbf{\hat{z}}$ | (12d) | Mo I |
| $\mathbf{B_{17}}$ | = | $\left(y_{3} + \frac{1}{4}\right) \, \mathbf{a}_{1}+\frac{1}{8} \, \mathbf{a}_{2}+y_{3} \, \mathbf{a}_{3}$ | = | $a \left(y_{3} + \frac{1}{4}\right) \,\mathbf{\hat{x}}+\frac{1}{8}a \,\mathbf{\hat{y}}+a y_{3} \,\mathbf{\hat{z}}$ | (12d) | Mo I |
| $\mathbf{B_{18}}$ | = | $\left(y_{3} + \frac{3}{4}\right) \, \mathbf{a}_{1}+\frac{3}{8} \, \mathbf{a}_{2}- y_{3} \, \mathbf{a}_{3}$ | = | $a \left(y_{3} + \frac{3}{4}\right) \,\mathbf{\hat{x}}+\frac{3}{8}a \,\mathbf{\hat{y}}- a y_{3} \,\mathbf{\hat{z}}$ | (12d) | Mo I |
| $\mathbf{B_{19}}$ | = | $- \left(y_{3} - \frac{1}{4}\right) \, \mathbf{a}_{1}+\frac{7}{8} \, \mathbf{a}_{2}+\left(y_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{3} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+\frac{7}{8}a \,\mathbf{\hat{y}}+a \left(y_{3} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (12d) | Mo I |
| $\mathbf{B_{20}}$ | = | $- \left(y_{3} - \frac{3}{4}\right) \, \mathbf{a}_{1}+\frac{5}{8} \, \mathbf{a}_{2}- \left(y_{3} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{3} - \frac{3}{4}\right) \,\mathbf{\hat{x}}+\frac{5}{8}a \,\mathbf{\hat{y}}- a \left(y_{3} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (12d) | Mo I |
| $\mathbf{B_{21}}$ | = | $y_{3} \, \mathbf{a}_{1}+\left(y_{3} + \frac{1}{4}\right) \, \mathbf{a}_{2}+\frac{1}{8} \, \mathbf{a}_{3}$ | = | $a y_{3} \,\mathbf{\hat{x}}+a \left(y_{3} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+\frac{1}{8}a \,\mathbf{\hat{z}}$ | (12d) | Mo I |
| $\mathbf{B_{22}}$ | = | $- y_{3} \, \mathbf{a}_{1}+\left(y_{3} + \frac{3}{4}\right) \, \mathbf{a}_{2}+\frac{3}{8} \, \mathbf{a}_{3}$ | = | $- a y_{3} \,\mathbf{\hat{x}}+a \left(y_{3} + \frac{3}{4}\right) \,\mathbf{\hat{y}}+\frac{3}{8}a \,\mathbf{\hat{z}}$ | (12d) | Mo I |
| $\mathbf{B_{23}}$ | = | $\left(y_{3} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{3} - \frac{1}{4}\right) \, \mathbf{a}_{2}+\frac{7}{8} \, \mathbf{a}_{3}$ | = | $a \left(y_{3} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(y_{3} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+\frac{7}{8}a \,\mathbf{\hat{z}}$ | (12d) | Mo I |
| $\mathbf{B_{24}}$ | = | $- \left(y_{3} - \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{3} - \frac{3}{4}\right) \, \mathbf{a}_{2}+\frac{5}{8} \, \mathbf{a}_{3}$ | = | $- a \left(y_{3} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(y_{3} - \frac{3}{4}\right) \,\mathbf{\hat{y}}+\frac{5}{8}a \,\mathbf{\hat{z}}$ | (12d) | Mo I |
References
- W. Jeitschko, H. Nowotny, and F. Benesovsky, Ein Beitrag zum Dreistoff: Molybdän-Aluminium-Kohlenstoff, Mh. Chem. 94, 247–251 (1963), doi:10.1007/BF00900244.
Found in
- J. Johnston, L. Toth, K. Kennedy, and E. R. Parker, Superconductivity of Mo$_{3}$Al$_{2}$C, Solid State Commun. 2, 123 (1964), doi:10.1016/0038-1098(64)90251-0.
Prototype Generator
aflow --proto=A2BC3_cP24_213_c_a_d --params=$a,x_{2},y_{3}$