Sr5Si3 Structure: A3B5_tI32_108_ac_a2c

Picture of Structure; Click for Big Picture
Prototype : Sr5Si3
AFLOW prototype label : A3B5_tI32_108_ac_a2c
Strukturbericht designation : None
Pearson symbol : tI32
Space group number : 108
Space group symbol : $I4cm$
AFLOW prototype command : aflow --proto=A3B5_tI32_108_ac_a2c
--params=
$a$,$c/a$,$z_{1}$,$z_{2}$,$x_{3}$,$z_{3}$,$x_{4}$,$z_{4}$,$x_{5}$,$z_{5}$



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

References

  • G. Nagorsen, G. Rocktäschel, H. Schäfer, and A. Weiss, Die Kristallstruktur der Phase Sr5Si3, Z. Naturforsch. B 22, 101–102 (1967), doi:10.1515/znb-1967-0122.
  • R. Nesper and F. Zürcher, Redetermination of the crystal structure of pentastrontium trisilicide, Sr5Si3, Z. Kristallogr. NCS 214, 19 (1999), doi:10.1515/ncrs-1999-0112.

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=A3B5_tI32_108_ac_a2c --params=

Species:

Running:

Output: