AFLOW Prototype: A3B2_cP20_213_d_c
Prototype | : | Mg3Ru2 |
AFLOW prototype label | : | A3B2_cP20_213_d_c |
Strukturbericht designation | : | None |
Pearson symbol | : | cP20 |
Space group number | : | 213 |
Space group symbol | : | $P4_{1}32$ |
AFLOW prototype command | : | aflow --proto=A3B2_cP20_213_d_c --params=$a$,$x_{1}$,$y_{2}$ |
Basis vectors:
\[ \begin{array}{ccccccc} & & \text{Lattice Coordinates} & & \text{Cartesian Coordinates} &\text{Wyckoff Position} & \text{Atom Type} \\ \mathbf{B}_{1} & = & x_{1} \, \mathbf{a}_{1} + x_{1} \, \mathbf{a}_{2} + x_{1} \, \mathbf{a}_{3} & = & x_{1}a \, \mathbf{\hat{x}} + x_{1}a \, \mathbf{\hat{y}} + x_{1}a \, \mathbf{\hat{z}} & \left(8c\right) & \text{Ru} \\ \mathbf{B}_{2} & = & \left(\frac{1}{2} - x_{1}\right) \, \mathbf{a}_{1}-x_{1} \, \mathbf{a}_{2} + \left(\frac{1}{2} +x_{1}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-x_{1}\right)a \, \mathbf{\hat{x}}-x_{1}a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +x_{1}\right)a \, \mathbf{\hat{z}} & \left(8c\right) & \text{Ru} \\ \mathbf{B}_{3} & = & -x_{1} \, \mathbf{a}_{1} + \left(\frac{1}{2} +x_{1}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - x_{1}\right) \, \mathbf{a}_{3} & = & -x_{1}a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +x_{1}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{2}-x_{1}\right)a \, \mathbf{\hat{z}} & \left(8c\right) & \text{Ru} \\ \mathbf{B}_{4} & = & \left(\frac{1}{2} +x_{1}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - x_{1}\right) \, \mathbf{a}_{2}-x_{1} \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +x_{1}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2}-x_{1}\right)a \, \mathbf{\hat{y}}-x_{1}a \, \mathbf{\hat{z}} & \left(8c\right) & \text{Ru} \\ \mathbf{B}_{5} & = & \left(\frac{3}{4} +x_{1}\right) \, \mathbf{a}_{1} + \left(\frac{1}{4} +x_{1}\right) \, \mathbf{a}_{2} + \left(\frac{1}{4} - x_{1}\right) \, \mathbf{a}_{3} & = & \left(\frac{3}{4} +x_{1}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4} +x_{1}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4}-x_{1}\right)a \, \mathbf{\hat{z}} & \left(8c\right) & \text{Ru} \\ \mathbf{B}_{6} & = & \left(\frac{3}{4} - x_{1}\right) \, \mathbf{a}_{1} + \left(\frac{3}{4} - x_{1}\right) \, \mathbf{a}_{2} + \left(\frac{3}{4} - x_{1}\right) \, \mathbf{a}_{3} & = & \left(\frac{3}{4}-x_{1}\right)a \, \mathbf{\hat{x}} + \left(\frac{3}{4}-x_{1}\right)a \, \mathbf{\hat{y}} + \left(\frac{3}{4}-x_{1}\right)a \, \mathbf{\hat{z}} & \left(8c\right) & \text{Ru} \\ \mathbf{B}_{7} & = & \left(\frac{1}{4} +x_{1}\right) \, \mathbf{a}_{1} + \left(\frac{1}{4} - x_{1}\right) \, \mathbf{a}_{2} + \left(\frac{3}{4} +x_{1}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4} +x_{1}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4}-x_{1}\right)a \, \mathbf{\hat{y}} + \left(\frac{3}{4} +x_{1}\right)a \, \mathbf{\hat{z}} & \left(8c\right) & \text{Ru} \\ \mathbf{B}_{8} & = & \left(\frac{1}{4} - x_{1}\right) \, \mathbf{a}_{1} + \left(\frac{3}{4} +x_{1}\right) \, \mathbf{a}_{2} + \left(\frac{1}{4} +x_{1}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4}-x_{1}\right)a \, \mathbf{\hat{x}} + \left(\frac{3}{4} +x_{1}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4} +x_{1}\right)a \, \mathbf{\hat{z}} & \left(8c\right) & \text{Ru} \\ \mathbf{B}_{9} & = & \frac{1}{8} \, \mathbf{a}_{1} + y_{2} \, \mathbf{a}_{2} + \left(\frac{1}{4} +y_{2}\right) \, \mathbf{a}_{3} & = & \frac{1}{8}a \, \mathbf{\hat{x}} + y_{2}a \, \mathbf{\hat{y}} + \left(\frac{1}{4} +y_{2}\right)a \, \mathbf{\hat{z}} & \left(12d\right) & \text{Mg} \\ \mathbf{B}_{10} & = & \frac{3}{8} \, \mathbf{a}_{1}-y_{2} \, \mathbf{a}_{2} + \left(\frac{3}{4} +y_{2}\right) \, \mathbf{a}_{3} & = & \frac{3}{8}a \, \mathbf{\hat{x}}-y_{2}a \, \mathbf{\hat{y}} + \left(\frac{3}{4} +y_{2}\right)a \, \mathbf{\hat{z}} & \left(12d\right) & \text{Mg} \\ \mathbf{B}_{11} & = & \frac{7}{8} \, \mathbf{a}_{1} + \left(\frac{1}{2} +y_{2}\right) \, \mathbf{a}_{2} + \left(\frac{1}{4} - y_{2}\right) \, \mathbf{a}_{3} & = & \frac{7}{8}a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +y_{2}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4}-y_{2}\right)a \, \mathbf{\hat{z}} & \left(12d\right) & \text{Mg} \\ \mathbf{B}_{12} & = & \frac{5}{8} \, \mathbf{a}_{1} + \left(\frac{1}{2} - y_{2}\right) \, \mathbf{a}_{2} + \left(\frac{3}{4} - y_{2}\right) \, \mathbf{a}_{3} & = & \frac{5}{8}a \, \mathbf{\hat{x}} + \left(\frac{1}{2}-y_{2}\right)a \, \mathbf{\hat{y}} + \left(\frac{3}{4}-y_{2}\right)a \, \mathbf{\hat{z}} & \left(12d\right) & \text{Mg} \\ \mathbf{B}_{13} & = & \left(\frac{1}{4} +y_{2}\right) \, \mathbf{a}_{1} + \frac{1}{8} \, \mathbf{a}_{2} + y_{2} \, \mathbf{a}_{3} & = & \left(\frac{1}{4} +y_{2}\right)a \, \mathbf{\hat{x}} + \frac{1}{8}a \, \mathbf{\hat{y}} + y_{2}a \, \mathbf{\hat{z}} & \left(12d\right) & \text{Mg} \\ \mathbf{B}_{14} & = & \left(\frac{3}{4} +y_{2}\right) \, \mathbf{a}_{1} + \frac{3}{8} \, \mathbf{a}_{2}-y_{2} \, \mathbf{a}_{3} & = & \left(\frac{3}{4} +y_{2}\right)a \, \mathbf{\hat{x}} + \frac{3}{8}a \, \mathbf{\hat{y}}-y_{2}a \, \mathbf{\hat{z}} & \left(12d\right) & \text{Mg} \\ \mathbf{B}_{15} & = & \left(\frac{1}{4} - y_{2}\right) \, \mathbf{a}_{1} + \frac{7}{8} \, \mathbf{a}_{2} + \left(\frac{1}{2} +y_{2}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4}-y_{2}\right)a \, \mathbf{\hat{x}} + \frac{7}{8}a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +y_{2}\right)a \, \mathbf{\hat{z}} & \left(12d\right) & \text{Mg} \\ \mathbf{B}_{16} & = & \left(\frac{3}{4} - y_{2}\right) \, \mathbf{a}_{1} + \frac{5}{8} \, \mathbf{a}_{2} + \left(\frac{1}{2} - y_{2}\right) \, \mathbf{a}_{3} & = & \left(\frac{3}{4}-y_{2}\right)a \, \mathbf{\hat{x}} + \frac{5}{8}a \, \mathbf{\hat{y}} + \left(\frac{1}{2}-y_{2}\right)a \, \mathbf{\hat{z}} & \left(12d\right) & \text{Mg} \\ \mathbf{B}_{17} & = & y_{2} \, \mathbf{a}_{1} + \left(\frac{1}{4} +y_{2}\right) \, \mathbf{a}_{2} + \frac{1}{8} \, \mathbf{a}_{3} & = & y_{2}a \, \mathbf{\hat{x}} + \left(\frac{1}{4} +y_{2}\right)a \, \mathbf{\hat{y}} + \frac{1}{8}a \, \mathbf{\hat{z}} & \left(12d\right) & \text{Mg} \\ \mathbf{B}_{18} & = & -y_{2} \, \mathbf{a}_{1} + \left(\frac{3}{4} +y_{2}\right) \, \mathbf{a}_{2} + \frac{3}{8} \, \mathbf{a}_{3} & = & -y_{2}a \, \mathbf{\hat{x}} + \left(\frac{3}{4} +y_{2}\right)a \, \mathbf{\hat{y}} + \frac{3}{8}a \, \mathbf{\hat{z}} & \left(12d\right) & \text{Mg} \\ \mathbf{B}_{19} & = & \left(\frac{1}{2} +y_{2}\right) \, \mathbf{a}_{1} + \left(\frac{1}{4} - y_{2}\right) \, \mathbf{a}_{2} + \frac{7}{8} \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +y_{2}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4}-y_{2}\right)a \, \mathbf{\hat{y}} + \frac{7}{8}a \, \mathbf{\hat{z}} & \left(12d\right) & \text{Mg} \\ \mathbf{B}_{20} & = & \left(\frac{1}{2} - y_{2}\right) \, \mathbf{a}_{1} + \left(\frac{3}{4} - y_{2}\right) \, \mathbf{a}_{2} + \frac{5}{8} \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-y_{2}\right)a \, \mathbf{\hat{x}} + \left(\frac{3}{4}-y_{2}\right)a \, \mathbf{\hat{y}} + \frac{5}{8}a \, \mathbf{\hat{z}} & \left(12d\right) & \text{Mg} \\ \end{array} \]