Hazelwoodite (Ni3S2, D5e) Structure: A3B2_hR5_155_e_c
| 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.