Ni$_{13}$Ga$_{3}$Ge$_{6}$ Structure: A3B6C13_hP66_152_ac_3c_a2b5c-001
| Prototype | Ga$_{3}$Ge$_{6}$Ni$_{13}$ |
| AFLOW prototype label | A3B6C13_hP66_152_ac_3c_a2b5c-001 |
| ICSD | 52177 |
| Pearson symbol | hP66 |
| Space group number | 152 |
| Space group symbol | $P3_121$ |
| AFLOW prototype command |
aflow --proto=A3B6C13_hP66_152_ac_3c_a2b5c-001
--params=$a, \allowbreak c/a, \allowbreak x_{1}, \allowbreak x_{2}, \allowbreak x_{3}, \allowbreak x_{4}, \allowbreak x_{5}, \allowbreak y_{5}, \allowbreak z_{5}, \allowbreak x_{6}, \allowbreak y_{6}, \allowbreak z_{6}, \allowbreak x_{7}, \allowbreak y_{7}, \allowbreak z_{7}, \allowbreak x_{8}, \allowbreak y_{8}, \allowbreak z_{8}, \allowbreak x_{9}, \allowbreak y_{9}, \allowbreak z_{9}, \allowbreak x_{10}, \allowbreak y_{10}, \allowbreak z_{10}, \allowbreak x_{11}, \allowbreak y_{11}, \allowbreak z_{11}, \allowbreak x_{12}, \allowbreak y_{12}, \allowbreak z_{12}, \allowbreak x_{13}, \allowbreak y_{13}, \allowbreak z_{13}$ |
- This structure can also exist in the enantiomorphic space group $P3_{2}21$ #154.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \,\mathbf{\hat{y}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $x_{1} \, \mathbf{a}_{1}+\frac{1}{3} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a x_{1} \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{1} \,\mathbf{\hat{y}}+\frac{1}{3}c \,\mathbf{\hat{z}}$ | (3a) | Ga I |
| $\mathbf{B_{2}}$ | = | $x_{1} \, \mathbf{a}_{2}+\frac{2}{3} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a x_{1} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{1} \,\mathbf{\hat{y}}+\frac{2}{3}c \,\mathbf{\hat{z}}$ | (3a) | Ga I |
| $\mathbf{B_{3}}$ | = | $- x_{1} \, \mathbf{a}_{1}- x_{1} \, \mathbf{a}_{2}$ | = | $- a x_{1} \,\mathbf{\hat{x}}$ | (3a) | Ga I |
| $\mathbf{B_{4}}$ | = | $x_{2} \, \mathbf{a}_{1}+\frac{1}{3} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a x_{2} \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{2} \,\mathbf{\hat{y}}+\frac{1}{3}c \,\mathbf{\hat{z}}$ | (3a) | Ni I |
| $\mathbf{B_{5}}$ | = | $x_{2} \, \mathbf{a}_{2}+\frac{2}{3} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a x_{2} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{2} \,\mathbf{\hat{y}}+\frac{2}{3}c \,\mathbf{\hat{z}}$ | (3a) | Ni I |
| $\mathbf{B_{6}}$ | = | $- x_{2} \, \mathbf{a}_{1}- x_{2} \, \mathbf{a}_{2}$ | = | $- a x_{2} \,\mathbf{\hat{x}}$ | (3a) | Ni I |
| $\mathbf{B_{7}}$ | = | $x_{3} \, \mathbf{a}_{1}+\frac{5}{6} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a x_{3} \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{3} \,\mathbf{\hat{y}}+\frac{5}{6}c \,\mathbf{\hat{z}}$ | (3b) | Ni II |
| $\mathbf{B_{8}}$ | = | $x_{3} \, \mathbf{a}_{2}+\frac{1}{6} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a x_{3} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{3} \,\mathbf{\hat{y}}+\frac{1}{6}c \,\mathbf{\hat{z}}$ | (3b) | Ni II |
| $\mathbf{B_{9}}$ | = | $- x_{3} \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (3b) | Ni II |
| $\mathbf{B_{10}}$ | = | $x_{4} \, \mathbf{a}_{1}+\frac{5}{6} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a x_{4} \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{4} \,\mathbf{\hat{y}}+\frac{5}{6}c \,\mathbf{\hat{z}}$ | (3b) | Ni III |
| $\mathbf{B_{11}}$ | = | $x_{4} \, \mathbf{a}_{2}+\frac{1}{6} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a x_{4} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{4} \,\mathbf{\hat{y}}+\frac{1}{6}c \,\mathbf{\hat{z}}$ | (3b) | Ni III |
| $\mathbf{B_{12}}$ | = | $- x_{4} \, \mathbf{a}_{1}- x_{4} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- a x_{4} \,\mathbf{\hat{x}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (3b) | Ni III |
| $\mathbf{B_{13}}$ | = | $x_{5} \, \mathbf{a}_{1}+y_{5} \, \mathbf{a}_{2}+z_{5} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{5} + y_{5}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \left(x_{5} - y_{5}\right) \,\mathbf{\hat{y}}+c z_{5} \,\mathbf{\hat{z}}$ | (6c) | Ga II |
| $\mathbf{B_{14}}$ | = | $- y_{5} \, \mathbf{a}_{1}+\left(x_{5} - y_{5}\right) \, \mathbf{a}_{2}+\left(z_{5} + \frac{1}{3}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{5} - 2 y_{5}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{5} \,\mathbf{\hat{y}}+c \left(z_{5} + \frac{1}{3}\right) \,\mathbf{\hat{z}}$ | (6c) | Ga II |
| $\mathbf{B_{15}}$ | = | $- \left(x_{5} - y_{5}\right) \, \mathbf{a}_{1}- x_{5} \, \mathbf{a}_{2}+\left(z_{5} + \frac{2}{3}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(2 x_{5} - y_{5}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a y_{5} \,\mathbf{\hat{y}}+\frac{1}{3}c \left(3 z_{5} + 2\right) \,\mathbf{\hat{z}}$ | (6c) | Ga II |
| $\mathbf{B_{16}}$ | = | $y_{5} \, \mathbf{a}_{1}+x_{5} \, \mathbf{a}_{2}- z_{5} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{5} + y_{5}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \left(x_{5} - y_{5}\right) \,\mathbf{\hat{y}}- c z_{5} \,\mathbf{\hat{z}}$ | (6c) | Ga II |
| $\mathbf{B_{17}}$ | = | $\left(x_{5} - y_{5}\right) \, \mathbf{a}_{1}- y_{5} \, \mathbf{a}_{2}- \left(z_{5} - \frac{2}{3}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{5} - 2 y_{5}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{5} \,\mathbf{\hat{y}}- \frac{1}{3}c \left(3 z_{5} - 2\right) \,\mathbf{\hat{z}}$ | (6c) | Ga II |
| $\mathbf{B_{18}}$ | = | $- x_{5} \, \mathbf{a}_{1}- \left(x_{5} - y_{5}\right) \, \mathbf{a}_{2}- \left(z_{5} - \frac{1}{3}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(2 x_{5} - y_{5}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a y_{5} \,\mathbf{\hat{y}}- c \left(z_{5} - \frac{1}{3}\right) \,\mathbf{\hat{z}}$ | (6c) | Ga II |
| $\mathbf{B_{19}}$ | = | $x_{6} \, \mathbf{a}_{1}+y_{6} \, \mathbf{a}_{2}+z_{6} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{6} + y_{6}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \left(x_{6} - y_{6}\right) \,\mathbf{\hat{y}}+c z_{6} \,\mathbf{\hat{z}}$ | (6c) | Ge I |
| $\mathbf{B_{20}}$ | = | $- y_{6} \, \mathbf{a}_{1}+\left(x_{6} - y_{6}\right) \, \mathbf{a}_{2}+\left(z_{6} + \frac{1}{3}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{6} - 2 y_{6}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{6} \,\mathbf{\hat{y}}+c \left(z_{6} + \frac{1}{3}\right) \,\mathbf{\hat{z}}$ | (6c) | Ge I |
| $\mathbf{B_{21}}$ | = | $- \left(x_{6} - y_{6}\right) \, \mathbf{a}_{1}- x_{6} \, \mathbf{a}_{2}+\left(z_{6} + \frac{2}{3}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(2 x_{6} - y_{6}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a y_{6} \,\mathbf{\hat{y}}+\frac{1}{3}c \left(3 z_{6} + 2\right) \,\mathbf{\hat{z}}$ | (6c) | Ge I |
| $\mathbf{B_{22}}$ | = | $y_{6} \, \mathbf{a}_{1}+x_{6} \, \mathbf{a}_{2}- z_{6} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{6} + y_{6}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \left(x_{6} - y_{6}\right) \,\mathbf{\hat{y}}- c z_{6} \,\mathbf{\hat{z}}$ | (6c) | Ge I |
| $\mathbf{B_{23}}$ | = | $\left(x_{6} - y_{6}\right) \, \mathbf{a}_{1}- y_{6} \, \mathbf{a}_{2}- \left(z_{6} - \frac{2}{3}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{6} - 2 y_{6}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{6} \,\mathbf{\hat{y}}- \frac{1}{3}c \left(3 z_{6} - 2\right) \,\mathbf{\hat{z}}$ | (6c) | Ge I |
| $\mathbf{B_{24}}$ | = | $- x_{6} \, \mathbf{a}_{1}- \left(x_{6} - y_{6}\right) \, \mathbf{a}_{2}- \left(z_{6} - \frac{1}{3}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(2 x_{6} - y_{6}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a y_{6} \,\mathbf{\hat{y}}- c \left(z_{6} - \frac{1}{3}\right) \,\mathbf{\hat{z}}$ | (6c) | Ge I |
| $\mathbf{B_{25}}$ | = | $x_{7} \, \mathbf{a}_{1}+y_{7} \, \mathbf{a}_{2}+z_{7} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{7} + y_{7}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \left(x_{7} - y_{7}\right) \,\mathbf{\hat{y}}+c z_{7} \,\mathbf{\hat{z}}$ | (6c) | Ge II |
| $\mathbf{B_{26}}$ | = | $- y_{7} \, \mathbf{a}_{1}+\left(x_{7} - y_{7}\right) \, \mathbf{a}_{2}+\left(z_{7} + \frac{1}{3}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{7} - 2 y_{7}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{7} \,\mathbf{\hat{y}}+c \left(z_{7} + \frac{1}{3}\right) \,\mathbf{\hat{z}}$ | (6c) | Ge II |
| $\mathbf{B_{27}}$ | = | $- \left(x_{7} - y_{7}\right) \, \mathbf{a}_{1}- x_{7} \, \mathbf{a}_{2}+\left(z_{7} + \frac{2}{3}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(2 x_{7} - y_{7}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a y_{7} \,\mathbf{\hat{y}}+\frac{1}{3}c \left(3 z_{7} + 2\right) \,\mathbf{\hat{z}}$ | (6c) | Ge II |
| $\mathbf{B_{28}}$ | = | $y_{7} \, \mathbf{a}_{1}+x_{7} \, \mathbf{a}_{2}- z_{7} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{7} + y_{7}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \left(x_{7} - y_{7}\right) \,\mathbf{\hat{y}}- c z_{7} \,\mathbf{\hat{z}}$ | (6c) | Ge II |
| $\mathbf{B_{29}}$ | = | $\left(x_{7} - y_{7}\right) \, \mathbf{a}_{1}- y_{7} \, \mathbf{a}_{2}- \left(z_{7} - \frac{2}{3}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{7} - 2 y_{7}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{7} \,\mathbf{\hat{y}}- \frac{1}{3}c \left(3 z_{7} - 2\right) \,\mathbf{\hat{z}}$ | (6c) | Ge II |
| $\mathbf{B_{30}}$ | = | $- x_{7} \, \mathbf{a}_{1}- \left(x_{7} - y_{7}\right) \, \mathbf{a}_{2}- \left(z_{7} - \frac{1}{3}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(2 x_{7} - y_{7}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a y_{7} \,\mathbf{\hat{y}}- c \left(z_{7} - \frac{1}{3}\right) \,\mathbf{\hat{z}}$ | (6c) | Ge II |
| $\mathbf{B_{31}}$ | = | $x_{8} \, \mathbf{a}_{1}+y_{8} \, \mathbf{a}_{2}+z_{8} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{8} + y_{8}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \left(x_{8} - y_{8}\right) \,\mathbf{\hat{y}}+c z_{8} \,\mathbf{\hat{z}}$ | (6c) | Ge III |
| $\mathbf{B_{32}}$ | = | $- y_{8} \, \mathbf{a}_{1}+\left(x_{8} - y_{8}\right) \, \mathbf{a}_{2}+\left(z_{8} + \frac{1}{3}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{8} - 2 y_{8}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{8} \,\mathbf{\hat{y}}+c \left(z_{8} + \frac{1}{3}\right) \,\mathbf{\hat{z}}$ | (6c) | Ge III |
| $\mathbf{B_{33}}$ | = | $- \left(x_{8} - y_{8}\right) \, \mathbf{a}_{1}- x_{8} \, \mathbf{a}_{2}+\left(z_{8} + \frac{2}{3}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(2 x_{8} - y_{8}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a y_{8} \,\mathbf{\hat{y}}+\frac{1}{3}c \left(3 z_{8} + 2\right) \,\mathbf{\hat{z}}$ | (6c) | Ge III |
| $\mathbf{B_{34}}$ | = | $y_{8} \, \mathbf{a}_{1}+x_{8} \, \mathbf{a}_{2}- z_{8} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{8} + y_{8}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \left(x_{8} - y_{8}\right) \,\mathbf{\hat{y}}- c z_{8} \,\mathbf{\hat{z}}$ | (6c) | Ge III |
| $\mathbf{B_{35}}$ | = | $\left(x_{8} - y_{8}\right) \, \mathbf{a}_{1}- y_{8} \, \mathbf{a}_{2}- \left(z_{8} - \frac{2}{3}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{8} - 2 y_{8}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{8} \,\mathbf{\hat{y}}- \frac{1}{3}c \left(3 z_{8} - 2\right) \,\mathbf{\hat{z}}$ | (6c) | Ge III |
| $\mathbf{B_{36}}$ | = | $- x_{8} \, \mathbf{a}_{1}- \left(x_{8} - y_{8}\right) \, \mathbf{a}_{2}- \left(z_{8} - \frac{1}{3}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(2 x_{8} - y_{8}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a y_{8} \,\mathbf{\hat{y}}- c \left(z_{8} - \frac{1}{3}\right) \,\mathbf{\hat{z}}$ | (6c) | Ge III |
| $\mathbf{B_{37}}$ | = | $x_{9} \, \mathbf{a}_{1}+y_{9} \, \mathbf{a}_{2}+z_{9} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{9} + y_{9}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \left(x_{9} - y_{9}\right) \,\mathbf{\hat{y}}+c z_{9} \,\mathbf{\hat{z}}$ | (6c) | Ni IV |
| $\mathbf{B_{38}}$ | = | $- y_{9} \, \mathbf{a}_{1}+\left(x_{9} - y_{9}\right) \, \mathbf{a}_{2}+\left(z_{9} + \frac{1}{3}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{9} - 2 y_{9}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{9} \,\mathbf{\hat{y}}+c \left(z_{9} + \frac{1}{3}\right) \,\mathbf{\hat{z}}$ | (6c) | Ni IV |
| $\mathbf{B_{39}}$ | = | $- \left(x_{9} - y_{9}\right) \, \mathbf{a}_{1}- x_{9} \, \mathbf{a}_{2}+\left(z_{9} + \frac{2}{3}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(2 x_{9} - y_{9}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a y_{9} \,\mathbf{\hat{y}}+\frac{1}{3}c \left(3 z_{9} + 2\right) \,\mathbf{\hat{z}}$ | (6c) | Ni IV |
| $\mathbf{B_{40}}$ | = | $y_{9} \, \mathbf{a}_{1}+x_{9} \, \mathbf{a}_{2}- z_{9} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{9} + y_{9}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \left(x_{9} - y_{9}\right) \,\mathbf{\hat{y}}- c z_{9} \,\mathbf{\hat{z}}$ | (6c) | Ni IV |
