Shandite (Ni3Pb2S2) Structure : A3B2C2_hR7_166_d_ab_c

Picture of Structure; Click for Big Picture
Prototype : Ni3Pb2S2
AFLOW prototype label : A3B2C2_hR7_166_d_ab_c
Strukturbericht designation : None
Pearson symbol : hR7
Space group number : 166
Space group symbol : $R\bar{3}m$
AFLOW prototype command : aflow --proto=A3B2C2_hR7_166_d_ab_c
--params=
$a$,$c/a$,$x_{3}$


Other compounds with this structure

  • Co3In2S2, Co3Sn2S2, Ni3In2S2, Ni3Sn2S2, and O3K2Sn2

Rhombohedral primitive vectors:

\[ \begin{array}{ccc} \mathbf{a}_1 & = & ~ \frac12 \, a \, \mathbf{\hat{x}} - \frac{1}{2\sqrt{3}} \, a \, \mathbf{\hat{y}} + \frac13 \, c \, \mathbf{\hat{z}} \\ \mathbf{a}_2 & = & \frac{1}{\sqrt{3}} \, a \, \mathbf{\hat{y}} + \frac13 \, c \, \mathbf{\hat{z}} \\ \mathbf{a}_3 & = & - \frac12 \, a \, \mathbf{\hat{x}} - \frac{1}{2\sqrt{3}} \, a \, \mathbf{\hat{y}} + \frac13 \, c \, \mathbf{\hat{z}} \\ \end{array} \]

Basis vectors:

\[ \begin{array}{ccccccc} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{Atom Type} \\ \mathbf{B}_{1} & = & 0 \, \mathbf{a}_{1} + 0 \, \mathbf{a}_{2} + 0 \, \mathbf{a}_{3} & = & 0 \, \mathbf{\hat{x}} + 0 \, \mathbf{\hat{y}} + 0 \, \mathbf{\hat{z}} & \left(1a\right) & \mbox{Pb I} \\ \mathbf{B}_{2} & = & \frac{1}{2} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{1}{2}c \, \mathbf{\hat{z}} & \left(1b\right) & \mbox{Pb II} \\ \mathbf{B}_{3} & = & x_{3} \, \mathbf{a}_{1} + x_{3} \, \mathbf{a}_{2} + x_{3} \, \mathbf{a}_{3} & = & x_{3}c \, \mathbf{\hat{z}} & \left(2c\right) & \mbox{S} \\ \mathbf{B}_{4} & = & -x_{3} \, \mathbf{a}_{1}-x_{3} \, \mathbf{a}_{2}-x_{3} \, \mathbf{a}_{3} & = & -x_{3}c \, \mathbf{\hat{z}} & \left(2c\right) & \mbox{S} \\ \mathbf{B}_{5} & = & \frac{1}{2} \, \mathbf{a}_{1} & = & \frac{1}{4}a \, \mathbf{\hat{x}}- \frac{1}{4\sqrt{3}}a \, \mathbf{\hat{y}} + \frac{1}{6}c \, \mathbf{\hat{z}} & \left(3d\right) & \mbox{Ni} \\ \mathbf{B}_{6} & = & \frac{1}{2} \, \mathbf{a}_{2} & = & \frac{1}{2\sqrt{3}}a \, \mathbf{\hat{y}} + \frac{1}{6}c \, \mathbf{\hat{z}} & \left(3d\right) & \mbox{Ni} \\ \mathbf{B}_{7} & = & \frac{1}{2} \, \mathbf{a}_{3} & = & - \frac{1}{4}a \, \mathbf{\hat{x}}- \frac{1}{4\sqrt{3}}a \, \mathbf{\hat{y}} + \frac{1}{6}c \, \mathbf{\hat{z}} & \left(3d\right) & \mbox{Ni} \\ \end{array} \]

References

  • R. Weihrich, S. F. Matar, V. Eyert, F. Rau, M. Zabel, M. Andratschke, I. Anusca, and T. Bernert, Structure, ordering, and bonding of half antiperovskites: PbNi3/2S and BiPd3/2S, Prog. Solid State Chem. 35, 309–327 (2007), doi:10.1016/j.progsolidstchem.2007.01.011.

Geometry files


Prototype Generator

aflow --proto=A3B2C2_hR7_166_d_ab_c --params=

Species:

Running:

Output: