Hazelwoodite (Ni$_{3}$S$_{2}$, $D5_{e}$) Structure: A3B2_hR5_155_e_c-001
| Prototype | Ni$_{3}$S$_{2}$ |
| AFLOW prototype label | A3B2_hR5_155_e_c-001 |
| Strukturbericht designation | $D5_{3}$ |
| Mineral name | hazelwoodite |
| ICSD | 23114 |
| Pearson symbol | hR5 |
| Space group number | 155 |
| Space group symbol | $R32$ |
| AFLOW prototype command |
aflow --proto=A3B2_hR5_155_e_c-001
--params=$a, \allowbreak c/a, \allowbreak x_{1}, \allowbreak y_{2}$ |
Other compounds with this structure
Ni$_{3}$Se$_{2}$
- 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.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+\frac{1}{3}c \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{\sqrt{3}}a \,\mathbf{\hat{y}}+\frac{1}{3}c \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&- \frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+\frac{1}{3}c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $x_{1} \, \mathbf{a}_{1}+x_{1} \, \mathbf{a}_{2}+x_{1} \, \mathbf{a}_{3}$ | = | $c x_{1} \,\mathbf{\hat{z}}$ | (2c) | S I |
| $\mathbf{B_{2}}$ | = | $- x_{1} \, \mathbf{a}_{1}- x_{1} \, \mathbf{a}_{2}- x_{1} \, \mathbf{a}_{3}$ | = | $- c x_{1} \,\mathbf{\hat{z}}$ | (2c) | S I |
| $\mathbf{B_{3}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+y_{2} \, \mathbf{a}_{2}- y_{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \left(2 y_{2} + 1\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{12}a \left(6 y_{2} - 1\right) \,\mathbf{\hat{y}}+\frac{1}{6}c \,\mathbf{\hat{z}}$ | (3e) | Ni I |
| $\mathbf{B_{4}}$ | = | $- y_{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+y_{2} \, \mathbf{a}_{3}$ | = | $- a y_{2} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+\frac{1}{6}c \,\mathbf{\hat{z}}$ | (3e) | Ni I |
| $\mathbf{B_{5}}$ | = | $y_{2} \, \mathbf{a}_{1}- y_{2} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \left(2 y_{2} - 1\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{12}a \left(6 y_{2} + 1\right) \,\mathbf{\hat{y}}+\frac{1}{6}c \,\mathbf{\hat{z}}$ | (3e) | Ni I |
References
- J. B. Parise, Structure of Hazelwoodite (Ni$_3$S$_2$, Acta Cryst. B36, 1179–1180 (1980), doi:10.1107/S0567740880005523.
Prototype Generator
aflow --proto=A3B2_hR5_155_e_c --params=$a,c/a,x_{1},y_{2}$