ζ-Hf$_{4}$N$_{3}$ Structure: AB_hR8_166_2c_abc-001
| Prototype | Hf$_{4}$N$_{3}$ |
| AFLOW prototype label | AB_hR8_166_2c_abc-001 |
| ICSD | 23572 |
| CCDC | 1599678 |
| Pearson symbol | hR8 |
| Space group number | 166 |
| Space group symbol | $R\overline{3}m$ |
| AFLOW prototype command |
aflow --proto=AB_hR8_166_2c_abc-001
--params=$a, \allowbreak c/a, \allowbreak x_{3}, \allowbreak x_{4}, \allowbreak x_{5}$ |
- The Hf-N phase diagram has three known phases (Rudy, 1970; Villars, 2023):
- HfN, stable up to the melting point of 3387$^\circ$C, is in the NaCl ($B1$) structure.
- $\epsilon$–Hf$_{3}$N$_{2}$ is stable up to 1970$^\circ$C.
- $\zeta$–Hf$_{4}$N$_{3}$ is stable in the range 1225-2300$^\circ$C.
- The N II (1b) and N III (2c) sites are only 2/3 occupied.
- 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 | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $0$ | = | $0$ | (1a) | N I |
| $\mathbf{B_{2}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}c \,\mathbf{\hat{z}}$ | (1b) | N II |
| $\mathbf{B_{3}}$ | = | $x_{3} \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{2}+x_{3} \, \mathbf{a}_{3}$ | = | $c x_{3} \,\mathbf{\hat{z}}$ | (2c) | Hf I |
| $\mathbf{B_{4}}$ | = | $- x_{3} \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}- x_{3} \, \mathbf{a}_{3}$ | = | $- c x_{3} \,\mathbf{\hat{z}}$ | (2c) | Hf I |
| $\mathbf{B_{5}}$ | = | $x_{4} \, \mathbf{a}_{1}+x_{4} \, \mathbf{a}_{2}+x_{4} \, \mathbf{a}_{3}$ | = | $c x_{4} \,\mathbf{\hat{z}}$ | (2c) | Hf II |
| $\mathbf{B_{6}}$ | = | $- x_{4} \, \mathbf{a}_{1}- x_{4} \, \mathbf{a}_{2}- x_{4} \, \mathbf{a}_{3}$ | = | $- c x_{4} \,\mathbf{\hat{z}}$ | (2c) | Hf II |
| $\mathbf{B_{7}}$ | = | $x_{5} \, \mathbf{a}_{1}+x_{5} \, \mathbf{a}_{2}+x_{5} \, \mathbf{a}_{3}$ | = | $c x_{5} \,\mathbf{\hat{z}}$ | (2c) | N III |
| $\mathbf{B_{8}}$ | = | $- x_{5} \, \mathbf{a}_{1}- x_{5} \, \mathbf{a}_{2}- x_{5} \, \mathbf{a}_{3}$ | = | $- c x_{5} \,\mathbf{\hat{z}}$ | (2c) | N III |
References
- E. Rudy, The Crystal Structures of Hf$_{3}$N$_{2}$ and Hf$_{4}$N$_{3}$, Metall. Trans. 1, 1249–1252 (1970), doi:10.1007/BF02900238.
- P. Villars, ed., PAULING FILE in: Inorganic Solid Phases, SpringerMaterials (online database) (Springer, Heidelberg, 2023), chap. Hf-N Binary Phase Diagram 0-100 at.% N c_0901275.
First cited in
- N. Anderson, M. J. Mehl, H. Eckert, S. Divilov, X. Campilongo, S. Curtarolo, The AFLOW Library of Crystallographic Prototypes: Part 5. Submitted to Computational Materials Science (2026).
Geometry files
Prototype Generator
aflow --proto=AB_hR8_166_2c_abc --params=$a,c/a,x_{3},x_{4},x_{5}$