Encyclopedia of Crystallographic Prototypes

AFLOW Prototype: A3B2C2_hR7_166_d_ab_c-001

This structure originally had the label A3B2C2_hR7_166_d_ab_c. Calls to that address will be redirected here.

If you are using this page, please cite:
D. Hicks, M.J. Mehl, M. Esters, C. Oses, O. Levy, G.L.W. Hart, C. Toher, and S. Curtarolo, The AFLOW Library of Crystallographic Prototypes: Part 3, Comp. Mat. Sci. 199, 110450 (2021). (doi=10.1016/j.commatsci.2021.110450)

Links to this page

https://aflow.org/p/SD1B
or https://aflow.org/p/A3B2C2_hR7_166_d_ab_c-001
or PDF Version

Shandite (Ni$_{3}$Pb$_{2}$S$_{2}$) Structure: A3B2C2_hR7_166_d_ab_c-001

Picture of Structure; Click for Big Picture
Prototype Ni$_{3}$Pb$_{2}$S$_{2}$
AFLOW prototype label A3B2C2_hR7_166_d_ab_c-001
Mineral name shandite
ICSD 417632
Pearson symbol hR7
Space group number 166
Space group symbol $R\overline{3}m$
AFLOW prototype command aflow --proto=A3B2C2_hR7_166_d_ab_c-001
--params=$a, \allowbreak c/a, \allowbreak x_{3}$

Other compounds with this structure

Co$_{3}$In$_{2}$S$_{2}$,  Co$_{3}$Sn$_{2}$S$_{2}$,  Ni$_{3}$In$_{2}$S$_{2}$,  Ni$_{3}$Sn$_{2}$S$_{2}$,  O$_{3}$K$_{2}$Sn$_{2}$,  Pd$_{3}$Bi$_{2}$S$_{2}$


\[ \begin{array}{ccc} \mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+\frac{1}{3}c \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{\sqrt{3}}a \,\mathbf{\hat{y}}+\frac{1}{3}c \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&- \frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+\frac{1}{3}c \,\mathbf{\hat{z}} \end{array}\]

Basis vectors

Lattice coordinates Cartesian coordinates Wyckoff position Atom type
$\mathbf{B_{1}}$ = $0$ = $0$ (1a) Pb I
$\mathbf{B_{2}}$ = $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ = $\frac{1}{2}c \,\mathbf{\hat{z}}$ (1b) Pb II
$\mathbf{B_{3}}$ = $x_{3} \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{2}+x_{3} \, \mathbf{a}_{3}$ = $c x_{3} \,\mathbf{\hat{z}}$ (2c) S I
$\mathbf{B_{4}}$ = $- x_{3} \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}- x_{3} \, \mathbf{a}_{3}$ = $- c x_{3} \,\mathbf{\hat{z}}$ (2c) S I
$\mathbf{B_{5}}$ = $\frac{1}{2} \, \mathbf{a}_{1}$ = $\frac{1}{4}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{12}a \,\mathbf{\hat{y}}+\frac{1}{6}c \,\mathbf{\hat{z}}$ (3d) Ni I
$\mathbf{B_{6}}$ = $\frac{1}{2} \, \mathbf{a}_{2}$ = $\frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+\frac{1}{6}c \,\mathbf{\hat{z}}$ (3d) Ni I
$\mathbf{B_{7}}$ = $\frac{1}{2} \, \mathbf{a}_{3}$ = $- \frac{1}{4}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{12}a \,\mathbf{\hat{y}}+\frac{1}{6}c \,\mathbf{\hat{z}}$ (3d) Ni I

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: PbNi$_{3/2}$S and BiPd$_{3/2}$S, Prog. Solid State Chem. 35, 309–322 (2007), doi:10.1016/j.progsolidstchem.2007.01.011.

Prototype Generator

aflow --proto=A3B2C2_hR7_166_d_ab_c --params=$a,c/a,x_{3}$

Species:

Running:

Output: