Trigonal (h') Al$_{5}$Mo Structure: A5B_hP60_143_7a7b6c10d_3a3b4c-001
| Prototype | Al$_{5}$Mo |
| AFLOW prototype label | A5B_hP60_143_7a7b6c10d_3a3b4c-001 |
| ICSD | 105519 |
| Pearson symbol | hP60 |
| Space group number | 143 |
| Space group symbol | $P3$ |
| AFLOW prototype command |
aflow --proto=A5B_hP60_143_7a7b6c10d_3a3b4c-001
--params=$a, \allowbreak c/a, \allowbreak z_{1}, \allowbreak z_{2}, \allowbreak z_{3}, \allowbreak z_{4}, \allowbreak z_{5}, \allowbreak z_{6}, \allowbreak z_{7}, \allowbreak z_{8}, \allowbreak z_{9}, \allowbreak z_{10}, \allowbreak z_{11}, \allowbreak z_{12}, \allowbreak z_{13}, \allowbreak z_{14}, \allowbreak z_{15}, \allowbreak z_{16}, \allowbreak z_{17}, \allowbreak z_{18}, \allowbreak z_{19}, \allowbreak z_{20}, \allowbreak z_{21}, \allowbreak z_{22}, \allowbreak z_{23}, \allowbreak z_{24}, \allowbreak z_{25}, \allowbreak z_{26}, \allowbreak z_{27}, \allowbreak z_{28}, \allowbreak z_{29}, \allowbreak z_{30}, \allowbreak x_{31}, \allowbreak y_{31}, \allowbreak z_{31}, \allowbreak x_{32}, \allowbreak y_{32}, \allowbreak z_{32}, \allowbreak x_{33}, \allowbreak y_{33}, \allowbreak z_{33}, \allowbreak x_{34}, \allowbreak y_{34}, \allowbreak z_{34}, \allowbreak x_{35}, \allowbreak y_{35}, \allowbreak z_{35}, \allowbreak x_{36}, \allowbreak y_{36}, \allowbreak z_{36}, \allowbreak x_{37}, \allowbreak y_{37}, \allowbreak z_{37}, \allowbreak x_{38}, \allowbreak y_{38}, \allowbreak z_{38}, \allowbreak x_{39}, \allowbreak y_{39}, \allowbreak z_{39}, \allowbreak x_{40}, \allowbreak y_{40}, \allowbreak z_{40}$ |
- Al$_{5}$Mo is known to have three phases (Schuster, 1991):
- Below 650K it is in a rhombohedral structure, Al$_{5}$Mo (r).
- Between 650K and 750-800K it is in a trigonal structure, Al$_{5}$Mo(h') (this structure).
- Above 750-800K up to 846K it is in the Al$_{5}$W structure.
- The Al$_{5}$Mo(h') atomic positions in (Schuster, 1991) are highly symmetric and approximate, and put the system in space group $P321$ #150. To show the correct $P3$ space group we slightly shifted the Al-I atom's $z$-coordinate. Presumably further refinement of the coordinates would let us determine the correct space group.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \,\mathbf{\hat{y}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $z_{1} \, \mathbf{a}_{3}$ | = | $c z_{1} \,\mathbf{\hat{z}}$ | (1a) | Al I |
| $\mathbf{B_{2}}$ | = | $z_{2} \, \mathbf{a}_{3}$ | = | $c z_{2} \,\mathbf{\hat{z}}$ | (1a) | Al II |
| $\mathbf{B_{3}}$ | = | $z_{3} \, \mathbf{a}_{3}$ | = | $c z_{3} \,\mathbf{\hat{z}}$ | (1a) | Al III |
| $\mathbf{B_{4}}$ | = | $z_{4} \, \mathbf{a}_{3}$ | = | $c z_{4} \,\mathbf{\hat{z}}$ | (1a) | Al IV |
| $\mathbf{B_{5}}$ | = | $z_{5} \, \mathbf{a}_{3}$ | = | $c z_{5} \,\mathbf{\hat{z}}$ | (1a) | Al V |
| $\mathbf{B_{6}}$ | = | $z_{6} \, \mathbf{a}_{3}$ | = | $c z_{6} \,\mathbf{\hat{z}}$ | (1a) | Al VI |
| $\mathbf{B_{7}}$ | = | $z_{7} \, \mathbf{a}_{3}$ | = | $c z_{7} \,\mathbf{\hat{z}}$ | (1a) | Al VII |
| $\mathbf{B_{8}}$ | = | $z_{8} \, \mathbf{a}_{3}$ | = | $c z_{8} \,\mathbf{\hat{z}}$ | (1a) | Mo I |
| $\mathbf{B_{9}}$ | = | $z_{9} \, \mathbf{a}_{3}$ | = | $c z_{9} \,\mathbf{\hat{z}}$ | (1a) | Mo II |
| $\mathbf{B_{10}}$ | = | $z_{10} \, \mathbf{a}_{3}$ | = | $c z_{10} \,\mathbf{\hat{z}}$ | (1a) | Mo III |
| $\mathbf{B_{11}}$ | = | $\frac{1}{3} \, \mathbf{a}_{1}+\frac{2}{3} \, \mathbf{a}_{2}+z_{11} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+c z_{11} \,\mathbf{\hat{z}}$ | (1b) | Al VIII |
| $\mathbf{B_{12}}$ | = | $\frac{1}{3} \, \mathbf{a}_{1}+\frac{2}{3} \, \mathbf{a}_{2}+z_{12} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+c z_{12} \,\mathbf{\hat{z}}$ | (1b) | Al IX |
| $\mathbf{B_{13}}$ | = | $\frac{1}{3} \, \mathbf{a}_{1}+\frac{2}{3} \, \mathbf{a}_{2}+z_{13} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+c z_{13} \,\mathbf{\hat{z}}$ | (1b) | Al X |
| $\mathbf{B_{14}}$ | = | $\frac{1}{3} \, \mathbf{a}_{1}+\frac{2}{3} \, \mathbf{a}_{2}+z_{14} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+c z_{14} \,\mathbf{\hat{z}}$ | (1b) | Al XI |
| $\mathbf{B_{15}}$ | = | $\frac{1}{3} \, \mathbf{a}_{1}+\frac{2}{3} \, \mathbf{a}_{2}+z_{15} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+c z_{15} \,\mathbf{\hat{z}}$ | (1b) | Al XII |
| $\mathbf{B_{16}}$ | = | $\frac{1}{3} \, \mathbf{a}_{1}+\frac{2}{3} \, \mathbf{a}_{2}+z_{16} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+c z_{16} \,\mathbf{\hat{z}}$ | (1b) | Al XIII |
| $\mathbf{B_{17}}$ | = | $\frac{1}{3} \, \mathbf{a}_{1}+\frac{2}{3} \, \mathbf{a}_{2}+z_{17} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+c z_{17} \,\mathbf{\hat{z}}$ | (1b) | Al XIV |
| $\mathbf{B_{18}}$ | = | $\frac{1}{3} \, \mathbf{a}_{1}+\frac{2}{3} \, \mathbf{a}_{2}+z_{18} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+c z_{18} \,\mathbf{\hat{z}}$ | (1b) | Mo IV |
| $\mathbf{B_{19}}$ | = | $\frac{1}{3} \, \mathbf{a}_{1}+\frac{2}{3} \, \mathbf{a}_{2}+z_{19} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+c z_{19} \,\mathbf{\hat{z}}$ | (1b) | Mo V |
| $\mathbf{B_{20}}$ | = | $\frac{1}{3} \, \mathbf{a}_{1}+\frac{2}{3} \, \mathbf{a}_{2}+z_{20} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+c z_{20} \,\mathbf{\hat{z}}$ | (1b) | Mo VI |
| $\mathbf{B_{21}}$ | = | $\frac{2}{3} \, \mathbf{a}_{1}+\frac{1}{3} \, \mathbf{a}_{2}+z_{21} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+c z_{21} \,\mathbf{\hat{z}}$ | (1c) | Al XV |
| $\mathbf{B_{22}}$ | = | $\frac{2}{3} \, \mathbf{a}_{1}+\frac{1}{3} \, \mathbf{a}_{2}+z_{22} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+c z_{22} \,\mathbf{\hat{z}}$ | (1c) | Al XVI |
| $\mathbf{B_{23}}$ | = | $\frac{2}{3} \, \mathbf{a}_{1}+\frac{1}{3} \, \mathbf{a}_{2}+z_{23} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+c z_{23} \,\mathbf{\hat{z}}$ | (1c) | Al XVII |
| $\mathbf{B_{24}}$ | = | $\frac{2}{3} \, \mathbf{a}_{1}+\frac{1}{3} \, \mathbf{a}_{2}+z_{24} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+c z_{24} \,\mathbf{\hat{z}}$ | (1c) | Al XVIII |
| $\mathbf{B_{25}}$ | = | $\frac{2}{3} \, \mathbf{a}_{1}+\frac{1}{3} \, \mathbf{a}_{2}+z_{25} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+c z_{25} \,\mathbf{\hat{z}}$ | (1c) | Al XIX |
| $\mathbf{B_{26}}$ | = | $\frac{2}{3} \, \mathbf{a}_{1}+\frac{1}{3} \, \mathbf{a}_{2}+z_{26} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+c z_{26} \,\mathbf{\hat{z}}$ | (1c) | Al XX |
| $\mathbf{B_{27}}$ | = | $\frac{2}{3} \, \mathbf{a}_{1}+\frac{1}{3} \, \mathbf{a}_{2}+z_{27} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+c z_{27} \,\mathbf{\hat{z}}$ | (1c) | Mo VII |
| $\mathbf{B_{28}}$ | = | $\frac{2}{3} \, \mathbf{a}_{1}+\frac{1}{3} \, \mathbf{a}_{2}+z_{28} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+c z_{28} \,\mathbf{\hat{z}}$ | (1c) | Mo VIII |
