Hazelwoodite (Ni3S2, $D5_{e}$) Structure: A3B2_hR5_155_e_c

Picture of Structure; Click for Big Picture
Prototype : Ni3S2
AFLOW prototype label : A3B2_hR5_155_e_c
Strukturbericht designation : $D5_{e}$
Pearson symbol : hR5
Space group number : 155
Space group symbol : $\mbox{R32}$
AFLOW prototype command : aflow --proto=A3B2_hR5_155_e_c [--hex]
--params=
$a$,$c/a$,$x_{1}$,$y_{2}$


Other compounds with this structure

  • Ni3Se2

  • This can be considered as a prototype for a high concentration of ordered vacancies in the hcp structure. We get the ideal hcp atomic positions when $z_{1}=1/3$ and $y_{2}=1/6$, leaving a vacancy at the origin. 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:

\[ \begin{array}{ccccccc} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{Atom Type} \\ \mathbf{B}_{1} & =& x_{1} \, \mathbf{a}_{1} + x_{1} \, \mathbf{a}_{2} + x_{1} \, \mathbf{a}_{3}& =& x_{1} \, c \, \mathbf{\hat{z}}& \left(2c\right) & \mbox{S} \\ \mathbf{B}_{2} & =& - x_{1} \, \mathbf{a}_{1} - x_{1} \, \mathbf{a}_{2} - x_{1} \, \mathbf{a}_{3}& =& - x_{1} \, c \, \mathbf{\hat{z}}& \left(2c\right) & \mbox{S} \\ \mathbf{B}_{3} & =&\frac12 \, \mathbf{a}_{1}+ y_{2} \, \mathbf{a}_{2}- y_{2} \, \mathbf{a}_{3}& =&\frac14 \left(1 + 2 \, y_{2}\right) \, a \, \mathbf{\hat{x}}+ \frac1{4\sqrt{3}} \left(6 \, y_{2} - 1\right) \, a \, \mathbf{\hat{y}}+ \frac16 \, c \, \mathbf{\hat{z}}& \left(3e\right) & \mbox{Ni} \\ \mathbf{B}_{4} & =&- y_{2} \, \mathbf{a}_{1}+ \frac12 \, \mathbf{a}_{2}+ y_{2} \, \mathbf{a}_{3}& =&- y_{2} \, a \, \mathbf{\hat{x}}+ \frac{1}{2\sqrt{3}} \, a \, \mathbf{\hat{y}}+ \frac16 \, c \, \mathbf{\hat{z}}& \left(3e\right) & \mbox{Ni} \\ \mathbf{B}_{5} & =&y_{2} \, \mathbf{a}_{1}- y_{2} \, \mathbf{a}_{2}+ \frac12 \, \mathbf{a}_{3}& =&\frac14 \left(2 \, y_{2} - 1\right) \, a \, \mathbf{\hat{x}}- \frac1{4\sqrt{3}} \left(1 + 6 \, y_{2}\right) \, a \, \mathbf{\hat{y}}+ \frac16 \, c \, \mathbf{\hat{z}}& \left(3e\right) & \mbox{Ni} \\ \end{array} \]

References

  • J. B. Parise, Structure of Hazelwoodite (Ni3S2), Acta Crystallogr. Sect. B Struct. Sci. B36, 1179–1180 (1980), doi:10.1107/S0567740880005523.

Geometry files


Prototype Generator

aflow --proto=A3B2_hR5_155_e_c --params=

Species:

Running:

Output: