Al$_{10}$V Structure: A10B_cF176_227_cfg_d-001
| Prototype | Al$_{10}$V |
| AFLOW prototype label | A10B_cF176_227_cfg_d-001 |
| ICSD | 58202 |
| Pearson symbol | cF176 |
| Space group number | 227 |
| Space group symbol | $Fd\overline{3}m$ |
| AFLOW prototype command |
aflow --proto=A10B_cF176_227_cfg_d-001
--params=$a, \allowbreak x_{3}, \allowbreak x_{4}, \allowbreak z_{4}$ |
- (Brown, 1957) gives the structural information in setting 1 of space group $Fd\overline{3}m$ #227. We shifted the origin by $(a/8$ $a/8$ $a/8)$ to change this to the standard setting 2.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $0$ | = | $0$ | (16c) | Al I |
| $\mathbf{B_{2}}$ | = | $\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}$ | (16c) | Al I |
| $\mathbf{B_{3}}$ | = | $\frac{1}{2} \, \mathbf{a}_{2}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (16c) | Al I |
| $\mathbf{B_{4}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}$ | = | $\frac{1}{4}a \,\mathbf{\hat{y}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (16c) | Al I |
| $\mathbf{B_{5}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}$ | (16d) | V I |
| $\mathbf{B_{6}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}$ | (16d) | V I |
| $\mathbf{B_{7}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (16d) | V I |
| $\mathbf{B_{8}}$ | = | $\frac{1}{2} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (16d) | V I |
| $\mathbf{B_{9}}$ | = | $- \left(x_{3} - \frac{1}{4}\right) \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{2}+x_{3} \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{x}}+\frac{1}{8}a \,\mathbf{\hat{y}}+\frac{1}{8}a \,\mathbf{\hat{z}}$ | (48f) | Al II |
| $\mathbf{B_{10}}$ | = | $x_{3} \, \mathbf{a}_{1}- \left(x_{3} - \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(x_{3} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{3} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+\frac{1}{8}a \,\mathbf{\hat{y}}+\frac{1}{8}a \,\mathbf{\hat{z}}$ | (48f) | Al II |
| $\mathbf{B_{11}}$ | = | $x_{3} \, \mathbf{a}_{1}- \left(x_{3} - \frac{1}{4}\right) \, \mathbf{a}_{2}+x_{3} \, \mathbf{a}_{3}$ | = | $\frac{1}{8}a \,\mathbf{\hat{x}}+a x_{3} \,\mathbf{\hat{y}}+\frac{1}{8}a \,\mathbf{\hat{z}}$ | (48f) | Al II |
| $\mathbf{B_{12}}$ | = | $- \left(x_{3} - \frac{1}{4}\right) \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{2}- \left(x_{3} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{8}a \,\mathbf{\hat{x}}- a \left(x_{3} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+\frac{1}{8}a \,\mathbf{\hat{z}}$ | (48f) | Al II |
| $\mathbf{B_{13}}$ | = | $x_{3} \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{2}- \left(x_{3} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{8}a \,\mathbf{\hat{x}}+\frac{1}{8}a \,\mathbf{\hat{y}}+a x_{3} \,\mathbf{\hat{z}}$ | (48f) | Al II |
| $\mathbf{B_{14}}$ | = | $- \left(x_{3} - \frac{1}{4}\right) \, \mathbf{a}_{1}- \left(x_{3} - \frac{1}{4}\right) \, \mathbf{a}_{2}+x_{3} \, \mathbf{a}_{3}$ | = | $\frac{1}{8}a \,\mathbf{\hat{x}}+\frac{1}{8}a \,\mathbf{\hat{y}}- a \left(x_{3} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (48f) | Al II |
| $\mathbf{B_{15}}$ | = | $\left(x_{3} + \frac{3}{4}\right) \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}+\left(x_{3} + \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $\frac{3}{8}a \,\mathbf{\hat{x}}+a \left(x_{3} + \frac{3}{4}\right) \,\mathbf{\hat{y}}+\frac{3}{8}a \,\mathbf{\hat{z}}$ | (48f) | Al II |
| $\mathbf{B_{16}}$ | = | $- x_{3} \, \mathbf{a}_{1}+\left(x_{3} + \frac{3}{4}\right) \, \mathbf{a}_{2}- x_{3} \, \mathbf{a}_{3}$ | = | $\frac{3}{8}a \,\mathbf{\hat{x}}- a x_{3} \,\mathbf{\hat{y}}+\frac{3}{8}a \,\mathbf{\hat{z}}$ | (48f) | Al II |
| $\mathbf{B_{17}}$ | = | $- x_{3} \, \mathbf{a}_{1}+\left(x_{3} + \frac{3}{4}\right) \, \mathbf{a}_{2}+\left(x_{3} + \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{3} + \frac{3}{4}\right) \,\mathbf{\hat{x}}+\frac{3}{8}a \,\mathbf{\hat{y}}+\frac{3}{8}a \,\mathbf{\hat{z}}$ | (48f) | Al II |
| $\mathbf{B_{18}}$ | = | $\left(x_{3} + \frac{3}{4}\right) \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}- x_{3} \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}+\frac{3}{8}a \,\mathbf{\hat{y}}+\frac{3}{8}a \,\mathbf{\hat{z}}$ | (48f) | Al II |
| $\mathbf{B_{19}}$ | = | $- x_{3} \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}+\left(x_{3} + \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $\frac{3}{8}a \,\mathbf{\hat{x}}+\frac{3}{8}a \,\mathbf{\hat{y}}- a x_{3} \,\mathbf{\hat{z}}$ | (48f) | Al II |
| $\mathbf{B_{20}}$ | = | $\left(x_{3} + \frac{3}{4}\right) \, \mathbf{a}_{1}+\left(x_{3} + \frac{3}{4}\right) \, \mathbf{a}_{2}- x_{3} \, \mathbf{a}_{3}$ | = | $\frac{3}{8}a \,\mathbf{\hat{x}}+\frac{3}{8}a \,\mathbf{\hat{y}}+a \left(x_{3} + \frac{3}{4}\right) \,\mathbf{\hat{z}}$ | (48f) | Al II |
| $\mathbf{B_{21}}$ | = | $z_{4} \, \mathbf{a}_{1}+z_{4} \, \mathbf{a}_{2}+\left(2 x_{4} - z_{4}\right) \, \mathbf{a}_{3}$ | = | $a x_{4} \,\mathbf{\hat{x}}+a x_{4} \,\mathbf{\hat{y}}+a z_{4} \,\mathbf{\hat{z}}$ | (96g) | Al III |
| $\mathbf{B_{22}}$ | = | $z_{4} \, \mathbf{a}_{1}+z_{4} \, \mathbf{a}_{2}- \left(2 x_{4} + z_{4} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{4} - \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(x_{4} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a z_{4} \,\mathbf{\hat{z}}$ | (96g) | Al III |
| $\mathbf{B_{23}}$ | = | $\left(2 x_{4} - z_{4}\right) \, \mathbf{a}_{1}- \left(2 x_{4} + z_{4} - \frac{1}{2}\right) \, \mathbf{a}_{2}+z_{4} \, \mathbf{a}_{3}$ | = | $- a \left(x_{4} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a x_{4} \,\mathbf{\hat{y}}- a \left(z_{4} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96g) | Al III |
| $\mathbf{B_{24}}$ | = | $- \left(2 x_{4} + z_{4} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(2 x_{4} - z_{4}\right) \, \mathbf{a}_{2}+z_{4} \, \mathbf{a}_{3}$ | = | $a x_{4} \,\mathbf{\hat{x}}- a \left(x_{4} - \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(z_{4} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96g) | Al III |
| $\mathbf{B_{25}}$ | = | $\left(2 x_{4} - z_{4}\right) \, \mathbf{a}_{1}+z_{4} \, \mathbf{a}_{2}+z_{4} \, \mathbf{a}_{3}$ | = | $a z_{4} \,\mathbf{\hat{x}}+a x_{4} \,\mathbf{\hat{y}}+a x_{4} \,\mathbf{\hat{z}}$ | (96g) | Al III |
| $\mathbf{B_{26}}$ | = | $- \left(2 x_{4} + z_{4} - \frac{1}{2}\right) \, \mathbf{a}_{1}+z_{4} \, \mathbf{a}_{2}+z_{4} \, \mathbf{a}_{3}$ | = | $a z_{4} \,\mathbf{\hat{x}}- a \left(x_{4} - \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(x_{4} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96g) | Al III |
| $\mathbf{B_{27}}$ | = | $z_{4} \, \mathbf{a}_{1}+\left(2 x_{4} - z_{4}\right) \, \mathbf{a}_{2}- \left(2 x_{4} + z_{4} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(z_{4} - \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(x_{4} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a x_{4} \,\mathbf{\hat{z}}$ | (96g) | Al III |
| $\mathbf{B_{28}}$ | = | $z_{4} \, \mathbf{a}_{1}- \left(2 x_{4} + z_{4} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(2 x_{4} - z_{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(z_{4} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a x_{4} \,\mathbf{\hat{y}}- a \left(x_{4} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96g) | Al III |
| $\mathbf{B_{29}}$ | = | $z_{4} \, \mathbf{a}_{1}+\left(2 x_{4} - z_{4}\right) \, \mathbf{a}_{2}+z_{4} \, \mathbf{a}_{3}$ | = | $a x_{4} \,\mathbf{\hat{x}}+a z_{4} \,\mathbf{\hat{y}}+a x_{4} \,\mathbf{\hat{z}}$ | (96g) | Al III |
| $\mathbf{B_{30}}$ | = | $z_{4} \, \mathbf{a}_{1}- \left(2 x_{4} + z_{4} - \frac{1}{2}\right) \, \mathbf{a}_{2}+z_{4} \, \mathbf{a}_{3}$ | = | $- a \left(x_{4} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a z_{4} \,\mathbf{\hat{y}}- a \left(x_{4} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96g) | Al III |
| $\mathbf{B_{31}}$ | = | $- \left(2 x_{4} + z_{4} - \frac{1}{2}\right) \, \mathbf{a}_{1}+z_{4} \, \mathbf{a}_{2}+\left(2 x_{4} - z_{4}\right) \, \mathbf{a}_{3}$ | = | $a x_{4} \,\mathbf{\hat{x}}- a \left(z_{4} - \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(x_{4} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96g) | Al III |
| $\mathbf{B_{32}}$ | = | $\left(2 x_{4} - z_{4}\right) \, \mathbf{a}_{1}+z_{4} \, \mathbf{a}_{2}- \left(2 x_{4} + z_{4} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{4} - \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(z_{4} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a x_{4} \,\mathbf{\hat{z}}$ | (96g) | Al III |
| $\mathbf{B_{33}}$ | = | $- z_{4} \, \mathbf{a}_{1}- z_{4} \, \mathbf{a}_{2}+\left(2 x_{4} + z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{4} + \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(x_{4} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a z_{4} \,\mathbf{\hat{z}}$ | (96g) | Al III |
| $\mathbf{B_{34}}$ | = | $- z_{4} \, \mathbf{a}_{1}- z_{4} \, \mathbf{a}_{2}- \left(2 x_{4} - z_{4}\right) \, \mathbf{a}_{3}$ | = | $- a x_{4} \,\mathbf{\hat{x}}- a x_{4} \,\mathbf{\hat{y}}- a z_{4} \,\mathbf{\hat{z}}$ | (96g) | Al III |
| $\mathbf{B_{35}}$ | = | $- \left(2 x_{4} - z_{4}\right) \, \mathbf{a}_{1}+\left(2 x_{4} + z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{2}- z_{4} \, \mathbf{a}_{3}$ | = | $a \left(x_{4} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a x_{4} \,\mathbf{\hat{y}}+a \left(z_{4} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96g) | Al III |
