Ta$_{3}$Ti$_{5}$ (BCC SQS-16) Structure: A3B5_oC32_38_abcd_abcef-001
| Prototype | Ta$_{3}$Ti$_{5}$ |
| AFLOW prototype label | A3B5_oC32_38_abcd_abcef-001 |
| ICSD | none |
| Pearson symbol | oC32 |
| Space group number | 38 |
| Space group symbol | $Amm2$ |
| AFLOW prototype command |
aflow --proto=A3B5_oC32_38_abcd_abcef-001
--params=$a, \allowbreak b/a, \allowbreak c/a, \allowbreak z_{1}, \allowbreak z_{2}, \allowbreak z_{3}, \allowbreak z_{4}, \allowbreak x_{5}, \allowbreak z_{5}, \allowbreak x_{6}, \allowbreak z_{6}, \allowbreak y_{7}, \allowbreak z_{7}, \allowbreak y_{8}, \allowbreak z_{8}, \allowbreak x_{9}, \allowbreak y_{9}, \allowbreak z_{9}$ |
- This is a special quasirandom structure with 16 atoms per unit cell (SQS-16) for a bcc binary substitutional alloy A$_{x}$B$_{1-x}$ (Jiang, 2004; Chakraborty, 2016)).
- Several compositions are available:
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&a \,\mathbf{\hat{x}}\\\mathbf{a_{2}}&=&\frac{1}{2}b \,\mathbf{\hat{y}}- \frac{1}{2}c \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&\frac{1}{2}b \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $- z_{1} \, \mathbf{a}_{2}+z_{1} \, \mathbf{a}_{3}$ | = | $c z_{1} \,\mathbf{\hat{z}}$ | (2a) | Ta I |
| $\mathbf{B_{2}}$ | = | $- z_{2} \, \mathbf{a}_{2}+z_{2} \, \mathbf{a}_{3}$ | = | $c z_{2} \,\mathbf{\hat{z}}$ | (2a) | Ti I |
| $\mathbf{B_{3}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}- z_{3} \, \mathbf{a}_{2}+z_{3} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+c z_{3} \,\mathbf{\hat{z}}$ | (2b) | Ta II |
| $\mathbf{B_{4}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}- z_{4} \, \mathbf{a}_{2}+z_{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+c z_{4} \,\mathbf{\hat{z}}$ | (2b) | Ti II |
| $\mathbf{B_{5}}$ | = | $x_{5} \, \mathbf{a}_{1}- z_{5} \, \mathbf{a}_{2}+z_{5} \, \mathbf{a}_{3}$ | = | $a x_{5} \,\mathbf{\hat{x}}+c z_{5} \,\mathbf{\hat{z}}$ | (4c) | Ta III |
| $\mathbf{B_{6}}$ | = | $- x_{5} \, \mathbf{a}_{1}- z_{5} \, \mathbf{a}_{2}+z_{5} \, \mathbf{a}_{3}$ | = | $- a x_{5} \,\mathbf{\hat{x}}+c z_{5} \,\mathbf{\hat{z}}$ | (4c) | Ta III |
| $\mathbf{B_{7}}$ | = | $x_{6} \, \mathbf{a}_{1}- z_{6} \, \mathbf{a}_{2}+z_{6} \, \mathbf{a}_{3}$ | = | $a x_{6} \,\mathbf{\hat{x}}+c z_{6} \,\mathbf{\hat{z}}$ | (4c) | Ti III |
| $\mathbf{B_{8}}$ | = | $- x_{6} \, \mathbf{a}_{1}- z_{6} \, \mathbf{a}_{2}+z_{6} \, \mathbf{a}_{3}$ | = | $- a x_{6} \,\mathbf{\hat{x}}+c z_{6} \,\mathbf{\hat{z}}$ | (4c) | Ti III |
