Shandite (Ni$_{3}$Pb$_{2}$S$_{2}$) Structure: A3B2C2_hR7_166_d_ab_c-001
| 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=$a,c/a,x_{3}$