| $\mathbf{B_{41}}$ | = | $\left(x_{9} - y_{9}\right) \, \mathbf{a}_{1}- y_{9} \, \mathbf{a}_{2}- \left(z_{9} - \frac{2}{3}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{9} - 2 y_{9}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{9} \,\mathbf{\hat{y}}- \frac{1}{3}c \left(3 z_{9} - 2\right) \,\mathbf{\hat{z}}$ | (6c) | Ni IV |
| $\mathbf{B_{42}}$ | = | $- x_{9} \, \mathbf{a}_{1}- \left(x_{9} - y_{9}\right) \, \mathbf{a}_{2}- \left(z_{9} - \frac{1}{3}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(2 x_{9} - y_{9}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a y_{9} \,\mathbf{\hat{y}}- c \left(z_{9} - \frac{1}{3}\right) \,\mathbf{\hat{z}}$ | (6c) | Ni IV |
| $\mathbf{B_{43}}$ | = | $x_{10} \, \mathbf{a}_{1}+y_{10} \, \mathbf{a}_{2}+z_{10} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{10} + y_{10}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \left(x_{10} - y_{10}\right) \,\mathbf{\hat{y}}+c z_{10} \,\mathbf{\hat{z}}$ | (6c) | Ni V |
| $\mathbf{B_{44}}$ | = | $- y_{10} \, \mathbf{a}_{1}+\left(x_{10} - y_{10}\right) \, \mathbf{a}_{2}+\left(z_{10} + \frac{1}{3}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{10} - 2 y_{10}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{10} \,\mathbf{\hat{y}}+c \left(z_{10} + \frac{1}{3}\right) \,\mathbf{\hat{z}}$ | (6c) | Ni V |
| $\mathbf{B_{45}}$ | = | $- \left(x_{10} - y_{10}\right) \, \mathbf{a}_{1}- x_{10} \, \mathbf{a}_{2}+\left(z_{10} + \frac{2}{3}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(2 x_{10} - y_{10}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a y_{10} \,\mathbf{\hat{y}}+\frac{1}{3}c \left(3 z_{10} + 2\right) \,\mathbf{\hat{z}}$ | (6c) | Ni V |
| $\mathbf{B_{46}}$ | = | $y_{10} \, \mathbf{a}_{1}+x_{10} \, \mathbf{a}_{2}- z_{10} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{10} + y_{10}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \left(x_{10} - y_{10}\right) \,\mathbf{\hat{y}}- c z_{10} \,\mathbf{\hat{z}}$ | (6c) | Ni V |
| $\mathbf{B_{47}}$ | = | $\left(x_{10} - y_{10}\right) \, \mathbf{a}_{1}- y_{10} \, \mathbf{a}_{2}- \left(z_{10} - \frac{2}{3}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{10} - 2 y_{10}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{10} \,\mathbf{\hat{y}}- \frac{1}{3}c \left(3 z_{10} - 2\right) \,\mathbf{\hat{z}}$ | (6c) | Ni V |
| $\mathbf{B_{48}}$ | = | $- x_{10} \, \mathbf{a}_{1}- \left(x_{10} - y_{10}\right) \, \mathbf{a}_{2}- \left(z_{10} - \frac{1}{3}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(2 x_{10} - y_{10}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a y_{10} \,\mathbf{\hat{y}}- c \left(z_{10} - \frac{1}{3}\right) \,\mathbf{\hat{z}}$ | (6c) | Ni V |
| $\mathbf{B_{49}}$ | = | $x_{11} \, \mathbf{a}_{1}+y_{11} \, \mathbf{a}_{2}+z_{11} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{11} + y_{11}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \left(x_{11} - y_{11}\right) \,\mathbf{\hat{y}}+c z_{11} \,\mathbf{\hat{z}}$ | (6c) | Ni VI |
