Al3Zr ($D0_{23}$) Structure: A3B_tI16_139_cde_e

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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=
$a$,$c/a$,$z_{3}$,$z_{4}$


  • When $c = 4a$, $z_{3} = 3/8$, and $z_{4} = 1/8$ the atoms are on the sites of a face-centered cubic lattice. This phase can also be described as a set of alternating L12 and D022 lattices.

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.

Geometry files


Prototype Generator

aflow --proto=A3B_tI16_139_cde_e --params=

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