Khatyrkite (Al2Cu, $C16$) Structure: A2B_tI12_140_h_a

Picture of Structure; Click for Big Picture
Prototype : Al2Cu
AFLOW prototype label : A2B_tI12_140_h_a
Strukturbericht designation : $C16$
Pearson symbol : tI12
Space group number : 140
Space group symbol : $\mbox{I4/mcm}$
AFLOW prototype command : aflow --proto=A2B_tI12_140_h_a
--params=
$a$,$c/a$,$x_{2}$


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:

\[ \begin{array}{ccccccc} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{Atom Type} \\ \mathbf{B}_{1} & =& \frac14 \, \mathbf{a}_{1} + \frac14 \, \mathbf{a}_{2}& =& \frac14 \, c \, \mathbf{\hat{z}}& \left(4a\right) & \mbox{Cu} \\ \mathbf{B}_{2} & =& \frac34 \, \mathbf{a}_{1} + \frac34 \, \mathbf{a}_{2}& =& \frac34 \, c \, \mathbf{\hat{z}}& \left(4a\right) & \mbox{Cu} \\ \mathbf{B}_{3} & =& \left(\frac12 + x_{2}\right) \, \mathbf{a}_{1} + x_{2} \, \mathbf{a}_{2} + \left(\frac12 + 2 x_{2}\right) \, \mathbf{a}_{3}& =& x_{2} \, a \, \mathbf{\hat{x}} + \left(\frac12 + x_{2}\right) \, a \, \mathbf{\hat{y}}& \left(8h\right) & \mbox{Al} \\ \mathbf{B}_{4} & =& \left(\frac12 - x_{2}\right) \, \mathbf{a}_{1} - x_{2} \, \mathbf{a}_{2} + \left(\frac12 - 2 x_{2}\right) \, \mathbf{a}_{3}& =& - x_{2} \, a \, \mathbf{\hat{x}} + \left(\frac12 - x_{2}\right) \, a \, \mathbf{\hat{y}}& \left(8h\right) & \mbox{Al} \\ \mathbf{B}_{5} & =& x_{2} \, \mathbf{a}_{1} + \left(\frac12 - x_{2}\right) \, \mathbf{a}_{2} + \frac12 \, \mathbf{a}_{3}& =& \left(\frac12 - x_{2}\right) \, a \, \mathbf{\hat{x}} + x_{2} \, a \, \mathbf{\hat{y}}& \left(8h\right) & \mbox{Al} \\ \mathbf{B}_{6} & =& - x_{2} \, \mathbf{a}_{1} + \left(\frac12 + x_{2}\right) \, \mathbf{a}_{2} + \frac12 \, \mathbf{a}_{3}& =& \left(\frac12 + x_{2}\right) \, a \, \mathbf{\hat{x}} - x_{2} \, a \, \mathbf{\hat{y}}& \left(8h\right) & \mbox{Al} \\ \end{array} \]

References

  • J. B. Friauf, The Crystal Structures of Two Intermetallic Compounds, J. Am. Chem. Soc. 49, 3107–3114 (1927), doi:10.1021/ja01411a017.

Geometry files


Prototype Generator

aflow --proto=A2B_tI12_140_h_a --params=

Species:

Running:

Output: