Mo$_{2}$B$_{5}$ ($D8_{i}$) Structure: A5B2_hR7_166_a2c_c-001
| Prototype | B$_{5}$Mo$_{2}$ |
| AFLOW prototype label | A5B2_hR7_166_a2c_c-001 |
| Strukturbericht designation | $D8_{i}$ |
| ICSD | 24282 |
| Pearson symbol | hR7 |
| Space group number | 166 |
| Space group symbol | $R\overline{3}m$ |
| AFLOW prototype command |
aflow --proto=A5B2_hR7_166_a2c_c-001
--params=$a, \allowbreak c/a, \allowbreak x_{2}, \allowbreak x_{3}, \allowbreak x_{4}$ |
Other compounds with this structure
InTlLi$_{5}$, Pb$_{2}$Na$_{5}$, Sn$_{2}$Li$_{5}$, Tl$_{2}$Li$_{5}$, V$_{2}$B$_{5}$
- The B-I and B-III atoms form buckled graphitic sheets, making this the rhombohedral form of $D8_{h}$. (Frotscher, 2007) suggest that the stable composition in this part of the molybdenum nitride system might be Mo$_{2}$B$_{4}$, which they describe as having a flattened $C12$ (CaSi$_{2}$) structure. Here we will describe the $D8_{i}$ structure, with the warning that this might not be the true structure.
- We have shifted the origin of this lattice so that the B-I atoms are at the (1a) Wyckoff positions. An earlier version of this page, included in (Mehl, 2017), shifted the B-I atom but neglected to shift the remaining atoms.
- 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) | B I |
| $\mathbf{B_{2}}$ | = | $x_{2} \, \mathbf{a}_{1}+x_{2} \, \mathbf{a}_{2}+x_{2} \, \mathbf{a}_{3}$ | = | $c x_{2} \,\mathbf{\hat{z}}$ | (2c) | B II |
| $\mathbf{B_{3}}$ | = | $- x_{2} \, \mathbf{a}_{1}- x_{2} \, \mathbf{a}_{2}- x_{2} \, \mathbf{a}_{3}$ | = | $- c x_{2} \,\mathbf{\hat{z}}$ | (2c) | B II |
| $\mathbf{B_{4}}$ | = | $x_{3} \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{2}+x_{3} \, \mathbf{a}_{3}$ | = | $c x_{3} \,\mathbf{\hat{z}}$ | (2c) | B III |
| $\mathbf{B_{5}}$ | = | $- x_{3} \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}- x_{3} \, \mathbf{a}_{3}$ | = | $- c x_{3} \,\mathbf{\hat{z}}$ | (2c) | B III |
| $\mathbf{B_{6}}$ | = | $x_{4} \, \mathbf{a}_{1}+x_{4} \, \mathbf{a}_{2}+x_{4} \, \mathbf{a}_{3}$ | = | $c x_{4} \,\mathbf{\hat{z}}$ | (2c) | Mo I |
| $\mathbf{B_{7}}$ | = | $- x_{4} \, \mathbf{a}_{1}- x_{4} \, \mathbf{a}_{2}- x_{4} \, \mathbf{a}_{3}$ | = | $- c x_{4} \,\mathbf{\hat{z}}$ | (2c) | Mo I |
References
- R. Kiessling, The Crystal Structures of Molybdenum and Tungsten Borides, Acta Chem. Scand. 1, 893–916 (1947), doi:10.3891/acta.chem.scand.01-0893.
- M. Frotscher, W. Klein, J. Bauer, C.-M. F., J.-F. Halet, A. Senyshyn, C. Baehtz, and B. Albert, M$_2$B$_5$ or M$_2$B$_4$? A Reinvestigation of the Mo/B and W/B System, Z. Anorganische und Allgemeine Chemie 633, 2626–2630 (2007), doi:10.1002/zaac.200700376.
- M. J. Mehl, D. Hicks, C. Toher, O. Levy, R. M. H., G. Hart, and S. Curtarolo, The AFLOW library of crystallographic prototypes: part 1, Comput. Mater. Sci. 136, S1–S828 (2017), doi:10.1016/j.commatsci.2017.01.017.
Prototype Generator
aflow --proto=A5B2_hR7_166_a2c_c --params=$a,c/a,x_{2},x_{3},x_{4}$