AFLOW Prototype: A4B_cI40_197_cde_c
Prototype | : | Ga4Ni |
AFLOW prototype label | : | A4B_cI40_197_cde_c |
Strukturbericht designation | : | None |
Pearson symbol | : | cI40 |
Space group number | : | 197 |
Space group symbol | : | $\text{I23}$ |
AFLOW prototype command | : | aflow --proto=A4B_cI40_197_cde_c --params=$a$,$x_{1}$,$x_{2}$,$x_{3}$,$x_{4}$ |
Basis vectors:
\[ \begin{array}{ccccccc} & & \text{Lattice Coordinates} & & \text{Cartesian Coordinates} &\text{Wyckoff Position} & \text{Atom Type} \\ \mathbf{B}_{1} & = &2 x_{1} \, \mathbf{a}_{1}+ 2 x_{1} \, \mathbf{a}_{2}+ 2 x_{1} \, \mathbf{a}_{3}& = &x_{1} \, a \, \mathbf{\hat{x}}+ x_{1} \, a \, \mathbf{\hat{y}}+ x_{1} \, a \, \mathbf{\hat{z}}& \left(8c\right) & \text{Ga I} \\ \mathbf{B}_{2} & = &- 2 x_{1} \, \mathbf{a}_{3}& = &- x_{1} \, a \, \mathbf{\hat{x}}- x_{1} \, a \, \mathbf{\hat{y}}+ x_{1} \, a \, \mathbf{\hat{z}}& \left(8c\right) & \text{Ga I} \\ \mathbf{B}_{3} & = &- 2 x_{1} \, \mathbf{a}_{2}& = &- x_{1} \, a \, \mathbf{\hat{x}}+ x_{1} \, a \, \mathbf{\hat{y}}- x_{1} \, a \, \mathbf{\hat{z}}& \left(8c\right) & \text{Ga I} \\ \mathbf{B}_{4} & = &- 2 x_{1} \, \mathbf{a}_{1}& = &x_{1} \, a \, \mathbf{\hat{x}}- x_{1} \, a \, \mathbf{\hat{y}}- x_{1} \, a \, \mathbf{\hat{z}}& \left(8c\right) & \text{Ga I} \\ \mathbf{B}_{5} & = &2 x_{2} \, \mathbf{a}_{1}+ 2 x_{2} \, \mathbf{a}_{2}+ 2 x_{2} \, \mathbf{a}_{3}& = &x_{2} \, a \, \mathbf{\hat{x}}+ x_{2} \, a \, \mathbf{\hat{y}}+ x_{2} \, a \, \mathbf{\hat{z}}& \left(8c\right) & \text{Ni} \\ \mathbf{B}_{6} & = &- 2 x_{2} \, \mathbf{a}_{3}& = &- x_{2} \, a \, \mathbf{\hat{x}}- x_{2} \, a \, \mathbf{\hat{y}}+ x_{2} \, a \, \mathbf{\hat{z}}& \left(8c\right) & \text{Ni} \\ \mathbf{B}_{7} & = &- 2 x_{2} \, \mathbf{a}_{2}& = &- x_{2} \, a \, \mathbf{\hat{x}}+ x_{2} \, a \, \mathbf{\hat{y}}- x_{2} \, a \, \mathbf{\hat{z}}& \left(8c\right) & \text{Ni} \\ \mathbf{B}_{8} & = &- 2 x_{2} \, \mathbf{a}_{1}& = &x_{2} \, a \, \mathbf{\hat{x}}- x_{2} \, a \, \mathbf{\hat{y}}- x_{2} \, a \, \mathbf{\hat{z}}& \left(8c\right) & \text{Ni} \\ \mathbf{B}_{9} & = &x_{3} \, \mathbf{a}_{2}+ x_{3} \, \mathbf{a}_{3}& = &x_{3} \, a \, \mathbf{\hat{x}}& \left(12d\right) & \text{Ga II} \\ \mathbf{B}_{10} & = &x_{3} \, \mathbf{a}_{1}+ x_{3} \, \mathbf{a}_{3}& = &x_{3} \, a \, \mathbf{\hat{y}}& \left(12d\right) & \text{Ga II} \\ \mathbf{B}_{11} & = &x_{3} \, \mathbf{a}_{1}+ x_{3} \, \mathbf{a}_{2}& = &x_{3} \, a \, \mathbf{\hat{z}}& \left(12d\right) & \text{Ga II} \\ \mathbf{B}_{12} & = &- x_{3} \, \mathbf{a}_{2}- x_{3} \, \mathbf{a}_{3}& = &- x_{3} \, a \, \mathbf{\hat{x}}& \left(12d\right) & \text{Ga II} \\ \mathbf{B}_{13} & = &- x_{3} \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{3}& = &- x_{3} \, a \, \mathbf{\hat{y}}& \left(12d\right) & \text{Ga II} \\ \mathbf{B}_{14} & = &- x_{3} \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}& = &- x_{3} \, a \, \mathbf{\hat{z}}& \left(12d\right) & \text{Ga II} \\ \mathbf{B}_{15} & = &\frac12 \, \mathbf{a}_{1}+ x_{4} \, \mathbf{a}_{2}+ \left(\frac12 + x_{4}\right) \, \mathbf{a}_{3}& = &x_{4} \, a \, \mathbf{\hat{x}}+ \frac12 \, a \, \mathbf{\hat{y}}& \left(12e\right) & \text{Ga III} \\ \mathbf{B}_{16} & = &\left(\frac12 + x_{4}\right) \, \mathbf{a}_{1}+ \frac12 \, \mathbf{a}_{2}+ x_{4} \, \mathbf{a}_{3}& = &x_{4} \, a \, \mathbf{\hat{y}}+ \frac12 \, a \, \mathbf{\hat{z}}& \left(12e\right) & \text{Ga III} \\ \mathbf{B}_{17} & = &x_{4} \, \mathbf{a}_{1}+ \left(\frac12 + x_{4}\right) \, \mathbf{a}_{2}+ \frac12 \, \mathbf{a}_{3}& = &\frac12 \, a \, \mathbf{\hat{x}}+ x_{4} \, a \, \mathbf{\hat{z}}& \left(12e\right) & \text{Ga III} \\ \mathbf{B}_{18} & = &\frac12 \, \mathbf{a}_{1}- x_{4} \, \mathbf{a}_{2}+ \left(\frac12 - x_{4}\right) \, \mathbf{a}_{3}& = &- x_{4} \, a \, \mathbf{\hat{x}}+ \frac12 \, a \, \mathbf{\hat{y}}& \left(12e\right) & \text{Ga III} \\ \mathbf{B}_{19} & = &\left(\frac12 - x_{4}\right) \, \mathbf{a}_{1}+ \frac12 \, \mathbf{a}_{2}- x_{4} \, \mathbf{a}_{3}& = &- x_{4} \, a \, \mathbf{\hat{y}}+ \frac12 \, a \, \mathbf{\hat{z}}& \left(12e\right) & \text{Ga III} \\ \mathbf{B}_{20} & = &- x_{4} \, \mathbf{a}_{1}+ \left(\frac12 - x_{4}\right) \, \mathbf{a}_{2}+ \frac12 \, \mathbf{a}_{3}& = &\frac12 \, a \, \mathbf{\hat{x}}- x_{4} \, a \, \mathbf{\hat{z}}& \left(12e\right) & \text{Ga III} \\ \end{array} \]