ZrSi2 ($C49$) Structure: A2B_oC12_63_2c_c

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Prototype : ZrSi2
AFLOW prototype label : A2B_oC12_63_2c_c
Strukturbericht designation : $C49$
Pearson symbol : oC12
Space group number : 63
Space group symbol : $\mbox{Cmcm}$
AFLOW prototype command : aflow --proto=A2B_oC12_63_2c_c
--params=
$a$,$b/a$,$c/a$,$y_{1}$,$y_{2}$,$y_{3}$


Base-centered Orthorhombic primitive vectors:

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

Basis vectors:

\[ \begin{array}{ccccccc} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{Atom Type} \\ \mathbf{B}_{1} & =& - y_{1} \, \mathbf{a}_{1} + y_{1} \, \mathbf{a}_{2} + \frac14 \, \mathbf{a}_{3}& =& y_{1} \, b \, \mathbf{\hat{y}} + \frac14 \, c \mathbf{\hat{z}}& \left(4c\right) & \mbox{Si I} \\ \mathbf{B}_{2} & =& y_{1} \, \mathbf{a}_{1} - y_{1} \, \mathbf{a}_{2} + \frac34 \, \mathbf{a}_{3}& =& - y_{1} \, b \, \mathbf{\hat{y}} + \frac34 \, c \mathbf{\hat{z}}& \left(4c\right) & \mbox{Si I} \\ \mathbf{B}_{3} & =& - y_{2} \, \mathbf{a}_{1} + y_{2} \, \mathbf{a}_{2} + \frac14 \, \mathbf{a}_{3}& =& y_{2} \, b \, \mathbf{\hat{y}} + \frac14 \, c \mathbf{\hat{z}}& \left(4c\right) & \mbox{Si II} \\ \mathbf{B}_{4} & =& y_{2} \, \mathbf{a}_{1} - y_{2} \, \mathbf{a}_{2} + \frac34 \, \mathbf{a}_{3}& =& - y_{2} \, b \, \mathbf{\hat{y}} + \frac34 \, c \mathbf{\hat{z}}& \left(4c\right) & \mbox{Si II} \\ \mathbf{B}_{5} & =& - y_{3} \, \mathbf{a}_{1} + y_{3} \, \mathbf{a}_{2} + \frac14 \, \mathbf{a}_{3}& =& y_{3} \, b \, \mathbf{\hat{y}} + \frac14 \, c \mathbf{\hat{z}}& \left(4c\right) & \mbox{Zr} \\ \mathbf{B}_{6} & =& y_{3} \, \mathbf{a}_{1} - y_{3} \, \mathbf{a}_{2} + \frac34 \, \mathbf{a}_{3}& =& - y_{3} \, b \, \mathbf{\hat{y}} + \frac34 \, c \mathbf{\hat{z}}& \left(4c\right) & \mbox{Zr} \\ \end{array} \]

References

  • P. G. Cotter, J. A. Kohn, and R. A. Potter, Physical and X–Ray Study of the Disilicides of Titanium, Zirconium, and Hafnium, J. Am. Ceram. Soc. 39, 11–12 (1956), doi:10.1111/j.1151-2916.1956.tb15590.x.

Found in

  • P. Villars, Material Phases Data System ((MPDS), CH–6354 Vitznau, Switzerland, 2014). Accessed through the Springer Materials site.

Geometry files


Prototype Generator

aflow --proto=A2B_oC12_63_2c_c --params=

Species:

Running:

Output: