Ti$_{3}$Cu$_{4}$ Structure: A4B3_tI14_139_2e_ae-001
| Prototype | Cu$_{4}$Ti$_{3}$ |
| AFLOW prototype label | A4B3_tI14_139_2e_ae-001 |
| ICSD | 103134 |
| Pearson symbol | tI14 |
| Space group number | 139 |
| Space group symbol | $I4/mmm$ |
| AFLOW prototype command |
aflow --proto=A4B3_tI14_139_2e_ae-001
--params=$a, \allowbreak c/a, \allowbreak z_{2}, \allowbreak z_{3}, \allowbreak z_{4}$ |
- When c = 7 a, z$_{2}$ = 1/7, z$_{3}$ = 3/7, and z$_{4}$ = 2/7 the atoms are on the sites of the bcc 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) | Ti I |
| $\mathbf{B_{2}}$ | = | $z_{2} \, \mathbf{a}_{1}+z_{2} \, \mathbf{a}_{2}$ | = | $c z_{2} \,\mathbf{\hat{z}}$ | (4e) | Cu I |
| $\mathbf{B_{3}}$ | = | $- z_{2} \, \mathbf{a}_{1}- z_{2} \, \mathbf{a}_{2}$ | = | $- c z_{2} \,\mathbf{\hat{z}}$ | (4e) | Cu I |
| $\mathbf{B_{4}}$ | = | $z_{3} \, \mathbf{a}_{1}+z_{3} \, \mathbf{a}_{2}$ | = | $c z_{3} \,\mathbf{\hat{z}}$ | (4e) | Cu II |
| $\mathbf{B_{5}}$ | = | $- z_{3} \, \mathbf{a}_{1}- z_{3} \, \mathbf{a}_{2}$ | = | $- c z_{3} \,\mathbf{\hat{z}}$ | (4e) | Cu II |
| $\mathbf{B_{6}}$ | = | $z_{4} \, \mathbf{a}_{1}+z_{4} \, \mathbf{a}_{2}$ | = | $c z_{4} \,\mathbf{\hat{z}}$ | (4e) | Ti II |
| $\mathbf{B_{7}}$ | = | $- z_{4} \, \mathbf{a}_{1}- z_{4} \, \mathbf{a}_{2}$ | = | $- c z_{4} \,\mathbf{\hat{z}}$ | (4e) | Ti II |
References
- K. Schubert, A. Raman, and W. Rossteutscher, Einige Strukturdaten metallischer Phasen (11), Naturwissenschaften 51, 507 (1964), doi:10.1007/BF00632207.
Found in
- J. M. Moya, A. M. Hallas, V. Loganathan, C.-L. Huang, L. Kish, A. A. Aczel, J. Beare, Y. Cai, G. M. Luke, F. Weickert, A. H. Nevidomskyy, C. D. Malliakas, M. G. Kanatzidis, K. Bayliff, and E. Morosan, Field-induced quantum critical point in the new itinerant antiferromagnet Ti$_{3}$Cu$_{4}$, Comm. Phys. 5, 136 (2022), doi:10.1038/s42005-022-00901-7.
Prototype Generator
aflow --proto=A4B3_tI14_139_2e_ae --params=$a,c/a,z_{2},z_{3},z_{4}$