Monoclinic Co$_{4}$Al$_{13}$ Structure: A13B4_mC102_8_17a11b_8a2b-001
| Prototype | Al$_{13}$Co$_{4}$ |
| AFLOW prototype label | A13B4_mC102_8_17a11b_8a2b-001 |
| ICSD | 57599 |
| Pearson symbol | mC102 |
| Space group number | 8 |
| Space group symbol | $Cm$ |
| AFLOW prototype command |
aflow --proto=A13B4_mC102_8_17a11b_8a2b-001
--params=$a, \allowbreak b/a, \allowbreak c/a, \allowbreak \beta, \allowbreak x_{1}, \allowbreak z_{1}, \allowbreak x_{2}, \allowbreak z_{2}, \allowbreak x_{3}, \allowbreak z_{3}, \allowbreak x_{4}, \allowbreak z_{4}, \allowbreak x_{5}, \allowbreak z_{5}, \allowbreak x_{6}, \allowbreak z_{6}, \allowbreak x_{7}, \allowbreak z_{7}, \allowbreak x_{8}, \allowbreak z_{8}, \allowbreak x_{9}, \allowbreak z_{9}, \allowbreak x_{10}, \allowbreak z_{10}, \allowbreak x_{11}, \allowbreak z_{11}, \allowbreak x_{12}, \allowbreak z_{12}, \allowbreak x_{13}, \allowbreak z_{13}, \allowbreak x_{14}, \allowbreak z_{14}, \allowbreak x_{15}, \allowbreak z_{15}, \allowbreak x_{16}, \allowbreak z_{16}, \allowbreak x_{17}, \allowbreak z_{17}, \allowbreak x_{18}, \allowbreak z_{18}, \allowbreak x_{19}, \allowbreak z_{19}, \allowbreak x_{20}, \allowbreak z_{20}, \allowbreak x_{21}, \allowbreak z_{21}, \allowbreak x_{22}, \allowbreak z_{22}, \allowbreak x_{23}, \allowbreak z_{23}, \allowbreak x_{24}, \allowbreak z_{24}, \allowbreak x_{25}, \allowbreak z_{25}, \allowbreak x_{26}, \allowbreak y_{26}, \allowbreak z_{26}, \allowbreak x_{27}, \allowbreak y_{27}, \allowbreak z_{27}, \allowbreak x_{28}, \allowbreak y_{28}, \allowbreak z_{28}, \allowbreak x_{29}, \allowbreak y_{29}, \allowbreak z_{29}, \allowbreak x_{30}, \allowbreak y_{30}, \allowbreak z_{30}, \allowbreak x_{31}, \allowbreak y_{31}, \allowbreak z_{31}, \allowbreak x_{32}, \allowbreak y_{32}, \allowbreak z_{32}, \allowbreak x_{33}, \allowbreak y_{33}, \allowbreak z_{33}, \allowbreak x_{34}, \allowbreak y_{34}, \allowbreak z_{34}, \allowbreak x_{35}, \allowbreak y_{35}, \allowbreak z_{35}, \allowbreak x_{36}, \allowbreak y_{36}, \allowbreak z_{36}, \allowbreak x_{37}, \allowbreak y_{37}, \allowbreak z_{37}, \allowbreak x_{38}, \allowbreak y_{38}, \allowbreak z_{38}$ |
- Following (Hudd, 1962), the Al-IV and Al-XIII sites are occupied 30% of the time, while the occupation of Al-VI, Al-IX, Al-XIV, and Al-XVII is 70%. This gives a nominal occupation of Al$_{91}$Co$_{30}$, though the authors state the actual composition is Al$_{68.3}$Co$_{24.4}$.
- Space group $Cm$ #8 allows an arbitrary choice for the origin of the $z$-axis. We follow (Hudd, 1962) and set $z_{26} = 0$.
