AlB4Mg Structure: AB4C_hP6_191_a_h_b
| Prototype | : | AlB4Mg |
| AFLOW prototype label | : | AB4C_hP6_191_a_h_b |
| Strukturbericht designation | : | None |
| Pearson symbol | : | hP6 |
| Space group number | : | 191 |
| Space group symbol | : | $\mbox{P6/mmm}$ |
| AFLOW prototype command | : | aflow --proto=AB4C_hP6_191_a_h_b --params=$a,c/a,z_{3}$ |
- Note that Table I of (Margadonna, 2002) mislabels the (1a) and (1b) Wyckoff positions.
Hexagonal primitive vectors:
\[
\begin{array}{ccc}
\mathbf{a}_1 & = & \frac12 \, a \, \mathbf{\hat{x}} - \frac{\sqrt3}2 \, a \, \mathbf{\hat{y}} \\
\mathbf{a}_2 & = & \frac12 \, a \, \mathbf{\hat{x}} + \frac{\sqrt3}2 \, a \, \mathbf{\hat{y}} \\
\mathbf{a}_3 & = & c \, \mathbf{\hat{z}}\\
\end{array}
\]
Basis vectors:
\[ \begin{array}{ccccccc} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{Atom Type} \\ \mathbf{B}_{1} & = & 0 \, \mathbf{a}_{1} + 0 \, \mathbf{a}_{2} + 0 \, \mathbf{a}_{3} & = & 0 \mathbf{\hat{x}} + 0 \mathbf{\hat{y}} + 0 \mathbf{\hat{z}} & \left(1a\right) & \mbox{Al} \\ \mathbf{B}_{2} & = & \frac12 \, \mathbf{a}_{3} & = & \frac12 \, c \, \mathbf{\hat{z}} & \left(1b\right) & \mbox{Mg} \\ \mathbf{B}_{3} & =&\frac13 \mathbf{a}_{1}+ \frac23 \mathbf{a}_{2}+ z_{3} \, \mathbf{a}_{3}& = &\frac12 \, a \, \mathbf{\hat{x}}+ \frac1{2\sqrt{3}} \, a \, \mathbf{\hat{y}}+ z_{3} \, c \, \mathbf{\hat{z}}& \left(4h\right) & \mbox{B} \\ \mathbf{B}_{4} & =&\frac23 \mathbf{a}_{1}+ \frac13 \mathbf{a}_{2}+ z_{3} \, \mathbf{a}_{3}& = &\frac12 \, a \, \mathbf{\hat{x}}- \frac1{2\sqrt{3}} \, a \, \mathbf{\hat{y}}+ z_{3} \, c \, \mathbf{\hat{z}}& \left(4h\right) & \mbox{B} \\ \mathbf{B}_{5} & =&\frac23 \mathbf{a}_{1}+ \frac13 \mathbf{a}_{2}- z_{3} \, \mathbf{a}_{3}& = &\frac12 \, a \, \mathbf{\hat{x}}- \frac1{2\sqrt{3}} \, a \, \mathbf{\hat{y}}- z_{3} \, c \, \mathbf{\hat{z}}& \left(4h\right) & \mbox{B} \\ \mathbf{B}_{6} & =&\frac13 \mathbf{a}_{1}+ \frac23 \mathbf{a}_{2}- z_{3} \, \mathbf{a}_{3}& = &\frac12 \, a \, \mathbf{\hat{x}}+ \frac1{2\sqrt{3}} \, a \, \mathbf{\hat{y}}- z_{3} \, c \, \mathbf{\hat{z}}& \left(4h\right) & \mbox{B} \\ \end{array} \]References
- S. Margadonna, K. Prassides, I. Arvanitidis, M. Pissas, G. Papavassiliou, and A. N. Fitch, Crystal structure of the Mg1–xAlxB2 superconductors near x ≈ 0.5, Phys. Rev. B 66, 014518 (2002), doi:10.1103/PhysRevB.66.014518.