Al4U ($D1_{b}$) Structure: A4B_oI20_74_beh_e

Picture of Structure; Click for Big Picture
Prototype : AlU
AFLOW prototype label : A4B_oI20_74_beh_e
Strukturbericht designation : $D1_{b}$
Pearson symbol : oI20
Space group number : 74
Space group symbol : $Imma$
AFLOW prototype command : aflow --proto=A4B_oI20_74_beh_e
--params=
$a$,$b/a$,$c/a$,$z_{2}$,$z_{3}$,$y_{4}$,$z_{4}$


Other compounds with this structure

  • Al4Gd, Al4Np, Al4Pu

Body-centered Orthorhombic primitive vectors:

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

Basis vectors:

\[ \begin{array}{ccccccc} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{Atom Type} \\ \mathbf{B}_{1} & = & \frac{1}{2} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{2} & = & \frac{1}{2}c \, \mathbf{\hat{z}} & \left(4b\right) & \mbox{Al I} \\ \mathbf{B}_{2} & = & \frac{1}{2} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} & \left(4b\right) & \mbox{Al I} \\ \mathbf{B}_{3} & = & \left(\frac{1}{4} +z_{2}\right) \, \mathbf{a}_{1} + z_{2} \, \mathbf{a}_{2} + \frac{1}{4} \, \mathbf{a}_{3} & = & \frac{1}{4}b \, \mathbf{\hat{y}} + z_{2}c \, \mathbf{\hat{z}} & \left(4e\right) & \mbox{Al II} \\ \mathbf{B}_{4} & = & \left(\frac{3}{4} - z_{2}\right) \, \mathbf{a}_{1}-z_{2} \, \mathbf{a}_{2} + \frac{3}{4} \, \mathbf{a}_{3} & = & \frac{3}{4}b \, \mathbf{\hat{y}}-z_{2}c \, \mathbf{\hat{z}} & \left(4e\right) & \mbox{Al II} \\ \mathbf{B}_{5} & = & \left(\frac{1}{4} +z_{3}\right) \, \mathbf{a}_{1} + z_{3} \, \mathbf{a}_{2} + \frac{1}{4} \, \mathbf{a}_{3} & = & \frac{1}{4}b \, \mathbf{\hat{y}} + z_{3}c \, \mathbf{\hat{z}} & \left(4e\right) & \mbox{U} \\ \mathbf{B}_{6} & = & \left(\frac{3}{4} - z_{3}\right) \, \mathbf{a}_{1}-z_{3} \, \mathbf{a}_{2} + \frac{3}{4} \, \mathbf{a}_{3} & = & \frac{3}{4}b \, \mathbf{\hat{y}}-z_{3}c \, \mathbf{\hat{z}} & \left(4e\right) & \mbox{U} \\ \mathbf{B}_{7} & = & \left(y_{4}+z_{4}\right) \, \mathbf{a}_{1} + z_{4} \, \mathbf{a}_{2} + y_{4} \, \mathbf{a}_{3} & = & y_{4}b \, \mathbf{\hat{y}} + z_{4}c \, \mathbf{\hat{z}} & \left(8h\right) & \mbox{Al III} \\ \mathbf{B}_{8} & = & \left(\frac{1}{2} - y_{4} + z_{4}\right) \, \mathbf{a}_{1} + z_{4} \, \mathbf{a}_{2} + \left(\frac{1}{2} - y_{4}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} - y_{4}\right)b \, \mathbf{\hat{y}} + z_{4}c \, \mathbf{\hat{z}} & \left(8h\right) & \mbox{Al III} \\ \mathbf{B}_{9} & = & \left(\frac{1}{2} +y_{4} - z_{4}\right) \, \mathbf{a}_{1}-z_{4} \, \mathbf{a}_{2} + \left(\frac{1}{2} +y_{4}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +y_{4}\right)b \, \mathbf{\hat{y}}-z_{4}c \, \mathbf{\hat{z}} & \left(8h\right) & \mbox{Al III} \\ \mathbf{B}_{10} & = & \left(-y_{4}-z_{4}\right) \, \mathbf{a}_{1}-z_{4} \, \mathbf{a}_{2}-y_{4} \, \mathbf{a}_{3} & = & -y_{4}b \, \mathbf{\hat{y}}-z_{4}c \, \mathbf{\hat{z}} & \left(8h\right) & \mbox{Al III} \\ \end{array} \]

References

  • H. U. Borgstedt and H. Wedemeyer, Gmelin Handbook of Inorganic Chemistry (Springer–Verlag, Berlin Heidelberg, 1989), vol. Supplement B 2, chap. 3, p. 144.

Geometry files


Prototype Generator

aflow --proto=A4B_oI20_74_beh_e --params=

Species:

Running:

Output: