TiFeSi Structure: ABC_oI36_46_ac_bc_3b

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Prototype : TiFeSi
AFLOW prototype label : ABC_oI36_46_ac_bc_3b
Strukturbericht designation : None
Pearson symbol : oI36
Space group number : 46
Space group symbol : $Ima2$
AFLOW prototype command : aflow --proto=ABC_oI36_46_ac_bc_3b
--params=
$a$,$b/a$,$c/a$,$z_{1}$,$y_{2}$,$z_{2}$,$y_{3}$,$z_{3}$,$y_{4}$,$z_{4}$,$y_{5}$,$z_{5}$,$x_{6}$,$y_{6}$,$z_{6}$,$x_{7}$,$y_{7}$,$z_{7}$


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} & = & z_{1} \, \mathbf{a}_{1} + z_{1} \, \mathbf{a}_{2} & = & z_{1}c \, \mathbf{\hat{z}} & \left(4a\right) & \mbox{Fe I} \\ \mathbf{B}_{2} & = & z_{1} \, \mathbf{a}_{1} + \left(\frac{1}{2} +z_{1}\right) \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + z_{1}c \, \mathbf{\hat{z}} & \left(4a\right) & \mbox{Fe I} \\ \mathbf{B}_{3} & = & \left(y_{2}+z_{2}\right) \, \mathbf{a}_{1} + \left(\frac{1}{4} +z_{2}\right) \, \mathbf{a}_{2} + \left(\frac{1}{4} +y_{2}\right) \, \mathbf{a}_{3} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + y_{2}b \, \mathbf{\hat{y}} + z_{2}c \, \mathbf{\hat{z}} & \left(4b\right) & \mbox{Si I} \\ \mathbf{B}_{4} & = & \left(-y_{2}+z_{2}\right) \, \mathbf{a}_{1} + \left(\frac{3}{4} +z_{2}\right) \, \mathbf{a}_{2} + \left(\frac{3}{4} - y_{2}\right) \, \mathbf{a}_{3} & = & \frac{3}{4}a \, \mathbf{\hat{x}}-y_{2}b \, \mathbf{\hat{y}} + z_{2}c \, \mathbf{\hat{z}} & \left(4b\right) & \mbox{Si I} \\ \mathbf{B}_{5} & = & \left(y_{3}+z_{3}\right) \, \mathbf{a}_{1} + \left(\frac{1}{4} +z_{3}\right) \, \mathbf{a}_{2} + \left(\frac{1}{4} +y_{3}\right) \, \mathbf{a}_{3} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + y_{3}b \, \mathbf{\hat{y}} + z_{3}c \, \mathbf{\hat{z}} & \left(4b\right) & \mbox{Ti I} \\ \mathbf{B}_{6} & = & \left(-y_{3}+z_{3}\right) \, \mathbf{a}_{1} + \left(\frac{3}{4} +z_{3}\right) \, \mathbf{a}_{2} + \left(\frac{3}{4} - y_{3}\right) \, \mathbf{a}_{3} & = & \frac{3}{4}a \, \mathbf{\hat{x}}-y_{3}b \, \mathbf{\hat{y}} + z_{3}c \, \mathbf{\hat{z}} & \left(4b\right) & \mbox{Ti I} \\ \mathbf{B}_{7} & = & \left(y_{4}+z_{4}\right) \, \mathbf{a}_{1} + \left(\frac{1}{4} +z_{4}\right) \, \mathbf{a}_{2} + \left(\frac{1}{4} +y_{4}\right) \, \mathbf{a}_{3} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + y_{4}b \, \mathbf{\hat{y}} + z_{4}c \, \mathbf{\hat{z}} & \left(4b\right) & \mbox{Ti II} \\ \mathbf{B}_{8} & = & \left(-y_{4}+z_{4}\right) \, \mathbf{a}_{1} + \left(\frac{3}{4} +z_{4}\right) \, \mathbf{a}_{2} + \left(\frac{3}{4} - y_{4}\right) \, \mathbf{a}_{3} & = & \frac{3}{4}a \, \mathbf{\hat{x}}-y_{4}b \, \mathbf{\hat{y}} + z_{4}c \, \mathbf{\hat{z}} & \left(4b\right) & \mbox{Ti II} \\ \mathbf{B}_{9} & = & \left(y_{5}+z_{5}\right) \, \mathbf{a}_{1} + \left(\frac{1}{4} +z_{5}\right) \, \mathbf{a}_{2} + \left(\frac{1}{4} +y_{5}\right) \, \mathbf{a}_{3} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + y_{5}b \, \mathbf{\hat{y}} + z_{5}c \, \mathbf{\hat{z}} & \left(4b\right) & \mbox{Ti III} \\ \mathbf{B}_{10} & = & \left(-y_{5}+z_{5}\right) \, \mathbf{a}_{1} + \left(\frac{3}{4} +z_{5}\right) \, \mathbf{a}_{2} + \left(\frac{3}{4} - y_{5}\right) \, \mathbf{a}_{3} & = & \frac{3}{4}a \, \mathbf{\hat{x}}-y_{5}b \, \mathbf{\hat{y}} + z_{5}c \, \mathbf{\hat{z}} & \left(4b\right) & \mbox{Ti III} \\ \mathbf{B}_{11} & = & \left(y_{6}+z_{6}\right) \, \mathbf{a}_{1} + \left(x_{6}+z_{6}\right) \, \mathbf{a}_{2} + \left(x_{6}+y_{6}\right) \, \mathbf{a}_{3} & = & x_{6}a \, \mathbf{\hat{x}} + y_{6}b \, \mathbf{\hat{y}} + z_{6}c \, \mathbf{\hat{z}} & \left(8c\right) & \mbox{Fe II} \\ \mathbf{B}_{12} & = & \left(-y_{6}+z_{6}\right) \, \mathbf{a}_{1} + \left(-x_{6}+z_{6}\right) \, \mathbf{a}_{2} + \left(-x_{6}-y_{6}\right) \, \mathbf{a}_{3} & = & -x_{6}a \, \mathbf{\hat{x}}-y_{6}b \, \mathbf{\hat{y}} + z_{6}c \, \mathbf{\hat{z}} & \left(8c\right) & \mbox{Fe II} \\ \mathbf{B}_{13} & = & \left(-y_{6}+z_{6}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +x_{6} + z_{6}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +x_{6} - y_{6}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +x_{6}\right)a \, \mathbf{\hat{x}}-y_{6}b \, \mathbf{\hat{y}} + z_{6}c \, \mathbf{\hat{z}} & \left(8c\right) & \mbox{Fe II} \\ \mathbf{B}_{14} & = & \left(y_{6}+z_{6}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - x_{6} + z_{6}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - x_{6} + y_{6}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} - x_{6}\right)a \, \mathbf{\hat{x}} + y_{6}b \, \mathbf{\hat{y}} + z_{6}c \, \mathbf{\hat{z}} & \left(8c\right) & \mbox{Fe II} \\ \mathbf{B}_{15} & = & \left(y_{7}+z_{7}\right) \, \mathbf{a}_{1} + \left(x_{7}+z_{7}\right) \, \mathbf{a}_{2} + \left(x_{7}+y_{7}\right) \, \mathbf{a}_{3} & = & x_{7}a \, \mathbf{\hat{x}} + y_{7}b \, \mathbf{\hat{y}} + z_{7}c \, \mathbf{\hat{z}} & \left(8c\right) & \mbox{Si II} \\ \mathbf{B}_{16} & = & \left(-y_{7}+z_{7}\right) \, \mathbf{a}_{1} + \left(-x_{7}+z_{7}\right) \, \mathbf{a}_{2} + \left(-x_{7}-y_{7}\right) \, \mathbf{a}_{3} & = & -x_{7}a \, \mathbf{\hat{x}}-y_{7}b \, \mathbf{\hat{y}} + z_{7}c \, \mathbf{\hat{z}} & \left(8c\right) & \mbox{Si II} \\ \mathbf{B}_{17} & = & \left(-y_{7}+z_{7}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +x_{7} + z_{7}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +x_{7} - y_{7}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +x_{7}\right)a \, \mathbf{\hat{x}}-y_{7}b \, \mathbf{\hat{y}} + z_{7}c \, \mathbf{\hat{z}} & \left(8c\right) & \mbox{Si II} \\ \mathbf{B}_{18} & = & \left(y_{7}+z_{7}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - x_{7} + z_{7}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - x_{7} + y_{7}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} - x_{7}\right)a \, \mathbf{\hat{x}} + y_{7}b \, \mathbf{\hat{y}} + z_{7}c \, \mathbf{\hat{z}} & \left(8c\right) & \mbox{Si II} \\ \end{array} \]

References

  • W. Jeitschko, The crystal structure of TiFeSi and related compounds, Acta Crystallogr. Sect. B Struct. Sci. 26, 815–822 (1970), doi:10.1107/S0567740870003163.

Found in

  • P. Villars and K. Cenzual, Pearson's Crystal Data – Crystal Structure Database for Inorganic Compounds, ASM International (2013).

Geometry files


Prototype Generator

aflow --proto=ABC_oI36_46_ac_bc_3b --params=

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