Mavlyanovite (Mn5Si3, $D8_{8}$) Structure: A5B3_hP16_193_dg_g

Picture of Structure; Click for Big Picture
Prototype : Mn5Si3
AFLOW prototype label : A5B3_hP16_193_dg_g
Strukturbericht designation : $D8_{8}$
Pearson symbol : hP16
Space group number : 193
Space group symbol : $P6_{3}/mcm$
AFLOW prototype command : aflow --proto=A5B3_hP16_193_dg_g
--params=
$a$,$c/a$,$x_{2}$,$x_{3}$


Hexagonal primitive vectors:

\[ \begin{array}{ccc} \mathbf{a}_1 & = & \frac12 \, a \, \mathbf{\hat{x}} - \frac{\sqrt3}2 \, a \, \mathbf{\hat{y}} \\ \mathbf{a}_2 & = & \frac12 \, a \, \mathbf{\hat{x}} + \frac{\sqrt3}2 \, a \, \mathbf{\hat{y}} \\ \mathbf{a}_3 & = & c \, \mathbf{\hat{z}} \\ \end{array} \]

Basis vectors:

\[ \begin{array}{ccccccc} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{Atom Type} \\ \mathbf{B}_{1} & = & \frac{1}{3} \, \mathbf{a}_{1} + \frac{2}{3} \, \mathbf{a}_{2} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + \frac{1}{2\sqrt{3}}a \, \mathbf{\hat{y}} & \left(4d\right) & \mbox{Mn I} \\ \mathbf{B}_{2} & = & \frac{2}{3} \, \mathbf{a}_{1} + \frac{1}{3} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}}- \frac{1}{2\sqrt{3}}a \, \mathbf{\hat{y}} + \frac{1}{2}c \, \mathbf{\hat{z}} & \left(4d\right) & \mbox{Mn I} \\ \mathbf{B}_{3} & = & \frac{2}{3} \, \mathbf{a}_{1} + \frac{1}{3} \, \mathbf{a}_{2} & = & \frac{1}{2}a \, \mathbf{\hat{x}}- \frac{1}{2\sqrt{3}}a \, \mathbf{\hat{y}} & \left(4d\right) & \mbox{Mn I} \\ \mathbf{B}_{4} & = & \frac{1}{3} \, \mathbf{a}_{1} + \frac{2}{3} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + \frac{1}{2\sqrt{3}}a \, \mathbf{\hat{y}} + \frac{1}{2}c \, \mathbf{\hat{z}} & \left(4d\right) & \mbox{Mn I} \\ \mathbf{B}_{5} & = & x_{2} \, \mathbf{a}_{1} + \frac{1}{4} \, \mathbf{a}_{3} & = & \frac{1}{2}x_{2}a \, \mathbf{\hat{x}}-\frac{\sqrt{3}}{2}x_{2}a \, \mathbf{\hat{y}} + \frac{1}{4}c \, \mathbf{\hat{z}} & \left(6g\right) & \mbox{Mn II} \\ \mathbf{B}_{6} & = & x_{2} \, \mathbf{a}_{2} + \frac{1}{4} \, \mathbf{a}_{3} & = & \frac{1}{2}x_{2}a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}x_{2}a \, \mathbf{\hat{y}} + \frac{1}{4}c \, \mathbf{\hat{z}} & \left(6g\right) & \mbox{Mn II} \\ \mathbf{B}_{7} & = & -x_{2} \, \mathbf{a}_{1}-x_{2} \, \mathbf{a}_{2} + \frac{1}{4} \, \mathbf{a}_{3} & = & -x_{2}a \, \mathbf{\hat{x}} + \frac{1}{4}c \, \mathbf{\hat{z}} & \left(6g\right) & \mbox{Mn II} \\ \mathbf{B}_{8} & = & -x_{2} \, \mathbf{a}_{1} + \frac{3}{4} \, \mathbf{a}_{3} & = & -\frac{1}{2}x_{2}a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}x_{2}a \, \mathbf{\hat{y}} + \frac{3}{4}c \, \mathbf{\hat{z}} & \left(6g\right) & \mbox{Mn II} \\ \mathbf{B}_{9} & = & -x_{2} \, \mathbf{a}_{2} + \frac{3}{4} \, \mathbf{a}_{3} & = & -\frac{1}{2}x_{2}a \, \mathbf{\hat{x}}-\frac{\sqrt{3}}{2}x_{2}a \, \mathbf{\hat{y}} + \frac{3}{4}c \, \mathbf{\hat{z}} & \left(6g\right) & \mbox{Mn II} \\ \mathbf{B}_{10} & = & x_{2} \, \mathbf{a}_{1} + x_{2} \, \mathbf{a}_{2} + \frac{3}{4} \, \mathbf{a}_{3} & = & x_{2}a \, \mathbf{\hat{x}} + \frac{3}{4}c \, \mathbf{\hat{z}} & \left(6g\right) & \mbox{Mn II} \\ \mathbf{B}_{11} & = & x_{3} \, \mathbf{a}_{1} + \frac{1}{4} \, \mathbf{a}_{3} & = & \frac{1}{2}x_{3}a \, \mathbf{\hat{x}}-\frac{\sqrt{3}}{2}x_{3}a \, \mathbf{\hat{y}} + \frac{1}{4}c \, \mathbf{\hat{z}} & \left(6g\right) & \mbox{Si} \\ \mathbf{B}_{12} & = & x_{3} \, \mathbf{a}_{2} + \frac{1}{4} \, \mathbf{a}_{3} & = & \frac{1}{2}x_{3}a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}x_{3}a \, \mathbf{\hat{y}} + \frac{1}{4}c \, \mathbf{\hat{z}} & \left(6g\right) & \mbox{Si} \\ \mathbf{B}_{13} & = & -x_{3} \, \mathbf{a}_{1}-x_{3} \, \mathbf{a}_{2} + \frac{1}{4} \, \mathbf{a}_{3} & = & -x_{3}a \, \mathbf{\hat{x}} + \frac{1}{4}c \, \mathbf{\hat{z}} & \left(6g\right) & \mbox{Si} \\ \mathbf{B}_{14} & = & -x_{3} \, \mathbf{a}_{1} + \frac{3}{4} \, \mathbf{a}_{3} & = & -\frac{1}{2}x_{3}a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}x_{3}a \, \mathbf{\hat{y}} + \frac{3}{4}c \, \mathbf{\hat{z}} & \left(6g\right) & \mbox{Si} \\ \mathbf{B}_{15} & = & -x_{3} \, \mathbf{a}_{2} + \frac{3}{4} \, \mathbf{a}_{3} & = & -\frac{1}{2}x_{3}a \, \mathbf{\hat{x}}-\frac{\sqrt{3}}{2}x_{3}a \, \mathbf{\hat{y}} + \frac{3}{4}c \, \mathbf{\hat{z}} & \left(6g\right) & \mbox{Si} \\ \mathbf{B}_{16} & = & x_{3} \, \mathbf{a}_{1} + x_{3} \, \mathbf{a}_{2} + \frac{3}{4} \, \mathbf{a}_{3} & = & x_{3}a \, \mathbf{\hat{x}} + \frac{3}{4}c \, \mathbf{\hat{z}} & \left(6g\right) & \mbox{Si} \\ \end{array} \]

References

  • B. Aronsson, A note on the compositions and crystal structures of MnB2, Mn3Si, Mn5Si3, and FeSi2, Acta Chem. Scand. 14, 1414–1418 (1960), doi:10.3891/acta.chem.scand.14-1414.

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=A5B3_hP16_193_dg_g --params=

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