Encyclopedia of Crystallographic Prototypes

AFLOW Prototype: A12B_cI26_204_g_a

  • 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)

Al12W Structure: A12B_cI26_204_g_a

Picture of Structure; Click for Big Picture
Prototype : Al12W
AFLOW prototype label : A12B_cI26_204_g_a
Strukturbericht designation : None
Pearson symbol : cI26
Space group number : 204
Space group symbol : $\text{Im}\bar{3}$
AFLOW prototype command : aflow --proto=A12B_cI26_204_g_a
--params=
$a$,$y_{2}$,$z_{2}$


Body-centered Cubic primitive vectors:

\[ \begin{array}{ccc} \mathbf{a}_1 & = & - \frac12 \, a \, \mathbf{\hat{x}} + \frac12 \, a \, \mathbf{\hat{y}} + \frac12 \, a \, \mathbf{\hat{z}} \\ \mathbf{a}_2 & = & ~ \frac12 \, a \, \mathbf{\hat{x}} - \frac12 \, a \, \mathbf{\hat{y}} + \frac12 \, a \, \mathbf{\hat{z}} \\ \mathbf{a}_3 & = & ~ \frac12 \, a \, \mathbf{\hat{x}} + \frac12 \, a \, \mathbf{\hat{y}} - \frac12 \, a \, \mathbf{\hat{z}} \\ \end{array} \]

Basis vectors:

\[ \begin{array}{ccccccc} & & \text{Lattice Coordinates} & & \text{Cartesian Coordinates} &\text{Wyckoff Position} & \text{Atom Type} \\ \mathbf{B}_{1} & = & 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(2a\right) & \text{W} \\ \mathbf{B}_{2} & = &\left(y_{2} + z_{2}\right) \, \mathbf{a}_{1}+ z_{2} \, \mathbf{a}_{2}+ y_{2} \, \mathbf{a}_{3}& = &y_{2} \, a \, \mathbf{\hat{y}}+ z_{2} \, a \, \mathbf{\hat{z}}& \left(24g\right) & \text{Al} \\ \mathbf{B}_{3} & = &\left(z_{2} - y_{2}\right) \, \mathbf{a}_{1}+ z_{2} \, \mathbf{a}_{2}- y_{2} \, \mathbf{a}_{3}& = &- y_{2} \, a \, \mathbf{\hat{y}}+ z_{2} \, a \, \mathbf{\hat{z}}& \left(24g\right) & \text{Al} \\ \mathbf{B}_{4} & = &\left(y_{2} - z_{2}\right) \, \mathbf{a}_{1}- z_{2} \, \mathbf{a}_{2}+ y_{2} \, \mathbf{a}_{3}& = &y_{2} \, a \, \mathbf{\hat{y}}- z_{2} \, a \, \mathbf{\hat{z}}& \left(24g\right) & \text{Al} \\ \mathbf{B}_{5} & = &- \left(y_{2} + z_{2}\right) \, \mathbf{a}_{1}- z_{2} \, \mathbf{a}_{2}- y_{2} \, \mathbf{a}_{3}& = &- y_{2} \, a \, \mathbf{\hat{y}}- z_{2} \, a \, \mathbf{\hat{z}}& \left(24g\right) & \text{Al} \\ \mathbf{B}_{6} & = &y_{2} \, \mathbf{a}_{1}+ \left(y_{2} + z_{2}\right) \, \mathbf{a}_{2}+ z_{2} \, \mathbf{a}_{3}& = &z_{2} \, a \, \mathbf{\hat{x}}+ y_{2} \, a \, \mathbf{\hat{z}}& \left(24g\right) & \text{Al} \\ \mathbf{B}_{7} & = &- y_{2} \, \mathbf{a}_{1}+ \left(z_{2} - y_{2}\right) \, \mathbf{a}_{2}+ z_{2} \, \mathbf{a}_{3}& = &z_{2} \, a \, \mathbf{\hat{x}}- y_{2} \, a \, \mathbf{\hat{z}}& \left(24g\right) & \text{Al} \\ \mathbf{B}_{8} & = &y_{2} \, \mathbf{a}_{1}+ \left(y_{2} - z_{2}\right) \, \mathbf{a}_{2}- z_{2} \, \mathbf{a}_{3}& = &- z_{2} \, a \, \mathbf{\hat{x}}+ y_{2} \, a \, \mathbf{\hat{z}}& \left(24g\right) & \text{Al} \\ \mathbf{B}_{9} & = &- y_{2} \, \mathbf{a}_{1}- \left(y_{2} + z_{2}\right) \, \mathbf{a}_{2}- z_{2} \, \mathbf{a}_{3}& = &- z_{2} \, a \, \mathbf{\hat{x}}- y_{2} \, a \, \mathbf{\hat{z}}& \left(24g\right) & \text{Al} \\ \mathbf{B}_{10} & = &z_{2} \, \mathbf{a}_{1}+ y_{2} \, \mathbf{a}_{2}+ \left(y_{2} + z_{2}\right) \, \mathbf{a}_{3}& = &y_{2} \, a \, \mathbf{\hat{x}}+ z_{2} \, a \, \mathbf{\hat{y}}& \left(24g\right) & \text{Al} \\ \mathbf{B}_{11} & = &z_{2} \, \mathbf{a}_{1}- y_{2} \, \mathbf{a}_{2}+ \left(z_{2} - y_{2}\right) \, \mathbf{a}_{3}& = &- y_{2} \, a \, \mathbf{\hat{x}}+ z_{2} \, a \, \mathbf{\hat{y}}& \left(24g\right) & \text{Al} \\ \mathbf{B}_{12} & = &- z_{2} \, \mathbf{a}_{1}+ y_{2} \, \mathbf{a}_{2}+ \left(y_{2} - z_{2}\right) \, \mathbf{a}_{3}& = &y_{2} \, a \, \mathbf{\hat{x}}- z_{2} \, a \, \mathbf{\hat{y}}& \left(24g\right) & \text{Al} \\ \mathbf{B}_{13} & = &- z_{2} \, \mathbf{a}_{1}- y_{2} \, \mathbf{a}_{2}- \left(y_{2} + z_{2}\right) \, \mathbf{a}_{3}& = &- y_{2} \, a \, \mathbf{\hat{x}}- z_{2} \, a \, \mathbf{\hat{y}}& \left(24g\right) & \text{Al} \\ \end{array} \]

References

  • J. Adam and J. B. Rich, The crystal structure of WAl12, MoAl12 and (Mn, Cr)Al12, Acta Cryst. 7, 813–816 (1954), doi:10.1107/S0365110X54002514.

Geometry files


Prototype Generator

aflow --proto=A12B_cI26_204_g_a --params=

Species:

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