Cr$_{4}$AlB$_{6}$ Structure: AB6C4_oC22_65_a_3g_2h-001
| Prototype | AlB$_{6}$Cr$_{4}$ |
| AFLOW prototype label | AB6C4_oC22_65_a_3g_2h-001 |
| ICSD | 251807 |
| Pearson symbol | oC22 |
| Space group number | 65 |
| Space group symbol | $Cmmm$ |
| AFLOW prototype command |
aflow --proto=AB6C4_oC22_65_a_3g_2h-001
--params=$a, \allowbreak b/a, \allowbreak c/a, \allowbreak x_{2}, \allowbreak x_{3}, \allowbreak x_{4}, \allowbreak x_{5}, \allowbreak x_{6}$ |
- (Ade, 2015) put set the origin so that the aluminum atoms were at the (2c) Wyckoff position. We shifted this so that the aluminum atoms are at the (2a) Wyckoff position, placing an aluminum atom at the origin.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{1}{2}b \,\mathbf{\hat{y}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}b \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \,\mathbf{\hat{z}}
\end{array}\]
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 |
| $\mathbf{B_{4}}$ | = | $x_{3} \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{2}$ | = | $a x_{3} \,\mathbf{\hat{x}}$ | (4g) | B II |
| $\mathbf{B_{5}}$ | = | $- x_{3} \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}$ | = | $- a x_{3} \,\mathbf{\hat{x}}$ | (4g) | B II |
| $\mathbf{B_{6}}$ | = | $x_{4} \, \mathbf{a}_{1}+x_{4} \, \mathbf{a}_{2}$ | = | $a x_{4} \,\mathbf{\hat{x}}$ | (4g) | B III |
| $\mathbf{B_{7}}$ | = | $- x_{4} \, \mathbf{a}_{1}- x_{4} \, \mathbf{a}_{2}$ | = | $- a x_{4} \,\mathbf{\hat{x}}$ | (4g) | B III |
| $\mathbf{B_{8}}$ | = | $x_{5} \, \mathbf{a}_{1}+x_{5} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $a x_{5} \,\mathbf{\hat{x}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (4h) | Cr I |
| $\mathbf{B_{9}}$ | = | $- x_{5} \, \mathbf{a}_{1}- x_{5} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- a x_{5} \,\mathbf{\hat{x}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (4h) | Cr I |
| $\mathbf{B_{10}}$ | = | $x_{6} \, \mathbf{a}_{1}+x_{6} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $a x_{6} \,\mathbf{\hat{x}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (4h) | Cr II |
| $\mathbf{B_{11}}$ | = | $- x_{6} \, \mathbf{a}_{1}- x_{6} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- a x_{6} \,\mathbf{\hat{x}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (4h) | Cr II |
References
- 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.
Found in
- H. Zhang, J. Kim, R. Su, P. Richardson, J. Xi, E. Kisi, J. O'Connor, L. Shi, and I. Szlufarska, Defect behavior and radiation tolerance of MAB phases (MoAlB and Fe$_{2}$AlB$_{2}$) with comparison to MAX phases, Acta Mater. 196, 505–515 (2020), doi:10.1016/j.actamat.2020.07.002.
Prototype Generator
aflow --proto=AB6C4_oC22_65_a_3g_2h --params=$a,b/a,c/a,x_{2},x_{3},x_{4},x_{5},x_{6}$