AlB$_{4}$Mg Structure: AB4C_hP6_191_a_h_b-001
| Prototype | AlB$_{4}$Mg |
| AFLOW prototype label | AB4C_hP6_191_a_h_b-001 |
| ICSD | 97224 |
| Pearson symbol | hP6 |
| Space group number | 191 |
| Space group symbol | $P6/mmm$ |
| AFLOW prototype command |
aflow --proto=AB4C_hP6_191_a_h_b-001
--params=$a, \allowbreak c/a, \allowbreak z_{3}$ |
- Note that Table I of (Margadonna, 2002) mislabels the (1a) and (1b) Wyckoff positions.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \,\mathbf{\hat{y}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $0$ | = | $0$ | (1a) | Al I |
| $\mathbf{B_{2}}$ | = | $\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}c \,\mathbf{\hat{z}}$ | (1b) | Mg I |
| $\mathbf{B_{3}}$ | = | $\frac{1}{3} \, \mathbf{a}_{1}+\frac{2}{3} \, \mathbf{a}_{2}+z_{3} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+c z_{3} \,\mathbf{\hat{z}}$ | (4h) | B I |
| $\mathbf{B_{4}}$ | = | $\frac{2}{3} \, \mathbf{a}_{1}+\frac{1}{3} \, \mathbf{a}_{2}+z_{3} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+c z_{3} \,\mathbf{\hat{z}}$ | (4h) | B I |
| $\mathbf{B_{5}}$ | = | $\frac{2}{3} \, \mathbf{a}_{1}+\frac{1}{3} \, \mathbf{a}_{2}- z_{3} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}- c z_{3} \,\mathbf{\hat{z}}$ | (4h) | B I |
| $\mathbf{B_{6}}$ | = | $\frac{1}{3} \, \mathbf{a}_{1}+\frac{2}{3} \, \mathbf{a}_{2}- z_{3} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}- c z_{3} \,\mathbf{\hat{z}}$ | (4h) | B I |
References
- S. Margadonna, K. Prassides, I. Arvanitidis, M. Pissas, G. Papavassiliou, and A. N. Fitch, Crystal structure of the Mg$_{1-x}$Al$_x$B$_2$ superconductors near $x \approx 0.5$, Phys. Rev. B 66, 014518 (2002), doi:10.1103/PhysRevB.66.014518.
Prototype Generator
aflow --proto=AB4C_hP6_191_a_h_b --params=$a,c/a,z_{3}$