- If we allow the rather large uncertainty of 0.3Å in the atomic positions, FINDSYM sets the symmetry as $C2/m$ #12. That crystal has the Al$_{13}$Fe$_{4}$ prototype.
- Co$_{4}$ has also been observed in a orthorhombic structure.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{1}{2}b \,\mathbf{\hat{y}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}b \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \cos{\beta} \,\mathbf{\hat{x}}+c \sin{\beta} \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $x_{1} \, \mathbf{a}_{1}+x_{1} \, \mathbf{a}_{2}+z_{1} \, \mathbf{a}_{3}$ | = | $\left(a x_{1} + c z_{1} \cos{\beta}\right) \,\mathbf{\hat{x}}+c z_{1} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | Al I |
| $\mathbf{B_{2}}$ | = | $x_{2} \, \mathbf{a}_{1}+x_{2} \, \mathbf{a}_{2}+z_{2} \, \mathbf{a}_{3}$ | = | $\left(a x_{2} + c z_{2} \cos{\beta}\right) \,\mathbf{\hat{x}}+c z_{2} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | Al II |
| $\mathbf{B_{3}}$ | = | $x_{3} \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{2}+z_{3} \, \mathbf{a}_{3}$ | = | $\left(a x_{3} + c z_{3} \cos{\beta}\right) \,\mathbf{\hat{x}}+c z_{3} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | Al III |
| $\mathbf{B_{4}}$ | = | $x_{4} \, \mathbf{a}_{1}+x_{4} \, \mathbf{a}_{2}+z_{4} \, \mathbf{a}_{3}$ | = | $\left(a x_{4} + c z_{4} \cos{\beta}\right) \,\mathbf{\hat{x}}+c z_{4} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | Al IV |
| $\mathbf{B_{5}}$ | = | $x_{5} \, \mathbf{a}_{1}+x_{5} \, \mathbf{a}_{2}+z_{5} \, \mathbf{a}_{3}$ | = | $\left(a x_{5} + c z_{5} \cos{\beta}\right) \,\mathbf{\hat{x}}+c z_{5} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | Al V |
| $\mathbf{B_{6}}$ | = | $x_{6} \, \mathbf{a}_{1}+x_{6} \, \mathbf{a}_{2}+z_{6} \, \mathbf{a}_{3}$ | = | $\left(a x_{6} + c z_{6} \cos{\beta}\right) \,\mathbf{\hat{x}}+c z_{6} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | Al VI |
| $\mathbf{B_{7}}$ | = | $x_{7} \, \mathbf{a}_{1}+x_{7} \, \mathbf{a}_{2}+z_{7} \, \mathbf{a}_{3}$ | = | $\left(a x_{7} + c z_{7} \cos{\beta}\right) \,\mathbf{\hat{x}}+c z_{7} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | Al VII |
| $\mathbf{B_{8}}$ | = | $x_{8} \, \mathbf{a}_{1}+x_{8} \, \mathbf{a}_{2}+z_{8} \, \mathbf{a}_{3}$ | = | $\left(a x_{8} + c z_{8} \cos{\beta}\right) \,\mathbf{\hat{x}}+c z_{8} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | Al VIII |
| $\mathbf{B_{9}}$ | = | $x_{9} \, \mathbf{a}_{1}+x_{9} \, \mathbf{a}_{2}+z_{9} \, \mathbf{a}_{3}$ | = | $\left(a x_{9} + c z_{9} \cos{\beta}\right) \,\mathbf{\hat{x}}+c z_{9} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | Al IX |
