AFLOW Prototype: A2BC3_cP24_213_c_a_d
Prototype | : | Al2CMo3 |
AFLOW prototype label | : | A2BC3_cP24_213_c_a_d |
Strukturbericht designation | : | None |
Pearson symbol | : | cP24 |
Space group number | : | 213 |
Space group symbol | : | $P4_{1}32$ |
AFLOW prototype command | : | aflow --proto=A2BC3_cP24_213_c_a_d --params=$a$,$x_{2}$,$y_{3}$ |
filled$\beta$–Mn ($A13$) structure, with the aluminum and molybdenum atoms almost exactly on the sites of the manganese atoms in $A13$.
Basis vectors:
\[ \begin{array}{ccccccc} & & \text{Lattice Coordinates} & & \text{Cartesian Coordinates} &\text{Wyckoff Position} & \text{Atom Type} \\ \mathbf{B}_{1} & = & \frac{3}{8} \, \mathbf{a}_{1} + \frac{3}{8} \, \mathbf{a}_{2} + \frac{3}{8} \, \mathbf{a}_{3} & = & \frac{3}{8}a \, \mathbf{\hat{x}} + \frac{3}{8}a \, \mathbf{\hat{y}} + \frac{3}{8}a \, \mathbf{\hat{z}} & \left(4a\right) & \text{C} \\ \mathbf{B}_{2} & = & \frac{1}{8} \, \mathbf{a}_{1} + \frac{5}{8} \, \mathbf{a}_{2} + \frac{7}{8} \, \mathbf{a}_{3} & = & \frac{1}{8}a \, \mathbf{\hat{x}} + \frac{5}{8}a \, \mathbf{\hat{y}} + \frac{7}{8}a \, \mathbf{\hat{z}} & \left(4a\right) & \text{C} \\ \mathbf{B}_{3} & = & \frac{5}{8} \, \mathbf{a}_{1} + \frac{7}{8} \, \mathbf{a}_{2} + \frac{1}{8} \, \mathbf{a}_{3} & = & \frac{5}{8}a \, \mathbf{\hat{x}} + \frac{7}{8}a \, \mathbf{\hat{y}} + \frac{1}{8}a \, \mathbf{\hat{z}} & \left(4a\right) & \text{C} \\ \mathbf{B}_{4} & = & \frac{7}{8} \, \mathbf{a}_{1} + \frac{1}{8} \, \mathbf{a}_{2} + \frac{5}{8} \, \mathbf{a}_{3} & = & \frac{7}{8}a \, \mathbf{\hat{x}} + \frac{1}{8}a \, \mathbf{\hat{y}} + \frac{5}{8}a \, \mathbf{\hat{z}} & \left(4a\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(8c\right) & \text{Al} \\ \mathbf{B}_{6} & = & \left(\frac{1}{2} - x_{2}\right) \, \mathbf{a}_{1}-x_{2} \, \mathbf{a}_{2} + \left(\frac{1}{2} +x_{2}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-x_{2}\right)a \, \mathbf{\hat{x}}-x_{2}a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +x_{2}\right)a \, \mathbf{\hat{z}} & \left(8c\right) & \text{Al} \\ \mathbf{B}_{7} & = & -x_{2} \, \mathbf{a}_{1} + \left(\frac{1}{2} +x_{2}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - x_{2}\right) \, \mathbf{a}_{3} & = & -x_{2}a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +x_{2}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{2}-x_{2}\right)a \, \mathbf{\hat{z}} & \left(8c\right) & \text{Al} \\ \mathbf{B}_{8} & = & \left(\frac{1}{2} +x_{2}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - x_{2}\right) \, \mathbf{a}_{2}-x_{2} \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +x_{2}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2}-x_{2}\right)a \, \mathbf{\hat{y}}-x_{2}a \, \mathbf{\hat{z}} & \left(8c\right) & \text{Al} \\ \mathbf{B}_{9} & = & \left(\frac{3}{4} +x_{2}\right) \, \mathbf{a}_{1} + \left(\frac{1}{4} +x_{2}\right) \, \mathbf{a}_{2} + \left(\frac{1}{4} - x_{2}\right) \, \mathbf{a}_{3} & = & \left(\frac{3}{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(8c\right) & \text{Al} \\ \mathbf{B}_{10} & = & \left(\frac{3}{4} - x_{2}\right) \, \mathbf{a}_{1} + \left(\frac{3}{4} - x_{2}\right) \, \mathbf{a}_{2} + \left(\frac{3}{4} - x_{2}\right) \, \mathbf{a}_{3} & = & \left(\frac{3}{4}-x_{2}\right)a \, \mathbf{\hat{x}} + \left(\frac{3}{4}-x_{2}\right)a \, \mathbf{\hat{y}} + \left(\frac{3}{4}-x_{2}\right)a \, \mathbf{\hat{z}} & \left(8c\right) & \text{Al} \\ \mathbf{B}_{11} & = & \left(\frac{1}{4} +x_{2}\right) \, \mathbf{a}_{1} + \left(\frac{1}{4} - x_{2}\right) \, \mathbf{a}_{2} + \left(\frac{3}{4} +x_{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{3}{4} +x_{2}\right)a \, \mathbf{\hat{z}} & \left(8c\right) & \text{Al} \\ \mathbf{B}_{12} & = & \left(\frac{1}{4} - x_{2}\right) \, \mathbf{a}_{1} + \left(\frac{3}{4} +x_{2}\right) \, \mathbf{a}_{2} + \left(\frac{1}{4} +x_{2}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4}-x_{2}\right)a \, \mathbf{\hat{x}} + \left(\frac{3}{4} +x_{2}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4} +x_{2}\right)a \, \mathbf{\hat{z}} & \left(8c\right) & \text{Al} \\ \mathbf{B}_{13} & = & \frac{1}{8} \, \mathbf{a}_{1} + y_{3} \, \mathbf{a}_{2} + \left(\frac{1}{4} +y_{3}\right) \, \mathbf{a}_{3} & = & \frac{1}{8}a \, \mathbf{\hat{x}} + y_{3}a \, \mathbf{\hat{y}} + \left(\frac{1}{4} +y_{3}\right)a \, \mathbf{\hat{z}} & \left(12d\right) & \text{Mo} \\ \mathbf{B}_{14} & = & \frac{3}{8} \, \mathbf{a}_{1}-y_{3} \, \mathbf{a}_{2} + \left(\frac{3}{4} +y_{3}\right) \, \mathbf{a}_{3} & = & \frac{3}{8}a \, \mathbf{\hat{x}}-y_{3}a \, \mathbf{\hat{y}} + \left(\frac{3}{4} +y_{3}\right)a \, \mathbf{\hat{z}} & \left(12d\right) & \text{Mo} \\ \mathbf{B}_{15} & = & \frac{7}{8} \, \mathbf{a}_{1} + \left(\frac{1}{2} +y_{3}\right) \, \mathbf{a}_{2} + \left(\frac{1}{4} - y_{3}\right) \, \mathbf{a}_{3} & = & \frac{7}{8}a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +y_{3}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4}-y_{3}\right)a \, \mathbf{\hat{z}} & \left(12d\right) & \text{Mo} \\ \mathbf{B}_{16} & = & \frac{5}{8} \, \mathbf{a}_{1} + \left(\frac{1}{2} - y_{3}\right) \, \mathbf{a}_{2} + \left(\frac{3}{4} - y_{3}\right) \, \mathbf{a}_{3} & = & \frac{5}{8}a \, \mathbf{\hat{x}} + \left(\frac{1}{2}-y_{3}\right)a \, \mathbf{\hat{y}} + \left(\frac{3}{4}-y_{3}\right)a \, \mathbf{\hat{z}} & \left(12d\right) & \text{Mo} \\ \mathbf{B}_{17} & = & \left(\frac{1}{4} +y_{3}\right) \, \mathbf{a}_{1} + \frac{1}{8} \, \mathbf{a}_{2} + y_{3} \, \mathbf{a}_{3} & = & \left(\frac{1}{4} +y_{3}\right)a \, \mathbf{\hat{x}} + \frac{1}{8}a \, \mathbf{\hat{y}} + y_{3}a \, \mathbf{\hat{z}} & \left(12d\right) & \text{Mo} \\ \mathbf{B}_{18} & = & \left(\frac{3}{4} +y_{3}\right) \, \mathbf{a}_{1} + \frac{3}{8} \, \mathbf{a}_{2}-y_{3} \, \mathbf{a}_{3} & = & \left(\frac{3}{4} +y_{3}\right)a \, \mathbf{\hat{x}} + \frac{3}{8}a \, \mathbf{\hat{y}}-y_{3}a \, \mathbf{\hat{z}} & \left(12d\right) & \text{Mo} \\ \mathbf{B}_{19} & = & \left(\frac{1}{4} - y_{3}\right) \, \mathbf{a}_{1} + \frac{7}{8} \, \mathbf{a}_{2} + \left(\frac{1}{2} +y_{3}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4}-y_{3}\right)a \, \mathbf{\hat{x}} + \frac{7}{8}a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +y_{3}\right)a \, \mathbf{\hat{z}} & \left(12d\right) & \text{Mo} \\ \mathbf{B}_{20} & = & \left(\frac{3}{4} - y_{3}\right) \, \mathbf{a}_{1} + \frac{5}{8} \, \mathbf{a}_{2} + \left(\frac{1}{2} - y_{3}\right) \, \mathbf{a}_{3} & = & \left(\frac{3}{4}-y_{3}\right)a \, \mathbf{\hat{x}} + \frac{5}{8}a \, \mathbf{\hat{y}} + \left(\frac{1}{2}-y_{3}\right)a \, \mathbf{\hat{z}} & \left(12d\right) & \text{Mo} \\ \mathbf{B}_{21} & = & y_{3} \, \mathbf{a}_{1} + \left(\frac{1}{4} +y_{3}\right) \, \mathbf{a}_{2} + \frac{1}{8} \, \mathbf{a}_{3} & = & y_{3}a \, \mathbf{\hat{x}} + \left(\frac{1}{4} +y_{3}\right)a \, \mathbf{\hat{y}} + \frac{1}{8}a \, \mathbf{\hat{z}} & \left(12d\right) & \text{Mo} \\ \mathbf{B}_{22} & = & -y_{3} \, \mathbf{a}_{1} + \left(\frac{3}{4} +y_{3}\right) \, \mathbf{a}_{2} + \frac{3}{8} \, \mathbf{a}_{3} & = & -y_{3}a \, \mathbf{\hat{x}} + \left(\frac{3}{4} +y_{3}\right)a \, \mathbf{\hat{y}} + \frac{3}{8}a \, \mathbf{\hat{z}} & \left(12d\right) & \text{Mo} \\ \mathbf{B}_{23} & = & \left(\frac{1}{2} +y_{3}\right) \, \mathbf{a}_{1} + \left(\frac{1}{4} - y_{3}\right) \, \mathbf{a}_{2} + \frac{7}{8} \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +y_{3}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4}-y_{3}\right)a \, \mathbf{\hat{y}} + \frac{7}{8}a \, \mathbf{\hat{z}} & \left(12d\right) & \text{Mo} \\ \mathbf{B}_{24} & = & \left(\frac{1}{2} - y_{3}\right) \, \mathbf{a}_{1} + \left(\frac{3}{4} - y_{3}\right) \, \mathbf{a}_{2} + \frac{5}{8} \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-y_{3}\right)a \, \mathbf{\hat{x}} + \left(\frac{3}{4}-y_{3}\right)a \, \mathbf{\hat{y}} + \frac{5}{8}a \, \mathbf{\hat{z}} & \left(12d\right) & \text{Mo} \\ \end{array} \]