AFLOW Prototype: A_tP16_138_j
Prototype | : | Cl |
AFLOW prototype label | : | A_tP16_138_j |
Strukturbericht designation | : | $A18$ |
Pearson symbol | : | tP16 |
Space group number | : | 138 |
Space group symbol | : | $\text{P4}_{2}\text{/ncm}$ |
AFLOW prototype command | : | aflow --proto=A_tP16_138_j --params=$a$,$c/a$,$x_{1}$,$y_{1}$,$z_{1}$ |
Basis vectors:
\[ \begin{array}{ccccccc} & & \text{Lattice Coordinates} & & \text{Cartesian Coordinates} &\text{Wyckoff Position} & \text{Atom Type} \\ \mathbf{B}_{1} & = &x_{1} \, \mathbf{a}_{1}+ y_{1} \, \mathbf{a}_{2}+ z_{1} \, \mathbf{a}_{3}& = &x_{1} \, a \, \mathbf{\hat{x}}+ y_{1} \, a \, \mathbf{\hat{y}}+ z_{1} \, c \, \mathbf{\hat{z}}& \left(16j\right) & \text{Cl} \\ \mathbf{B}_{2} & = &\left(\frac12 - x_{1}\right) \, \mathbf{a}_{1}+ \left(\frac12 - y_{1}\right) \, \mathbf{a}_{2}+ z_{1} \, \mathbf{a}_{3}& = &\left(\frac12 - x_{1}\right) \, a \, \mathbf{\hat{x}}+ \left(\frac12 - y_{1}\right) \, a \, \mathbf{\hat{y}}+ z_{1} \, c \, \mathbf{\hat{z}}& \left(16j\right) & \text{Cl} \\ \mathbf{B}_{3} & = &\left(\frac12 - y_{1}\right) \, \mathbf{a}_{1}+ x_{1} \, \mathbf{a}_{2}+ \left(\frac12 + z_{1}\right) \, \mathbf{a}_{3}& = &\left(\frac12 - y_{1}\right) \, a \, \mathbf{\hat{x}}+ x_{1} \, a \, \mathbf{\hat{y}}+ \left(\frac12 + z_{1}\right) \, c \, \mathbf{\hat{z}}& \left(16j\right) & \text{Cl} \\ \mathbf{B}_{4} & = &y_{1} \, \mathbf{a}_{1}+ \left(\frac12 - x_{1}\right) \, \mathbf{a}_{2}+ \left(\frac12 + z_{1}\right) \, \mathbf{a}_{3}& = &y_{1} \, a \, \mathbf{\hat{x}}+ \left(\frac12 - x_{1}\right) \, a \, \mathbf{\hat{y}}+ \left(\frac12 + z_{1}\right) \, c \, \mathbf{\hat{z}}& \left(16j\right) & \text{Cl} \\ \mathbf{B}_{5} & = &- x_{1} \, \mathbf{a}_{1}+ \left(\frac12 + y_{1}\right) \, \mathbf{a}_{2}+ \left(\frac12 - z_{1}\right) \, \mathbf{a}_{3}& = &- x_{1} \, a \, \mathbf{\hat{x}}+ \left(\frac12 + y_{1}\right) \, a \, \mathbf{\hat{y}}+ \left(\frac12 - z_{1}\right) \, c \, \mathbf{\hat{z}}& \left(16j\right) & \text{Cl} \\ \mathbf{B}_{6} & = &\left(\frac12 + x_{1}\right) \, \mathbf{a}_{1}- y_{1} \, \mathbf{a}_{2}+ \left(\frac12 - z_{1}\right) \, \mathbf{a}_{3}& = &\left(\frac12 + x_{1}\right) \, a \, \mathbf{\hat{x}}- y_{1} \, a \, \mathbf{\hat{y}}+ \left(\frac12 - z_{1}\right) \, c \, \mathbf{\hat{z}}& \left(16j\right) & \text{Cl} \\ \mathbf{B}_{7} & = &\left(\frac12 + y_{1}\right) \, \mathbf{a}_{1}+ \left(\frac12 + x_{1}\right) \, \mathbf{a}_{2}- z_{1} \, \mathbf{a}_{3}& = &\left(\frac12 + y_{1}\right) \, a \, \mathbf{\hat{x}}+ \left(\frac12 + x_{1}\right) \, a \, \mathbf{\hat{y}}- z_{1} \, c \, \mathbf{\hat{z}}& \left(16j\right) & \text{Cl} \\ \mathbf{B}_{8} & = &- y_{1} \, \mathbf{a}_{1}- x_{1} \, \mathbf{a}_{2}- z_{1} \, \mathbf{a}_{3}& = &- y_{1} \, a \, \mathbf{\hat{x}}- x_{1} \, a \, \mathbf{\hat{y}}- z_{1} \, c \, \mathbf{\hat{z}}& \left(16j\right) & \text{Cl} \\ \mathbf{B}_{9} & = &- x_{1} \, \mathbf{a}_{1}- y_{1} \, \mathbf{a}_{2}- z_{1} \, \mathbf{a}_{3}& = &- x_{1} \, a \, \mathbf{\hat{x}}- y_{1} \, a \, \mathbf{\hat{y}}- z_{1} \, c \, \mathbf{\hat{z}}& \left(16j\right) & \text{Cl} \\ \mathbf{B}_{10} & = &\left(\frac12 + x_{1}\right) \, \mathbf{a}_{1}+ \left(\frac12 + y_{1}\right) \, \mathbf{a}_{2}- z_{1} \, \mathbf{a}_{3}& = &\left(\frac12 + x_{1}\right) \, a \, \mathbf{\hat{x}}+ \left(\frac12 + y_{1}\right) \, a \, \mathbf{\hat{y}}- z_{1} \, c \, \mathbf{\hat{z}}& \left(16j\right) & \text{Cl} \\ \mathbf{B}_{11} & = &\left(\frac12 + y_{1}\right) \, \mathbf{a}_{1}- x_{1} \, \mathbf{a}_{2}+ \left(\frac12 - z_{1}\right) \, \mathbf{a}_{3}& = &\left(\frac12 + y_{1}\right) \, a \, \mathbf{\hat{x}}- x_{1} \, a \, \mathbf{\hat{y}}+ \left(\frac12 - z_{1}\right) \, c \, \mathbf{\hat{z}}& \left(16j\right) & \text{Cl} \\ \mathbf{B}_{12} & = &- y_{1} \, \mathbf{a}_{1}+ \left(\frac12 + x_{1}\right) \, \mathbf{a}_{2}+ \left(\frac12 - z_{1}\right) \, \mathbf{a}_{3}& = &- y_{1} \, a \, \mathbf{\hat{x}}+ \left(\frac12 + x_{1}\right) \, a \, \mathbf{\hat{y}}+ \left(\frac12 - z_{1}\right) \, c \, \mathbf{\hat{z}}& \left(16j\right) & \text{Cl} \\ \mathbf{B}_{13} & = &x_{1} \, \mathbf{a}_{1}+ \left(\frac12 - y_{1}\right) \, \mathbf{a}_{2}+ \left(\frac12 + z_{1}\right) \, \mathbf{a}_{3}& = &x_{1} \, a \, \mathbf{\hat{x}}+ \left(\frac12 - y_{1}\right) \, a \, \mathbf{\hat{y}}+ \left(\frac12 + z_{1}\right) \, c \, \mathbf{\hat{z}}& \left(16j\right) & \text{Cl} \\ \mathbf{B}_{14} & = &\left(\frac12 - x_{1}\right) \, \mathbf{a}_{1}+ y_{1} \, \mathbf{a}_{2}+ \left(\frac12 + z_{1}\right) \, \mathbf{a}_{3}& = &\left(\frac12 - x_{1}\right) \, a \, \mathbf{\hat{x}}+ y_{1} \, a \, \mathbf{\hat{y}}+ \left(\frac12 + z_{1}\right) \, c \, \mathbf{\hat{z}}& \left(16j\right) & \text{Cl} \\ \mathbf{B}_{15} & = &\left(\frac12 - y_{1}\right) \, \mathbf{a}_{1}+ \left(\frac12 - x_{1}\right) \, \mathbf{a}_{2}+ z_{1} \, \mathbf{a}_{3}& = &\left(\frac12 - y_{1}\right) \, a \, \mathbf{\hat{x}}+ \left(\frac12 - x_{1}\right) \, a \, \mathbf{\hat{y}}+ z_{1} \, c \, \mathbf{\hat{z}}& \left(16j\right) & \text{Cl} \\ \mathbf{B}_{16} & = &y_{1} \, \mathbf{a}_{1}+ x_{1} \, \mathbf{a}_{2}+ z_{1} \, \mathbf{a}_{3}& = &y_{1} \, a \, \mathbf{\hat{x}}+ x_{1} \, a \, \mathbf{\hat{y}}+ z_{1} \, c \, \mathbf{\hat{z}}& \left(16j\right) & \text{Cl} \\ \end{array} \]