| $\mathbf{B_{10}}$ | = | $x_{10} \, \mathbf{a}_{1}+x_{10} \, \mathbf{a}_{2}+z_{10} \, \mathbf{a}_{3}$ | = | $\left(a x_{10} + c z_{10} \cos{\beta}\right) \,\mathbf{\hat{x}}+c z_{10} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | Al X |
| $\mathbf{B_{11}}$ | = | $x_{11} \, \mathbf{a}_{1}+x_{11} \, \mathbf{a}_{2}+z_{11} \, \mathbf{a}_{3}$ | = | $\left(a x_{11} + c z_{11} \cos{\beta}\right) \,\mathbf{\hat{x}}+c z_{11} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | Al XI |
| $\mathbf{B_{12}}$ | = | $x_{12} \, \mathbf{a}_{1}+x_{12} \, \mathbf{a}_{2}+z_{12} \, \mathbf{a}_{3}$ | = | $\left(a x_{12} + c z_{12} \cos{\beta}\right) \,\mathbf{\hat{x}}+c z_{12} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | Al XII |
| $\mathbf{B_{13}}$ | = | $x_{13} \, \mathbf{a}_{1}+x_{13} \, \mathbf{a}_{2}+z_{13} \, \mathbf{a}_{3}$ | = | $\left(a x_{13} + c z_{13} \cos{\beta}\right) \,\mathbf{\hat{x}}+c z_{13} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | Al XIII |
| $\mathbf{B_{14}}$ | = | $x_{14} \, \mathbf{a}_{1}+x_{14} \, \mathbf{a}_{2}+z_{14} \, \mathbf{a}_{3}$ | = | $\left(a x_{14} + c z_{14} \cos{\beta}\right) \,\mathbf{\hat{x}}+c z_{14} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | Al XIV |
| $\mathbf{B_{15}}$ | = | $x_{15} \, \mathbf{a}_{1}+x_{15} \, \mathbf{a}_{2}+z_{15} \, \mathbf{a}_{3}$ | = | $\left(a x_{15} + c z_{15} \cos{\beta}\right) \,\mathbf{\hat{x}}+c z_{15} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | Al XV |
| $\mathbf{B_{16}}$ | = | $x_{16} \, \mathbf{a}_{1}+x_{16} \, \mathbf{a}_{2}+z_{16} \, \mathbf{a}_{3}$ | = | $\left(a x_{16} + c z_{16} \cos{\beta}\right) \,\mathbf{\hat{x}}+c z_{16} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | Al XVI |
| $\mathbf{B_{17}}$ | = | $x_{17} \, \mathbf{a}_{1}+x_{17} \, \mathbf{a}_{2}+z_{17} \, \mathbf{a}_{3}$ | = | $\left(a x_{17} + c z_{17} \cos{\beta}\right) \,\mathbf{\hat{x}}+c z_{17} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | Al XVII |
| $\mathbf{B_{18}}$ | = | $x_{18} \, \mathbf{a}_{1}+x_{18} \, \mathbf{a}_{2}+z_{18} \, \mathbf{a}_{3}$ | = | $\left(a x_{18} + c z_{18} \cos{\beta}\right) \,\mathbf{\hat{x}}+c z_{18} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | Co I |
| $\mathbf{B_{19}}$ | = | $x_{19} \, \mathbf{a}_{1}+x_{19} \, \mathbf{a}_{2}+z_{19} \, \mathbf{a}_{3}$ | = | $\left(a x_{19} + c z_{19} \cos{\beta}\right) \,\mathbf{\hat{x}}+c z_{19} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | Co II |
| $\mathbf{B_{20}}$ | = | $x_{20} \, \mathbf{a}_{1}+x_{20} \, \mathbf{a}_{2}+z_{20} \, \mathbf{a}_{3}$ | = | $\left(a x_{20} + c z_{20} \cos{\beta}\right) \,\mathbf{\hat{x}}+c z_{20} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | Co III |
| $\mathbf{B_{21}}$ | = | $x_{21} \, \mathbf{a}_{1}+x_{21} \, \mathbf{a}_{2}+z_{21} \, \mathbf{a}_{3}$ | = | $\left(a x_{21} + c z_{21} \cos{\beta}\right) \,\mathbf{\hat{x}}+c z_{21} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | Co IV |
| $\mathbf{B_{22}}$ | = | $x_{22} \, \mathbf{a}_{1}+x_{22} \, \mathbf{a}_{2}+z_{22} \, \mathbf{a}_{3}$ | = | $\left(a x_{22} + c z_{22} \cos{\beta}\right) \,\mathbf{\hat{x}}+c z_{22} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | Co V |
| $\mathbf{B_{23}}$ | = | $x_{23} \, \mathbf{a}_{1}+x_{23} \, \mathbf{a}_{2}+z_{23} \, \mathbf{a}_{3}$ | = | $\left(a x_{23} + c z_{23} \cos{\beta}\right) \,\mathbf{\hat{x}}+c z_{23} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | Co VI |
| $\mathbf{B_{24}}$ | = | $x_{24} \, \mathbf{a}_{1}+x_{24} \, \mathbf{a}_{2}+z_{24} \, \mathbf{a}_{3}$ | = | $\left(a x_{24} + c z_{24} \cos{\beta}\right) \,\mathbf{\hat{x}}+c z_{24} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | Co VII |
| $\mathbf{B_{25}}$ | = | $x_{25} \, \mathbf{a}_{1}+x_{25} \, \mathbf{a}_{2}+z_{25} \, \mathbf{a}_{3}$ | = | $\left(a x_{25} + c z_{25} \cos{\beta}\right) \,\mathbf{\hat{x}}+c z_{25} \sin{\beta} \,\mathbf{\hat{z}}$ | (2a) | Co VIII |
| $\mathbf{B_{26}}$ | = | $\left(x_{26} - y_{26}\right) \, \mathbf{a}_{1}+\left(x_{26} + y_{26}\right) \, \mathbf{a}_{2}+z_{26} \, \mathbf{a}_{3}$ | = | $\left(a x_{26} + c z_{26} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{26} \,\mathbf{\hat{y}}+c z_{26} \sin{\beta} \,\mathbf{\hat{z}}$ | (4b) | Al XVIII |
| $\mathbf{B_{27}}$ | = | $\left(x_{26} + y_{26}\right) \, \mathbf{a}_{1}+\left(x_{26} - y_{26}\right) \, \mathbf{a}_{2}+z_{26} \, \mathbf{a}_{3}$ | = | $\left(a x_{26} + c z_{26} \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{26} \,\mathbf{\hat{y}}+c z_{26} \sin{\beta} \,\mathbf{\hat{z}}$ | (4b) | Al XVIII |
| $\mathbf{B_{28}}$ | = | $\left(x_{27} - y_{27}\right) \, \mathbf{a}_{1}+\left(x_{27} + y_{27}\right) \, \mathbf{a}_{2}+z_{27} \, \mathbf{a}_{3}$ | = | $\left(a x_{27} + c z_{27} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{27} \,\mathbf{\hat{y}}+c z_{27} \sin{\beta} \,\mathbf{\hat{z}}$ | (4b) | Al XIX |
| $\mathbf{B_{29}}$ | = | $\left(x_{27} + y_{27}\right) \, \mathbf{a}_{1}+\left(x_{27} - y_{27}\right) \, \mathbf{a}_{2}+z_{27} \, \mathbf{a}_{3}$ | = | $\left(a x_{27} + c z_{27} \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{27} \,\mathbf{\hat{y}}+c z_{27} \sin{\beta} \,\mathbf{\hat{z}}$ | (4b) | Al XIX |
| $\mathbf{B_{30}}$ | = | $\left(x_{28} - y_{28}\right) \, \mathbf{a}_{1}+\left(x_{28} + y_{28}\right) \, \mathbf{a}_{2}+z_{28} \, \mathbf{a}_{3}$ | = | $\left(a x_{28} + c z_{28} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{28} \,\mathbf{\hat{y}}+c z_{28} \sin{\beta} \,\mathbf{\hat{z}}$ | (4b) | Al XX |
| $\mathbf{B_{31}}$ | = | $\left(x_{28} + y_{28}\right) \, \mathbf{a}_{1}+\left(x_{28} - y_{28}\right) \, \mathbf{a}_{2}+z_{28} \, \mathbf{a}_{3}$ | = | $\left(a x_{28} + c z_{28} \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{28} \,\mathbf{\hat{y}}+c z_{28} \sin{\beta} \,\mathbf{\hat{z}}$ | (4b) | Al XX |
| $\mathbf{B_{32}}$ | = | $\left(x_{29} - y_{29}\right) \, \mathbf{a}_{1}+\left(x_{29} + y_{29}\right) \, \mathbf{a}_{2}+z_{29} \, \mathbf{a}_{3}$ | = | $\left(a x_{29} + c z_{29} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{29} \,\mathbf{\hat{y}}+c z_{29} \sin{\beta} \,\mathbf{\hat{z}}$ | (4b) | Al XXI |
| $\mathbf{B_{33}}$ | = | $\left(x_{29} + y_{29}\right) \, \mathbf{a}_{1}+\left(x_{29} - y_{29}\right) \, \mathbf{a}_{2}+z_{29} \, \mathbf{a}_{3}$ | = | $\left(a x_{29} + c z_{29} \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{29} \,\mathbf{\hat{y}}+c z_{29} \sin{\beta} \,\mathbf{\hat{z}}$ | (4b) | Al XXI |
| $\mathbf{B_{34}}$ | = | $\left(x_{30} - y_{30}\right) \, \mathbf{a}_{1}+\left(x_{30} + y_{30}\right) \, \mathbf{a}_{2}+z_{30} \, \mathbf{a}_{3}$ | = | $\left(a x_{30} + c z_{30} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{30} \,\mathbf{\hat{y}}+c z_{30} \sin{\beta} \,\mathbf{\hat{z}}$ | (4b) | Al XXII |
| $\mathbf{B_{35}}$ | = | $\left(x_{30} + y_{30}\right) \, \mathbf{a}_{1}+\left(x_{30} - y_{30}\right) \, \mathbf{a}_{2}+z_{30} \, \mathbf{a}_{3}$ | = | $\left(a x_{30} + c z_{30} \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{30} \,\mathbf{\hat{y}}+c z_{30} \sin{\beta} \,\mathbf{\hat{z}}$ | (4b) | Al XXII |
| $\mathbf{B_{36}}$ | = | $\left(x_{31} - y_{31}\right) \, \mathbf{a}_{1}+\left(x_{31} + y_{31}\right) \, \mathbf{a}_{2}+z_{31} \, \mathbf{a}_{3}$ | = | $\left(a x_{31} + c z_{31} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{31} \,\mathbf{\hat{y}}+c z_{31} \sin{\beta} \,\mathbf{\hat{z}}$ | (4b) | Al XXIII |
| $\mathbf{B_{37}}$ | = | $\left(x_{31} + y_{31}\right) \, \mathbf{a}_{1}+\left(x_{31} - y_{31}\right) \, \mathbf{a}_{2}+z_{31} \, \mathbf{a}_{3}$ | = | $\left(a x_{31} + c z_{31} \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{31} \,\mathbf{\hat{y}}+c z_{31} \sin{\beta} \,\mathbf{\hat{z}}$ | (4b) | Al XXIII |
| $\mathbf{B_{38}}$ | = | $\left(x_{32} - y_{32}\right) \, \mathbf{a}_{1}+\left(x_{32} + y_{32}\right) \, \mathbf{a}_{2}+z_{32} \, \mathbf{a}_{3}$ | = | $\left(a x_{32} + c z_{32} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{32} \,\mathbf{\hat{y}}+c z_{32} \sin{\beta} \,\mathbf{\hat{z}}$ | (4b) | Al XXIV |