| $\mathbf{B_{29}}$ | = | $\frac{2}{3} \, \mathbf{a}_{1}+\frac{1}{3} \, \mathbf{a}_{2}+z_{29} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+c z_{29} \,\mathbf{\hat{z}}$ | (1c) | Mo IX |
| $\mathbf{B_{30}}$ | = | $\frac{2}{3} \, \mathbf{a}_{1}+\frac{1}{3} \, \mathbf{a}_{2}+z_{30} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+c z_{30} \,\mathbf{\hat{z}}$ | (1c) | Mo X |
| $\mathbf{B_{31}}$ | = | $x_{31} \, \mathbf{a}_{1}+y_{31} \, \mathbf{a}_{2}+z_{31} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{31} + y_{31}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \left(x_{31} - y_{31}\right) \,\mathbf{\hat{y}}+c z_{31} \,\mathbf{\hat{z}}$ | (3d) | Al XXI |
| $\mathbf{B_{32}}$ | = | $- y_{31} \, \mathbf{a}_{1}+\left(x_{31} - y_{31}\right) \, \mathbf{a}_{2}+z_{31} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{31} - 2 y_{31}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{31} \,\mathbf{\hat{y}}+c z_{31} \,\mathbf{\hat{z}}$ | (3d) | Al XXI |
| $\mathbf{B_{33}}$ | = | $- \left(x_{31} - y_{31}\right) \, \mathbf{a}_{1}- x_{31} \, \mathbf{a}_{2}+z_{31} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(2 x_{31} - y_{31}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a y_{31} \,\mathbf{\hat{y}}+c z_{31} \,\mathbf{\hat{z}}$ | (3d) | Al XXI |
| $\mathbf{B_{34}}$ | = | $x_{32} \, \mathbf{a}_{1}+y_{32} \, \mathbf{a}_{2}+z_{32} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{32} + y_{32}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \left(x_{32} - y_{32}\right) \,\mathbf{\hat{y}}+c z_{32} \,\mathbf{\hat{z}}$ | (3d) | Al XXII |
| $\mathbf{B_{35}}$ | = | $- y_{32} \, \mathbf{a}_{1}+\left(x_{32} - y_{32}\right) \, \mathbf{a}_{2}+z_{32} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{32} - 2 y_{32}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{32} \,\mathbf{\hat{y}}+c z_{32} \,\mathbf{\hat{z}}$ | (3d) | Al XXII |
| $\mathbf{B_{36}}$ | = | $- \left(x_{32} - y_{32}\right) \, \mathbf{a}_{1}- x_{32} \, \mathbf{a}_{2}+z_{32} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(2 x_{32} - y_{32}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a y_{32} \,\mathbf{\hat{y}}+c z_{32} \,\mathbf{\hat{z}}$ | (3d) | Al XXII |
| $\mathbf{B_{37}}$ | = | $x_{33} \, \mathbf{a}_{1}+y_{33} \, \mathbf{a}_{2}+z_{33} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{33} + y_{33}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \left(x_{33} - y_{33}\right) \,\mathbf{\hat{y}}+c z_{33} \,\mathbf{\hat{z}}$ | (3d) | Al XXIII |
| $\mathbf{B_{38}}$ | = | $- y_{33} \, \mathbf{a}_{1}+\left(x_{33} - y_{33}\right) \, \mathbf{a}_{2}+z_{33} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{33} - 2 y_{33}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{33} \,\mathbf{\hat{y}}+c z_{33} \,\mathbf{\hat{z}}$ | (3d) | Al XXIII |
| $\mathbf{B_{39}}$ | = | $- \left(x_{33} - y_{33}\right) \, \mathbf{a}_{1}- x_{33} \, \mathbf{a}_{2}+z_{33} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(2 x_{33} - y_{33}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a y_{33} \,\mathbf{\hat{y}}+c z_{33} \,\mathbf{\hat{z}}$ | (3d) | Al XXIII |
| $\mathbf{B_{40}}$ | = | $x_{34} \, \mathbf{a}_{1}+y_{34} \, \mathbf{a}_{2}+z_{34} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{34} + y_{34}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \left(x_{34} - y_{34}\right) \,\mathbf{\hat{y}}+c z_{34} \,\mathbf{\hat{z}}$ | (3d) | Al XXIV |
| $\mathbf{B_{41}}$ | = | $- y_{34} \, \mathbf{a}_{1}+\left(x_{34} - y_{34}\right) \, \mathbf{a}_{2}+z_{34} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{34} - 2 y_{34}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{34} \,\mathbf{\hat{y}}+c z_{34} \,\mathbf{\hat{z}}$ | (3d) | Al XXIV |
| $\mathbf{B_{42}}$ | = | $- \left(x_{34} - y_{34}\right) \, \mathbf{a}_{1}- x_{34} \, \mathbf{a}_{2}+z_{34} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(2 x_{34} - y_{34}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a y_{34} \,\mathbf{\hat{y}}+c z_{34} \,\mathbf{\hat{z}}$ | (3d) | Al XXIV |
| $\mathbf{B_{43}}$ | = | $x_{35} \, \mathbf{a}_{1}+y_{35} \, \mathbf{a}_{2}+z_{35} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{35} + y_{35}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \left(x_{35} - y_{35}\right) \,\mathbf{\hat{y}}+c z_{35} \,\mathbf{\hat{z}}$ | (3d) | Al XXV |
| $\mathbf{B_{44}}$ | = | $- y_{35} \, \mathbf{a}_{1}+\left(x_{35} - y_{35}\right) \, \mathbf{a}_{2}+z_{35} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{35} - 2 y_{35}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{35} \,\mathbf{\hat{y}}+c z_{35} \,\mathbf{\hat{z}}$ | (3d) | Al XXV |
| $\mathbf{B_{45}}$ | = | $- \left(x_{35} - y_{35}\right) \, \mathbf{a}_{1}- x_{35} \, \mathbf{a}_{2}+z_{35} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(2 x_{35} - y_{35}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a y_{35} \,\mathbf{\hat{y}}+c z_{35} \,\mathbf{\hat{z}}$ | (3d) | Al XXV |
| $\mathbf{B_{46}}$ | = | $x_{36} \, \mathbf{a}_{1}+y_{36} \, \mathbf{a}_{2}+z_{36} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{36} + y_{36}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \left(x_{36} - y_{36}\right) \,\mathbf{\hat{y}}+c z_{36} \,\mathbf{\hat{z}}$ | (3d) | Al XXVI |
| $\mathbf{B_{47}}$ | = | $- y_{36} \, \mathbf{a}_{1}+\left(x_{36} - y_{36}\right) \, \mathbf{a}_{2}+z_{36} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{36} - 2 y_{36}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{36} \,\mathbf{\hat{y}}+c z_{36} \,\mathbf{\hat{z}}$ | (3d) | Al XXVI |
| $\mathbf{B_{48}}$ | = | $- \left(x_{36} - y_{36}\right) \, \mathbf{a}_{1}- x_{36} \, \mathbf{a}_{2}+z_{36} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(2 x_{36} - y_{36}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a y_{36} \,\mathbf{\hat{y}}+c z_{36} \,\mathbf{\hat{z}}$ | (3d) | Al XXVI |
| $\mathbf{B_{49}}$ | = | $x_{37} \, \mathbf{a}_{1}+y_{37} \, \mathbf{a}_{2}+z_{37} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{37} + y_{37}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \left(x_{37} - y_{37}\right) \,\mathbf{\hat{y}}+c z_{37} \,\mathbf{\hat{z}}$ | (3d) | Al XXVII |
| $\mathbf{B_{50}}$ | = | $- y_{37} \, \mathbf{a}_{1}+\left(x_{37} - y_{37}\right) \, \mathbf{a}_{2}+z_{37} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{37} - 2 y_{37}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{37} \,\mathbf{\hat{y}}+c z_{37} \,\mathbf{\hat{z}}$ | (3d) | Al XXVII |
| $\mathbf{B_{51}}$ | = | $- \left(x_{37} - y_{37}\right) \, \mathbf{a}_{1}- x_{37} \, \mathbf{a}_{2}+z_{37} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(2 x_{37} - y_{37}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a y_{37} \,\mathbf{\hat{y}}+c z_{37} \,\mathbf{\hat{z}}$ | (3d) | Al XXVII |
