Orthorhombic Co$_{4}$Al$_{13}$ Structure (Approximate Quasicrystal): A13B4_oP102_31_17a11b_8a2b-001
| Prototype | Al$_{13}$Co$_{4}$ |
| AFLOW prototype label | A13B4_oP102_31_17a11b_8a2b-001 |
| ICSD | 104638 |
| Pearson symbol | oP102 |
| Space group number | 31 |
| Space group symbol | $Pmn2_1$ |
| AFLOW prototype command |
aflow --proto=A13B4_oP102_31_17a11b_8a2b-001
--params=$a, \allowbreak b/a, \allowbreak c/a, \allowbreak y_{1}, \allowbreak z_{1}, \allowbreak y_{2}, \allowbreak z_{2}, \allowbreak y_{3}, \allowbreak z_{3}, \allowbreak y_{4}, \allowbreak z_{4}, \allowbreak y_{5}, \allowbreak z_{5}, \allowbreak y_{6}, \allowbreak z_{6}, \allowbreak y_{7}, \allowbreak z_{7}, \allowbreak y_{8}, \allowbreak z_{8}, \allowbreak y_{9}, \allowbreak z_{9}, \allowbreak y_{10}, \allowbreak z_{10}, \allowbreak y_{11}, \allowbreak z_{11}, \allowbreak y_{12}, \allowbreak z_{12}, \allowbreak y_{13}, \allowbreak z_{13}, \allowbreak y_{14}, \allowbreak z_{14}, \allowbreak y_{15}, \allowbreak z_{15}, \allowbreak y_{16}, \allowbreak z_{16}, \allowbreak y_{17}, \allowbreak z_{17}, \allowbreak y_{18}, \allowbreak z_{18}, \allowbreak y_{19}, \allowbreak z_{19}, \allowbreak y_{20}, \allowbreak z_{20}, \allowbreak y_{21}, \allowbreak z_{21}, \allowbreak y_{22}, \allowbreak z_{22}, \allowbreak y_{23}, \allowbreak z_{23}, \allowbreak y_{24}, \allowbreak z_{24}, \allowbreak y_{25}, \allowbreak z_{25}, \allowbreak x_{26}, \allowbreak y_{26}, \allowbreak z_{26}, \allowbreak x_{27}, \allowbreak y_{27}, \allowbreak z_{27}, \allowbreak x_{28}, \allowbreak y_{28}, \allowbreak z_{28}, \allowbreak x_{29}, \allowbreak y_{29}, \allowbreak z_{29}, \allowbreak x_{30}, \allowbreak y_{30}, \allowbreak z_{30}, \allowbreak x_{31}, \allowbreak y_{31}, \allowbreak z_{31}, \allowbreak x_{32}, \allowbreak y_{32}, \allowbreak z_{32}, \allowbreak x_{33}, \allowbreak y_{33}, \allowbreak z_{33}, \allowbreak x_{34}, \allowbreak y_{34}, \allowbreak z_{34}, \allowbreak x_{35}, \allowbreak y_{35}, \allowbreak z_{35}, \allowbreak x_{36}, \allowbreak y_{36}, \allowbreak z_{36}, \allowbreak x_{37}, \allowbreak y_{37}, \allowbreak z_{37}, \allowbreak x_{38}, \allowbreak y_{38}, \allowbreak z_{38}$ |
- (Addou, 2009) consider this as an
approximate of the decagonal Al-Ni-Co quasicrystal.
- Co$_{4}$ has also been observed in a monoclinic structure which has a large number of vacancies on the aluminum sites.
- Space group $Pmn2_{1}$ #31 allows an arbitrary choice for the origin of the $z$-axis. We follow (Grin, 1994) and set the $z_{25} = 0$.
- If we allow the rather large uncertainty of 0.6Å in the atomic positions, FINDSYM sets the symmetry as $Pnnm$ #58.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&a \,\mathbf{\hat{x}}\\\mathbf{a_{2}}&=&b \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $y_{1} \, \mathbf{a}_{2}+z_{1} \, \mathbf{a}_{3}$ | = | $b y_{1} \,\mathbf{\hat{y}}+c z_{1} \,\mathbf{\hat{z}}$ | (2a) | Al I |
| $\mathbf{B_{2}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}- y_{1} \, \mathbf{a}_{2}+\left(z_{1} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- b y_{1} \,\mathbf{\hat{y}}+c \left(z_{1} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (2a) | Al I |
| $\mathbf{B_{3}}$ | = | $y_{2} \, \mathbf{a}_{2}+z_{2} \, \mathbf{a}_{3}$ | = | $b y_{2} \,\mathbf{\hat{y}}+c z_{2} \,\mathbf{\hat{z}}$ | (2a) | Al II |
| $\mathbf{B_{4}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}- y_{2} \, \mathbf{a}_{2}+\left(z_{2} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- b y_{2} \,\mathbf{\hat{y}}+c \left(z_{2} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (2a) | Al II |
| $\mathbf{B_{5}}$ | = | $y_{3} \, \mathbf{a}_{2}+z_{3} \, \mathbf{a}_{3}$ | = | $b y_{3} \,\mathbf{\hat{y}}+c z_{3} \,\mathbf{\hat{z}}$ | (2a) | Al III |
| $\mathbf{B_{6}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}- y_{3} \, \mathbf{a}_{2}+\left(z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- b y_{3} \,\mathbf{\hat{y}}+c \left(z_{3} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (2a) | Al III |
| $\mathbf{B_{7}}$ | = | $y_{4} \, \mathbf{a}_{2}+z_{4} \, \mathbf{a}_{3}$ | = | $b y_{4} \,\mathbf{\hat{y}}+c z_{4} \,\mathbf{\hat{z}}$ | (2a) | Al IV |
| $\mathbf{B_{8}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}- y_{4} \, \mathbf{a}_{2}+\left(z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- b y_{4} \,\mathbf{\hat{y}}+c \left(z_{4} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (2a) | Al IV |
| $\mathbf{B_{9}}$ | = | $y_{5} \, \mathbf{a}_{2}+z_{5} \, \mathbf{a}_{3}$ | = | $b y_{5} \,\mathbf{\hat{y}}+c z_{5} \,\mathbf{\hat{z}}$ | (2a) | Al V |
| $\mathbf{B_{10}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}- y_{5} \, \mathbf{a}_{2}+\left(z_{5} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- b y_{5} \,\mathbf{\hat{y}}+c \left(z_{5} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (2a) | Al V |
| $\mathbf{B_{11}}$ | = | $y_{6} \, \mathbf{a}_{2}+z_{6} \, \mathbf{a}_{3}$ | = | $b y_{6} \,\mathbf{\hat{y}}+c z_{6} \,\mathbf{\hat{z}}$ | (2a) | Al VI |
| $\mathbf{B_{12}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}- y_{6} \, \mathbf{a}_{2}+\left(z_{6} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- b y_{6} \,\mathbf{\hat{y}}+c \left(z_{6} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (2a) | Al VI |
| $\mathbf{B_{13}}$ | = | $y_{7} \, \mathbf{a}_{2}+z_{7} \, \mathbf{a}_{3}$ | = | $b y_{7} \,\mathbf{\hat{y}}+c z_{7} \,\mathbf{\hat{z}}$ | (2a) | Al VII |
| $\mathbf{B_{14}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}- y_{7} \, \mathbf{a}_{2}+\left(z_{7} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- b y_{7} \,\mathbf{\hat{y}}+c \left(z_{7} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (2a) | Al VII |
| $\mathbf{B_{15}}$ | = | $y_{8} \, \mathbf{a}_{2}+z_{8} \, \mathbf{a}_{3}$ | = | $b y_{8} \,\mathbf{\hat{y}}+c z_{8} \,\mathbf{\hat{z}}$ | (2a) | Al VIII |
| $\mathbf{B_{16}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}- y_{8} \, \mathbf{a}_{2}+\left(z_{8} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- b y_{8} \,\mathbf{\hat{y}}+c \left(z_{8} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (2a) | Al VIII |
| $\mathbf{B_{17}}$ | = | $y_{9} \, \mathbf{a}_{2}+z_{9} \, \mathbf{a}_{3}$ | = | $b y_{9} \,\mathbf{\hat{y}}+c z_{9} \,\mathbf{\hat{z}}$ | (2a) | Al IX |
| $\mathbf{B_{18}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}- y_{9} \, \mathbf{a}_{2}+\left(z_{9} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- b y_{9} \,\mathbf{\hat{y}}+c \left(z_{9} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (2a) | Al IX |
| $\mathbf{B_{19}}$ | = | $y_{10} \, \mathbf{a}_{2}+z_{10} \, \mathbf{a}_{3}$ | = | $b y_{10} \,\mathbf{\hat{y}}+c z_{10} \,\mathbf{\hat{z}}$ | (2a) | Al X |
| $\mathbf{B_{20}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}- y_{10} \, \mathbf{a}_{2}+\left(z_{10} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- b y_{10} \,\mathbf{\hat{y}}+c \left(z_{10} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (2a) | Al X |
| $\mathbf{B_{21}}$ | = | $y_{11} \, \mathbf{a}_{2}+z_{11} \, \mathbf{a}_{3}$ | = | $b y_{11} \,\mathbf{\hat{y}}+c z_{11} \,\mathbf{\hat{z}}$ | (2a) | Al XI |
| $\mathbf{B_{22}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}- y_{11} \, \mathbf{a}_{2}+\left(z_{11} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- b y_{11} \,\mathbf{\hat{y}}+c \left(z_{11} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (2a) | Al XI |
| $\mathbf{B_{23}}$ | = | $y_{12} \, \mathbf{a}_{2}+z_{12} \, \mathbf{a}_{3}$ | = | $b y_{12} \,\mathbf{\hat{y}}+c z_{12} \,\mathbf{\hat{z}}$ | (2a) | Al XII |
| $\mathbf{B_{24}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}- y_{12} \, \mathbf{a}_{2}+\left(z_{12} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- b y_{12} \,\mathbf{\hat{y}}+c \left(z_{12} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (2a) | Al XII |
| $\mathbf{B_{25}}$ | = | $y_{13} \, \mathbf{a}_{2}+z_{13} \, \mathbf{a}_{3}$ | = | $b y_{13} \,\mathbf{\hat{y}}+c z_{13} \,\mathbf{\hat{z}}$ | (2a) | Al XIII |
| $\mathbf{B_{26}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}- y_{13} \, \mathbf{a}_{2}+\left(z_{13} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- b y_{13} \,\mathbf{\hat{y}}+c \left(z_{13} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (2a) | Al XIII |
| $\mathbf{B_{27}}$ | = | $y_{14} \, \mathbf{a}_{2}+z_{14} \, \mathbf{a}_{3}$ | = | $b y_{14} \,\mathbf{\hat{y}}+c z_{14} \,\mathbf{\hat{z}}$ | (2a) | Al XIV |
| $\mathbf{B_{28}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}- y_{14} \, \mathbf{a}_{2}+\left(z_{14} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- b y_{14} \,\mathbf{\hat{y}}+c \left(z_{14} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (2a) | Al XIV |
| $\mathbf{B_{29}}$ | = | $y_{15} \, \mathbf{a}_{2}+z_{15} \, \mathbf{a}_{3}$ | = | $b y_{15} \,\mathbf{\hat{y}}+c z_{15} \,\mathbf{\hat{z}}$ | (2a) | Al XV |
| $\mathbf{B_{30}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}- y_{15} \, \mathbf{a}_{2}+\left(z_{15} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- b y_{15} \,\mathbf{\hat{y}}+c \left(z_{15} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (2a) | Al XV |
| $\mathbf{B_{31}}$ | = | $y_{16} \, \mathbf{a}_{2}+z_{16} \, \mathbf{a}_{3}$ | = | $b y_{16} \,\mathbf{\hat{y}}+c z_{16} \,\mathbf{\hat{z}}$ | (2a) | Al XVI |
| $\mathbf{B_{32}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}- y_{16} \, \mathbf{a}_{2}+\left(z_{16} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- b y_{16} \,\mathbf{\hat{y}}+c \left(z_{16} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (2a) | Al XVI |
| $\mathbf{B_{33}}$ | = | $y_{17} \, \mathbf{a}_{2}+z_{17} \, \mathbf{a}_{3}$ | = | $b y_{17} \,\mathbf{\hat{y}}+c z_{17} \,\mathbf{\hat{z}}$ | (2a) | Al XVII |
| $\mathbf{B_{34}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}- y_{17} \, \mathbf{a}_{2}+\left(z_{17} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- b y_{17} \,\mathbf{\hat{y}}+c \left(z_{17} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (2a) | Al XVII |
| $\mathbf{B_{35}}$ | = | $y_{18} \, \mathbf{a}_{2}+z_{18} \, \mathbf{a}_{3}$ | = | $b y_{18} \,\mathbf{\hat{y}}+c z_{18} \,\mathbf{\hat{z}}$ | (2a) | Co I |
| $\mathbf{B_{36}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}- y_{18} \, \mathbf{a}_{2}+\left(z_{18} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- b y_{18} \,\mathbf{\hat{y}}+c \left(z_{18} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (2a) | Co I |
| $\mathbf{B_{37}}$ | = | $y_{19} \, \mathbf{a}_{2}+z_{19} \, \mathbf{a}_{3}$ | = | $b y_{19} \,\mathbf{\hat{y}}+c z_{19} \,\mathbf{\hat{z}}$ | (2a) | Co II |
| $\mathbf{B_{38}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}- y_{19} \, \mathbf{a}_{2}+\left(z_{19} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- b y_{19} \,\mathbf{\hat{y}}+c \left(z_{19} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (2a) | Co II |
| $\mathbf{B_{39}}$ | = | $y_{20} \, \mathbf{a}_{2}+z_{20} \, \mathbf{a}_{3}$ | = | $b y_{20} \,\mathbf{\hat{y}}+c z_{20} \,\mathbf{\hat{z}}$ | (2a) | Co III |
| $\mathbf{B_{40}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}- y_{20} \, \mathbf{a}_{2}+\left(z_{20} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- b y_{20} \,\mathbf{\hat{y}}+c \left(z_{20} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (2a) | Co III |
| $\mathbf{B_{41}}$ | = | $y_{21} \, \mathbf{a}_{2}+z_{21} \, \mathbf{a}_{3}$ | = | $b y_{21} \,\mathbf{\hat{y}}+c z_{21} \,\mathbf{\hat{z}}$ | (2a) | Co IV |
| $\mathbf{B_{42}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}- y_{21} \, \mathbf{a}_{2}+\left(z_{21} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- b y_{21} \,\mathbf{\hat{y}}+c \left(z_{21} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (2a) | Co IV |
| $\mathbf{B_{43}}$ | = | $y_{22} \, \mathbf{a}_{2}+z_{22} \, \mathbf{a}_{3}$ | = | $b y_{22} \,\mathbf{\hat{y}}+c z_{22} \,\mathbf{\hat{z}}$ | (2a) | Co V |
| $\mathbf{B_{44}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}- y_{22} \, \mathbf{a}_{2}+\left(z_{22} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- b y_{22} \,\mathbf{\hat{y}}+c \left(z_{22} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (2a) | Co V |
| $\mathbf{B_{45}}$ | = | $y_{23} \, \mathbf{a}_{2}+z_{23} \, \mathbf{a}_{3}$ | = | $b y_{23} \,\mathbf{\hat{y}}+c z_{23} \,\mathbf{\hat{z}}$ | (2a) | Co VI |
| $\mathbf{B_{46}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}- y_{23} \, \mathbf{a}_{2}+\left(z_{23} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- b y_{23} \,\mathbf{\hat{y}}+c \left(z_{23} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (2a) | Co VI |
| $\mathbf{B_{47}}$ | = | $y_{24} \, \mathbf{a}_{2}+z_{24} \, \mathbf{a}_{3}$ | = | $b y_{24} \,\mathbf{\hat{y}}+c z_{24} \,\mathbf{\hat{z}}$ | (2a) | Co VII |
| $\mathbf{B_{48}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}- y_{24} \, \mathbf{a}_{2}+\left(z_{24} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- b y_{24} \,\mathbf{\hat{y}}+c \left(z_{24} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (2a) | Co VII |
| $\mathbf{B_{49}}$ | = | $y_{25} \, \mathbf{a}_{2}+z_{25} \, \mathbf{a}_{3}$ | = | $b y_{25} \,\mathbf{\hat{y}}+c z_{25} \,\mathbf{\hat{z}}$ | (2a) | Co VIII |
| $\mathbf{B_{50}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}- y_{25} \, \mathbf{a}_{2}+\left(z_{25} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- b y_{25} \,\mathbf{\hat{y}}+c \left(z_{25} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (2a) | Co VIII |
| $\mathbf{B_{51}}$ | = | $x_{26} \, \mathbf{a}_{1}+y_{26} \, \mathbf{a}_{2}+z_{26} \, \mathbf{a}_{3}$ | = | $a x_{26} \,\mathbf{\hat{x}}+b y_{26} \,\mathbf{\hat{y}}+c z_{26} \,\mathbf{\hat{z}}$ | (4b) | Al XVIII |
| $\mathbf{B_{52}}$ | = | $- \left(x_{26} - \frac{1}{2}\right) \, \mathbf{a}_{1}- y_{26} \, \mathbf{a}_{2}+\left(z_{26} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{26} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- b y_{26} \,\mathbf{\hat{y}}+c \left(z_{26} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4b) | Al XVIII |
