Heusler (L21) Structure: AB2C_cF16_225_a_c_b
| Prototype | : | AlCu2Mn |
| AFLOW prototype label | : | AB2C_cF16_225_a_c_b |
| Strukturbericht designation | : | $L2_{1}$ |
| Pearson symbol | : | cF16 |
| Space group number | : | 225 |
| Space group symbol | : | $\mbox{Fm}\bar{3}\mbox{m}$ |
| AFLOW prototype command | : | aflow --proto=AB2C_cF16_225_a_c_b --params=$a$ |
Other compounds with this structure
- AlNi2Ti, AlNi2Hf
- All of the atoms are located on the sites of a body-centered cubic lattice. If we replace the Mn atom by another copper atom, the structure reduces to the crystallographically equivalent D03 lattice. Also see the C1b
half–Heusler
structure.
Face-centered Cubic primitive vectors:
\[
\begin{array}{ccc}
\mathbf{a}_1 & = & \frac12 \, a \, \mathbf{\hat{y}} + \frac12 \, a \, \mathbf{\hat{z}} \\
\mathbf{a}_2 & = & \frac12 \, a \, \mathbf{\hat{x}} + \frac12 \, a \, \mathbf{\hat{z}} \\
\mathbf{a}_3 & = & \frac12 \, a \, \mathbf{\hat{x}} + \frac12 \, a \, \mathbf{\hat{y}} \\
\end{array}
\]
Basis vectors:
\[ \begin{array}{ccccccc} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{Atom Type} \\ \mathbf{B_1} & = & 0 \, \mathbf{a}_{1} + 0 \, \mathbf{a}_{2} + 0 \, \mathbf{a}_{3} & = & 0 \mathbf{\hat{x}} + 0 \mathbf{\hat{y}} + 0 \mathbf{\hat{z}} & \left(4a\right) & \mbox{Al} \\ \mathbf{B_2} & =& \frac12 \mathbf{a}_{1} + \frac12 \mathbf{a}_{2} + \frac12\mathbf{a}_{3}& =& \frac12 \, a \, \mathbf{\hat{x}} + \frac12 \, a \, \mathbf{\hat{y}} + \frac12 \, a \, \mathbf{\hat{z}}& \left(4b\right) & \mbox{Mn} \\ \mathbf{B_3} & =& \frac14 \mathbf{a}_{1} + \frac14 \mathbf{a}_{2} + \frac14\mathbf{a}_{3}& =& \frac14 \, a \, \mathbf{\hat{x}} + \frac14 \, a \, \mathbf{\hat{y}} + \frac14 \, a \, \mathbf{\hat{z}}& \left(8c\right) & \mbox{Cu} \\ \mathbf{B_4} & =& \frac34 \mathbf{a}_{1} + \frac34 \mathbf{a}_{2} + \frac34\mathbf{a}_{3}& =& \frac34 \, a \, \mathbf{\hat{x}} + \frac34 \, a \, \mathbf{\hat{y}} + \frac34 \, a \, \mathbf{\hat{z}}& \left(8c\right) & \mbox{Cu} \\ \end{array} \]References
- A. J. Bradley and J. W. Rodgers, The Crystal Structure of Heusler Alloys, Proc. R. Soc. A Math. Phys. Eng. Sci. 144, 340–359 (1934), doi:10.1098/rspa.1934.0053.