Encyclopedia of Crystallographic Prototypes

AFLOW Prototype: A3B_tI16_139_cde_e

  • M. J. Mehl, D. Hicks, C. Toher, O. Levy, R. M. Hanson, G. L. W. Hart, and S. Curtarolo, The AFLOW Library of Crystallographic Prototypes: Part 1, Comp. Mat. Sci. 136, S1-S828 (2017). (doi=10.1016/j.commatsci.2017.01.017)
  • D. Hicks, M. J. Mehl, E. Gossett, C. Toher, O. Levy, R. M. Hanson, G. L. W. Hart, and S. Curtarolo, The AFLOW Library of Crystallographic Prototypes: Part 2, Comp. Mat. Sci. 161, S1-S1011 (2019). (doi=10.1016/j.commatsci.2018.10.043)
  • D. Hicks, M.J. Mehl, M. Esters, C. Oses, O. Levy, G.L.W. Hart, C. Toher, and S. Curtarolo, The AFLOW Library of Crystallographic Prototypes: Part 3, Comp. Mat. Sci. 199, 110450 (2021). (doi=10.1016/j.commatsci.2021.110450)

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

Picture of Structure; Click for Big Picture
Prototype : Al3Zr
AFLOW prototype label : A3B_tI16_139_cde_e
Strukturbericht designation : $D0_{23}$
Pearson symbol : tI16
Space group number : 139
Space group symbol : $\text{I4/mmm}$
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:

\[ \begin{array}{ccccccc} & & \text{Lattice Coordinates} & & \text{Cartesian Coordinates} &\text{Wyckoff Position} & \text{Atom Type} \\ \mathbf{B}_{1} & =&\frac12 \, \mathbf{a}_{1}+ \frac12 \, \mathbf{a}_{3}& =&\frac12 \, a \, \mathbf{\hat{y}}& \left(4c\right) & \text{Al I} \\ \mathbf{B}_{2} & =&\frac12 \, \mathbf{a}_{2}+ \frac12 \, \mathbf{a}_{3}& =&\frac12 \, a \, \mathbf{\hat{x}}& \left(4c\right) & \text{Al I} \\ \mathbf{B}_{3} & =&\frac34 \, \mathbf{a}_{1}+ \frac14 \, \mathbf{a}_{2}+ \frac12 \, \mathbf{a}_{3}& =&\frac12 \, a \, \mathbf{\hat{y}}+ \frac14 \, c \, \mathbf{\hat{z}}& \left(4d\right) & \text{Al II} \\ \mathbf{B}_{4} & =&\frac14 \, \mathbf{a}_{1}+ \frac34 \, \mathbf{a}_{2}+ \frac12 \, \mathbf{a}_{3}& =&\frac12 \, a \, \mathbf{\hat{x}}+ \frac14 \, c \, \mathbf{\hat{z}}& \left(4d\right) & \text{Al II} \\ \mathbf{B}_{5} & =&z_{3} \, \mathbf{a}_{1}+ z_{3} \, \mathbf{a}_{2}& =&+ z_{3} \, c \, \mathbf{\hat{z}}& \left(4e\right) & \text{Al III} \\ \mathbf{B}_{6} & =&- z_{3} \, \mathbf{a}_{1}- z_{3} \, \mathbf{a}_{2}& =&- z_{3} \, c \, \mathbf{\hat{z}}& \left(4e\right) & \text{Al III} \\ \mathbf{B}_{7} & =&z_{4} \, \mathbf{a}_{1}+ z_{4} \, \mathbf{a}_{2}& =&+ z_{4} \, c \, \mathbf{\hat{z}}& \left(4e\right) & \text{Zr} \\ \mathbf{B}_{8} & =&- z_{4} \, \mathbf{a}_{1}- z_{4} \, \mathbf{a}_{2}& =&- z_{4} \, c \, \mathbf{\hat{z}}& \left(4e\right) & \text{Zr} \\ \end{array} \]

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=

Species:

Running:

Output: