TiSi2 ($C54$) Structure: A2B_oF24_70_e_a

Picture of Structure; Click for Big Picture
Prototype : TiSi2
AFLOW prototype label : A2B_oF24_70_e_a
Strukturbericht designation : $C54$
Pearson symbol : oF24
Space group number : 70
Space group symbol : $\mbox{Fddd}$
AFLOW prototype command : aflow --proto=A2B_oF24_70_e_a
--params=
$a$,$b/a$,$c/a$,$x_{2}$


Face-centered Orthorhombic primitive vectors:

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

Basis vectors:

\[ \begin{array}{ccccccc} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{Atom Type} \\ \mathbf{B}_{1} & =& \frac18 \, \mathbf{a}_{1} + \frac18 \, \mathbf{a}_{2} + \frac18 \, \mathbf{a}_{3}& =& \frac18 \, a \, \mathbf{\hat{x}} + \frac18 \, b \, \mathbf{\hat{y}} + \frac18 \, c \, \mathbf{\hat{z}}& \left(8a\right) & \mbox{Ti} \\ \mathbf{B}_{2} & =& \frac78 \, \mathbf{a}_{1} + \frac78 \, \mathbf{a}_{2} + \frac78 \, \mathbf{a}_{3}& =& \frac78 \, a \, \mathbf{\hat{x}} + \frac78 \, b \, \mathbf{\hat{y}} + \frac78 \, c \, \mathbf{\hat{z}}& \left(8a\right) & \mbox{Ti} \\ \mathbf{B}_{3} & =& \left(\frac14 - x_{2}\right) \, \mathbf{a}_{1} + x_{2} \, \mathbf{a}_{2} + x_{2} \, \mathbf{a}_{3}& =& x_{2} \, a \, \mathbf{\hat{x}} + \frac18 \, b \, \mathbf{\hat{y}} + \frac18 \, c \, \mathbf{\hat{z}}& \left(16e\right) & \mbox{Si} \\ \mathbf{B}_{4} & =& x_{2} \, \mathbf{a}_{1} + \left(\frac14 - x_{2}\right) \, \mathbf{a}_{2} + \left(\frac14 - x_{2}\right) \, \mathbf{a}_{3}& =& \left(\frac14 - x_{2}\right) \, a \, \mathbf{\hat{x}} + \frac18 \, b \, \mathbf{\hat{y}} + \frac18 \, c \, \mathbf{\hat{z}}& \left(16e\right) & \mbox{Si} \\ \mathbf{B}_{5} & =& \left(\frac34 + x_{2}\right) \, \mathbf{a}_{1} - x_{2} \, \mathbf{a}_{2} + - x_{2} \, \mathbf{a}_{3}& =& - x_{2} \, a \, \mathbf{\hat{x}} + \frac38 \, b \, \mathbf{\hat{y}} + \frac38 \, c \, \mathbf{\hat{z}}& \left(16e\right) & \mbox{Si} \\ \mathbf{B}_{6} & =& -x_{2} \, \mathbf{a}_{1} + \left(\frac34 + x_{2}\right) \, \mathbf{a}_{2} + \left(\frac34 + x_{2}\right) \, \mathbf{a}_{3}& =& \left(\frac34 + x_{2}\right) \, a \, \mathbf{\hat{x}} + \frac38 \, b \, \mathbf{\hat{y}} + \frac38 \, c \, \mathbf{\hat{z}}& \left(16e\right) & \mbox{Si} \\ \end{array} \]

References

  • W. Jeitschko, Refinement of the crystal structure of TiSi2 and some comments on bonding in TiSi2 and related compounds, Acta Crystallogr. Sect. B Struct. Sci. 33, 2347–2348 (1977), doi:10.1107/S0567740877008462.

Geometry files


Prototype Generator

aflow --proto=A2B_oF24_70_e_a --params=

Species:

Running:

Output: