W5Si3 ($D8_{m}$) Structure: A3B5_tI32_140_ah_bk

Picture of Structure; Click for Big Picture
Prototype : W5Si3
AFLOW prototype label : A3B5_tI32_140_ah_bk
Strukturbericht designation : $D8_{m}$
Pearson symbol : tI32
Space group number : 140
Space group symbol : $I4/mcm$
AFLOW prototype command : aflow --proto=A3B5_tI32_140_ah_bk
--params=
$a$,$c/a$,$x_{3}$,$x_{4}$,$y_{4}$


Other compounds with this structure

  • Cr5Ge3, Cr5Si3, Mo5Si3, Nb5Si3, Ta5Si3, V5Si3, Ti3Sb, Hf5Co1-$x$Sb2+$x$, Hf5Cr1-$x$Sb2+$x$, Hf5Cu1-$x$Sb2+$x$, Hf5Fe1-$x$Sb2+$x$, Hf5Ni1-$x$Sb2+$x$, Hf5Pd1-$x$Sb2+$x$, Hf5Rh1-$x$Sb2+$x$, Hf5Ru1-$x$Sb2+$x$, Hf5V1-$x$Sb2+$x$, Zr5Co0.5Sb2.5, Zr5Cr1-$x$Bi2+$x$, Zr5Cr1-$x$Sb2+$x$, Zr5Fe0.5Sb2.5, Zr5Mn1-$x$Bi2+$x$, Zr5Mn1-$x$Sb2+$x$, Zr5Ni0.5Sb2.5, Zr5Rh0.5Sb2.5, and Zr5Ru0.5Sb2.5


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

References

Geometry files


Prototype Generator

aflow --proto=A3B5_tI32_140_ah_bk --params=

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