AFLOW Prototype: A3B_tI32_82_3g_g
Prototype | : | Ni3P |
AFLOW prototype label | : | A3B_tI32_82_3g_g |
Strukturbericht designation | : | $D0_{e}$ |
Pearson symbol | : | tI32 |
Space group number | : | 82 |
Space group symbol | : | $I\bar{4}$ |
AFLOW prototype command | : | aflow --proto=A3B_tI32_82_3g_g --params=$a$,$c/a$,$x_{1}$,$y_{1}$,$z_{1}$,$x_{2}$,$y_{2}$,$z_{2}$,$x_{3}$,$y_{3}$,$z_{3}$,$x_{4}$,$y_{4}$,$z_{4}$ |
Basis vectors:
\[ \begin{array}{ccccccc} & & \text{Lattice Coordinates} & & \text{Cartesian Coordinates} &\text{Wyckoff Position} & \text{Atom Type} \\ \mathbf{B}_{1} & = & \left(y_{1}+z_{1}\right) \, \mathbf{a}_{1} + \left(x_{1}+z_{1}\right) \, \mathbf{a}_{2} + \left(x_{1}+y_{1}\right) \, \mathbf{a}_{3} & = & x_{1}a \, \mathbf{\hat{x}} + y_{1}a \, \mathbf{\hat{y}} + z_{1}c \, \mathbf{\hat{z}} & \left(8g\right) & \text{Ni I} \\ \mathbf{B}_{2} & = & \left(-y_{1}+z_{1}\right) \, \mathbf{a}_{1} + \left(-x_{1}+z_{1}\right) \, \mathbf{a}_{2} + \left(-x_{1}-y_{1}\right) \, \mathbf{a}_{3} & = & -x_{1}a \, \mathbf{\hat{x}}-y_{1}a \, \mathbf{\hat{y}} + z_{1}c \, \mathbf{\hat{z}} & \left(8g\right) & \text{Ni I} \\ \mathbf{B}_{3} & = & \left(-x_{1}-z_{1}\right) \, \mathbf{a}_{1} + \left(y_{1}-z_{1}\right) \, \mathbf{a}_{2} + \left(-x_{1}+y_{1}\right) \, \mathbf{a}_{3} & = & y_{1}a \, \mathbf{\hat{x}}-x_{1}a \, \mathbf{\hat{y}}-z_{1}c \, \mathbf{\hat{z}} & \left(8g\right) & \text{Ni I} \\ \mathbf{B}_{4} & = & \left(x_{1}-z_{1}\right) \, \mathbf{a}_{1} + \left(-y_{1}-z_{1}\right) \, \mathbf{a}_{2} + \left(x_{1}-y_{1}\right) \, \mathbf{a}_{3} & = & -y_{1}a \, \mathbf{\hat{x}} + x_{1}a \, \mathbf{\hat{y}}-z_{1}c \, \mathbf{\hat{z}} & \left(8g\right) & \text{Ni I} \\ \mathbf{B}_{5} & = & \left(y_{2}+z_{2}\right) \, \mathbf{a}_{1} + \left(x_{2}+z_{2}\right) \, \mathbf{a}_{2} + \left(x_{2}+y_{2}\right) \, \mathbf{a}_{3} & = & x_{2}a \, \mathbf{\hat{x}} + y_{2}a \, \mathbf{\hat{y}} + z_{2}c \, \mathbf{\hat{z}} & \left(8g\right) & \text{Ni II} \\ \mathbf{B}_{6} & = & \left(-y_{2}+z_{2}\right) \, \mathbf{a}_{1} + \left(-x_{2}+z_{2}\right) \, \mathbf{a}_{2} + \left(-x_{2}-y_{2}\right) \, \mathbf{a}_{3} & = & -x_{2}a \, \mathbf{\hat{x}}-y_{2}a \, \mathbf{\hat{y}} + z_{2}c \, \mathbf{\hat{z}} & \left(8g\right) & \text{Ni II} \\ \mathbf{B}_{7} & = & \left(-x_{2}-z_{2}\right) \, \mathbf{a}_{1} + \left(y_{2}-z_{2}\right) \, \mathbf{a}_{2} + \left(-x_{2}+y_{2}\right) \, \mathbf{a}_{3} & = & y_{2}a \, \mathbf{\hat{x}}-x_{2}a \, \mathbf{\hat{y}}-z_{2}c \, \mathbf{\hat{z}} & \left(8g\right) & \text{Ni II} \\ \mathbf{B}_{8} & = & \left(x_{2}-z_{2}\right) \, \mathbf{a}_{1} + \left(-y_{2}-z_{2}\right) \, \mathbf{a}_{2} + \left(x_{2}-y_{2}\right) \, \mathbf{a}_{3} & = & -y_{2}a \, \mathbf{\hat{x}} + x_{2}a \, \mathbf{\hat{y}}-z_{2}c \, \mathbf{\hat{z}} & \left(8g\right) & \text{Ni II} \\ \mathbf{B}_{9} & = & \left(y_{3}+z_{3}\right) \, \mathbf{a}_{1} + \left(x_{3}+z_{3}\right) \, \mathbf{a}_{2} + \left(x_{3}+y_{3}\right) \, \mathbf{a}_{3} & = & x_{3}a \, \mathbf{\hat{x}} + y_{3}a \, \mathbf{\hat{y}} + z_{3}c \, \mathbf{\hat{z}} & \left(8g\right) & \text{Ni III} \\ \mathbf{B}_{10} & = & \left(-y_{3}+z_{3}\right) \, \mathbf{a}_{1} + \left(-x_{3}+z_{3}\right) \, \mathbf{a}_{2} + \left(-x_{3}-y_{3}\right) \, \mathbf{a}_{3} & = & -x_{3}a \, \mathbf{\hat{x}}-y_{3}a \, \mathbf{\hat{y}} + z_{3}c \, \mathbf{\hat{z}} & \left(8g\right) & \text{Ni III} \\ \mathbf{B}_{11} & = & \left(-x_{3}-z_{3}\right) \, \mathbf{a}_{1} + \left(y_{3}-z_{3}\right) \, \mathbf{a}_{2} + \left(-x_{3}+y_{3}\right) \, \mathbf{a}_{3} & = & y_{3}a \, \mathbf{\hat{x}}-x_{3}a \, \mathbf{\hat{y}}-z_{3}c \, \mathbf{\hat{z}} & \left(8g\right) & \text{Ni III} \\ \mathbf{B}_{12} & = & \left(x_{3}-z_{3}\right) \, \mathbf{a}_{1} + \left(-y_{3}-z_{3}\right) \, \mathbf{a}_{2} + \left(x_{3}-y_{3}\right) \, \mathbf{a}_{3} & = & -y_{3}a \, \mathbf{\hat{x}} + x_{3}a \, \mathbf{\hat{y}}-z_{3}c \, \mathbf{\hat{z}} & \left(8g\right) & \text{Ni III} \\ \mathbf{B}_{13} & = & \left(y_{4}+z_{4}\right) \, \mathbf{a}_{1} + \left(x_{4}+z_{4}\right) \, \mathbf{a}_{2} + \left(x_{4}+y_{4}\right) \, \mathbf{a}_{3} & = & x_{4}a \, \mathbf{\hat{x}} + y_{4}a \, \mathbf{\hat{y}} + z_{4}c \, \mathbf{\hat{z}} & \left(8g\right) & \text{P} \\ \mathbf{B}_{14} & = & \left(-y_{4}+z_{4}\right) \, \mathbf{a}_{1} + \left(-x_{4}+z_{4}\right) \, \mathbf{a}_{2} + \left(-x_{4}-y_{4}\right) \, \mathbf{a}_{3} & = & -x_{4}a \, \mathbf{\hat{x}}-y_{4}a \, \mathbf{\hat{y}} + z_{4}c \, \mathbf{\hat{z}} & \left(8g\right) & \text{P} \\ \mathbf{B}_{15} & = & \left(-x_{4}-z_{4}\right) \, \mathbf{a}_{1} + \left(y_{4}-z_{4}\right) \, \mathbf{a}_{2} + \left(-x_{4}+y_{4}\right) \, \mathbf{a}_{3} & = & y_{4}a \, \mathbf{\hat{x}}-x_{4}a \, \mathbf{\hat{y}}-z_{4}c \, \mathbf{\hat{z}} & \left(8g\right) & \text{P} \\ \mathbf{B}_{16} & = & \left(x_{4}-z_{4}\right) \, \mathbf{a}_{1} + \left(-y_{4}-z_{4}\right) \, \mathbf{a}_{2} + \left(x_{4}-y_{4}\right) \, \mathbf{a}_{3} & = & -y_{4}a \, \mathbf{\hat{x}} + x_{4}a \, \mathbf{\hat{y}}-z_{4}c \, \mathbf{\hat{z}} & \left(8g\right) & \text{P} \\ \end{array} \]