Al3Zr (D023) Structure: A3B_tI16_139_cde_e
| Prototype | : | Al3Zr |
| AFLOW prototype label | : | A3B_tI16_139_cde_e |
| Strukturbericht designation | : | $D0_{23}$ |
| Pearson symbol | : | tI16 |
| Space group number | : | 139 |
| Space group symbol | : | $\mbox{I4/mmm}$ |
| AFLOW prototype command | : | aflow --proto=A3B_tI16_139_cde_e --params=$a,c/a,z_{3},z_{4}$ |
Body-centered Tetragonal primitive vectors:
\[
\begin{array}{ccc}
\mathbf{a}_1 & = & - \frac12 \, a \, \mathbf{\hat{x}} + \frac12 \, a \, \mathbf{\hat{y}} + \frac12 \, c \, \mathbf{\hat{z}}\\
\mathbf{a}_2 & = & ~ \frac12 \, a \, \mathbf{\hat{x}} - \frac12 \, a \, \mathbf{\hat{y}} + \frac12 \, c \, \mathbf{\hat{z}}\\
\mathbf{a}_3 & = & ~ \frac12 \, a \, \mathbf{\hat{x}} + \frac12 \, a \, \mathbf{\hat{y}} - \frac12 \, c \, \mathbf{\hat{z}}\\
\end{array}
\]
Basis vectors:
\[ \begin{array}{ccccccc} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{Atom Type} \\ \mathbf{B}_{1} & =&\frac12 \, \mathbf{a}_{1}+ \frac12 \, \mathbf{a}_{3}& =&\frac12 \, a \, \mathbf{\hat{y}}& \left(4c\right) & \mbox{Al I} \\ \mathbf{B}_{2} & =&\frac12 \, \mathbf{a}_{2}+ \frac12 \, \mathbf{a}_{3}& =&\frac12 \, a \, \mathbf{\hat{x}}& \left(4c\right) & \mbox{Al I} \\ \mathbf{B}_{3} & =&\frac34 \, \mathbf{a}_{1}+ \frac14 \, \mathbf{a}_{2}+ \frac12 \, \mathbf{a}_{3}& =&\frac12 \, a \, \mathbf{\hat{y}}+ \frac14 \, c \, \mathbf{\hat{z}}& \left(4d\right) & \mbox{Al II} \\ \mathbf{B}_{4} & =&\frac14 \, \mathbf{a}_{1}+ \frac34 \, \mathbf{a}_{2}+ \frac12 \, \mathbf{a}_{3}& =&\frac12 \, a \, \mathbf{\hat{x}}+ \frac14 \, c \, \mathbf{\hat{z}}& \left(4d\right) & \mbox{Al II} \\ \mathbf{B}_{5} & =&z_{3} \, \mathbf{a}_{1}+ z_{3} \, \mathbf{a}_{2}& =&+ z_{3} \, c \, \mathbf{\hat{z}}& \left(4e\right) & \mbox{Al III} \\ \mathbf{B}_{6} & =&- z_{3} \, \mathbf{a}_{1}- z_{3} \, \mathbf{a}_{2}& =&- z_{3} \, c \, \mathbf{\hat{z}}& \left(4e\right) & \mbox{Al III} \\ \mathbf{B}_{7} & =&z_{4} \, \mathbf{a}_{1}+ z_{4} \, \mathbf{a}_{2}& =&+ z_{4} \, c \, \mathbf{\hat{z}}& \left(4e\right) & \mbox{Zr} \\ \mathbf{B}_{8} & =&- z_{4} \, \mathbf{a}_{1}- z_{4} \, \mathbf{a}_{2}& =&- z_{4} \, c \, \mathbf{\hat{z}}& \left(4e\right) & \mbox{Zr} \\ \end{array} \]References
- Y. Ma, C. Romming, B. Lebech, J. Gjonnes, and J. Tafto, Structure Refinement of Al3Zr using Single–Crystal X–ray Diffraction, Powder Neutron Diffraction and CBED, Acta Crystallogr. Sect. B Struct. Sci. B48, 11–16 (1992), doi:10.1107/S0108768191010467.
Found in
- G. Ghosh and M. Asta, First–principles calculation of structural energetics of Al–TM (TM = Ti, Zr, Hf) intermetallics, Acta Mater. 53, 3225–3252 (2005), doi:10.1016/j.actamat.2005.03.028.