AFLOW Prototype: A3B_cP16_198_b_a
Prototype | : | NH3 |
AFLOW prototype label | : | A3B_cP16_198_b_a |
Strukturbericht designation | : | $D0_{1}$ |
Pearson symbol | : | cP16 |
Space group number | : | 198 |
Space group symbol | : | $\text{P2}_{1}\text{3}$ |
AFLOW prototype command | : | aflow --proto=A3B_cP16_198_b_a --params=$a$,$x_{1}$,$x_{2}$,$y_{2}$,$z_{2}$ |
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}+ x_{1} \, \mathbf{a}_{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(4a\right) & \text{N} \\ \mathbf{B}_{2} & = &\left(\frac12 - x_{1}\right) \, \mathbf{a}_{1}- x_{1} \, \mathbf{a}_{2}+ \left(\frac12 + x_{1}\right) \, \mathbf{a}_{3}& = &\left(\frac12 - x_{1}\right) \, a \, \mathbf{\hat{x}}- x_{1} \, a \, \mathbf{\hat{y}}+ \left(\frac12 + x_{1}\right) \, a \, \mathbf{\hat{z}}& \left(4a\right) & \text{N} \\ \mathbf{B}_{3} & = &- x_{1} \, \mathbf{a}_{1}+ \left(\frac12 + x_{1}\right) \, \mathbf{a}_{2}+ \left(\frac12 - x_{1}\right) \, \mathbf{a}_{3}& = &- x_{1} \, a \, \mathbf{\hat{x}}+ \left(\frac12 + x_{1}\right) \, a \, \mathbf{\hat{y}}+ \left(\frac12 - x_{1}\right) \, a \, \mathbf{\hat{z}}& \left(4a\right) & \text{N} \\ \mathbf{B}_{4} & = &+ \left(\frac12 + x_{1}\right) \, \mathbf{a}_{1}+ \left(\frac12 - x_{1}\right) \, \mathbf{a}_{2}- x_{1} \, \mathbf{a}_{3}& = &+ \left(\frac12 + x_{1}\right) \, a \, \mathbf{\hat{x}}+ \left(\frac12 - x_{1}\right) \, a \, \mathbf{\hat{y}}- x_{1} \, a \, \mathbf{\hat{z}}& \left(4a\right) & \text{N} \\ \mathbf{B}_{5} & = &x_{2} \, \mathbf{a}_{1}+ y_{2} \, \mathbf{a}_{2}+ z_{2} \, \mathbf{a}_{3}& = &x_{2} \, a \, \mathbf{\hat{x}}+ y_{2} \, a \, \mathbf{\hat{y}}+ z_{2} \, a \, \mathbf{\hat{z}}& \left(12b\right) & \text{H} \\ \mathbf{B}_{6} & = &\left(\frac12 - x_{2}\right) \, \mathbf{a}_{1}- y_{2} \, \mathbf{a}_{2}+ \left(\frac12 + z_{2}\right) \, \mathbf{a}_{3}& = &\left(\frac12 - x_{2}\right) \, a \, \mathbf{\hat{x}}- y_{2} \, a \, \mathbf{\hat{y}}+ \left(\frac12 + z_{2}\right) \, a \, \mathbf{\hat{z}}& \left(12b\right) & \text{H} \\ \mathbf{B}_{7} & = &- x_{2} \, \mathbf{a}_{1}+ \left(\frac12 + y_{2}\right) \, \mathbf{a}_{2}+ \left(\frac12 - z_{2}\right) \, \mathbf{a}_{3}& = &- x_{2} \, a \, \mathbf{\hat{x}}+ \left(\frac12 + y_{2}\right) \, a \, \mathbf{\hat{y}}+ \left(\frac12 - z_{2}\right) \, a \, \mathbf{\hat{z}}& \left(12b\right) & \text{H} \\ \mathbf{B}_{8} & = &+ \left(\frac12 + x_{2}\right) \, \mathbf{a}_{1}+ \left(\frac12 - y_{2}\right) \, \mathbf{a}_{2}- z_{2} \, \mathbf{a}_{3}& = &+ \left(\frac12 + x_{2}\right) \, a \, \mathbf{\hat{x}}+ \left(\frac12 - y_{2}\right) \, a \, \mathbf{\hat{y}}- z_{2} \, a \, \mathbf{\hat{z}}& \left(12b\right) & \text{H} \\ \mathbf{B}_{9} & = &z_{2} \, \mathbf{a}_{1}+ x_{2} \, \mathbf{a}_{2}+ y_{2} \, \mathbf{a}_{3}& = &z_{2} \, a \, \mathbf{\hat{x}}+ x_{2} \, a \, \mathbf{\hat{y}}+ y_{2} \, a \, \mathbf{\hat{z}}& \left(12b\right) & \text{H} \\ \mathbf{B}_{10} & = &\left(\frac12 - z_{2}\right) \, \mathbf{a}_{1}- x_{2} \, \mathbf{a}_{2}+ \left(\frac12 + y_{2}\right) \, \mathbf{a}_{3}& = &\left(\frac12 - z_{2}\right) \, a \, \mathbf{\hat{x}}- x_{2} \, a \, \mathbf{\hat{y}}+ \left(\frac12 + y_{2}\right) \, a \, \mathbf{\hat{z}}& \left(12b\right) & \text{H} \\ \mathbf{B}_{11} & = &- z_{2} \, \mathbf{a}_{1}+ \left(\frac12 + x_{2}\right) \, \mathbf{a}_{2}+ \left(\frac12 - y_{2}\right) \, \mathbf{a}_{3}& = &- z_{2} \, a \, \mathbf{\hat{x}}+ \left(\frac12 + x_{2}\right) \, a \, \mathbf{\hat{y}}+ \left(\frac12 - y_{2}\right) \, a \, \mathbf{\hat{z}}& \left(12b\right) & \text{H} \\ \mathbf{B}_{12} & = &+ \left(\frac12 + z_{2}\right) \, \mathbf{a}_{1}+ \left(\frac12 - x_{2}\right) \, \mathbf{a}_{2}- y_{2} \, \mathbf{a}_{3}& = &+ \left(\frac12 + z_{2}\right) \, a \, \mathbf{\hat{x}}+ \left(\frac12 - x_{2}\right) \, a \, \mathbf{\hat{y}}- y_{2} \, a \, \mathbf{\hat{z}}& \left(12b\right) & \text{H} \\ \mathbf{B}_{13} & = &y_{2} \, \mathbf{a}_{1}+ z_{2} \, \mathbf{a}_{2}+ x_{2} \, \mathbf{a}_{3}& = &y_{2} \, a \, \mathbf{\hat{x}}+ z_{2} \, a \, \mathbf{\hat{y}}+ x_{2} \, a \, \mathbf{\hat{z}}& \left(12b\right) & \text{H} \\ \mathbf{B}_{14} & = &\left(\frac12 - y_{2}\right) \, \mathbf{a}_{1}- z_{2} \, \mathbf{a}_{2}+ \left(\frac12 + x_{2}\right) \, \mathbf{a}_{3}& = &\left(\frac12 - y_{2}\right) \, a \, \mathbf{\hat{x}}- z_{2} \, a \, \mathbf{\hat{y}}+ \left(\frac12 + x_{2}\right) \, a \, \mathbf{\hat{z}}& \left(12b\right) & \text{H} \\ \mathbf{B}_{15} & = &- y_{2} \, \mathbf{a}_{1}+ \left(\frac12 + z_{2}\right) \, \mathbf{a}_{2}+ \left(\frac12 - x_{2}\right) \, \mathbf{a}_{3}& = &- y_{2} \, a \, \mathbf{\hat{x}}+ \left(\frac12 + z_{2}\right) \, a \, \mathbf{\hat{y}}+ \left(\frac12 - x_{2}\right) \, a \, \mathbf{\hat{z}}& \left(12b\right) & \text{H} \\ \mathbf{B}_{16} & = &+ \left(\frac12 + y_{2}\right) \, \mathbf{a}_{1}+ \left(\frac12 - z_{2}\right) \, \mathbf{a}_{2}- x_{2} \, \mathbf{a}_{3}& = &+ \left(\frac12 + y_{2}\right) \, a \, \mathbf{\hat{x}}+ \left(\frac12 - z_{2}\right) \, a \, \mathbf{\hat{y}}- x_{2} \, a \, \mathbf{\hat{z}}& \left(12b\right) & \text{H} \\ \end{array} \]