| $\mathbf{B_{53}}$ | = | $\left(x_{26} + \frac{1}{2}\right) \, \mathbf{a}_{1}- y_{26} \, \mathbf{a}_{2}+\left(z_{26} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{26} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- b y_{26} \,\mathbf{\hat{y}}+c \left(z_{26} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4b) | Al XVIII |
| $\mathbf{B_{54}}$ | = | $- x_{26} \, \mathbf{a}_{1}+y_{26} \, \mathbf{a}_{2}+z_{26} \, \mathbf{a}_{3}$ | = | $- a x_{26} \,\mathbf{\hat{x}}+b y_{26} \,\mathbf{\hat{y}}+c z_{26} \,\mathbf{\hat{z}}$ | (4b) | Al XVIII |
| $\mathbf{B_{55}}$ | = | $x_{27} \, \mathbf{a}_{1}+y_{27} \, \mathbf{a}_{2}+z_{27} \, \mathbf{a}_{3}$ | = | $a x_{27} \,\mathbf{\hat{x}}+b y_{27} \,\mathbf{\hat{y}}+c z_{27} \,\mathbf{\hat{z}}$ | (4b) | Al XIX |
| $\mathbf{B_{56}}$ | = | $- \left(x_{27} - \frac{1}{2}\right) \, \mathbf{a}_{1}- y_{27} \, \mathbf{a}_{2}+\left(z_{27} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{27} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- b y_{27} \,\mathbf{\hat{y}}+c \left(z_{27} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4b) | Al XIX |
| $\mathbf{B_{57}}$ | = | $\left(x_{27} + \frac{1}{2}\right) \, \mathbf{a}_{1}- y_{27} \, \mathbf{a}_{2}+\left(z_{27} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{27} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- b y_{27} \,\mathbf{\hat{y}}+c \left(z_{27} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4b) | Al XIX |
| $\mathbf{B_{58}}$ | = | $- x_{27} \, \mathbf{a}_{1}+y_{27} \, \mathbf{a}_{2}+z_{27} \, \mathbf{a}_{3}$ | = | $- a x_{27} \,\mathbf{\hat{x}}+b y_{27} \,\mathbf{\hat{y}}+c z_{27} \,\mathbf{\hat{z}}$ | (4b) | Al XIX |
| $\mathbf{B_{59}}$ | = | $x_{28} \, \mathbf{a}_{1}+y_{28} \, \mathbf{a}_{2}+z_{28} \, \mathbf{a}_{3}$ | = | $a x_{28} \,\mathbf{\hat{x}}+b y_{28} \,\mathbf{\hat{y}}+c z_{28} \,\mathbf{\hat{z}}$ | (4b) | Al XX |
| $\mathbf{B_{60}}$ | = | $- \left(x_{28} - \frac{1}{2}\right) \, \mathbf{a}_{1}- y_{28} \, \mathbf{a}_{2}+\left(z_{28} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{28} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- b y_{28} \,\mathbf{\hat{y}}+c \left(z_{28} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4b) | Al XX |
| $\mathbf{B_{61}}$ | = | $\left(x_{28} + \frac{1}{2}\right) \, \mathbf{a}_{1}- y_{28} \, \mathbf{a}_{2}+\left(z_{28} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{28} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- b y_{28} \,\mathbf{\hat{y}}+c \left(z_{28} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4b) | Al XX |
| $\mathbf{B_{62}}$ | = | $- x_{28} \, \mathbf{a}_{1}+y_{28} \, \mathbf{a}_{2}+z_{28} \, \mathbf{a}_{3}$ | = | $- a x_{28} \,\mathbf{\hat{x}}+b y_{28} \,\mathbf{\hat{y}}+c z_{28} \,\mathbf{\hat{z}}$ | (4b) | Al XX |
| $\mathbf{B_{63}}$ | = | $x_{29} \, \mathbf{a}_{1}+y_{29} \, \mathbf{a}_{2}+z_{29} \, \mathbf{a}_{3}$ | = | $a x_{29} \,\mathbf{\hat{x}}+b y_{29} \,\mathbf{\hat{y}}+c z_{29} \,\mathbf{\hat{z}}$ | (4b) | Al XXI |
| $\mathbf{B_{64}}$ | = | $- \left(x_{29} - \frac{1}{2}\right) \, \mathbf{a}_{1}- y_{29} \, \mathbf{a}_{2}+\left(z_{29} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{29} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- b y_{29} \,\mathbf{\hat{y}}+c \left(z_{29} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4b) | Al XXI |
| $\mathbf{B_{65}}$ | = | $\left(x_{29} + \frac{1}{2}\right) \, \mathbf{a}_{1}- y_{29} \, \mathbf{a}_{2}+\left(z_{29} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{29} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- b y_{29} \,\mathbf{\hat{y}}+c \left(z_{29} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4b) | Al XXI |
| $\mathbf{B_{66}}$ | = | $- x_{29} \, \mathbf{a}_{1}+y_{29} \, \mathbf{a}_{2}+z_{29} \, \mathbf{a}_{3}$ | = | $- a x_{29} \,\mathbf{\hat{x}}+b y_{29} \,\mathbf{\hat{y}}+c z_{29} \,\mathbf{\hat{z}}$ | (4b) | Al XXI |
| $\mathbf{B_{67}}$ | = | $x_{30} \, \mathbf{a}_{1}+y_{30} \, \mathbf{a}_{2}+z_{30} \, \mathbf{a}_{3}$ | = | $a x_{30} \,\mathbf{\hat{x}}+b y_{30} \,\mathbf{\hat{y}}+c z_{30} \,\mathbf{\hat{z}}$ | (4b) | Al XXII |
| $\mathbf{B_{68}}$ | = | $- \left(x_{30} - \frac{1}{2}\right) \, \mathbf{a}_{1}- y_{30} \, \mathbf{a}_{2}+\left(z_{30} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{30} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- b y_{30} \,\mathbf{\hat{y}}+c \left(z_{30} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4b) | Al XXII |
| $\mathbf{B_{69}}$ | = | $\left(x_{30} + \frac{1}{2}\right) \, \mathbf{a}_{1}- y_{30} \, \mathbf{a}_{2}+\left(z_{30} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{30} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- b y_{30} \,\mathbf{\hat{y}}+c \left(z_{30} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4b) | Al XXII |
| $\mathbf{B_{70}}$ | = | $- x_{30} \, \mathbf{a}_{1}+y_{30} \, \mathbf{a}_{2}+z_{30} \, \mathbf{a}_{3}$ | = | $- a x_{30} \,\mathbf{\hat{x}}+b y_{30} \,\mathbf{\hat{y}}+c z_{30} \,\mathbf{\hat{z}}$ | (4b) | Al XXII |
| $\mathbf{B_{71}}$ | = | $x_{31} \, \mathbf{a}_{1}+y_{31} \, \mathbf{a}_{2}+z_{31} \, \mathbf{a}_{3}$ | = | $a x_{31} \,\mathbf{\hat{x}}+b y_{31} \,\mathbf{\hat{y}}+c z_{31} \,\mathbf{\hat{z}}$ | (4b) | Al XXIII |
| $\mathbf{B_{72}}$ | = | $- \left(x_{31} - \frac{1}{2}\right) \, \mathbf{a}_{1}- y_{31} \, \mathbf{a}_{2}+\left(z_{31} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{31} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- b y_{31} \,\mathbf{\hat{y}}+c \left(z_{31} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4b) | Al XXIII |
| $\mathbf{B_{73}}$ | = | $\left(x_{31} + \frac{1}{2}\right) \, \mathbf{a}_{1}- y_{31} \, \mathbf{a}_{2}+\left(z_{31} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{31} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- b y_{31} \,\mathbf{\hat{y}}+c \left(z_{31} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4b) | Al XXIII |
| $\mathbf{B_{74}}$ | = | $- x_{31} \, \mathbf{a}_{1}+y_{31} \, \mathbf{a}_{2}+z_{31} \, \mathbf{a}_{3}$ | = | $- a x_{31} \,\mathbf{\hat{x}}+b y_{31} \,\mathbf{\hat{y}}+c z_{31} \,\mathbf{\hat{z}}$ | (4b) | Al XXIII |
| $\mathbf{B_{75}}$ | = | $x_{32} \, \mathbf{a}_{1}+y_{32} \, \mathbf{a}_{2}+z_{32} \, \mathbf{a}_{3}$ | = | $a x_{32} \,\mathbf{\hat{x}}+b y_{32} \,\mathbf{\hat{y}}+c z_{32} \,\mathbf{\hat{z}}$ | (4b) | Al XXIV |
| $\mathbf{B_{76}}$ | = | $- \left(x_{32} - \frac{1}{2}\right) \, \mathbf{a}_{1}- y_{32} \, \mathbf{a}_{2}+\left(z_{32} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{32} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- b y_{32} \,\mathbf{\hat{y}}+c \left(z_{32} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4b) | Al XXIV |
| $\mathbf{B_{77}}$ | = | $\left(x_{32} + \frac{1}{2}\right) \, \mathbf{a}_{1}- y_{32} \, \mathbf{a}_{2}+\left(z_{32} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{32} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- b y_{32} \,\mathbf{\hat{y}}+c \left(z_{32} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4b) | Al XXIV |
| $\mathbf{B_{78}}$ | = | $- x_{32} \, \mathbf{a}_{1}+y_{32} \, \mathbf{a}_{2}+z_{32} \, \mathbf{a}_{3}$ | = | $- a x_{32} \,\mathbf{\hat{x}}+b y_{32} \,\mathbf{\hat{y}}+c z_{32} \,\mathbf{\hat{z}}$ | (4b) | Al XXIV |
| $\mathbf{B_{79}}$ | = | $x_{33} \, \mathbf{a}_{1}+y_{33} \, \mathbf{a}_{2}+z_{33} \, \mathbf{a}_{3}$ | = | $a x_{33} \,\mathbf{\hat{x}}+b y_{33} \,\mathbf{\hat{y}}+c z_{33} \,\mathbf{\hat{z}}$ | (4b) | Al XXV |
| $\mathbf{B_{80}}$ | = | $- \left(x_{33} - \frac{1}{2}\right) \, \mathbf{a}_{1}- y_{33} \, \mathbf{a}_{2}+\left(z_{33} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{33} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- b y_{33} \,\mathbf{\hat{y}}+c \left(z_{33} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4b) | Al XXV |
| $\mathbf{B_{81}}$ | = | $\left(x_{33} + \frac{1}{2}\right) \, \mathbf{a}_{1}- y_{33} \, \mathbf{a}_{2}+\left(z_{33} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{33} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- b y_{33} \,\mathbf{\hat{y}}+c \left(z_{33} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4b) | Al XXV |
| $\mathbf{B_{82}}$ | = | $- x_{33} \, \mathbf{a}_{1}+y_{33} \, \mathbf{a}_{2}+z_{33} \, \mathbf{a}_{3}$ | = | $- a x_{33} \,\mathbf{\hat{x}}+b y_{33} \,\mathbf{\hat{y}}+c z_{33} \,\mathbf{\hat{z}}$ | (4b) | Al XXV |
| $\mathbf{B_{83}}$ | = | $x_{34} \, \mathbf{a}_{1}+y_{34} \, \mathbf{a}_{2}+z_{34} \, \mathbf{a}_{3}$ | = | $a x_{34} \,\mathbf{\hat{x}}+b y_{34} \,\mathbf{\hat{y}}+c z_{34} \,\mathbf{\hat{z}}$ | (4b) | Al XXVI |
| $\mathbf{B_{84}}$ | = | $- \left(x_{34} - \frac{1}{2}\right) \, \mathbf{a}_{1}- y_{34} \, \mathbf{a}_{2}+\left(z_{34} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{34} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- b y_{34} \,\mathbf{\hat{y}}+c \left(z_{34} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4b) | Al XXVI |
| $\mathbf{B_{85}}$ | = | $\left(x_{34} + \frac{1}{2}\right) \, \mathbf{a}_{1}- y_{34} \, \mathbf{a}_{2}+\left(z_{34} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{34} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- b y_{34} \,\mathbf{\hat{y}}+c \left(z_{34} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4b) | Al XXVI |
| $\mathbf{B_{86}}$ | = | $- x_{34} \, \mathbf{a}_{1}+y_{34} \, \mathbf{a}_{2}+z_{34} \, \mathbf{a}_{3}$ | = | $- a x_{34} \,\mathbf{\hat{x}}+b y_{34} \,\mathbf{\hat{y}}+c z_{34} \,\mathbf{\hat{z}}$ | (4b) | Al XXVI |
| $\mathbf{B_{87}}$ | = | $x_{35} \, \mathbf{a}_{1}+y_{35} \, \mathbf{a}_{2}+z_{35} \, \mathbf{a}_{3}$ | = | $a x_{35} \,\mathbf{\hat{x}}+b y_{35} \,\mathbf{\hat{y}}+c z_{35} \,\mathbf{\hat{z}}$ | (4b) | Al XXVII |
| $\mathbf{B_{88}}$ | = | $- \left(x_{35} - \frac{1}{2}\right) \, \mathbf{a}_{1}- y_{35} \, \mathbf{a}_{2}+\left(z_{35} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{35} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- b y_{35} \,\mathbf{\hat{y}}+c \left(z_{35} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4b) | Al XXVII |
| $\mathbf{B_{89}}$ | = | $\left(x_{35} + \frac{1}{2}\right) \, \mathbf{a}_{1}- y_{35} \, \mathbf{a}_{2}+\left(z_{35} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{35} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- b y_{35} \,\mathbf{\hat{y}}+c \left(z_{35} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4b) | Al XXVII |
| $\mathbf{B_{90}}$ | = | $- x_{35} \, \mathbf{a}_{1}+y_{35} \, \mathbf{a}_{2}+z_{35} \, \mathbf{a}_{3}$ | = | $- a x_{35} \,\mathbf{\hat{x}}+b y_{35} \,\mathbf{\hat{y}}+c z_{35} \,\mathbf{\hat{z}}$ | (4b) | Al XXVII |
| $\mathbf{B_{91}}$ | = | $x_{36} \, \mathbf{a}_{1}+y_{36} \, \mathbf{a}_{2}+z_{36} \, \mathbf{a}_{3}$ | = | $a x_{36} \,\mathbf{\hat{x}}+b y_{36} \,\mathbf{\hat{y}}+c z_{36} \,\mathbf{\hat{z}}$ | (4b) | Al XXVIII |
| $\mathbf{B_{92}}$ | = | $- \left(x_{36} - \frac{1}{2}\right) \, \mathbf{a}_{1}- y_{36} \, \mathbf{a}_{2}+\left(z_{36} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{36} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- b y_{36} \,\mathbf{\hat{y}}+c \left(z_{36} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4b) | Al XXVIII |
