$\alpha$–ThSi2 ($C_{c}$) Structure: A2B_tI12_141_e_a

Picture of Structure; Click for Big Picture
Prototype : ThSi2
AFLOW prototype label : A2B_tI12_141_e_a
Strukturbericht designation : $C_{c}$
Pearson symbol : tI12
Space group number : 141
Space group symbol : $I4_{1}/amd$
AFLOW prototype command : aflow --proto=A2B_tI12_141_e_a
--params=
$a$,$c/a$,$z_{2}$


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:

\[ \begin{array}{ccccccc} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{Atom Type} \\ \mathbf{B}_{1} & = & \frac{7}{8} \, \mathbf{a}_{1} + \frac{1}{8} \, \mathbf{a}_{2} + \frac{3}{4} \, \mathbf{a}_{3} & = & \frac{3}{4}a \, \mathbf{\hat{y}} + \frac{1}{8}c \, \mathbf{\hat{z}} & \left(4a\right) & \mbox{Th} \\ \mathbf{B}_{2} & = & \frac{1}{8} \, \mathbf{a}_{1} + \frac{7}{8} \, \mathbf{a}_{2} + \frac{1}{4} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + \frac{3}{4}a \, \mathbf{\hat{y}} + \frac{3}{8}c \, \mathbf{\hat{z}} & \left(4a\right) & \mbox{Th} \\ \mathbf{B}_{3} & = & \left(\frac{1}{4} +z_{2}\right) \, \mathbf{a}_{1} + z_{2} \, \mathbf{a}_{2} + \frac{1}{4} \, \mathbf{a}_{3} & = & \frac{1}{4}a \, \mathbf{\hat{y}} + z_{2}c \, \mathbf{\hat{z}} & \left(8e\right) & \mbox{Si} \\ \mathbf{B}_{4} & = & z_{2} \, \mathbf{a}_{1} + \left(\frac{1}{4} +z_{2}\right) \, \mathbf{a}_{2} + \frac{3}{4} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + \frac{1}{4}a \, \mathbf{\hat{y}} + \left(- \frac{1}{4} +z_{2}\right)c \, \mathbf{\hat{z}} & \left(8e\right) & \mbox{Si} \\ \mathbf{B}_{5} & = & \left(\frac{3}{4} - z_{2}\right) \, \mathbf{a}_{1}-z_{2} \, \mathbf{a}_{2} + \frac{3}{4} \, \mathbf{a}_{3} & = & \frac{3}{4}a \, \mathbf{\hat{y}}-z_{2}c \, \mathbf{\hat{z}} & \left(8e\right) & \mbox{Si} \\ \mathbf{B}_{6} & = & -z_{2} \, \mathbf{a}_{1} + \left(\frac{3}{4} - z_{2}\right) \, \mathbf{a}_{2} + \frac{1}{4} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + \frac{3}{4}a \, \mathbf{\hat{y}} + \left(\frac{1}{4} - z_{2}\right)c \, \mathbf{\hat{z}} & \left(8e\right) & \mbox{Si} \\ \end{array} \]

References

  • G. Brauer and A. Mitius, Die Kristallstruktur des Thoriumsilicids ThSi2, Z. Anorg. Allg. Chem. 249, 325–339 (1942), doi:10.1002/zaac.19422490401.

Found in

  • W. B. Pearson, The Crystal Chemistry and Physics of Metals and Alloys (Wiley Interscience, New York, London, Sydney, Tornoto, 1972).

Geometry files


Prototype Generator

aflow --proto=A2B_tI12_141_e_a --params=

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