Hypothetical SiO$_{2}$-like WN$_{2}$ structure: A2B_cI36_229_h_d-001
| Prototype | N$_{2}$W |
| AFLOW prototype label | A2B_cI36_229_h_d-001 |
| Pearson symbol | cI36 |
| Space group number | 229 |
| Space group symbol | $Im\overline{3}m$ |
| AFLOW prototype command |
aflow --proto=A2B_cI36_229_h_d-001
--params=$a, \allowbreak y_{2}$ |
- This structure was studied by (Mehl, 2015) as part of an effort to understand vacancy formation in the N$_{1-x}$W$_{x}$ system. It was produced by removing 4 nitrogen and 10 tungsten atoms from a 64-atom supercell of the rock salt ($B1$) structure. The resulting structure leaves four nitrogen atoms forming a tetrahedron around each tungsten atom, with the perfect regular tetrahedron occuring when y$_{2}$ = 1/$\sqrt{8}$ with an N-W-N bond angle of 109.47$^\circ$. It is similar to the idealized $\beta$-cristobalite SiO$_{2}$ structure, although the current structure has never been reported for any compound.
- The y$_{2}$-value for this structure reported in (Mehl, 2015) Table VI should be replaced by 1/2 - y$_{2}$, as we do here.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&- \frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}- \frac{1}{2}a \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{z}}$ | (12d) | W I |
| $\mathbf{B_{2}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}$ | (12d) | W I |
| $\mathbf{B_{3}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}$ | (12d) | W I |
| $\mathbf{B_{4}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}$ | (12d) | W I |
| $\mathbf{B_{5}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (12d) | W I |
| $\mathbf{B_{6}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (12d) | W I |
| $\mathbf{B_{7}}$ | = | $2 y_{2} \, \mathbf{a}_{1}+y_{2} \, \mathbf{a}_{2}+y_{2} \, \mathbf{a}_{3}$ | = | $a y_{2} \,\mathbf{\hat{y}}+a y_{2} \,\mathbf{\hat{z}}$ | (24h) | N I |
| $\mathbf{B_{8}}$ | = | $y_{2} \, \mathbf{a}_{2}- y_{2} \, \mathbf{a}_{3}$ | = | $- a y_{2} \,\mathbf{\hat{y}}+a y_{2} \,\mathbf{\hat{z}}$ | (24h) | N I |
| $\mathbf{B_{9}}$ | = | $- y_{2} \, \mathbf{a}_{2}+y_{2} \, \mathbf{a}_{3}$ | = | $a y_{2} \,\mathbf{\hat{y}}- a y_{2} \,\mathbf{\hat{z}}$ | (24h) | N I |
| $\mathbf{B_{10}}$ | = | $- 2 y_{2} \, \mathbf{a}_{1}- y_{2} \, \mathbf{a}_{2}- y_{2} \, \mathbf{a}_{3}$ | = | $- a y_{2} \,\mathbf{\hat{y}}- a y_{2} \,\mathbf{\hat{z}}$ | (24h) | N I |
| $\mathbf{B_{11}}$ | = | $y_{2} \, \mathbf{a}_{1}+2 y_{2} \, \mathbf{a}_{2}+y_{2} \, \mathbf{a}_{3}$ | = | $a y_{2} \,\mathbf{\hat{x}}+a y_{2} \,\mathbf{\hat{z}}$ | (24h) | N I |
| $\mathbf{B_{12}}$ | = | $- y_{2} \, \mathbf{a}_{1}+y_{2} \, \mathbf{a}_{3}$ | = | $a y_{2} \,\mathbf{\hat{x}}- a y_{2} \,\mathbf{\hat{z}}$ | (24h) | N I |
| $\mathbf{B_{13}}$ | = | $y_{2} \, \mathbf{a}_{1}- y_{2} \, \mathbf{a}_{3}$ | = | $- a y_{2} \,\mathbf{\hat{x}}+a y_{2} \,\mathbf{\hat{z}}$ | (24h) | N I |
| $\mathbf{B_{14}}$ | = | $- y_{2} \, \mathbf{a}_{1}- 2 y_{2} \, \mathbf{a}_{2}- y_{2} \, \mathbf{a}_{3}$ | = | $- a y_{2} \,\mathbf{\hat{x}}- a y_{2} \,\mathbf{\hat{z}}$ | (24h) | N I |
| $\mathbf{B_{15}}$ | = | $y_{2} \, \mathbf{a}_{1}+y_{2} \, \mathbf{a}_{2}+2 y_{2} \, \mathbf{a}_{3}$ | = | $a y_{2} \,\mathbf{\hat{x}}+a y_{2} \,\mathbf{\hat{y}}$ | (24h) | N I |
| $\mathbf{B_{16}}$ | = | $y_{2} \, \mathbf{a}_{1}- y_{2} \, \mathbf{a}_{2}$ | = | $- a y_{2} \,\mathbf{\hat{x}}+a y_{2} \,\mathbf{\hat{y}}$ | (24h) | N I |
| $\mathbf{B_{17}}$ | = | $- y_{2} \, \mathbf{a}_{1}+y_{2} \, \mathbf{a}_{2}$ | = | $a y_{2} \,\mathbf{\hat{x}}- a y_{2} \,\mathbf{\hat{y}}$ | (24h) | N I |
| $\mathbf{B_{18}}$ | = | $- y_{2} \, \mathbf{a}_{1}- y_{2} \, \mathbf{a}_{2}- 2 y_{2} \, \mathbf{a}_{3}$ | = | $- a y_{2} \,\mathbf{\hat{x}}- a y_{2} \,\mathbf{\hat{y}}$ | (24h) | N I |
References
- M. J. Mehl, D. Finkenstadt, C. Dane, G. L. W. Hart, and S. Curtarolo, Finding the stable structures of N$_{1-x}$W$_{x}$ with an {\em ab initio} high-throughput approach, Phys. Rev. B 91, 184110 (2015), doi:10.1103/PhysRevB.91.184110.
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=A2B_cI36_229_h_d --params=$a,y_{2}$