Millerite (NiS, $B13$) Structure: AB_hR6_160_b_b-001
| Prototype | NiS |
| AFLOW prototype label | AB_hR6_160_b_b-001 |
| Strukturbericht designation | $B13$ |
| Mineral name | millerite |
| ICSD | 40054 |
| Pearson symbol | hR6 |
| Space group number | 160 |
| Space group symbol | $R3m$ |
| AFLOW prototype command |
aflow --proto=AB_hR6_160_b_b-001
--params=$a, \allowbreak c/a, \allowbreak x_{1}, \allowbreak z_{1}, \allowbreak x_{2}, \allowbreak z_{2}$ |
Other compounds with this structure
$\beta$-FeS, NiSe
- Hexagonal settings of this structure can be obtained with the option
--hex.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+\frac{1}{3}c \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{\sqrt{3}}a \,\mathbf{\hat{y}}+\frac{1}{3}c \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&- \frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+\frac{1}{3}c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $x_{1} \, \mathbf{a}_{1}+x_{1} \, \mathbf{a}_{2}+z_{1} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{1} - z_{1}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(x_{1} - z_{1}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(2 x_{1} + z_{1}\right) \,\mathbf{\hat{z}}$ | (3b) | Ni I |
| $\mathbf{B_{2}}$ | = | $z_{1} \, \mathbf{a}_{1}+x_{1} \, \mathbf{a}_{2}+x_{1} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{1} - z_{1}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(x_{1} - z_{1}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(2 x_{1} + z_{1}\right) \,\mathbf{\hat{z}}$ | (3b) | Ni I |
| $\mathbf{B_{3}}$ | = | $x_{1} \, \mathbf{a}_{1}+z_{1} \, \mathbf{a}_{2}+x_{1} \, \mathbf{a}_{3}$ | = | $- \frac{1}{\sqrt{3}}a \left(x_{1} - z_{1}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(2 x_{1} + z_{1}\right) \,\mathbf{\hat{z}}$ | (3b) | Ni I |
| $\mathbf{B_{4}}$ | = | $x_{2} \, \mathbf{a}_{1}+x_{2} \, \mathbf{a}_{2}+z_{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{2} - z_{2}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(x_{2} - z_{2}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(2 x_{2} + z_{2}\right) \,\mathbf{\hat{z}}$ | (3b) | S I |
| $\mathbf{B_{5}}$ | = | $z_{2} \, \mathbf{a}_{1}+x_{2} \, \mathbf{a}_{2}+x_{2} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{2} - z_{2}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(x_{2} - z_{2}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(2 x_{2} + z_{2}\right) \,\mathbf{\hat{z}}$ | (3b) | S I |
| $\mathbf{B_{6}}$ | = | $x_{2} \, \mathbf{a}_{1}+z_{2} \, \mathbf{a}_{2}+x_{2} \, \mathbf{a}_{3}$ | = | $- \frac{1}{\sqrt{3}}a \left(x_{2} - z_{2}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(2 x_{2} + z_{2}\right) \,\mathbf{\hat{z}}$ | (3b) | S I |
References
- V. Rajamani and C. T. Prewitt, The Crystal Structure of Millerite, Can. Mineral. 12, 253–257 (1974).
Found in
- R. T. Downs and M. Hall-Wallace, The American Mineralogist Crystal Structure Database, Am. Mineral. 88, 247–250 (2003).
Prototype Generator
aflow --proto=AB_hR6_160_b_b --params=$a,c/a,x_{1},z_{1},x_{2},z_{2}$