| $\mathbf{B_{36}}$ | = | $\left(2 x_{4} + z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(2 x_{4} - z_{4}\right) \, \mathbf{a}_{2}- z_{4} \, \mathbf{a}_{3}$ | = | $- a x_{4} \,\mathbf{\hat{x}}+a \left(x_{4} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(z_{4} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96g) | Al III |
| $\mathbf{B_{37}}$ | = | $- \left(2 x_{4} - z_{4}\right) \, \mathbf{a}_{1}- z_{4} \, \mathbf{a}_{2}+\left(2 x_{4} + z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{4} + \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(z_{4} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a x_{4} \,\mathbf{\hat{z}}$ | (96g) | Al III |
| $\mathbf{B_{38}}$ | = | $\left(2 x_{4} + z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{1}- z_{4} \, \mathbf{a}_{2}- \left(2 x_{4} - z_{4}\right) \, \mathbf{a}_{3}$ | = | $- a x_{4} \,\mathbf{\hat{x}}+a \left(z_{4} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(x_{4} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96g) | Al III |
| $\mathbf{B_{39}}$ | = | $- z_{4} \, \mathbf{a}_{1}- \left(2 x_{4} - z_{4}\right) \, \mathbf{a}_{2}- z_{4} \, \mathbf{a}_{3}$ | = | $- a x_{4} \,\mathbf{\hat{x}}- a z_{4} \,\mathbf{\hat{y}}- a x_{4} \,\mathbf{\hat{z}}$ | (96g) | Al III |
| $\mathbf{B_{40}}$ | = | $- z_{4} \, \mathbf{a}_{1}+\left(2 x_{4} + z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{2}- z_{4} \, \mathbf{a}_{3}$ | = | $a \left(x_{4} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a z_{4} \,\mathbf{\hat{y}}+a \left(x_{4} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96g) | Al III |
| $\mathbf{B_{41}}$ | = | $- z_{4} \, \mathbf{a}_{1}- \left(2 x_{4} - z_{4}\right) \, \mathbf{a}_{2}+\left(2 x_{4} + z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(z_{4} + \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(x_{4} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a x_{4} \,\mathbf{\hat{z}}$ | (96g) | Al III |
| $\mathbf{B_{42}}$ | = | $- z_{4} \, \mathbf{a}_{1}+\left(2 x_{4} + z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(2 x_{4} - z_{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(z_{4} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a x_{4} \,\mathbf{\hat{y}}+a \left(x_{4} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96g) | Al III |
| $\mathbf{B_{43}}$ | = | $\left(2 x_{4} + z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{1}- z_{4} \, \mathbf{a}_{2}- z_{4} \, \mathbf{a}_{3}$ | = | $- a z_{4} \,\mathbf{\hat{x}}+a \left(x_{4} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(x_{4} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96g) | Al III |
| $\mathbf{B_{44}}$ | = | $- \left(2 x_{4} - z_{4}\right) \, \mathbf{a}_{1}- z_{4} \, \mathbf{a}_{2}- z_{4} \, \mathbf{a}_{3}$ | = | $- a z_{4} \,\mathbf{\hat{x}}- a x_{4} \,\mathbf{\hat{y}}- a x_{4} \,\mathbf{\hat{z}}$ | (96g) | Al III |
References
- P. J. Brown, The Structure of α(V-Al), Acta Cryst. 10, 133–135 (1957), doi:10.1107/S0365110X57000389.
Found in
- F. Wang, Y.-L. Chiu, D. Eskin, W. Du, and P. R. Shearing, A grain refinement mechanism of cast commercial purity aluminium by vanadium, Mater. Charact 181, 111468 (2021), doi:10.1016/j.matchar.2021.111468.
Prototype Generator
aflow --proto=A10B_cF176_227_cfg_d --params=$a,x_{3},x_{4},z_{4}$