Ti$_{2}$Ga$_{3}$ Structure: A3B2_tP10_83_adj_k-001
| Prototype | Ga$_{3}$Ti$_{2}$ |
| AFLOW prototype label | A3B2_tP10_83_adj_k-001 |
| ICSD | 197271 |
| Pearson symbol | tP10 |
| Space group number | 83 |
| Space group symbol | $P4/m$ |
| AFLOW prototype command |
aflow --proto=A3B2_tP10_83_adj_k-001
--params=$a, \allowbreak c/a, \allowbreak x_{3}, \allowbreak y_{3}, \allowbreak x_{4}, \allowbreak y_{4}$ |
- We originally listed this structure as Ti$_{2}$Ge$_{3}$ (Hicks, 2019), but Ti$_{2}$Ga$_{3}$ is the correct compound.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&a \,\mathbf{\hat{x}}\\\mathbf{a_{2}}&=&a \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $0$ | = | $0$ | (1a) | Ga I |
| $\mathbf{B_{2}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (1d) | Ga II |
| $\mathbf{B_{3}}$ | = | $x_{3} \, \mathbf{a}_{1}+y_{3} \, \mathbf{a}_{2}$ | = | $a x_{3} \,\mathbf{\hat{x}}+a y_{3} \,\mathbf{\hat{y}}$ | (4j) | Ga III |
| $\mathbf{B_{4}}$ | = | $- x_{3} \, \mathbf{a}_{1}- y_{3} \, \mathbf{a}_{2}$ | = | $- a x_{3} \,\mathbf{\hat{x}}- a y_{3} \,\mathbf{\hat{y}}$ | (4j) | Ga III |
| $\mathbf{B_{5}}$ | = | $- y_{3} \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{2}$ | = | $- a y_{3} \,\mathbf{\hat{x}}+a x_{3} \,\mathbf{\hat{y}}$ | (4j) | Ga III |
| $\mathbf{B_{6}}$ | = | $y_{3} \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}$ | = | $a y_{3} \,\mathbf{\hat{x}}- a x_{3} \,\mathbf{\hat{y}}$ | (4j) | Ga III |
| $\mathbf{B_{7}}$ | = | $x_{4} \, \mathbf{a}_{1}+y_{4} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $a x_{4} \,\mathbf{\hat{x}}+a y_{4} \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (4k) | Ti I |
| $\mathbf{B_{8}}$ | = | $- x_{4} \, \mathbf{a}_{1}- y_{4} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- a x_{4} \,\mathbf{\hat{x}}- a y_{4} \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (4k) | Ti I |
| $\mathbf{B_{9}}$ | = | $- y_{4} \, \mathbf{a}_{1}+x_{4} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- a y_{4} \,\mathbf{\hat{x}}+a x_{4} \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (4k) | Ti I |
| $\mathbf{B_{10}}$ | = | $y_{4} \, \mathbf{a}_{1}- x_{4} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $a y_{4} \,\mathbf{\hat{x}}- a x_{4} \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (4k) | Ti I |
References
- K. Schubert, H. G. Meissner, M. Pötzschke, W. Rossteutscher, and E. Stolz, Einige Strukturdaten metallischer Phasen (7), Naturwissenschaften 49, 57 (1962), doi:10.1007/BF00595382.
- D. Hicks, M. J. Mehl, E. Gossett, C. Toher, O. Levy, R. M. Hanson, G. Hart, and S. Curtarolo, The AFLOW Library of Crystallographic Prototypes: Part 2, Comput. Mater. Sci. 161, S1–S1011 (2019), doi:10.1016/j.commatsci.2018.10.043.
Found in
- P. Villars and K. Cenzual, Pearson's Crystal Data – Crystal Structure Database for Inorganic Compounds (2013). ASM International.
Prototype Generator
aflow --proto=A3B2_tP10_83_adj_k --params=$a,c/a,x_{3},y_{3},x_{4},y_{4}$