| $\mathbf{B_{9}}$ | = | $\left(y_{7} - z_{7}\right) \, \mathbf{a}_{2}+\left(y_{7} + z_{7}\right) \, \mathbf{a}_{3}$ | = | $b y_{7} \,\mathbf{\hat{y}}+c z_{7} \,\mathbf{\hat{z}}$ | (4d) | Ta IV |
| $\mathbf{B_{10}}$ | = | $- \left(y_{7} + z_{7}\right) \, \mathbf{a}_{2}- \left(y_{7} - z_{7}\right) \, \mathbf{a}_{3}$ | = | $- b y_{7} \,\mathbf{\hat{y}}+c z_{7} \,\mathbf{\hat{z}}$ | (4d) | Ta IV |
| $\mathbf{B_{11}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\left(y_{8} - z_{8}\right) \, \mathbf{a}_{2}+\left(y_{8} + z_{8}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+b y_{8} \,\mathbf{\hat{y}}+c z_{8} \,\mathbf{\hat{z}}$ | (4e) | Ti IV |
| $\mathbf{B_{12}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}- \left(y_{8} + z_{8}\right) \, \mathbf{a}_{2}- \left(y_{8} - z_{8}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- b y_{8} \,\mathbf{\hat{y}}+c z_{8} \,\mathbf{\hat{z}}$ | (4e) | Ti IV |
| $\mathbf{B_{13}}$ | = | $x_{9} \, \mathbf{a}_{1}+\left(y_{9} - z_{9}\right) \, \mathbf{a}_{2}+\left(y_{9} + z_{9}\right) \, \mathbf{a}_{3}$ | = | $a x_{9} \,\mathbf{\hat{x}}+b y_{9} \,\mathbf{\hat{y}}+c z_{9} \,\mathbf{\hat{z}}$ | (8f) | Ti V |
| $\mathbf{B_{14}}$ | = | $- x_{9} \, \mathbf{a}_{1}- \left(y_{9} + z_{9}\right) \, \mathbf{a}_{2}- \left(y_{9} - z_{9}\right) \, \mathbf{a}_{3}$ | = | $- a x_{9} \,\mathbf{\hat{x}}- b y_{9} \,\mathbf{\hat{y}}+c z_{9} \,\mathbf{\hat{z}}$ | (8f) | Ti V |
| $\mathbf{B_{15}}$ | = | $x_{9} \, \mathbf{a}_{1}- \left(y_{9} + z_{9}\right) \, \mathbf{a}_{2}- \left(y_{9} - z_{9}\right) \, \mathbf{a}_{3}$ | = | $a x_{9} \,\mathbf{\hat{x}}- b y_{9} \,\mathbf{\hat{y}}+c z_{9} \,\mathbf{\hat{z}}$ | (8f) | Ti V |
| $\mathbf{B_{16}}$ | = | $- x_{9} \, \mathbf{a}_{1}+\left(y_{9} - z_{9}\right) \, \mathbf{a}_{2}+\left(y_{9} + z_{9}\right) \, \mathbf{a}_{3}$ | = | $- a x_{9} \,\mathbf{\hat{x}}+b y_{9} \,\mathbf{\hat{y}}+c z_{9} \,\mathbf{\hat{z}}$ | (8f) | Ti V |
References
- C. Jiang, C. Wolverton, J. Sofo, L.-Q. Chen, and Z.-K. Liu, First-principles study of binary bcc alloys using special quasirandom structures, Phys. Rev. B 69, 214202 (2004), doi:10.1103/PhysRevB.69.214202.
- T. Chakraborty, J. Rogal, and R. Drautz, Unraveling the composition dependence of the martensitic transformation temperature: A first-principles study of Ti-Ta alloys, Phys. Rev. B 94, 224104 (2016), doi:10.1103/PhysRevB.94.224104.
Prototype Generator
aflow --proto=A3B5_oC32_38_abcd_abcef --params=$a,b/a,c/a,z_{1},z_{2},z_{3},z_{4},x_{5},z_{5},x_{6},z_{6},y_{7},z_{7},y_{8},z_{8},x_{9},y_{9},z_{9}$