| $\mathbf{B_{39}}$ | = | $\left(x_{32} + y_{32}\right) \, \mathbf{a}_{1}+\left(x_{32} - y_{32}\right) \, \mathbf{a}_{2}+z_{32} \, \mathbf{a}_{3}$ | = | $\left(a x_{32} + c z_{32} \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{32} \,\mathbf{\hat{y}}+c z_{32} \sin{\beta} \,\mathbf{\hat{z}}$ | (4b) | Al XXIV |
| $\mathbf{B_{40}}$ | = | $\left(x_{33} - y_{33}\right) \, \mathbf{a}_{1}+\left(x_{33} + y_{33}\right) \, \mathbf{a}_{2}+z_{33} \, \mathbf{a}_{3}$ | = | $\left(a x_{33} + c z_{33} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{33} \,\mathbf{\hat{y}}+c z_{33} \sin{\beta} \,\mathbf{\hat{z}}$ | (4b) | Al XXV |
| $\mathbf{B_{41}}$ | = | $\left(x_{33} + y_{33}\right) \, \mathbf{a}_{1}+\left(x_{33} - y_{33}\right) \, \mathbf{a}_{2}+z_{33} \, \mathbf{a}_{3}$ | = | $\left(a x_{33} + c z_{33} \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{33} \,\mathbf{\hat{y}}+c z_{33} \sin{\beta} \,\mathbf{\hat{z}}$ | (4b) | Al XXV |
| $\mathbf{B_{42}}$ | = | $\left(x_{34} - y_{34}\right) \, \mathbf{a}_{1}+\left(x_{34} + y_{34}\right) \, \mathbf{a}_{2}+z_{34} \, \mathbf{a}_{3}$ | = | $\left(a x_{34} + c z_{34} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{34} \,\mathbf{\hat{y}}+c z_{34} \sin{\beta} \,\mathbf{\hat{z}}$ | (4b) | Al XXVI |
| $\mathbf{B_{43}}$ | = | $\left(x_{34} + y_{34}\right) \, \mathbf{a}_{1}+\left(x_{34} - y_{34}\right) \, \mathbf{a}_{2}+z_{34} \, \mathbf{a}_{3}$ | = | $\left(a x_{34} + c z_{34} \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{34} \,\mathbf{\hat{y}}+c z_{34} \sin{\beta} \,\mathbf{\hat{z}}$ | (4b) | Al XXVI |
| $\mathbf{B_{44}}$ | = | $\left(x_{35} - y_{35}\right) \, \mathbf{a}_{1}+\left(x_{35} + y_{35}\right) \, \mathbf{a}_{2}+z_{35} \, \mathbf{a}_{3}$ | = | $\left(a x_{35} + c z_{35} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{35} \,\mathbf{\hat{y}}+c z_{35} \sin{\beta} \,\mathbf{\hat{z}}$ | (4b) | Al XXVII |
| $\mathbf{B_{45}}$ | = | $\left(x_{35} + y_{35}\right) \, \mathbf{a}_{1}+\left(x_{35} - y_{35}\right) \, \mathbf{a}_{2}+z_{35} \, \mathbf{a}_{3}$ | = | $\left(a x_{35} + c z_{35} \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{35} \,\mathbf{\hat{y}}+c z_{35} \sin{\beta} \,\mathbf{\hat{z}}$ | (4b) | Al XXVII |
| $\mathbf{B_{46}}$ | = | $\left(x_{36} - y_{36}\right) \, \mathbf{a}_{1}+\left(x_{36} + y_{36}\right) \, \mathbf{a}_{2}+z_{36} \, \mathbf{a}_{3}$ | = | $\left(a x_{36} + c z_{36} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{36} \,\mathbf{\hat{y}}+c z_{36} \sin{\beta} \,\mathbf{\hat{z}}$ | (4b) | Al XXVIII |
