C-AlRuNi (Al$_{20}$Ni$_{3}$Ru$_{5}$) Structure: A23B2C6_cP31_200_cij_ab_f-001
| Prototype | Al$_{20}$Ni$_{3}$Ru$_{5}$ |
| AFLOW prototype label | A23B2C6_cP31_200_cij_ab_f-001 |
| ICSD | 230569 |
| Pearson symbol | cP31 |
| Space group number | 200 |
| Space group symbol | $Pm\overline{3}$ |
| AFLOW prototype command |
aflow --proto=A23B2C6_cP31_200_cij_ab_f-001
--params=$a, \allowbreak x_{4}, \allowbreak x_{5}, \allowbreak y_{6}, \allowbreak z_{6}$ |
- Most of these sites are partially or contained a mixture of species. We label them by the majority species:
- Ni-I (1a) is 79% nickel and 21% ruthenium,
- Ni-II (1b) is 100% nickel,
- Al-I (3c) is 77% aluminum and 23% vacancies,
- Ru-I (6g) is 81.4% ruthenium and 18.6% nickel,
- Al-II (8i) is 74% aluminum and 26% vacancies, and
- Al-III (12k) is 100% aluminum.
- This gives an actual composition of Al$_{20.23}$Ni$_{2.906}$Ru$_{5.094}$, which we simplify to Al$_{20}$Ni$_{3}$Ru$_{5}$.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&a \,\mathbf{\hat{x}}\\\mathbf{a_{2}}&=&a \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&a \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $0$ | = | $0$ | (1a) | Ni I |
| $\mathbf{B_{2}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}$ | (1b) | Ni II |
| $\mathbf{B_{3}}$ | = | $\frac{1}{2} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}$ | (3c) | Al I |
| $\mathbf{B_{4}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{z}}$ | (3c) | Al I |
| $\mathbf{B_{5}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}$ | (3c) | Al I |
| $\mathbf{B_{6}}$ | = | $x_{4} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $a x_{4} \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{z}}$ | (6f) | Ru I |
| $\mathbf{B_{7}}$ | = | $- x_{4} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- a x_{4} \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{z}}$ | (6f) | Ru I |
| $\mathbf{B_{8}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+x_{4} \, \mathbf{a}_{2}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+a x_{4} \,\mathbf{\hat{y}}$ | (6f) | Ru I |
| $\mathbf{B_{9}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}- x_{4} \, \mathbf{a}_{2}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- a x_{4} \,\mathbf{\hat{y}}$ | (6f) | Ru I |
| $\mathbf{B_{10}}$ | = | $\frac{1}{2} \, \mathbf{a}_{2}+x_{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{y}}+a x_{4} \,\mathbf{\hat{z}}$ | (6f) | Ru I |
| $\mathbf{B_{11}}$ | = | $\frac{1}{2} \, \mathbf{a}_{2}- x_{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{y}}- a x_{4} \,\mathbf{\hat{z}}$ | (6f) | Ru I |
| $\mathbf{B_{12}}$ | = | $x_{5} \, \mathbf{a}_{1}+x_{5} \, \mathbf{a}_{2}+x_{5} \, \mathbf{a}_{3}$ | = | $a x_{5} \,\mathbf{\hat{x}}+a x_{5} \,\mathbf{\hat{y}}+a x_{5} \,\mathbf{\hat{z}}$ | (8i) | Al II |
| $\mathbf{B_{13}}$ | = | $- x_{5} \, \mathbf{a}_{1}- x_{5} \, \mathbf{a}_{2}+x_{5} \, \mathbf{a}_{3}$ | = | $- a x_{5} \,\mathbf{\hat{x}}- a x_{5} \,\mathbf{\hat{y}}+a x_{5} \,\mathbf{\hat{z}}$ | (8i) | Al II |
| $\mathbf{B_{14}}$ | = | $- x_{5} \, \mathbf{a}_{1}+x_{5} \, \mathbf{a}_{2}- x_{5} \, \mathbf{a}_{3}$ | = | $- a x_{5} \,\mathbf{\hat{x}}+a x_{5} \,\mathbf{\hat{y}}- a x_{5} \,\mathbf{\hat{z}}$ | (8i) | Al II |
| $\mathbf{B_{15}}$ | = | $x_{5} \, \mathbf{a}_{1}- x_{5} \, \mathbf{a}_{2}- x_{5} \, \mathbf{a}_{3}$ | = | $a x_{5} \,\mathbf{\hat{x}}- a x_{5} \,\mathbf{\hat{y}}- a x_{5} \,\mathbf{\hat{z}}$ | (8i) | Al II |
| $\mathbf{B_{16}}$ | = | $- x_{5} \, \mathbf{a}_{1}- x_{5} \, \mathbf{a}_{2}- x_{5} \, \mathbf{a}_{3}$ | = | $- a x_{5} \,\mathbf{\hat{x}}- a x_{5} \,\mathbf{\hat{y}}- a x_{5} \,\mathbf{\hat{z}}$ | (8i) | Al II |
| $\mathbf{B_{17}}$ | = | $x_{5} \, \mathbf{a}_{1}+x_{5} \, \mathbf{a}_{2}- x_{5} \, \mathbf{a}_{3}$ | = | $a x_{5} \,\mathbf{\hat{x}}+a x_{5} \,\mathbf{\hat{y}}- a x_{5} \,\mathbf{\hat{z}}$ | (8i) | Al II |
| $\mathbf{B_{18}}$ | = | $x_{5} \, \mathbf{a}_{1}- x_{5} \, \mathbf{a}_{2}+x_{5} \, \mathbf{a}_{3}$ | = | $a x_{5} \,\mathbf{\hat{x}}- a x_{5} \,\mathbf{\hat{y}}+a x_{5} \,\mathbf{\hat{z}}$ | (8i) | Al II |
| $\mathbf{B_{19}}$ | = | $- x_{5} \, \mathbf{a}_{1}+x_{5} \, \mathbf{a}_{2}+x_{5} \, \mathbf{a}_{3}$ | = | $- a x_{5} \,\mathbf{\hat{x}}+a x_{5} \,\mathbf{\hat{y}}+a x_{5} \,\mathbf{\hat{z}}$ | (8i) | Al II |
| $\mathbf{B_{20}}$ | = | $y_{6} \, \mathbf{a}_{2}+z_{6} \, \mathbf{a}_{3}$ | = | $a y_{6} \,\mathbf{\hat{y}}+a z_{6} \,\mathbf{\hat{z}}$ | (12j) | Al III |
| $\mathbf{B_{21}}$ | = | $- y_{6} \, \mathbf{a}_{2}+z_{6} \, \mathbf{a}_{3}$ | = | $- a y_{6} \,\mathbf{\hat{y}}+a z_{6} \,\mathbf{\hat{z}}$ | (12j) | Al III |
| $\mathbf{B_{22}}$ | = | $y_{6} \, \mathbf{a}_{2}- z_{6} \, \mathbf{a}_{3}$ | = | $a y_{6} \,\mathbf{\hat{y}}- a z_{6} \,\mathbf{\hat{z}}$ | (12j) | Al III |
| $\mathbf{B_{23}}$ | = | $- y_{6} \, \mathbf{a}_{2}- z_{6} \, \mathbf{a}_{3}$ | = | $- a y_{6} \,\mathbf{\hat{y}}- a z_{6} \,\mathbf{\hat{z}}$ | (12j) | Al III |
| $\mathbf{B_{24}}$ | = | $z_{6} \, \mathbf{a}_{1}+y_{6} \, \mathbf{a}_{3}$ | = | $a z_{6} \,\mathbf{\hat{x}}+a y_{6} \,\mathbf{\hat{z}}$ | (12j) | Al III |
| $\mathbf{B_{25}}$ | = | $z_{6} \, \mathbf{a}_{1}- y_{6} \, \mathbf{a}_{3}$ | = | $a z_{6} \,\mathbf{\hat{x}}- a y_{6} \,\mathbf{\hat{z}}$ | (12j) | Al III |
| $\mathbf{B_{26}}$ | = | $- z_{6} \, \mathbf{a}_{1}+y_{6} \, \mathbf{a}_{3}$ | = | $- a z_{6} \,\mathbf{\hat{x}}+a y_{6} \,\mathbf{\hat{z}}$ | (12j) | Al III |
| $\mathbf{B_{27}}$ | = | $- z_{6} \, \mathbf{a}_{1}- y_{6} \, \mathbf{a}_{3}$ | = | $- a z_{6} \,\mathbf{\hat{x}}- a y_{6} \,\mathbf{\hat{z}}$ | (12j) | Al III |
| $\mathbf{B_{28}}$ | = | $y_{6} \, \mathbf{a}_{1}+z_{6} \, \mathbf{a}_{2}$ | = | $a y_{6} \,\mathbf{\hat{x}}+a z_{6} \,\mathbf{\hat{y}}$ | (12j) | Al III |
| $\mathbf{B_{29}}$ | = | $- y_{6} \, \mathbf{a}_{1}+z_{6} \, \mathbf{a}_{2}$ | = | $- a y_{6} \,\mathbf{\hat{x}}+a z_{6} \,\mathbf{\hat{y}}$ | (12j) | Al III |
| $\mathbf{B_{30}}$ | = | $y_{6} \, \mathbf{a}_{1}- z_{6} \, \mathbf{a}_{2}$ | = | $a y_{6} \,\mathbf{\hat{x}}- a z_{6} \,\mathbf{\hat{y}}$ | (12j) | Al III |
| $\mathbf{B_{31}}$ | = | $- y_{6} \, \mathbf{a}_{1}- z_{6} \, \mathbf{a}_{2}$ | = | $- a y_{6} \,\mathbf{\hat{x}}- a z_{6} \,\mathbf{\hat{y}}$ | (12j) | Al III |
References
- R. Simura, K. Sugiyama, S. Suzuki, and T. Kawamata, Crystal Structure of the C-AlRuNi Phase, Mater. Trans. 58, 1101–1105 (2017), doi:10.2320/matertrans.M2017106.
Prototype Generator
aflow --proto=A23B2C6_cP31_200_cij_ab_f --params=$a,x_{4},x_{5},y_{6},z_{6}$