Ti2Ge3 Structure: A3B2_tP10_83_adk_j

Picture of Structure; Click for Big Picture
Prototype : Ti2Ge3
AFLOW prototype label : A3B2_tP10_83_adk_j
Strukturbericht designation : None
Pearson symbol : tP10
Space group number : 83
Space group symbol : $P4/m$
AFLOW prototype command : aflow --proto=A3B2_tP10_83_adk_j
--params=
$a$,$c/a$,$x_{3}$,$y_{3}$,$x_{4}$,$y_{4}$


Simple Tetragonal primitive vectors:

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

Basis vectors:

\[ \begin{array}{ccccccc} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{Atom Type} \\ \mathbf{B}_{1} & = & 0 \, \mathbf{a}_{1} + 0 \, \mathbf{a}_{2} + 0 \, \mathbf{a}_{3} & = & 0 \, \mathbf{\hat{x}} + 0 \, \mathbf{\hat{y}} + 0 \, \mathbf{\hat{z}} & \left(1a\right) & \mbox{Ge I} \\ \mathbf{B}_{2} & = & \frac{1}{2} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + \frac{1}{2}a \, \mathbf{\hat{y}} + \frac{1}{2}c \, \mathbf{\hat{z}} & \left(1d\right) & \mbox{Ge II} \\ \mathbf{B}_{3} & = & x_{3} \, \mathbf{a}_{1} + y_{3} \, \mathbf{a}_{2} & = & x_{3}a \, \mathbf{\hat{x}} + y_{3}a \, \mathbf{\hat{y}} & \left(4j\right) & \mbox{Ti} \\ \mathbf{B}_{4} & = & -x_{3} \, \mathbf{a}_{1}-y_{3} \, \mathbf{a}_{2} & = & -x_{3}a \, \mathbf{\hat{x}}-y_{3}a \, \mathbf{\hat{y}} & \left(4j\right) & \mbox{Ti} \\ \mathbf{B}_{5} & = & -y_{3} \, \mathbf{a}_{1} + x_{3} \, \mathbf{a}_{2} & = & -y_{3}a \, \mathbf{\hat{x}} + x_{3}a \, \mathbf{\hat{y}} & \left(4j\right) & \mbox{Ti} \\ \mathbf{B}_{6} & = & y_{3} \, \mathbf{a}_{1}-x_{3} \, \mathbf{a}_{2} & = & y_{3}a \, \mathbf{\hat{x}}-x_{3}a \, \mathbf{\hat{y}} & \left(4j\right) & \mbox{Ti} \\ \mathbf{B}_{7} & = & x_{4} \, \mathbf{a}_{1} + y_{4} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & x_{4}a \, \mathbf{\hat{x}} + y_{4}a \, \mathbf{\hat{y}} + \frac{1}{2}c \, \mathbf{\hat{z}} & \left(4k\right) & \mbox{Ge III} \\ \mathbf{B}_{8} & = & -x_{4} \, \mathbf{a}_{1}-y_{4} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & -x_{4}a \, \mathbf{\hat{x}}-y_{4}a \, \mathbf{\hat{y}} + \frac{1}{2}c \, \mathbf{\hat{z}} & \left(4k\right) & \mbox{Ge III} \\ \mathbf{B}_{9} & = & -y_{4} \, \mathbf{a}_{1} + x_{4} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & -y_{4}a \, \mathbf{\hat{x}} + x_{4}a \, \mathbf{\hat{y}} + \frac{1}{2}c \, \mathbf{\hat{z}} & \left(4k\right) & \mbox{Ge III} \\ \mathbf{B}_{10} & = & y_{4} \, \mathbf{a}_{1}-x_{4} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & y_{4}a \, \mathbf{\hat{x}}-x_{4}a \, \mathbf{\hat{y}} + \frac{1}{2}c \, \mathbf{\hat{z}} & \left(4k\right) & \mbox{Ge III} \\ \end{array} \]

References

  • K. Schubert, H. G. Meissner, M. Pötzschke, W. Rossteutscher, and E. Stolz, Einige Strukturdaten metallischer Phasen (7), Naturwissenschaften 49, 57–57 (1962), doi:10.1007/BF00595382.

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=A3B2_tP10_83_adk_j --params=

Species:

Running:

Output: