Re$_{3}$N Structure: AB3_hP4_187_a_bh-001
| Prototype | NRe$_{3}$ |
| AFLOW prototype label | AB3_hP4_187_a_bh-001 |
| ICSD | 169884 |
| Pearson symbol | hP4 |
| Space group number | 187 |
| Space group symbol | $P\overline{6}m2$ |
| AFLOW prototype command |
aflow --proto=AB3_hP4_187_a_bh-001
--params=$a, \allowbreak c/a, \allowbreak z_{3}$ |
- The reference presents both experimental findings and the results of density functional theory calculations. We obtain our data from the density functional theory calculations at equilibrium ($P = 0$), which are consistent with the lattice constants found experimentally.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \,\mathbf{\hat{y}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $0$ | = | $0$ | (1a) | N I |
| $\mathbf{B_{2}}$ | = | $\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}c \,\mathbf{\hat{z}}$ | (1b) | Re I |
| $\mathbf{B_{3}}$ | = | $\frac{1}{3} \, \mathbf{a}_{1}+\frac{2}{3} \, \mathbf{a}_{2}+z_{3} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+c z_{3} \,\mathbf{\hat{z}}$ | (2h) | Re II |
| $\mathbf{B_{4}}$ | = | $\frac{1}{3} \, \mathbf{a}_{1}+\frac{2}{3} \, \mathbf{a}_{2}- z_{3} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}- c z_{3} \,\mathbf{\hat{z}}$ | (2h) | Re II |
References
- A. Friedrich, B. Winkler, L. Bayarjargal, W. Morgenroth, E. A. Juarez-Arellano, V. Milman, K. Refson, M. Kunz, and K. Chen, Novel Rhenium Nitrides, Phys. Rev. Lett. 105, 085504 (2010), doi:10.1103/PhysRevLett.105.085504. August.
Prototype Generator
aflow --proto=AB3_hP4_187_a_bh --params=$a,c/a,z_{3}$