Ga$_{4}$Ni$_{3}$ Structure: A4B3_cI112_230_af_g-001
| Prototype | Ga$_{4}$Ni$_{3}$ |
| AFLOW prototype label | A4B3_cI112_230_af_g-001 |
| ICSD | 103864 |
| Pearson symbol | cI112 |
| Space group number | 230 |
| Space group symbol | $Ia\overline{3}d$ |
| AFLOW prototype command |
aflow --proto=A4B3_cI112_230_af_g-001
--params=$a, \allowbreak x_{2}, \allowbreak y_{3}$ |
- This is a simple defect superstructure of the CsCl ($B2$) structure. If GaNi $B2$ is expanded into a 128 atom supercell, we can describe it using space group $Ia\overline{3}d$ #230, with Ga atoms on the (16a) and (48f) Wyckoff sites and Ni atoms on the (16b) and (48g) sites. Removing the Ni atoms from the (16b) sites yields this structure.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&- \frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}- \frac{1}{2}a \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $0$ | = | $0$ | (16a) | Ga I |
| $\mathbf{B_{2}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{y}}$ | (16a) | Ga I |
| $\mathbf{B_{3}}$ | = | $\frac{1}{2} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}$ | (16a) | Ga I |
| $\mathbf{B_{4}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}$ | = | $\frac{1}{2}a \,\mathbf{\hat{z}}$ | (16a) | Ga I |
| $\mathbf{B_{5}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}$ | = | $- \frac{1}{4}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (16a) | Ga I |
| $\mathbf{B_{6}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (16a) | Ga I |
| $\mathbf{B_{7}}$ | = | $\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}- \frac{1}{4}a \,\mathbf{\hat{z}}$ | (16a) | Ga I |
| $\mathbf{B_{8}}$ | = | $\frac{1}{2} \, \mathbf{a}_{2}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}- \frac{1}{4}a \,\mathbf{\hat{y}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (16a) | Ga I |
| $\mathbf{B_{9}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+\left(x_{2} + \frac{1}{4}\right) \, \mathbf{a}_{2}+x_{2} \, \mathbf{a}_{3}$ | = | $a x_{2} \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (48f) | Ga II |
| $\mathbf{B_{10}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}- \left(x_{2} - \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(x_{2} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{2} \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (48f) | Ga II |
| $\mathbf{B_{11}}$ | = | $x_{2} \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}+\left(x_{2} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+a x_{2} \,\mathbf{\hat{y}}$ | (48f) | Ga II |
| $\mathbf{B_{12}}$ | = | $- \left(x_{2} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}- \left(x_{2} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}- a x_{2} \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}$ | (48f) | Ga II |
| $\mathbf{B_{13}}$ | = | $\left(x_{2} + \frac{1}{4}\right) \, \mathbf{a}_{1}+x_{2} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{y}}+a x_{2} \,\mathbf{\hat{z}}$ | (48f) | Ga II |
| $\mathbf{B_{14}}$ | = | $- \left(x_{2} - \frac{1}{4}\right) \, \mathbf{a}_{1}- \left(x_{2} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}- a x_{2} \,\mathbf{\hat{z}}$ | (48f) | Ga II |
| $\mathbf{B_{15}}$ | = | $\left(x_{2} + \frac{1}{4}\right) \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}+x_{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+a \left(x_{2} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}$ | (48f) | Ga II |
| $\mathbf{B_{16}}$ | = | $- \left(x_{2} - \frac{1}{4}\right) \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}- \left(x_{2} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}- a \left(x_{2} - \frac{1}{4}\right) \,\mathbf{\hat{y}}$ | (48f) | Ga II |
| $\mathbf{B_{17}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}+x_{2} \, \mathbf{a}_{2}+\left(x_{2} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{2} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (48f) | Ga II |
| $\mathbf{B_{18}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}- \left(x_{2} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{2} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{2} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (48f) | Ga II |
| $\mathbf{B_{19}}$ | = | $- \left(x_{2} - \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{2} - \frac{1}{4}\right) \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{y}}- a \left(x_{2} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (48f) | Ga II |
| $\mathbf{B_{20}}$ | = | $x_{2} \, \mathbf{a}_{1}+\left(x_{2} + \frac{1}{4}\right) \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+a \left(x_{2} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (48f) | Ga II |
| $\mathbf{B_{21}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}- \left(x_{2} - \frac{3}{4}\right) \, \mathbf{a}_{2}- x_{2} \, \mathbf{a}_{3}$ | = | $- a x_{2} \,\mathbf{\hat{x}}+\frac{3}{4}a \,\mathbf{\hat{z}}$ | (48f) | Ga II |
| $\mathbf{B_{22}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+\left(x_{2} + \frac{3}{4}\right) \, \mathbf{a}_{2}+\left(x_{2} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{2} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (48f) | Ga II |
| $\mathbf{B_{23}}$ | = | $- x_{2} \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}- \left(x_{2} - \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $\frac{3}{4}a \,\mathbf{\hat{x}}- a x_{2} \,\mathbf{\hat{y}}$ | (48f) | Ga II |
| $\mathbf{B_{24}}$ | = | $\left(x_{2} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}+\left(x_{2} + \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+a \left(x_{2} + \frac{1}{2}\right) \,\mathbf{\hat{y}}$ | (48f) | Ga II |
| $\mathbf{B_{25}}$ | = | $- \left(x_{2} - \frac{3}{4}\right) \, \mathbf{a}_{1}- x_{2} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{3}{4}a \,\mathbf{\hat{y}}- a x_{2} \,\mathbf{\hat{z}}$ | (48f) | Ga II |
| $\mathbf{B_{26}}$ | = | $\left(x_{2} + \frac{3}{4}\right) \, \mathbf{a}_{1}+\left(x_{2} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{y}}+a \left(x_{2} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (48f) | Ga II |
| $\mathbf{B_{27}}$ | = | $- \left(x_{2} - \frac{3}{4}\right) \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}- x_{2} \, \mathbf{a}_{3}$ | = | $- \frac{1}{4}a \,\mathbf{\hat{x}}- a \left(x_{2} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}$ | (48f) | Ga II |
| $\mathbf{B_{28}}$ | = | $\left(x_{2} + \frac{3}{4}\right) \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}+\left(x_{2} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+a \left(x_{2} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}$ | (48f) | Ga II |
| $\mathbf{B_{29}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}- x_{2} \, \mathbf{a}_{2}- \left(x_{2} - \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{2} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}- \frac{1}{4}a \,\mathbf{\hat{z}}$ | (48f) | Ga II |
| $\mathbf{B_{30}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}+\left(x_{2} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{2} + \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{2} + \frac{1}{4}\right) \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (48f) | Ga II |
| $\mathbf{B_{31}}$ | = | $\left(x_{2} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{2} + \frac{3}{4}\right) \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+a \left(x_{2} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (48f) | Ga II |
| $\mathbf{B_{32}}$ | = | $- x_{2} \, \mathbf{a}_{1}- \left(x_{2} - \frac{3}{4}\right) \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{1}{4}a \,\mathbf{\hat{y}}- a \left(x_{2} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (48f) | Ga II |
| $\mathbf{B_{33}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}- \left(y_{3} - \frac{3}{8}\right) \, \mathbf{a}_{2}+\left(y_{3} + \frac{1}{8}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{8}a \,\mathbf{\hat{x}}+a y_{3} \,\mathbf{\hat{y}}- a \left(y_{3} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (48g) | Ni I |
| $\mathbf{B_{34}}$ | = | $- \left(2 y_{3} - \frac{3}{4}\right) \, \mathbf{a}_{1}- \left(y_{3} - \frac{1}{8}\right) \, \mathbf{a}_{2}- \left(y_{3} - \frac{3}{8}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{8}a \,\mathbf{\hat{x}}- a \left(y_{3} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(y_{3} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (48g) | Ni I |
| $\mathbf{B_{35}}$ | = | $\left(2 y_{3} + \frac{3}{4}\right) \, \mathbf{a}_{1}+\left(y_{3} + \frac{1}{8}\right) \, \mathbf{a}_{2}+\left(y_{3} + \frac{3}{8}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{8}a \,\mathbf{\hat{x}}+a \left(y_{3} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+a \left(y_{3} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (48g) | Ni I |
| $\mathbf{B_{36}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+\left(y_{3} + \frac{3}{8}\right) \, \mathbf{a}_{2}- \left(y_{3} - \frac{1}{8}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{8}a \,\mathbf{\hat{x}}- a y_{3} \,\mathbf{\hat{y}}+a \left(y_{3} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (48g) | Ni I |
| $\mathbf{B_{37}}$ | = | $\left(y_{3} + \frac{1}{8}\right) \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}- \left(y_{3} - \frac{3}{8}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{3} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+\frac{1}{8}a \,\mathbf{\hat{y}}+a y_{3} \,\mathbf{\hat{z}}$ | (48g) | Ni I |
| $\mathbf{B_{38}}$ | = | $- \left(y_{3} - \frac{3}{8}\right) \, \mathbf{a}_{1}- \left(2 y_{3} - \frac{3}{4}\right) \, \mathbf{a}_{2}- \left(y_{3} - \frac{1}{8}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{3} - \frac{1}{4}\right) \,\mathbf{\hat{x}}- \frac{1}{8}a \,\mathbf{\hat{y}}- a \left(y_{3} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (48g) | Ni I |
| $\mathbf{B_{39}}$ | = | $\left(y_{3} + \frac{3}{8}\right) \, \mathbf{a}_{1}+\left(2 y_{3} + \frac{3}{4}\right) \, \mathbf{a}_{2}+\left(y_{3} + \frac{1}{8}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{3} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- \frac{1}{8}a \,\mathbf{\hat{y}}+a \left(y_{3} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (48g) | Ni I |
| $\mathbf{B_{40}}$ | = | $- \left(y_{3} - \frac{1}{8}\right) \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}+\left(y_{3} + \frac{3}{8}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{3} + \frac{1}{4}\right) \,\mathbf{\hat{x}}+\frac{1}{8}a \,\mathbf{\hat{y}}- a y_{3} \,\mathbf{\hat{z}}$ | (48g) | Ni I |
| $\mathbf{B_{41}}$ | = | $- \left(y_{3} - \frac{3}{8}\right) \, \mathbf{a}_{1}+\left(y_{3} + \frac{1}{8}\right) \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $a y_{3} \,\mathbf{\hat{x}}- a \left(y_{3} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+\frac{1}{8}a \,\mathbf{\hat{z}}$ | (48g) | Ni I |
| $\mathbf{B_{42}}$ | = | $- \left(y_{3} - \frac{1}{8}\right) \, \mathbf{a}_{1}- \left(y_{3} - \frac{3}{8}\right) \, \mathbf{a}_{2}- \left(2 y_{3} - \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{3} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(y_{3} - \frac{1}{4}\right) \,\mathbf{\hat{y}}- \frac{1}{8}a \,\mathbf{\hat{z}}$ | (48g) | Ni I |
| $\mathbf{B_{43}}$ | = | $\left(y_{3} + \frac{1}{8}\right) \, \mathbf{a}_{1}+\left(y_{3} + \frac{3}{8}\right) \, \mathbf{a}_{2}+\left(2 y_{3} + \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{3} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(y_{3} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- \frac{1}{8}a \,\mathbf{\hat{z}}$ | (48g) | Ni I |
| $\mathbf{B_{44}}$ | = | $\left(y_{3} + \frac{3}{8}\right) \, \mathbf{a}_{1}- \left(y_{3} - \frac{1}{8}\right) \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $- a y_{3} \,\mathbf{\hat{x}}+a \left(y_{3} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+\frac{1}{8}a \,\mathbf{\hat{z}}$ | (48g) | Ni I |
| $\mathbf{B_{45}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}+\left(y_{3} + \frac{5}{8}\right) \, \mathbf{a}_{2}- \left(y_{3} - \frac{7}{8}\right) \, \mathbf{a}_{3}$ | = | $\frac{3}{8}a \,\mathbf{\hat{x}}- a \left(y_{3} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+a \left(y_{3} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (48g) | Ni I |
