AFLOW Prototype: AB2_cF96_227_e_cf
Prototype | : | NiTi2 |
AFLOW prototype label | : | AB2_cF96_227_e_cf |
Strukturbericht designation | : | None |
Pearson symbol | : | cF96 |
Space group number | : | 227 |
Space group symbol | : | $\text{Fd}\bar{3}\text{m}$ |
AFLOW prototype command | : | aflow --proto=AB2_cF96_227_e_cf --params=$a$,$x_{2}$,$x_{3}$ |
Basis vectors:
\[ \begin{array}{ccccccc} & & \text{Lattice Coordinates} & & \text{Cartesian Coordinates} &\text{Wyckoff Position} & \text{Atom Type} \\ \mathbf{B}_{1} & = &0 \, \mathbf{a}_{1} + 0 \, \mathbf{a}_{2} + 0 \, \mathbf{a}_{3} & = &0 \mathbf{\hat{x}} + 0 \mathbf{\hat{y}} + 0 \mathbf{\hat{z}} & \left(16c\right) & \text{Ti I} \\ \mathbf{B}_{2} & = &\frac12 \mathbf{a}_{3}& = &\frac14 \, a \, \mathbf{\hat{x}}+ \frac14 \, a \, \mathbf{\hat{y}}& \left(16c\right) & \text{Ti I} \\ \mathbf{B}_{3} & = &\frac12 \mathbf{a}_{2}& = &\frac14 \, a \, \mathbf{\hat{x}}+ \frac14 \, a \, \mathbf{\hat{z}}& \left(16c\right) & \text{Ti I} \\ \mathbf{B}_{4} & = &\frac12 \mathbf{a}_{1}& = &\frac14 \, a \, \mathbf{\hat{y}}+ \frac14 \, a \, \mathbf{\hat{z}}& \left(16c\right) & \text{Ti I} \\ \mathbf{B}_{5} & = &x_{2} \mathbf{a}_{1}+ x_{2} \mathbf{a}_{2}+ x_{2} \mathbf{a}_{3}& = &x_{2} \, a \, \mathbf{\hat{x}}+ x_{2} \, a \, \mathbf{\hat{y}}+ x_{2} \, a \, \mathbf{\hat{z}}& \left(32e\right) & \text{Ni} \\ \mathbf{B}_{6} & = &x_{2} \mathbf{a}_{1}+ x_{2} \mathbf{a}_{2}+ \left(\frac12 - 3 \, x_{2}\right) \mathbf{a}_{3}& = &\left(\frac14 - x_{2}\right) \, a \, \mathbf{\hat{x}}+ \left(\frac14 - x_{2}\right) \, a \, \mathbf{\hat{y}}+ x_{2} \, a \, \mathbf{\hat{z}}& \left(32e\right) & \text{Ni} \\ \mathbf{B}_{7} & = &x_{2} \mathbf{a}_{1}+ \left(\frac12 - 3 \, x_{2}\right) \mathbf{a}_{2}+ x_{2} \mathbf{a}_{3}& = &\left(\frac14 - x_{2}\right) \, a \, \mathbf{\hat{x}}+ x_{2} \, a \, \mathbf{\hat{y}}+ \left(\frac14 - x_{2}\right) \, a \, \mathbf{\hat{z}}& \left(32e\right) & \text{Ni} \\ \mathbf{B}_{8} & = &\left(\frac12 - 3 \, x_{2}\right) \mathbf{a}_{1}+ x_{2} \mathbf{a}_{2}+ x_{2} \mathbf{a}_{3}& = &x_{2} \, a \, \mathbf{\hat{x}}+ \left(\frac14 - x_{2}\right) \, a \, \mathbf{\hat{y}}+ \left(\frac14 - x_{2}\right) \, a \, \mathbf{\hat{z}}& \left(32e\right) & \text{Ni} \\ \mathbf{B}_{9} & = &- x_{2} \mathbf{a}_{1}- x_{2} \mathbf{a}_{2}+ \left(\frac12 + 3 \, x_{2}\right) \mathbf{a}_{3}& = &\left(\frac14 + x_{2}\right) \, a \, \mathbf{\hat{x}}+ \left(\frac14 + x_{2}\right) \, a \, \mathbf{\hat{y}}- x_{2} \, a \, \mathbf{\hat{z}}& \left(32e\right) & \text{Ni} \\ \mathbf{B}_{10} & = &- x_{2} \mathbf{a}_{1}- x_{2} \mathbf{a}_{2}- x_{2} \mathbf{a}_{3}& = &- x_{2} \, a \, \mathbf{\hat{x}}- x_{2} \, a \, \mathbf{\hat{y}}- x_{2} \, a \, \mathbf{\hat{z}}& \left(32e\right) & \text{Ni} \\ \mathbf{B}_{11} & = &- x_{2} \mathbf{a}_{1}+ \left(\frac12 + 3 \, x_{2}\right) \mathbf{a}_{2}- x_{2} \mathbf{a}_{3}& = &\left(\frac14 + x_{2}\right) \, a \, \mathbf{\hat{x}}- x_{2} \, a \, \mathbf{\hat{y}}+ \left(\frac14 + x_{2}\right) \, a \, \mathbf{\hat{z}}& \left(32e\right) & \text{Ni} \\ \mathbf{B}_{12} & = &\left(\frac12 + 3 \, x_{2}\right) \mathbf{a}_{1}- x_{2} \mathbf{a}_{2}- x_{2} \mathbf{a}_{3}& = &- x_{2} \, a \, \mathbf{\hat{x}}+ \left(\frac14 + x_{2}\right) \, a \, \mathbf{\hat{y}}+ \left(\frac14 + x_{2}\right) \, a \, \mathbf{\hat{z}}& \left(32e\right) & \text{Ni} \\ \mathbf{B}_{13} & = &\left(\frac14 - x_{3}\right) \mathbf{a}_{1}+ x_{3} \mathbf{a}_{2}+ x_{3} \mathbf{a}_{3}& = &x_{3} \, a \, \mathbf{\hat{x}}+ \frac18 \, a \, \mathbf{\hat{y}}+ \frac18 \, a \, \mathbf{\hat{z}}& \left(48f\right) & \text{Ti II} \\ \mathbf{B}_{14} & = &x_{3} \mathbf{a}_{1}+ \left(\frac14 - x_{3}\right) \mathbf{a}_{2}+ \left(\frac14 - x_{3}\right) \mathbf{a}_{3}& = &\left(\frac14 - x_{3}\right) \, a \, \mathbf{\hat{x}}+ \frac18 \, a \, \mathbf{\hat{y}}+ \frac18 \, a \, \mathbf{\hat{z}}& \left(48f\right) & \text{Ti II} \\ \mathbf{B}_{15} & = &x_{3} \mathbf{a}_{1}+ \left(\frac14 - x_{3}\right) \mathbf{a}_{2}+ x_{3} \mathbf{a}_{3}& = &\frac18 \, a \, \mathbf{\hat{x}}+ x_{3} \, a \, \mathbf{\hat{y}}+ \frac18 \, a \, \mathbf{\hat{z}}& \left(48f\right) & \text{Ti II} \\ \mathbf{B}_{16} & = &\left(\frac14 - x_{3}\right) \mathbf{a}_{1}+ x_{3} \mathbf{a}_{2}+ \left(\frac14 - x_{3}\right) \mathbf{a}_{3}& = &\frac18 \, a \, \mathbf{\hat{x}}+ \left(\frac14 - x_{3}\right) \, a \, \mathbf{\hat{y}}+ \frac18 \, a \, \mathbf{\hat{z}}& \left(48f\right) & \text{Ti II} \\ \mathbf{B}_{17} & = &x_{3} \mathbf{a}_{1}+ x_{3} \mathbf{a}_{2}+ \left(\frac14 - x_{3}\right) \mathbf{a}_{3}& = &\frac18 \, a \, \mathbf{\hat{x}}+ \frac18 \, a \, \mathbf{\hat{y}}+ x_{3} \, a \, \mathbf{\hat{z}}& \left(48f\right) & \text{Ti II} \\ \mathbf{B}_{18} & = &\left(\frac14 - x_{3}\right) \mathbf{a}_{1}+ \left(\frac14 - x_{3}\right) \mathbf{a}_{2}+ x_{3} \mathbf{a}_{3}& = &\frac18 \, a \, \mathbf{\hat{x}}+ \frac18 \, a \, \mathbf{\hat{y}}+ \left(\frac14 - x_{3}\right) \, a \, \mathbf{\hat{z}}& \left(48f\right) & \text{Ti II} \\ \mathbf{B}_{19} & = &\left(x_{3} + \frac34\right) \mathbf{a}_{1}- x_{3} \mathbf{a}_{2}+ \left(x_{3} + \frac34\right) \mathbf{a}_{3}& = &\frac38 \, a \, \mathbf{\hat{x}}+ \left(x_{3} + \frac34\right) \, a \, \mathbf{\hat{y}}+ \frac38 \, a \, \mathbf{\hat{z}}& \left(48f\right) & \text{Ti II} \\ \mathbf{B}_{20} & = &- x_{3} \mathbf{a}_{1}+ \left(x_{3} + \frac34\right) \mathbf{a}_{2}- x_{3} \mathbf{a}_{3}& = &\frac38 \, a \, \mathbf{\hat{x}}- x_{3} \, a \, \mathbf{\hat{y}}+ \frac38 \, a \, \mathbf{\hat{z}}& \left(48f\right) & \text{Ti II} \\ \mathbf{B}_{21} & = &- x_{3} \mathbf{a}_{1}+ \left(x_{3} + \frac34\right) \mathbf{a}_{2}+ \left(x_{3} + \frac34\right) \mathbf{a}_{3}& = &\left(x_{3} + \frac34\right) \, a \, \mathbf{\hat{x}}+ \frac38 \, a \, \mathbf{\hat{y}}+ \frac38 \, a \, \mathbf{\hat{z}}& \left(48f\right) & \text{Ti II} \\ \mathbf{B}_{22} & = &\left(x_{3} + \frac34\right) \mathbf{a}_{1}- x_{3} \mathbf{a}_{2}- x_{3} \mathbf{a}_{3}& = &- x_{3} \, a \, \mathbf{\hat{x}}+ \frac38 \, a \, \mathbf{\hat{y}}+ \frac38 \, a \, \mathbf{\hat{z}}& \left(48f\right) & \text{Ti II} \\ \mathbf{B}_{23} & = &- x_{3} \mathbf{a}_{1}- x_{3} \mathbf{a}_{2}+ \left(x_{3} + \frac34\right) \mathbf{a}_{3}& = &\frac38 \, a \, \mathbf{\hat{x}}+ \frac38 \, a \, \mathbf{\hat{y}}- x_{3} \, a \, \mathbf{\hat{z}}& \left(48f\right) & \text{Ti II} \\ \mathbf{B}_{24} & = &+ \left(x_{3} + \frac34\right) \mathbf{a}_{1}+ \left(x_{3} + \frac34\right) \mathbf{a}_{2}- x_{3} \mathbf{a}_{3}& = &\frac38 \, a \, \mathbf{\hat{x}}+ \frac38 \, a \, \mathbf{\hat{y}}+ \left(x_{3} + \frac34\right) \, a \, \mathbf{\hat{z}}& \left(48f\right) & \text{Ti II} \\ \end{array} \]