AFLOW Prototype: A4B3_cI28_220_c_a
Prototype | : | Th3P4 |
AFLOW prototype label | : | A4B3_cI28_220_c_a |
Strukturbericht designation | : | $D7_{3}$ |
Pearson symbol | : | cI28 |
Space group number | : | 220 |
Space group symbol | : | $I\bar{4}3d$ |
AFLOW prototype command | : | aflow --proto=A4B3_cI28_220_c_a --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{5}{8} \, \mathbf{a}_{2} + \frac{3}{8} \, \mathbf{a}_{3} & = & \frac{3}{8}a \, \mathbf{\hat{x}} + \frac{1}{4}a \, \mathbf{\hat{z}} & \left(12a\right) & \text{Th} \\ \mathbf{B}_{2} & = & \frac{3}{4} \, \mathbf{a}_{1} + \frac{7}{8} \, \mathbf{a}_{2} + \frac{1}{8} \, \mathbf{a}_{3} & = & \frac{1}{8}a \, \mathbf{\hat{x}} + \frac{3}{4}a \, \mathbf{\hat{z}} & \left(12a\right) & \text{Th} \\ \mathbf{B}_{3} & = & \frac{3}{8} \, \mathbf{a}_{1} + \frac{1}{4} \, \mathbf{a}_{2} + \frac{5}{8} \, \mathbf{a}_{3} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + \frac{3}{8}a \, \mathbf{\hat{y}} & \left(12a\right) & \text{Th} \\ \mathbf{B}_{4} & = & \frac{1}{8} \, \mathbf{a}_{1} + \frac{3}{4} \, \mathbf{a}_{2} + \frac{7}{8} \, \mathbf{a}_{3} & = & \frac{3}{4}a \, \mathbf{\hat{x}} + \frac{1}{8}a \, \mathbf{\hat{y}} & \left(12a\right) & \text{Th} \\ \mathbf{B}_{5} & = & \frac{5}{8} \, \mathbf{a}_{1} + \frac{3}{8} \, \mathbf{a}_{2} + \frac{1}{4} \, \mathbf{a}_{3} & = & \frac{1}{4}a \, \mathbf{\hat{y}} + \frac{3}{8}a \, \mathbf{\hat{z}} & \left(12a\right) & \text{Th} \\ \mathbf{B}_{6} & = & \frac{7}{8} \, \mathbf{a}_{1} + \frac{1}{8} \, \mathbf{a}_{2} + \frac{3}{4} \, \mathbf{a}_{3} & = & \frac{3}{4}a \, \mathbf{\hat{y}} + \frac{1}{8}a \, \mathbf{\hat{z}} & \left(12a\right) & \text{Th} \\ \mathbf{B}_{7} & = & 2x_{2} \, \mathbf{a}_{1} + 2x_{2} \, \mathbf{a}_{2} + 2x_{2} \, \mathbf{a}_{3} & = & x_{2}a \, \mathbf{\hat{x}} + x_{2}a \, \mathbf{\hat{y}} + x_{2}a \, \mathbf{\hat{z}} & \left(16c\right) & \text{P} \\ \mathbf{B}_{8} & = & \frac{1}{2} \, \mathbf{a}_{1} + \left(\frac{1}{2} - 2x_{2}\right) \, \mathbf{a}_{3} & = & -x_{2}a \, \mathbf{\hat{x}} + \left(\frac{1}{2} - x_{2}\right)a \, \mathbf{\hat{y}} + x_{2}a \, \mathbf{\hat{z}} & \left(16c\right) & \text{P} \\ \mathbf{B}_{9} & = & \left(\frac{1}{2} - 2x_{2}\right) \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \left(\frac{1}{2} - x_{2}\right)a \, \mathbf{\hat{x}} + x_{2}a \, \mathbf{\hat{y}}-x_{2}a \, \mathbf{\hat{z}} & \left(16c\right) & \text{P} \\ \mathbf{B}_{10} & = & \left(\frac{1}{2} - 2x_{2}\right) \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{2} & = & x_{2}a \, \mathbf{\hat{x}}-x_{2}a \, \mathbf{\hat{y}} + \left(\frac{1}{2} - x_{2}\right)a \, \mathbf{\hat{z}} & \left(16c\right) & \text{P} \\ \mathbf{B}_{11} & = & \left(\frac{1}{2} +2x_{2}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +2x_{2}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +2x_{2}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4} +x_{2}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4} +x_{2}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4} +x_{2}\right)a \, \mathbf{\hat{z}} & \left(16c\right) & \text{P} \\ \mathbf{B}_{12} & = & \frac{1}{2} \, \mathbf{a}_{1}-2x_{2} \, \mathbf{a}_{3} & = & -a\left(x_{2}+\frac{1}{4}\right) \, \mathbf{\hat{x}} + \left(\frac{1}{4} - x_{2}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4} +x_{2}\right)a \, \mathbf{\hat{z}} & \left(16c\right) & \text{P} \\ \mathbf{B}_{13} & = & -2x_{2} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{2} & = & \left(\frac{1}{4} +x_{2}\right)a \, \mathbf{\hat{x}}-a\left(x_{2}+\frac{1}{4}\right) \, \mathbf{\hat{y}} + \left(\frac{1}{4} - x_{2}\right)a \, \mathbf{\hat{z}} & \left(16c\right) & \text{P} \\ \mathbf{B}_{14} & = & -2x_{2} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \left(\frac{1}{4} - x_{2}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4} +x_{2}\right)a \, \mathbf{\hat{y}}-a\left(x_{2}+\frac{1}{4}\right) \, \mathbf{\hat{z}} & \left(16c\right) & \text{P} \\ \end{array} \]