| $\mathbf{B_{50}}$ | = | $- y_{11} \, \mathbf{a}_{1}+\left(x_{11} - y_{11}\right) \, \mathbf{a}_{2}+\left(z_{11} + \frac{1}{3}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{11} - 2 y_{11}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{11} \,\mathbf{\hat{y}}+c \left(z_{11} + \frac{1}{3}\right) \,\mathbf{\hat{z}}$ | (6c) | Ni VI |
| $\mathbf{B_{51}}$ | = | $- \left(x_{11} - y_{11}\right) \, \mathbf{a}_{1}- x_{11} \, \mathbf{a}_{2}+\left(z_{11} + \frac{2}{3}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(2 x_{11} - y_{11}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a y_{11} \,\mathbf{\hat{y}}+\frac{1}{3}c \left(3 z_{11} + 2\right) \,\mathbf{\hat{z}}$ | (6c) | Ni VI |
| $\mathbf{B_{52}}$ | = | $y_{11} \, \mathbf{a}_{1}+x_{11} \, \mathbf{a}_{2}- z_{11} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{11} + y_{11}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \left(x_{11} - y_{11}\right) \,\mathbf{\hat{y}}- c z_{11} \,\mathbf{\hat{z}}$ | (6c) | Ni VI |
| $\mathbf{B_{53}}$ | = | $\left(x_{11} - y_{11}\right) \, \mathbf{a}_{1}- y_{11} \, \mathbf{a}_{2}- \left(z_{11} - \frac{2}{3}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{11} - 2 y_{11}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{11} \,\mathbf{\hat{y}}- \frac{1}{3}c \left(3 z_{11} - 2\right) \,\mathbf{\hat{z}}$ | (6c) | Ni VI |
| $\mathbf{B_{54}}$ | = | $- x_{11} \, \mathbf{a}_{1}- \left(x_{11} - y_{11}\right) \, \mathbf{a}_{2}- \left(z_{11} - \frac{1}{3}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(2 x_{11} - y_{11}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a y_{11} \,\mathbf{\hat{y}}- c \left(z_{11} - \frac{1}{3}\right) \,\mathbf{\hat{z}}$ | (6c) | Ni VI |
| $\mathbf{B_{55}}$ | = | $x_{12} \, \mathbf{a}_{1}+y_{12} \, \mathbf{a}_{2}+z_{12} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{12} + y_{12}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \left(x_{12} - y_{12}\right) \,\mathbf{\hat{y}}+c z_{12} \,\mathbf{\hat{z}}$ | (6c) | Ni VII |
| $\mathbf{B_{56}}$ | = | $- y_{12} \, \mathbf{a}_{1}+\left(x_{12} - y_{12}\right) \, \mathbf{a}_{2}+\left(z_{12} + \frac{1}{3}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{12} - 2 y_{12}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{12} \,\mathbf{\hat{y}}+c \left(z_{12} + \frac{1}{3}\right) \,\mathbf{\hat{z}}$ | (6c) | Ni VII |
| $\mathbf{B_{57}}$ | = | $- \left(x_{12} - y_{12}\right) \, \mathbf{a}_{1}- x_{12} \, \mathbf{a}_{2}+\left(z_{12} + \frac{2}{3}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(2 x_{12} - y_{12}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a y_{12} \,\mathbf{\hat{y}}+\frac{1}{3}c \left(3 z_{12} + 2\right) \,\mathbf{\hat{z}}$ | (6c) | Ni VII |
| $\mathbf{B_{58}}$ | = | $y_{12} \, \mathbf{a}_{1}+x_{12} \, \mathbf{a}_{2}- z_{12} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{12} + y_{12}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \left(x_{12} - y_{12}\right) \,\mathbf{\hat{y}}- c z_{12} \,\mathbf{\hat{z}}$ | (6c) | Ni VII |
| $\mathbf{B_{59}}$ | = | $\left(x_{12} - y_{12}\right) \, \mathbf{a}_{1}- y_{12} \, \mathbf{a}_{2}- \left(z_{12} - \frac{2}{3}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{12} - 2 y_{12}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{12} \,\mathbf{\hat{y}}- \frac{1}{3}c \left(3 z_{12} - 2\right) \,\mathbf{\hat{z}}$ | (6c) | Ni VII |
| $\mathbf{B_{60}}$ | = | $- x_{12} \, \mathbf{a}_{1}- \left(x_{12} - y_{12}\right) \, \mathbf{a}_{2}- \left(z_{12} - \frac{1}{3}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(2 x_{12} - y_{12}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a y_{12} \,\mathbf{\hat{y}}- c \left(z_{12} - \frac{1}{3}\right) \,\mathbf{\hat{z}}$ | (6c) | Ni VII |
| $\mathbf{B_{61}}$ | = | $x_{13} \, \mathbf{a}_{1}+y_{13} \, \mathbf{a}_{2}+z_{13} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{13} + y_{13}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \left(x_{13} - y_{13}\right) \,\mathbf{\hat{y}}+c z_{13} \,\mathbf{\hat{z}}$ | (6c) | Ni VIII |
| $\mathbf{B_{62}}$ | = | $- y_{13} \, \mathbf{a}_{1}+\left(x_{13} - y_{13}\right) \, \mathbf{a}_{2}+\left(z_{13} + \frac{1}{3}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{13} - 2 y_{13}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{13} \,\mathbf{\hat{y}}+c \left(z_{13} + \frac{1}{3}\right) \,\mathbf{\hat{z}}$ | (6c) | Ni VIII |
| $\mathbf{B_{63}}$ | = | $- \left(x_{13} - y_{13}\right) \, \mathbf{a}_{1}- x_{13} \, \mathbf{a}_{2}+\left(z_{13} + \frac{2}{3}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(2 x_{13} - y_{13}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a y_{13} \,\mathbf{\hat{y}}+\frac{1}{3}c \left(3 z_{13} + 2\right) \,\mathbf{\hat{z}}$ | (6c) | Ni VIII |
| $\mathbf{B_{64}}$ | = | $y_{13} \, \mathbf{a}_{1}+x_{13} \, \mathbf{a}_{2}- z_{13} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{13} + y_{13}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \left(x_{13} - y_{13}\right) \,\mathbf{\hat{y}}- c z_{13} \,\mathbf{\hat{z}}$ | (6c) | Ni VIII |
| $\mathbf{B_{65}}$ | = | $\left(x_{13} - y_{13}\right) \, \mathbf{a}_{1}- y_{13} \, \mathbf{a}_{2}- \left(z_{13} - \frac{2}{3}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{13} - 2 y_{13}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{13} \,\mathbf{\hat{y}}- \frac{1}{3}c \left(3 z_{13} - 2\right) \,\mathbf{\hat{z}}$ | (6c) | Ni VIII |
| $\mathbf{B_{66}}$ | = | $- x_{13} \, \mathbf{a}_{1}- \left(x_{13} - y_{13}\right) \, \mathbf{a}_{2}- \left(z_{13} - \frac{1}{3}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(2 x_{13} - y_{13}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a y_{13} \,\mathbf{\hat{y}}- c \left(z_{13} - \frac{1}{3}\right) \,\mathbf{\hat{z}}$ | (6c) | Ni VIII |
References
- G. Nover and K. Schubert, Crystal Structure of Ni$_{13}$Ga$_{3}$Ge$_{6}$, Z. Metallkd. 72, 26–29 (1981), doi:10.1515/ijmr-1981-720104.
Found in
- P. Villars, H. Okamoto, and K. Cenzual, eds., ASM Alloy Phase Diagram Database (ASM International, 2018), chap. Gallium-Germanium-Nickel Ternary, Isothermal Section (1973 Ellner M.). Copyright © 2006-2018 ASM International.
Prototype Generator
aflow --proto=A3B6C13_hP66_152_ac_3c_a2b5c --params=$a,c/a,x_{1},x_{2},x_{3},x_{4},x_{5},y_{5},z_{5},x_{6},y_{6},z_{6},x_{7},y_{7},z_{7},x_{8},y_{8},z_{8},x_{9},y_{9},z_{9},x_{10},y_{10},z_{10},x_{11},y_{11},z_{11},x_{12},y_{12},z_{12},x_{13},y_{13},z_{13}$