AFLOW Prototype: AB2_cF48_227_c_e
Prototype | : | CTi2 |
AFLOW prototype label | : | AB2_cF48_227_c_e |
Strukturbericht designation | : | None |
Pearson symbol | : | cF48 |
Space group number | : | 227 |
Space group symbol | : | $\text{Fd}\bar{3}\text{m}$ |
AFLOW prototype command | : | aflow --proto=AB2_cF48_227_c_e --params=$a$,$x_{2}$ |
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{C} \\ \mathbf{B}_{2} & = &\frac12 \mathbf{a}_{3}& = &\frac14 \, a \, \mathbf{\hat{x}}+ \frac14 \, a \, \mathbf{\hat{y}}& \left(16c\right) & \text{C} \\ \mathbf{B}_{3} & = &\frac12 \mathbf{a}_{2}& = &\frac14 \, a \, \mathbf{\hat{x}}+ \frac14 \, a \, \mathbf{\hat{z}}& \left(16c\right) & \text{C} \\ \mathbf{B}_{4} & = &\frac12 \mathbf{a}_{1}& = &\frac14 \, a \, \mathbf{\hat{y}}+ \frac14 \, a \, \mathbf{\hat{z}}& \left(16c\right) & \text{C} \\ \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{Ti} \\ \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{Ti} \\ \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{Ti} \\ \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{Ti} \\ \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{Ti} \\ \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{Ti} \\ \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{Ti} \\ \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{Ti} \\ \end{array} \]