Millerite (NiS, $B13$) Structure: AB_hR6_160_b_b

Picture of Structure; Click for Big Picture
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).

Geometry files


Prototype Generator

aflow --proto=AB_hR6_160_b_b --params=

Species:

Running:

Output: