β-Mo$_{2}$N$_{1-x}$ Structure: A2B_tI12_141_e_a-003
| Prototype | Mo$_{2}$N |
| AFLOW prototype label | A2B_tI12_141_e_a-003 |
| ICSD | 30593 |
| CCDC | 1604846 |
| Pearson symbol | tI12 |
| Space group number | 141 |
| Space group symbol | $I4_1/amd$ |
| AFLOW prototype command |
aflow --proto=A2B_tI12_141_e_a-003
--params=$a, \allowbreak c/a, \allowbreak z_{2}$ |
- Mo$_{2}$N$_{1-x}$ is found in three forms (Jehn, 1978; Jauberteau, 2015):
- In $\alpha$–Mo$_{2}$N$_{1-x}$ the molybdenum atoms retain their body-centered cubic (bcc) structure with nitrogen absorbed on random sites.
- The ground state $\beta$–Mo$_{2}$N$_{1-x}$ is this tetragonal structure, and
- $\gamma$–Mo$_{2}$N$_{1{\pm}x}$ or Mo$_{2}$N$_{2-x}$ is in the rock salt ($B1$) structure with the nitrogen atoms randomly distributed.
- The transition temperature between the $\beta$ and $\gamma$ structures is about 850$^\circ$C when x = 0.286 and drops to about 400$^\circ$C when x = 0.34 (Ettmayer, 1970).
- In $\beta$–Mo$_{2}$N$_{1-x}$ the nitrogen atoms randomly occupy the (4a) Wyckoff sites.
- (Ettmayer, 1970) gives the atomic positions in setting 1 of space group $I4_{1}/amd$ #141. AFLOW transforms this to the standard setting 2.
- Anatase TiO$_{2}$ ($C5$), $\alpha$–ThSi$_{2}$ ($C_{c}$), and $\beta$–Mo$_{2}$N share the same AFLOW prototype label, A2B_tI12_141_e_a. The structures are generated by the same symmetry operations with different sets of parameters (
--params) specified in their corresponding CIF files.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&- \frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}- \frac{1}{2}c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $\frac{7}{8} \, \mathbf{a}_{1}+\frac{1}{8} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{3}{4}a \,\mathbf{\hat{y}}+\frac{1}{8}c \,\mathbf{\hat{z}}$ | (4a) | N I |
| $\mathbf{B_{2}}$ | = | $\frac{1}{8} \, \mathbf{a}_{1}+\frac{7}{8} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{1}{4}a \,\mathbf{\hat{y}}+\frac{3}{8}c \,\mathbf{\hat{z}}$ | (4a) | N I |
| $\mathbf{B_{3}}$ | = | $\left(z_{2} + \frac{1}{4}\right) \, \mathbf{a}_{1}+z_{2} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{y}}+c z_{2} \,\mathbf{\hat{z}}$ | (8e) | Mo I |
| $\mathbf{B_{4}}$ | = | $z_{2} \, \mathbf{a}_{1}+\left(z_{2} + \frac{1}{4}\right) \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+c \left(z_{2} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (8e) | Mo I |
| $\mathbf{B_{5}}$ | = | $- \left(z_{2} - \frac{3}{4}\right) \, \mathbf{a}_{1}- z_{2} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{3}{4}a \,\mathbf{\hat{y}}- c z_{2} \,\mathbf{\hat{z}}$ | (8e) | Mo I |
| $\mathbf{B_{6}}$ | = | $- z_{2} \, \mathbf{a}_{1}- \left(z_{2} - \frac{3}{4}\right) \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{1}{4}a \,\mathbf{\hat{y}}- c \left(z_{2} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (8e) | Mo I |
References
- P. Ettmayer, Das System Molybdän - Stickstoff, Monatsh. Chem. 101, 127–140 (1970), doi:10.1007/BF00907533.
- D. A. Evans and K. H. Jack, The $\gamma \leftrightarrow \beta$ phase transformation in the Mo-N system, Acta Cryst. 10, 833–834 (1957), doi:10.1107/S0365110X57002649. Abstract 13.5.
- H. Jehn and P. Ettmayer, The Molybdenum-Nitrogen Phase Diagram, J. Less-Common Met. 58, 85–98 (1978), doi:10.1016/0022-5088(78)90073-5.
- I. Jauberteau, A. Bessaudou, R. Mayet, J. Cornette, J. L. Jauberteau, P. Carles, and T. Merle-Méjean, Molybdenum Nitride Films: Crystal Structures, Synthesis, Mechanical, Electrical and Some Other Properties, Coatings 5, 656–687 (2015), doi:10.3390/coatings5040656.
Found in
- AFLOW Database}, \href{https://aflow.org}{https://aflow.org}. Mo$_{2$N, ICSD entry 30593.
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_tI12_141_e_a --params=$a,c/a,z_{2}$