Mn$_{2}$AlB$_{2}$ Structure: AB2C2_oC10_65_a_g_h-001
| Prototype | AlB$_{2}$Mn$_{2}$ |
| AFLOW prototype label | AB2C2_oC10_65_a_g_h-001 |
| ICSD | 25518 |
| Pearson symbol | oC10 |
| Space group number | 65 |
| Space group symbol | $Cmmm$ |
| AFLOW prototype command |
aflow --proto=AB2C2_oC10_65_a_g_h-001
--params=$a, \allowbreak b/a, \allowbreak c/a, \allowbreak x_{2}, \allowbreak x_{3}$ |
Other compounds with this structure
Cr$_{2}$AlB$_{2}$, Fe$_{2}$AlB$_{2}$
- (Becher, 1966) give the space group as $C222$ #20, but their Wyckoff positions are obviously from space group $Cmmm$ #65, a result which was confirmed by (Ade, 2015).
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{1}{2}b \,\mathbf{\hat{y}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}b \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $0$ | = | $0$ | (2a) | Al I |
| $\mathbf{B_{2}}$ | = | $x_{2} \, \mathbf{a}_{1}+x_{2} \, \mathbf{a}_{2}$ | = | $a x_{2} \,\mathbf{\hat{x}}$ | (4g) | B I |
| $\mathbf{B_{3}}$ | = | $- x_{2} \, \mathbf{a}_{1}- x_{2} \, \mathbf{a}_{2}$ | = | $- a x_{2} \,\mathbf{\hat{x}}$ | (4g) | B I |
| $\mathbf{B_{4}}$ | = | $x_{3} \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{x}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (4h) | Mn I |
| $\mathbf{B_{5}}$ | = | $- x_{3} \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (4h) | Mn I |
References
- H. J. Becher, K. Krogmann, and E. Peisker, Über das ternáre Borid Mn$_{2}$AlB$_{2}$, Z. Anorganische und Allgemeine Chemie 344, 140–147 (1966), doi:10.1002/zaac.19663440304.
- K. Cenzual, L. M. Gelato, M. Penzo, and E. Parthé, Inorganic structure types with revised space groups. I, Acta Crystallogr. Sect. B 47, 433–439 (1991), doi:10.1107/S0108768191000903.
- M. Ade and H. Hillebrecht, Ternary Borides Cr$_{2}$AlB$_{2}$, Cr$_{2}$AlB$_{4}$, and Cr$_{4}$AlB$_{6}$: The First Members of the Series (CrB$_{2}$)$_{n}$CrAl with $n = 1, 2, 3$ and a Unifying Concept for Ternary Borides as MAB-Phases, Inorg. Chem. 54, 6122–6135 (2015), doi:10.1021/acs.inorgchem.5b00049.
Found in
- M. Ade and H. Hillebrecht, Ternary Borides Cr$_{2}$AlB$_{2}$, Cr$_{2}$AlB$_{4}$, and Cr$_{4}$AlB$_{6}$: The First Members of the Series (CrB$_{2}$)$_{n}$CrAl with $n = 1, 2, 3$ and a Unifying Concept for Ternary Borides as MAB-Phases, Inorg. Chem. 54, 6122–6135 (2015), doi:10.1021/acs.inorgchem.5b00049.
- D. Hicks, C. Toher, D. C. Ford, F. Rose, C. D. Santo, O. Levy, M. J. Mehl, and S. Curtarolo, AFLOW-XtalFinder: a reliable choice to identify crystalline prototypes 7, 30 (2021), doi:10.1038/s41524-020-00483-4.
Prototype Generator
aflow --proto=AB2C2_oC10_65_a_g_h --params=$a,b/a,c/a,x_{2},x_{3}$