| $\mathbf{B_{46}}$ | = | $\left(2 y_{3} + \frac{1}{4}\right) \, \mathbf{a}_{1}+\left(y_{3} + \frac{7}{8}\right) \, \mathbf{a}_{2}+\left(y_{3} + \frac{5}{8}\right) \, \mathbf{a}_{3}$ | = | $\frac{5}{8}a \,\mathbf{\hat{x}}+a y_{3} \,\mathbf{\hat{y}}+a \left(y_{3} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (48g) | Ni I |
| $\mathbf{B_{47}}$ | = | $- \left(2 y_{3} - \frac{1}{4}\right) \, \mathbf{a}_{1}- \left(y_{3} - \frac{7}{8}\right) \, \mathbf{a}_{2}- \left(y_{3} - \frac{5}{8}\right) \, \mathbf{a}_{3}$ | = | $\frac{5}{8}a \,\mathbf{\hat{x}}- a y_{3} \,\mathbf{\hat{y}}- a \left(y_{3} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (48g) | Ni I |
| $\mathbf{B_{48}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}- \left(y_{3} - \frac{5}{8}\right) \, \mathbf{a}_{2}+\left(y_{3} + \frac{7}{8}\right) \, \mathbf{a}_{3}$ | = | $\frac{3}{8}a \,\mathbf{\hat{x}}+a \left(y_{3} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(y_{3} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (48g) | Ni I |
| $\mathbf{B_{49}}$ | = | $- \left(y_{3} - \frac{7}{8}\right) \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}+\left(y_{3} + \frac{5}{8}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{3} + \frac{1}{4}\right) \,\mathbf{\hat{x}}+\frac{3}{8}a \,\mathbf{\hat{y}}- a \left(y_{3} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (48g) | Ni I |
| $\mathbf{B_{50}}$ | = | $\left(y_{3} + \frac{5}{8}\right) \, \mathbf{a}_{1}+\left(2 y_{3} + \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(y_{3} + \frac{7}{8}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{3} + \frac{1}{4}\right) \,\mathbf{\hat{x}}+\frac{5}{8}a \,\mathbf{\hat{y}}+a y_{3} \,\mathbf{\hat{z}}$ | (48g) | Ni I |
| $\mathbf{B_{51}}$ | = | $- \left(y_{3} - \frac{5}{8}\right) \, \mathbf{a}_{1}- \left(2 y_{3} - \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(y_{3} - \frac{7}{8}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{3} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+\frac{5}{8}a \,\mathbf{\hat{y}}- a y_{3} \,\mathbf{\hat{z}}$ | (48g) | Ni I |
| $\mathbf{B_{52}}$ | = | $\left(y_{3} + \frac{7}{8}\right) \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}- \left(y_{3} - \frac{5}{8}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{3} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+\frac{3}{8}a \,\mathbf{\hat{y}}+a \left(y_{3} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (48g) | Ni I |
| $\mathbf{B_{53}}$ | = | $\left(y_{3} + \frac{5}{8}\right) \, \mathbf{a}_{1}- \left(y_{3} - \frac{7}{8}\right) \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $- a \left(y_{3} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(y_{3} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+\frac{3}{8}a \,\mathbf{\hat{z}}$ | (48g) | Ni I |
| $\mathbf{B_{54}}$ | = | $\left(y_{3} + \frac{7}{8}\right) \, \mathbf{a}_{1}+\left(y_{3} + \frac{5}{8}\right) \, \mathbf{a}_{2}+\left(2 y_{3} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $a y_{3} \,\mathbf{\hat{x}}+a \left(y_{3} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+\frac{5}{8}a \,\mathbf{\hat{z}}$ | (48g) | Ni I |
| $\mathbf{B_{55}}$ | = | $- \left(y_{3} - \frac{7}{8}\right) \, \mathbf{a}_{1}- \left(y_{3} - \frac{5}{8}\right) \, \mathbf{a}_{2}- \left(2 y_{3} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $- a y_{3} \,\mathbf{\hat{x}}- a \left(y_{3} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+\frac{5}{8}a \,\mathbf{\hat{z}}$ | (48g) | Ni I |
| $\mathbf{B_{56}}$ | = | $- \left(y_{3} - \frac{5}{8}\right) \, \mathbf{a}_{1}+\left(y_{3} + \frac{7}{8}\right) \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $a \left(y_{3} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(y_{3} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+\frac{3}{8}a \,\mathbf{\hat{z}}$ | (48g) | Ni I |
References
- M. Ellner, K. Best, H. Jacobi, and K. Schubert, Struktur von Ni$_3$Ga$_4$, J. Less-Common Met. 19, 294–296 (1969), doi:10.1016/0022-5088(69)90109-X.
Found in
- P. Villars and K. Cenzual, eds., Structure Types. Part 1: Space Groups (230) Ia-3d – (219) F43-c} (Springer-Verlag, Berlin Heidelberg, 2004), chap. Ni$_{3}$Ga$_{4$.
Prototype Generator
aflow --proto=A4B3_cI112_230_af_g --params=$a,x_{2},y_{3}$