Millerite (NiS, B13) Structure: AB_hR6_160_b_b
| Prototype | : | NiS |
| AFLOW prototype label | : | AB_hR6_160_b_b |
| Strukturbericht designation | : | $B13$ |
| Pearson symbol | : | hR6 |
| Space group number | : | 160 |
| Space group symbol | : | $\mbox{R3m}$ |
| AFLOW prototype command | : | aflow --proto=AB_hR6_160_b_b [--hex] --params=$a,c/a,x_{1},z_{1},x_{2},z_{2}$ |
Other compounds with this structure
- beta–FeS
- Hexagonal settings of this structure can be obtained with the option ––hex.
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:
\[ \begin{array}{ccccccc} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{Atom Type} \\ \mathbf{B}_{1} & =&x_{1} \, \mathbf{a}_{1}+ x_{1} \, \mathbf{a}_{2}+ z_{1} \, \mathbf{a}_{3}& =&\frac12 \left(x_{1} - z_{1}\right) \, a \, \mathbf{\hat{x}}+ \frac1{2 \sqrt3} \left(x_{1} - z_{1}\right) \, a \, \mathbf{\hat{y}}+ \frac13 \left(2 x_{1} + z_{1}\right) \, c \, \mathbf{\hat{z}}& \left(3b\right) & \mbox{Ni} \\ \mathbf{B}_{2} & =&z_{1} \, \mathbf{a}_{1}+ x_{1} \, \mathbf{a}_{2}+ x_{1} \, \mathbf{a}_{3}& =&\frac12 \left(z_{1} - x_{1}\right) \, a \, \mathbf{\hat{x}}+ \frac1{2 \sqrt3} \left(x_{1} - z_{1}\right) \, a \, \mathbf{\hat{y}}+ \frac13 \left(2 x_{1} + z_{1}\right) \, c \, \mathbf{\hat{z}}& \left(3b\right) & \mbox{Ni} \\ \mathbf{B}_{3} & =&x_{1} \, \mathbf{a}_{1}+ z_{1} \, \mathbf{a}_{2}+ x_{1} \, \mathbf{a}_{3}& =&\frac1{\sqrt3} \left(z_{1} - x_{1}\right) \, a \, \mathbf{\hat{y}}+ \frac13 \left(2 x_{1} + z_{1}\right) \, c \, \mathbf{\hat{z}}& \left(3b\right) & \mbox{Ni} \\ \mathbf{B}_{4} & =&x_{2} \, \mathbf{a}_{1}+ x_{2} \, \mathbf{a}_{2}+ z_{2} \, \mathbf{a}_{3}& =&\frac12 \left(x_{2} - z_{2}\right) \, a \, \mathbf{\hat{x}}+ \frac1{2 \sqrt3} \left(x_{2} - z_{2}\right) \, a \, \mathbf{\hat{y}}+ \frac13 \left(2 x_{2} + z_{2}\right) \, c \, \mathbf{\hat{z}}& \left(3b\right) & \mbox{S} \\ \mathbf{B}_{5} & =&z_{2} \, \mathbf{a}_{1}+ x_{2} \, \mathbf{a}_{2}+ x_{2} \, \mathbf{a}_{3}& =&\frac12 \left(z_{2} - x_{2}\right) \, a \, \mathbf{\hat{x}}+ \frac1{2 \sqrt3} \left(x_{2} - z_{2}\right) \, a \, \mathbf{\hat{y}}+ \frac13 \left(2 x_{2} + z_{2}\right) \, c \, \mathbf{\hat{z}}& \left(3b\right) & \mbox{S} \\ \mathbf{B}_{6} & =&x_{2} \, \mathbf{a}_{1}+ z_{2} \, \mathbf{a}_{2}+ x_{2} \, \mathbf{a}_{3}& =&\frac1{\sqrt3} \left(z_{2} - x_{2}\right) \, a \, \mathbf{\hat{y}}+ \frac13 \left(2 x_{2} + z_{2}\right) \, c \, \mathbf{\hat{z}}& \left(3b\right) & \mbox{S} \\ \end{array} \]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).