| $\mathbf{B_{47}}$ | = | $\left(x_{36} + y_{36}\right) \, \mathbf{a}_{1}+\left(x_{36} - y_{36}\right) \, \mathbf{a}_{2}+z_{36} \, \mathbf{a}_{3}$ | = | $\left(a x_{36} + c z_{36} \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{36} \,\mathbf{\hat{y}}+c z_{36} \sin{\beta} \,\mathbf{\hat{z}}$ | (4b) | Al XXVIII |
| $\mathbf{B_{48}}$ | = | $\left(x_{37} - y_{37}\right) \, \mathbf{a}_{1}+\left(x_{37} + y_{37}\right) \, \mathbf{a}_{2}+z_{37} \, \mathbf{a}_{3}$ | = | $\left(a x_{37} + c z_{37} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{37} \,\mathbf{\hat{y}}+c z_{37} \sin{\beta} \,\mathbf{\hat{z}}$ | (4b) | Co IX |
| $\mathbf{B_{49}}$ | = | $\left(x_{37} + y_{37}\right) \, \mathbf{a}_{1}+\left(x_{37} - y_{37}\right) \, \mathbf{a}_{2}+z_{37} \, \mathbf{a}_{3}$ | = | $\left(a x_{37} + c z_{37} \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{37} \,\mathbf{\hat{y}}+c z_{37} \sin{\beta} \,\mathbf{\hat{z}}$ | (4b) | Co IX |
| $\mathbf{B_{50}}$ | = | $\left(x_{38} - y_{38}\right) \, \mathbf{a}_{1}+\left(x_{38} + y_{38}\right) \, \mathbf{a}_{2}+z_{38} \, \mathbf{a}_{3}$ | = | $\left(a x_{38} + c z_{38} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{38} \,\mathbf{\hat{y}}+c z_{38} \sin{\beta} \,\mathbf{\hat{z}}$ | (4b) | Co X |
| $\mathbf{B_{51}}$ | = | $\left(x_{38} + y_{38}\right) \, \mathbf{a}_{1}+\left(x_{38} - y_{38}\right) \, \mathbf{a}_{2}+z_{38} \, \mathbf{a}_{3}$ | = | $\left(a x_{38} + c z_{38} \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{38} \,\mathbf{\hat{y}}+c z_{38} \sin{\beta} \,\mathbf{\hat{z}}$ | (4b) | Co X |
References
- R. C. Hudd and W. H. Taylor, The Structure of Co$_{4}$Al$_{13}$, Acta Cryst. 15, 441–442 (1962), doi:10.1107/S0365110X62001103.
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.
- T. B. Massalski, H. Okamoto, P. R. Subramanian, and L. Kacprzak, eds., Binary Alloy Phase Diagrams}, vol. 1 (ASM International, Materials Park, Ohio, USA, 1990), 2$^{nd$ edn. Ac-Ag to Ca-Zn.
Prototype Generator
aflow --proto=A13B4_mC102_8_17a11b_8a2b --params=$a,b/a,c/a,\beta,x_{1},z_{1},x_{2},z_{2},x_{3},z_{3},x_{4},z_{4},x_{5},z_{5},x_{6},z_{6},x_{7},z_{7},x_{8},z_{8},x_{9},z_{9},x_{10},z_{10},x_{11},z_{11},x_{12},z_{12},x_{13},z_{13},x_{14},z_{14},x_{15},z_{15},x_{16},z_{16},x_{17},z_{17},x_{18},z_{18},x_{19},z_{19},x_{20},z_{20},x_{21},z_{21},x_{22},z_{22},x_{23},z_{23},x_{24},z_{24},x_{25},z_{25},x_{26},y_{26},z_{26},x_{27},y_{27},z_{27},x_{28},y_{28},z_{28},x_{29},y_{29},z_{29},x_{30},y_{30},z_{30},x_{31},y_{31},z_{31},x_{32},y_{32},z_{32},x_{33},y_{33},z_{33},x_{34},y_{34},z_{34},x_{35},y_{35},z_{35},x_{36},y_{36},z_{36},x_{37},y_{37},z_{37},x_{38},y_{38},z_{38}$