Au$_{2}$Nb$_{3}$ Structure: A2B3_tI10_139_e_ae-001
| Prototype | Au$_{2}$Nb$_{3}$ |
| AFLOW prototype label | A2B3_tI10_139_e_ae-001 |
| ICSD | 58559 |
| Pearson symbol | tI10 |
| Space group number | 139 |
| Space group symbol | $I4/mmm$ |
| AFLOW prototype command |
aflow --proto=A2B3_tI10_139_e_ae-001
--params=$a, \allowbreak c/a, \allowbreak z_{2}, \allowbreak z_{3}$ |
Other compounds with this structure
Os$_{2}$Al$_{3}$, Ti$_{2}$Cu$_{3}$
- (Schubert, 1960) listed the lattice constants in
kX
units. We used the conversion factor 1.00207789 to convert their units into Ångstroms (Arblaster, 1997). (We had previously (Hicks, 2021) divided instead of multiplied. This has been corrected.) - When $c/a = 5, z_{2} = 1/5$ and $z_{3} = 2/5$, the atoms are on the sites of a body-centered cubic lattice.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&- \frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}- \frac{1}{2}c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $0$ | = | $0$ | (2a) | Nb I |
| $\mathbf{B_{2}}$ | = | $z_{2} \, \mathbf{a}_{1}+z_{2} \, \mathbf{a}_{2}$ | = | $c z_{2} \,\mathbf{\hat{z}}$ | (4e) | Au I |
| $\mathbf{B_{3}}$ | = | $- z_{2} \, \mathbf{a}_{1}- z_{2} \, \mathbf{a}_{2}$ | = | $- c z_{2} \,\mathbf{\hat{z}}$ | (4e) | Au I |
| $\mathbf{B_{4}}$ | = | $z_{3} \, \mathbf{a}_{1}+z_{3} \, \mathbf{a}_{2}$ | = | $c z_{3} \,\mathbf{\hat{z}}$ | (4e) | Nb II |
| $\mathbf{B_{5}}$ | = | $- z_{3} \, \mathbf{a}_{1}- z_{3} \, \mathbf{a}_{2}$ | = | $- c z_{3} \,\mathbf{\hat{z}}$ | (4e) | Nb II |
References
- K. Schubert, T. R. Anantharaman, H. O. K. Ata, H. G. Meissner, M. Pötzschke, W. Rossteutscher, and E. Stolz, Einige strukturelle Ergebnisse an metallischen Phasen (6), Naturwissenschaften 47, 512 (1960), doi:10.1007/BF00641115.
- J. W. Arblaster, Crystallographic Properties of Platinum, Platinum Metals Rev. 41, 12–21 (1997).
- D. Hicks, M. J.Mehl, M. Esters, C. Oses, O. Levy, G. L. W. Hart, C. Toher, and S. Curtarolo, The AFLOW Library of Crystallographic Prototypes: Part 3, Comput. Mater. Sci. 199, 110450 (2021), doi:10.1016/j.commatsci.2021.110450.
Found in
- L.-E. Edshammar, The Crystal Structures of Os$_{2}$Al$_{3}$ and OsAl$_{2}$, Acta Chem. Scand. 19, 871–874 (1965), doi:10.3891/acta.chem.scand.19-0871.
Prototype Generator
aflow --proto=A2B3_tI10_139_e_ae --params=$a,c/a,z_{2},z_{3}$