Co5Ge7 Structure: A5B7_tI24_107_ac_abd

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Prototype : Co5Ge7
AFLOW prototype label : A5B7_tI24_107_ac_abd
Strukturbericht designation : None
Pearson symbol : tI24
Space group number : 107
Space group symbol : $I4mm$
AFLOW prototype command : aflow --proto=A5B7_tI24_107_ac_abd
--params=
$a$,$c/a$,$z_{1}$,$z_{2}$,$z_{3}$,$x_{4}$,$z_{4}$,$x_{5}$,$z_{5}$


  • The origin of the $z$ axis is arbitrary. We have chosen to place the Ge (2a) atom at the origin, taking $z_{1} = 0$. (Schubert, 1960) instead set $z_{4} = 0$.

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} & = & z_{1} \, \mathbf{a}_{1} + z_{1} \, \mathbf{a}_{2} & = & z_{1}c \, \mathbf{\hat{z}} & \left(2a\right) & \mbox{Co I} \\ \mathbf{B}_{2} & = & z_{2} \, \mathbf{a}_{1} + z_{2} \, \mathbf{a}_{2} & = & z_{2}c \, \mathbf{\hat{z}} & \left(2a\right) & \mbox{Ge I} \\ \mathbf{B}_{3} & = & \left(\frac{1}{2} +z_{3}\right) \, \mathbf{a}_{1} + z_{3} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{y}} + z_{3}c \, \mathbf{\hat{z}} & \left(4b\right) & \mbox{Ge II} \\ \mathbf{B}_{4} & = & z_{3} \, \mathbf{a}_{1} + \left(\frac{1}{2} +z_{3}\right) \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + z_{3}c \, \mathbf{\hat{z}} & \left(4b\right) & \mbox{Ge II} \\ \mathbf{B}_{5} & = & \left(x_{4}+z_{4}\right) \, \mathbf{a}_{1} + \left(x_{4}+z_{4}\right) \, \mathbf{a}_{2} + 2x_{4} \, \mathbf{a}_{3} & = & x_{4}a \, \mathbf{\hat{x}} + x_{4}a \, \mathbf{\hat{y}} + z_{4}c \, \mathbf{\hat{z}} & \left(8c\right) & \mbox{Co II} \\ \mathbf{B}_{6} & = & \left(-x_{4}+z_{4}\right) \, \mathbf{a}_{1} + \left(-x_{4}+z_{4}\right) \, \mathbf{a}_{2}-2x_{4} \, \mathbf{a}_{3} & = & -x_{4}a \, \mathbf{\hat{x}}-x_{4}a \, \mathbf{\hat{y}} + z_{4}c \, \mathbf{\hat{z}} & \left(8c\right) & \mbox{Co II} \\ \mathbf{B}_{7} & = & \left(x_{4}+z_{4}\right) \, \mathbf{a}_{1} + \left(-x_{4}+z_{4}\right) \, \mathbf{a}_{2} & = & -x_{4}a \, \mathbf{\hat{x}} + x_{4}a \, \mathbf{\hat{y}} + z_{4}c \, \mathbf{\hat{z}} & \left(8c\right) & \mbox{Co II} \\ \mathbf{B}_{8} & = & \left(-x_{4}+z_{4}\right) \, \mathbf{a}_{1} + \left(x_{4}+z_{4}\right) \, \mathbf{a}_{2} & = & x_{4}a \, \mathbf{\hat{x}}-x_{4}a \, \mathbf{\hat{y}} + z_{4}c \, \mathbf{\hat{z}} & \left(8c\right) & \mbox{Co II} \\ \mathbf{B}_{9} & = & z_{5} \, \mathbf{a}_{1} + \left(x_{5}+z_{5}\right) \, \mathbf{a}_{2} + x_{5} \, \mathbf{a}_{3} & = & x_{5}a \, \mathbf{\hat{x}} + z_{5}c \, \mathbf{\hat{z}} & \left(8d\right) & \mbox{Ge III} \\ \mathbf{B}_{10} & = & z_{5} \, \mathbf{a}_{1} + \left(-x_{5}+z_{5}\right) \, \mathbf{a}_{2}-x_{5} \, \mathbf{a}_{3} & = & -x_{5}a \, \mathbf{\hat{x}} + z_{5}c \, \mathbf{\hat{z}} & \left(8d\right) & \mbox{Ge III} \\ \mathbf{B}_{11} & = & \left(x_{5}+z_{5}\right) \, \mathbf{a}_{1} + z_{5} \, \mathbf{a}_{2} + x_{5} \, \mathbf{a}_{3} & = & x_{5}a \, \mathbf{\hat{y}} + z_{5}c \, \mathbf{\hat{z}} & \left(8d\right) & \mbox{Ge III} \\ \mathbf{B}_{12} & = & \left(-x_{5}+z_{5}\right) \, \mathbf{a}_{1} + z_{5} \, \mathbf{a}_{2}-x_{5} \, \mathbf{a}_{3} & = & -x_{5}a \, \mathbf{\hat{y}} + z_{5}c \, \mathbf{\hat{z}} & \left(8d\right) & \mbox{Ge III} \\ \end{array} \]

References

  • K. Schubert, T. R. Anantharaman, H. O. K. Ata, H. G. Meissner, M. Pötzschke, W. Rossteutscher, and E. Stolz, Einige strukturelle Ergebnisse an metallischen Phasen (6), Naturwissenschaften 47, 512 (1960), doi:10.1007/BF00641115.

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=A5B7_tI24_107_ac_abd --params=

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