| $\mathbf{B_{93}}$ | = | $\left(x_{36} + \frac{1}{2}\right) \, \mathbf{a}_{1}- y_{36} \, \mathbf{a}_{2}+\left(z_{36} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{36} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- b y_{36} \,\mathbf{\hat{y}}+c \left(z_{36} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4b) | Al XXVIII |
| $\mathbf{B_{94}}$ | = | $- x_{36} \, \mathbf{a}_{1}+y_{36} \, \mathbf{a}_{2}+z_{36} \, \mathbf{a}_{3}$ | = | $- a x_{36} \,\mathbf{\hat{x}}+b y_{36} \,\mathbf{\hat{y}}+c z_{36} \,\mathbf{\hat{z}}$ | (4b) | Al XXVIII |
| $\mathbf{B_{95}}$ | = | $x_{37} \, \mathbf{a}_{1}+y_{37} \, \mathbf{a}_{2}+z_{37} \, \mathbf{a}_{3}$ | = | $a x_{37} \,\mathbf{\hat{x}}+b y_{37} \,\mathbf{\hat{y}}+c z_{37} \,\mathbf{\hat{z}}$ | (4b) | Co IX |
| $\mathbf{B_{96}}$ | = | $- \left(x_{37} - \frac{1}{2}\right) \, \mathbf{a}_{1}- y_{37} \, \mathbf{a}_{2}+\left(z_{37} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{37} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- b y_{37} \,\mathbf{\hat{y}}+c \left(z_{37} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4b) | Co IX |
| $\mathbf{B_{97}}$ | = | $\left(x_{37} + \frac{1}{2}\right) \, \mathbf{a}_{1}- y_{37} \, \mathbf{a}_{2}+\left(z_{37} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{37} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- b y_{37} \,\mathbf{\hat{y}}+c \left(z_{37} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4b) | Co IX |
| $\mathbf{B_{98}}$ | = | $- x_{37} \, \mathbf{a}_{1}+y_{37} \, \mathbf{a}_{2}+z_{37} \, \mathbf{a}_{3}$ | = | $- a x_{37} \,\mathbf{\hat{x}}+b y_{37} \,\mathbf{\hat{y}}+c z_{37} \,\mathbf{\hat{z}}$ | (4b) | Co IX |
| $\mathbf{B_{99}}$ | = | $x_{38} \, \mathbf{a}_{1}+y_{38} \, \mathbf{a}_{2}+z_{38} \, \mathbf{a}_{3}$ | = | $a x_{38} \,\mathbf{\hat{x}}+b y_{38} \,\mathbf{\hat{y}}+c z_{38} \,\mathbf{\hat{z}}$ | (4b) | Co X |
| $\mathbf{B_{100}}$ | = | $- \left(x_{38} - \frac{1}{2}\right) \, \mathbf{a}_{1}- y_{38} \, \mathbf{a}_{2}+\left(z_{38} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{38} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- b y_{38} \,\mathbf{\hat{y}}+c \left(z_{38} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4b) | Co X |
| $\mathbf{B_{101}}$ | = | $\left(x_{38} + \frac{1}{2}\right) \, \mathbf{a}_{1}- y_{38} \, \mathbf{a}_{2}+\left(z_{38} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{38} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- b y_{38} \,\mathbf{\hat{y}}+c \left(z_{38} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4b) | Co X |
| $\mathbf{B_{102}}$ | = | $- x_{38} \, \mathbf{a}_{1}+y_{38} \, \mathbf{a}_{2}+z_{38} \, \mathbf{a}_{3}$ | = | $- a x_{38} \,\mathbf{\hat{x}}+b y_{38} \,\mathbf{\hat{y}}+c z_{38} \,\mathbf{\hat{z}}$ | (4b) | Co X |
References
- J. Grin, U. Burkhard, M. Ellner, and K. Peters, Crystal structure of orthorhombic Co$_{4}$Al$_{13}$, J. Alloys Compd. 206, 243–247 (1994), doi:10.1016/0925-8388(94)90043-4.
Found in
- R. Addou, E. Gaudry, T. Deniozou, M. Heggen, M. Feuerbacher, P. Gille, Y. Grin, R. Widmer, O. Gröning, V. Fournée, J.-M. Dubois, , and J. Ledieu, Structure investigation of the (100) surface of the orthorhombic Al$_{13}$Co$_{4}$ crystal, Phys. Rev. B 80, 014203 (2009), doi:10.1103/PhysRevB.80.014203.
Prototype Generator
aflow --proto=A13B4_oP102_31_17a11b_8a2b --params=$a,b/a,c/a,y_{1},z_{1},y_{2},z_{2},y_{3},z_{3},y_{4},z_{4},y_{5},z_{5},y_{6},z_{6},y_{7},z_{7},y_{8},z_{8},y_{9},z_{9},y_{10},z_{10},y_{11},z_{11},y_{12},z_{12},y_{13},z_{13},y_{14},z_{14},y_{15},z_{15},y_{16},z_{16},y_{17},z_{17},y_{18},z_{18},y_{19},z_{19},y_{20},z_{20},y_{21},z_{21},y_{22},z_{22},y_{23},z_{23},y_{24},z_{24},y_{25},z_{25},x_{26},y_{26},z_{26},x_{27},y_{27},z_{27},x_{28},y_{28},z_{28},x_{29},y_{29},z_{29},x_{30},y_{30},z_{30},x_{31},y_{31},z_{31},x_{32},y_{32},z_{32},x_{33},y_{33},z_{33},x_{34},y_{34},z_{34},x_{35},y_{35},z_{35},x_{36},y_{36},z_{36},x_{37},y_{37},z_{37},x_{38},y_{38},z_{38}$