AFLOW Prototype: A3B_cP16_208_j_b
Prototype | : | PH3 |
AFLOW prototype label | : | A3B_cP16_208_j_b |
Strukturbericht designation | : | None |
Pearson symbol | : | cP16 |
Space group number | : | 208 |
Space group symbol | : | $P4_{2}32$ |
AFLOW prototype command | : | aflow --proto=A3B_cP16_208_j_b --params=$a$,$x_{2}$ |
Basis vectors:
\[ \begin{array}{ccccccc} & & \text{Lattice Coordinates} & & \text{Cartesian Coordinates} &\text{Wyckoff Position} & \text{Atom Type} \\ \mathbf{B}_{1} & = & \frac{1}{4} \, \mathbf{a}_{1} + \frac{1}{4} \, \mathbf{a}_{2} + \frac{1}{4} \, \mathbf{a}_{3} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + \frac{1}{4}a \, \mathbf{\hat{y}} + \frac{1}{4}a \, \mathbf{\hat{z}} & \left(4b\right) & \text{P} \\ \mathbf{B}_{2} & = & \frac{3}{4} \, \mathbf{a}_{1} + \frac{3}{4} \, \mathbf{a}_{2} + \frac{1}{4} \, \mathbf{a}_{3} & = & \frac{3}{4}a \, \mathbf{\hat{x}} + \frac{3}{4}a \, \mathbf{\hat{y}} + \frac{1}{4}a \, \mathbf{\hat{z}} & \left(4b\right) & \text{P} \\ \mathbf{B}_{3} & = & \frac{3}{4} \, \mathbf{a}_{1} + \frac{1}{4} \, \mathbf{a}_{2} + \frac{3}{4} \, \mathbf{a}_{3} & = & \frac{3}{4}a \, \mathbf{\hat{x}} + \frac{1}{4}a \, \mathbf{\hat{y}} + \frac{3}{4}a \, \mathbf{\hat{z}} & \left(4b\right) & \text{P} \\ \mathbf{B}_{4} & = & \frac{1}{4} \, \mathbf{a}_{1} + \frac{3}{4} \, \mathbf{a}_{2} + \frac{3}{4} \, \mathbf{a}_{3} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + \frac{3}{4}a \, \mathbf{\hat{y}} + \frac{3}{4}a \, \mathbf{\hat{z}} & \left(4b\right) & \text{P} \\ \mathbf{B}_{5} & = & x_{2} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{2} & = & x_{2}a \, \mathbf{\hat{x}} + \frac{1}{2}a \, \mathbf{\hat{y}} & \left(12j\right) & \text{H} \\ \mathbf{B}_{6} & = & -x_{2} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{2} & = & -x_{2}a \, \mathbf{\hat{x}} + \frac{1}{2}a \, \mathbf{\hat{y}} & \left(12j\right) & \text{H} \\ \mathbf{B}_{7} & = & x_{2} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & x_{2}a \, \mathbf{\hat{y}} + \frac{1}{2}a \, \mathbf{\hat{z}} & \left(12j\right) & \text{H} \\ \mathbf{B}_{8} & = & -x_{2} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & -x_{2}a \, \mathbf{\hat{y}} + \frac{1}{2}a \, \mathbf{\hat{z}} & \left(12j\right) & \text{H} \\ \mathbf{B}_{9} & = & \frac{1}{2} \, \mathbf{a}_{1} + x_{2} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + x_{2}a \, \mathbf{\hat{z}} & \left(12j\right) & \text{H} \\ \mathbf{B}_{10} & = & \frac{1}{2} \, \mathbf{a}_{1}-x_{2} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}}-x_{2}a \, \mathbf{\hat{z}} & \left(12j\right) & \text{H} \\ \mathbf{B}_{11} & = & \left(\frac{1}{2} +x_{2}\right) \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +x_{2}\right)a \, \mathbf{\hat{y}} + \frac{1}{2}a \, \mathbf{\hat{z}} & \left(12j\right) & \text{H} \\ \mathbf{B}_{12} & = & \left(\frac{1}{2} - x_{2}\right) \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \left(\frac{1}{2} - x_{2}\right)a \, \mathbf{\hat{y}} + \frac{1}{2}a \, \mathbf{\hat{z}} & \left(12j\right) & \text{H} \\ \mathbf{B}_{13} & = & \left(\frac{1}{2} +x_{2}\right) \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{2} & = & \left(\frac{1}{2} +x_{2}\right)a \, \mathbf{\hat{x}} + \frac{1}{2}a \, \mathbf{\hat{y}} & \left(12j\right) & \text{H} \\ \mathbf{B}_{14} & = & \left(\frac{1}{2} - x_{2}\right) \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{2} & = & \left(\frac{1}{2} - x_{2}\right)a \, \mathbf{\hat{x}} + \frac{1}{2}a \, \mathbf{\hat{y}} & \left(12j\right) & \text{H} \\ \mathbf{B}_{15} & = & \frac{1}{2} \, \mathbf{a}_{1} + \left(\frac{1}{2} - x_{2}\right) \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + \left(\frac{1}{2} - x_{2}\right)a \, \mathbf{\hat{z}} & \left(12j\right) & \text{H} \\ \mathbf{B}_{16} & = & \frac{1}{2} \, \mathbf{a}_{1} + \left(\frac{1}{2} +x_{2}\right) \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +x_{2}\right)a \, \mathbf{\hat{z}} & \left(12j\right) & \text{H} \\ \end{array} \]