AFLOW Prototype: AB2_cI36_199_b_c
Prototype | : | NO2 |
AFLOW prototype label | : | AB2_cI36_199_b_c |
Strukturbericht designation | : | $C26_{a}$ |
Pearson symbol | : | cI36 |
Space group number | : | 199 |
Space group symbol | : | $I2_{1}3$ |
AFLOW prototype command | : | aflow --proto=AB2_cI36_199_b_c --params=$a$,$x_{1}$,$x_{2}$,$y_{2}$,$z_{2}$ |
making this proposed structure very unlikely.
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} + \left(\frac{1}{4} +x_{1}\right) \, \mathbf{a}_{2} + x_{1} \, \mathbf{a}_{3} & = & x_{1}a \, \mathbf{\hat{x}} + \frac{1}{4}a \, \mathbf{\hat{z}} & \left(12b\right) & \text{N} \\ \mathbf{B}_{2} & = & \frac{3}{4} \, \mathbf{a}_{1} + \left(\frac{1}{4} - x_{1}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - x_{1}\right) \, \mathbf{a}_{3} & = & -x_{1}a \, \mathbf{\hat{x}} + \frac{1}{2}a \, \mathbf{\hat{y}} + \frac{1}{4}a \, \mathbf{\hat{z}} & \left(12b\right) & \text{N} \\ \mathbf{B}_{3} & = & x_{1} \, \mathbf{a}_{1} + \frac{1}{4} \, \mathbf{a}_{2} + \left(\frac{1}{4} +x_{1}\right) \, \mathbf{a}_{3} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + x_{1}a \, \mathbf{\hat{y}} & \left(12b\right) & \text{N} \\ \mathbf{B}_{4} & = & \left(\frac{1}{2} - x_{1}\right) \, \mathbf{a}_{1} + \frac{3}{4} \, \mathbf{a}_{2} + \left(\frac{1}{4} - x_{1}\right) \, \mathbf{a}_{3} & = & \frac{1}{4}a \, \mathbf{\hat{x}}-x_{1}a \, \mathbf{\hat{y}} + \frac{1}{2}a \, \mathbf{\hat{z}} & \left(12b\right) & \text{N} \\ \mathbf{B}_{5} & = & \left(\frac{1}{4} +x_{1}\right) \, \mathbf{a}_{1} + x_{1} \, \mathbf{a}_{2} + \frac{1}{4} \, \mathbf{a}_{3} & = & \frac{1}{4}a \, \mathbf{\hat{y}} + x_{1}a \, \mathbf{\hat{z}} & \left(12b\right) & \text{N} \\ \mathbf{B}_{6} & = & \left(\frac{1}{4} - x_{1}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - x_{1}\right) \, \mathbf{a}_{2} + \frac{3}{4} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + \frac{1}{4}a \, \mathbf{\hat{y}}-x_{1}a \, \mathbf{\hat{z}} & \left(12b\right) & \text{N} \\ \mathbf{B}_{7} & = & \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}a \, \mathbf{\hat{z}} & \left(24c\right) & \text{O} \\ \mathbf{B}_{8} & = & \left(\frac{1}{2} - y_{2} + z_{2}\right) \, \mathbf{a}_{1} + \left(-x_{2}+z_{2}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - x_{2} - y_{2}\right) \, \mathbf{a}_{3} & = & -x_{2}a \, \mathbf{\hat{x}} + \left(\frac{1}{2}-y_{2}\right)a \, \mathbf{\hat{y}} + z_{2}a \, \mathbf{\hat{z}} & \left(24c\right) & \text{O} \\ \mathbf{B}_{9} & = & \left(y_{2}-z_{2}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - x_{2} - z_{2}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - x_{2} + y_{2}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-x_{2}\right)a \, \mathbf{\hat{x}} + y_{2}a \, \mathbf{\hat{y}}-z_{2}a \, \mathbf{\hat{z}} & \left(24c\right) & \text{O} \\ \mathbf{B}_{10} & = & \left(\frac{1}{2} - y_{2} - z_{2}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +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}} + \left(\frac{1}{2}-z_{2}\right)a \, \mathbf{\hat{z}} & \left(24c\right) & \text{O} \\ \mathbf{B}_{11} & = & \left(x_{2}+y_{2}\right) \, \mathbf{a}_{1} + \left(y_{2}+z_{2}\right) \, \mathbf{a}_{2} + \left(x_{2}+z_{2}\right) \, \mathbf{a}_{3} & = & z_{2}a \, \mathbf{\hat{x}} + x_{2}a \, \mathbf{\hat{y}} + y_{2}a \, \mathbf{\hat{z}} & \left(24c\right) & \text{O} \\ \mathbf{B}_{12} & = & \left(\frac{1}{2} - x_{2} - y_{2}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - y_{2} + z_{2}\right) \, \mathbf{a}_{2} + \left(-x_{2}+z_{2}\right) \, \mathbf{a}_{3} & = & z_{2}a \, \mathbf{\hat{x}}-x_{2}a \, \mathbf{\hat{y}} + \left(\frac{1}{2}-y_{2}\right)a \, \mathbf{\hat{z}} & \left(24c\right) & \text{O} \\ \mathbf{B}_{13} & = & \left(\frac{1}{2} - x_{2} + y_{2}\right) \, \mathbf{a}_{1} + \left(y_{2}-z_{2}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - x_{2} - z_{2}\right) \, \mathbf{a}_{3} & = & -z_{2}a \, \mathbf{\hat{x}} + \left(\frac{1}{2}-x_{2}\right)a \, \mathbf{\hat{y}} + y_{2}a \, \mathbf{\hat{z}} & \left(24c\right) & \text{O} \\ \mathbf{B}_{14} & = & \left(x_{2}-y_{2}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - y_{2} - z_{2}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +x_{2} - z_{2}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-z_{2}\right)a \, \mathbf{\hat{x}} + x_{2}a \, \mathbf{\hat{y}}-y_{2}a \, \mathbf{\hat{z}} & \left(24c\right) & \text{O} \\ \mathbf{B}_{15} & = & \left(x_{2}+z_{2}\right) \, \mathbf{a}_{1} + \left(x_{2}+y_{2}\right) \, \mathbf{a}_{2} + \left(y_{2}+z_{2}\right) \, \mathbf{a}_{3} & = & y_{2}a \, \mathbf{\hat{x}} + z_{2}a \, \mathbf{\hat{y}} + x_{2}a \, \mathbf{\hat{z}} & \left(24c\right) & \text{O} \\ \mathbf{B}_{16} & = & \left(-x_{2}+z_{2}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - x_{2} - y_{2}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - y_{2} + z_{2}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-y_{2}\right)a \, \mathbf{\hat{x}} + z_{2}a \, \mathbf{\hat{y}}-x_{2}a \, \mathbf{\hat{z}} & \left(24c\right) & \text{O} \\ \mathbf{B}_{17} & = & \left(\frac{1}{2} - x_{2} - z_{2}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - x_{2} + y_{2}\right) \, \mathbf{a}_{2} + \left(y_{2}-z_{2}\right) \, \mathbf{a}_{3} & = & y_{2}a \, \mathbf{\hat{x}}-z_{2}a \, \mathbf{\hat{y}} + \left(\frac{1}{2}-x_{2}\right)a \, \mathbf{\hat{z}} & \left(24c\right) & \text{O} \\ \mathbf{B}_{18} & = & \left(\frac{1}{2} +x_{2} - z_{2}\right) \, \mathbf{a}_{1} + \left(x_{2}-y_{2}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - y_{2} - z_{2}\right) \, \mathbf{a}_{3} & = & -y_{2}a \, \mathbf{\hat{x}} + \left(\frac{1}{2}-z_{2}\right)a \, \mathbf{\hat{y}} + x_{2}a \, \mathbf{\hat{z}} & \left(24c\right) & \text{O} \\ \end{array} \]