Ti$_{2}$InB$_{2}$ Structure: A2BC2_hP5_187_ac_b_i-001
| Prototype | B$_{2}$InTi$_{2}$ |
| AFLOW prototype label | A2BC2_hP5_187_ac_b_i-001 |
| Pearson symbol | hP5 |
| Space group number | 187 |
| Space group symbol | $P\overline{6}m2$ |
| AFLOW prototype command |
aflow --proto=A2BC2_hP5_187_ac_b_i-001
--params=$a, \allowbreak c/a, \allowbreak z_{4}$ |
Other compounds with this structure
Hf$_{2}$InB$_{2}$, Hf$_{2}$SnB$_{2}$, Zr$_{2}$InB$_{2}$, Zr$_{2}$TlB$_{2}$
- (Wang, 2019) synthesized Ti$_{2}$InB$_{2}$ and found it was in space group $P\overline{6}m2$ #187, but did not give experimental positions of the atoms. Instead we use their computational results.
- We shifted the origin of the (Wang, 2019) primitive cell so that one of the boron atoms is at the origin.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \,\mathbf{\hat{y}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $0$ | = | $0$ | (1a) | B I |
| $\mathbf{B_{2}}$ | = | $\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}c \,\mathbf{\hat{z}}$ | (1b) | In I |
| $\mathbf{B_{3}}$ | = | $\frac{1}{3} \, \mathbf{a}_{1}+\frac{2}{3} \, \mathbf{a}_{2}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}$ | (1c) | B II |
| $\mathbf{B_{4}}$ | = | $\frac{2}{3} \, \mathbf{a}_{1}+\frac{1}{3} \, \mathbf{a}_{2}+z_{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+c z_{4} \,\mathbf{\hat{z}}$ | (2i) | Ti I |
| $\mathbf{B_{5}}$ | = | $\frac{2}{3} \, \mathbf{a}_{1}+\frac{1}{3} \, \mathbf{a}_{2}- z_{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}- c z_{4} \,\mathbf{\hat{z}}$ | (2i) | Ti I |
References
- J. Wang, T.-N. Ye, Y. Gong, J. Wu, N. Miao, T. Tada, and H. Hosono, Discovery of hexagonal ternary phase Ti$_{2}$InB$_{2}$ and its evolution to layered boride TiB, Nat. Commun. 10, 2284 (2019), doi:10.1038/s41467-019-10297-8.
Found in
- M. A. Ali, M. M. Hossain, M. M. Uddin, A. K. M. A. Islam, and S. H. Naqib, Understanding the improvement of thermo-mechanical and optical properties of 212 MAX phase borides Zr$_{2}$AB$_{2}$ (A = In, Tl), J. Mater. Res. Tech. 15, 2227–2239 (2021), doi:10.1016/j.jmrt.2021.09.042.
First cited in
- H. Eckert, S. Divilov, M. J. Mehl, D. Hicks, A. C. Zettel, M. Esters, X. Campilongo, and S. Curtarolo, The AFLOW Library of Crystallographic Prototypes: Part 4, Comp. Mat. Sci. 240, 112988 (2024). (doi=10.1016/j.commatsci.2021.110450)
Geometry files
Prototype Generator
aflow --proto=A2BC2_hP5_187_ac_b_i --params=$a,c/a,z_{4}$