| $\mathbf{B_{52}}$ | = | $x_{38} \, \mathbf{a}_{1}+y_{38} \, \mathbf{a}_{2}+z_{38} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{38} + y_{38}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \left(x_{38} - y_{38}\right) \,\mathbf{\hat{y}}+c z_{38} \,\mathbf{\hat{z}}$ | (3d) | Al XXVIII |
| $\mathbf{B_{53}}$ | = | $- y_{38} \, \mathbf{a}_{1}+\left(x_{38} - y_{38}\right) \, \mathbf{a}_{2}+z_{38} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{38} - 2 y_{38}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{38} \,\mathbf{\hat{y}}+c z_{38} \,\mathbf{\hat{z}}$ | (3d) | Al XXVIII |
| $\mathbf{B_{54}}$ | = | $- \left(x_{38} - y_{38}\right) \, \mathbf{a}_{1}- x_{38} \, \mathbf{a}_{2}+z_{38} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(2 x_{38} - y_{38}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a y_{38} \,\mathbf{\hat{y}}+c z_{38} \,\mathbf{\hat{z}}$ | (3d) | Al XXVIII |
| $\mathbf{B_{55}}$ | = | $x_{39} \, \mathbf{a}_{1}+y_{39} \, \mathbf{a}_{2}+z_{39} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{39} + y_{39}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \left(x_{39} - y_{39}\right) \,\mathbf{\hat{y}}+c z_{39} \,\mathbf{\hat{z}}$ | (3d) | Al XXIX |
| $\mathbf{B_{56}}$ | = | $- y_{39} \, \mathbf{a}_{1}+\left(x_{39} - y_{39}\right) \, \mathbf{a}_{2}+z_{39} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{39} - 2 y_{39}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{39} \,\mathbf{\hat{y}}+c z_{39} \,\mathbf{\hat{z}}$ | (3d) | Al XXIX |
| $\mathbf{B_{57}}$ | = | $- \left(x_{39} - y_{39}\right) \, \mathbf{a}_{1}- x_{39} \, \mathbf{a}_{2}+z_{39} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(2 x_{39} - y_{39}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a y_{39} \,\mathbf{\hat{y}}+c z_{39} \,\mathbf{\hat{z}}$ | (3d) | Al XXIX |
| $\mathbf{B_{58}}$ | = | $x_{40} \, \mathbf{a}_{1}+y_{40} \, \mathbf{a}_{2}+z_{40} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{40} + y_{40}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \left(x_{40} - y_{40}\right) \,\mathbf{\hat{y}}+c z_{40} \,\mathbf{\hat{z}}$ | (3d) | Al XXX |
| $\mathbf{B_{59}}$ | = | $- y_{40} \, \mathbf{a}_{1}+\left(x_{40} - y_{40}\right) \, \mathbf{a}_{2}+z_{40} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{40} - 2 y_{40}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{40} \,\mathbf{\hat{y}}+c z_{40} \,\mathbf{\hat{z}}$ | (3d) | Al XXX |
| $\mathbf{B_{60}}$ | = | $- \left(x_{40} - y_{40}\right) \, \mathbf{a}_{1}- x_{40} \, \mathbf{a}_{2}+z_{40} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(2 x_{40} - y_{40}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a y_{40} \,\mathbf{\hat{y}}+c z_{40} \,\mathbf{\hat{z}}$ | (3d) | Al XXX |
References
- J. C. Schuster and H. Ipser, The Al-Al$_{8}$Mo$_{3}$ section of the binary system aluminum-molybdenum, Metall. Trans. A 22, 1729–1736 (1991), doi:10.1007/BF02646496.
Prototype Generator
aflow --proto=A5B_hP60_143_7a7b6c10d_3a3b4c --params=$a,c/a,z_{1},z_{2},z_{3},z_{4},z_{5},z_{6},z_{7},z_{8},z_{9},z_{10},z_{11},z_{12},z_{13},z_{14},z_{15},z_{16},z_{17},z_{18},z_{19},z_{20},z_{21},z_{22},z_{23},z_{24},z_{25},z_{26},z_{27},z_{28},z_{29},z_{30},x_{31},y_{31},z_{31},x_{32},y_{32},z_{32},x_{33},y_{33},z_{33},x_{34},y_{34},z_{34},x_{35},y_{35},z_{35},x_{36},y_{36},z_{36},x_{37},y_{37},z_{37},x_{38},y_{38},z_{38},x_{39},y_{39},z_{39},x_{40},y_{40},z_{40}$