AFLOW Prototype: A4B9_cP52_215_ei_3efgi
Prototype | : | Cu9Al4 |
AFLOW prototype label | : | A4B9_cP52_215_ei_3efgi |
Strukturbericht designation | : | $D8_{3}$ |
Pearson symbol | : | cP52 |
Space group number | : | 215 |
Space group symbol | : | $P\bar{4}3m$ |
AFLOW prototype command | : | aflow --proto=A4B9_cP52_215_ei_3efgi --params=$a$,$x_{1}$,$x_{2}$,$x_{3}$,$x_{4}$,$x_{5}$,$x_{6}$,$x_{7}$,$z_{7}$,$x_{8}$,$z_{8}$ |
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(4e\right) & \text{Al I} \\ \mathbf{B}_{2} & = & -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(4e\right) & \text{Al I} \\ \mathbf{B}_{3} & = & -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(4e\right) & \text{Al I} \\ \mathbf{B}_{4} & = & 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(4e\right) & \text{Al 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(4e\right) & \text{Cu I} \\ \mathbf{B}_{6} & = & -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(4e\right) & \text{Cu I} \\ \mathbf{B}_{7} & = & -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(4e\right) & \text{Cu I} \\ \mathbf{B}_{8} & = & 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(4e\right) & \text{Cu I} \\ \mathbf{B}_{9} & = & x_{3} \, \mathbf{a}_{1} + x_{3} \, \mathbf{a}_{2} + x_{3} \, \mathbf{a}_{3} & = & x_{3}a \, \mathbf{\hat{x}} + x_{3}a \, \mathbf{\hat{y}} + x_{3}a \, \mathbf{\hat{z}} & \left(4e\right) & \text{Cu II} \\ \mathbf{B}_{10} & = & -x_{3} \, \mathbf{a}_{1}-x_{3} \, \mathbf{a}_{2} + x_{3} \, \mathbf{a}_{3} & = & -x_{3}a \, \mathbf{\hat{x}}-x_{3}a \, \mathbf{\hat{y}} + x_{3}a \, \mathbf{\hat{z}} & \left(4e\right) & \text{Cu II} \\ \mathbf{B}_{11} & = & -x_{3} \, \mathbf{a}_{1} + x_{3} \, \mathbf{a}_{2}-x_{3} \, \mathbf{a}_{3} & = & -x_{3}a \, \mathbf{\hat{x}} + x_{3}a \, \mathbf{\hat{y}}-x_{3}a \, \mathbf{\hat{z}} & \left(4e\right) & \text{Cu II} \\ \mathbf{B}_{12} & = & x_{3} \, \mathbf{a}_{1}-x_{3} \, \mathbf{a}_{2}-x_{3} \, \mathbf{a}_{3} & = & x_{3}a \, \mathbf{\hat{x}}-x_{3}a \, \mathbf{\hat{y}}-x_{3}a \, \mathbf{\hat{z}} & \left(4e\right) & \text{Cu II} \\ \mathbf{B}_{13} & = & x_{4} \, \mathbf{a}_{1} + x_{4} \, \mathbf{a}_{2} + x_{4} \, \mathbf{a}_{3} & = & x_{4}a \, \mathbf{\hat{x}} + x_{4}a \, \mathbf{\hat{y}} + x_{4}a \, \mathbf{\hat{z}} & \left(4e\right) & \text{Cu III} \\ \mathbf{B}_{14} & = & -x_{4} \, \mathbf{a}_{1}-x_{4} \, \mathbf{a}_{2} + x_{4} \, \mathbf{a}_{3} & = & -x_{4}a \, \mathbf{\hat{x}}-x_{4}a \, \mathbf{\hat{y}} + x_{4}a \, \mathbf{\hat{z}} & \left(4e\right) & \text{Cu III} \\ \mathbf{B}_{15} & = & -x_{4} \, \mathbf{a}_{1} + x_{4} \, \mathbf{a}_{2}-x_{4} \, \mathbf{a}_{3} & = & -x_{4}a \, \mathbf{\hat{x}} + x_{4}a \, \mathbf{\hat{y}}-x_{4}a \, \mathbf{\hat{z}} & \left(4e\right) & \text{Cu III} \\ \mathbf{B}_{16} & = & x_{4} \, \mathbf{a}_{1}-x_{4} \, \mathbf{a}_{2}-x_{4} \, \mathbf{a}_{3} & = & x_{4}a \, \mathbf{\hat{x}}-x_{4}a \, \mathbf{\hat{y}}-x_{4}a \, \mathbf{\hat{z}} & \left(4e\right) & \text{Cu III} \\ \mathbf{B}_{17} & = & x_{5} \, \mathbf{a}_{1} & = & x_{5}a \, \mathbf{\hat{x}} & \left(6f\right) & \text{Cu IV} \\ \mathbf{B}_{18} & = & -x_{5} \, \mathbf{a}_{1} & = & -x_{5}a \, \mathbf{\hat{x}} & \left(6f\right) & \text{Cu IV} \\ \mathbf{B}_{19} & = & x_{5} \, \mathbf{a}_{2} & = & x_{5}a \, \mathbf{\hat{y}} & \left(6f\right) & \text{Cu IV} \\ \mathbf{B}_{20} & = & -x_{5} \, \mathbf{a}_{2} & = & -x_{5}a \, \mathbf{\hat{y}} & \left(6f\right) & \text{Cu IV} \\ \mathbf{B}_{21} & = & x_{5} \, \mathbf{a}_{3} & = & x_{5}a \, \mathbf{\hat{z}} & \left(6f\right) & \text{Cu IV} \\ \mathbf{B}_{22} & = & -x_{5} \, \mathbf{a}_{3} & = & -x_{5}a \, \mathbf{\hat{z}} & \left(6f\right) & \text{Cu IV} \\ \mathbf{B}_{23} & = & x_{6} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & x_{6}a \, \mathbf{\hat{x}} + \frac{1}{2}a \, \mathbf{\hat{y}} + \frac{1}{2}a \, \mathbf{\hat{z}} & \left(6g\right) & \text{Cu V} \\ \mathbf{B}_{24} & = & -x_{6} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & -x_{6}a \, \mathbf{\hat{x}} + \frac{1}{2}a \, \mathbf{\hat{y}} + \frac{1}{2}a \, \mathbf{\hat{z}} & \left(6g\right) & \text{Cu V} \\ \mathbf{B}_{25} & = & \frac{1}{2} \, \mathbf{a}_{1} + x_{6} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + x_{6}a \, \mathbf{\hat{y}} + \frac{1}{2}a \, \mathbf{\hat{z}} & \left(6g\right) & \text{Cu V} \\ \mathbf{B}_{26} & = & \frac{1}{2} \, \mathbf{a}_{1}-x_{6} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}}-x_{6}a \, \mathbf{\hat{y}} + \frac{1}{2}a \, \mathbf{\hat{z}} & \left(6g\right) & \text{Cu V} \\ \mathbf{B}_{27} & = & \frac{1}{2} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{2} + x_{6} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + \frac{1}{2}a \, \mathbf{\hat{y}} + x_{6}a \, \mathbf{\hat{z}} & \left(6g\right) & \text{Cu V} \\ \mathbf{B}_{28} & = & \frac{1}{2} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{2}-x_{6} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + \frac{1}{2}a \, \mathbf{\hat{y}}-x_{6}a \, \mathbf{\hat{z}} & \left(6g\right) & \text{Cu V} \\ \mathbf{B}_{29} & = & x_{7} \, \mathbf{a}_{1} + x_{7} \, \mathbf{a}_{2} + z_{7} \, \mathbf{a}_{3} & = & x_{7}a \, \mathbf{\hat{x}} + x_{7}a \, \mathbf{\hat{y}} + z_{7}a \, \mathbf{\hat{z}} & \left(12i\right) & \text{Al II} \\ \mathbf{B}_{30} & = & -x_{7} \, \mathbf{a}_{1}-x_{7} \, \mathbf{a}_{2} + z_{7} \, \mathbf{a}_{3} & = & -x_{7}a \, \mathbf{\hat{x}}-x_{7}a \, \mathbf{\hat{y}} + z_{7}a \, \mathbf{\hat{z}} & \left(12i\right) & \text{Al II} \\ \mathbf{B}_{31} & = & -x_{7} \, \mathbf{a}_{1} + x_{7} \, \mathbf{a}_{2}-z_{7} \, \mathbf{a}_{3} & = & -x_{7}a \, \mathbf{\hat{x}} + x_{7}a \, \mathbf{\hat{y}}-z_{7}a \, \mathbf{\hat{z}} & \left(12i\right) & \text{Al II} \\ \mathbf{B}_{32} & = & x_{7} \, \mathbf{a}_{1}-x_{7} \, \mathbf{a}_{2}-z_{7} \, \mathbf{a}_{3} & = & x_{7}a \, \mathbf{\hat{x}}-x_{7}a \, \mathbf{\hat{y}}-z_{7}a \, \mathbf{\hat{z}} & \left(12i\right) & \text{Al II} \\ \mathbf{B}_{33} & = & z_{7} \, \mathbf{a}_{1} + x_{7} \, \mathbf{a}_{2} + x_{7} \, \mathbf{a}_{3} & = & z_{7}a \, \mathbf{\hat{x}} + x_{7}a \, \mathbf{\hat{y}} + x_{7}a \, \mathbf{\hat{z}} & \left(12i\right) & \text{Al II} \\ \mathbf{B}_{34} & = & z_{7} \, \mathbf{a}_{1}-x_{7} \, \mathbf{a}_{2}-x_{7} \, \mathbf{a}_{3} & = & z_{7}a \, \mathbf{\hat{x}}-x_{7}a \, \mathbf{\hat{y}}-x_{7}a \, \mathbf{\hat{z}} & \left(12i\right) & \text{Al II} \\ \mathbf{B}_{35} & = & -z_{7} \, \mathbf{a}_{1}-x_{7} \, \mathbf{a}_{2} + x_{7} \, \mathbf{a}_{3} & = & -z_{7}a \, \mathbf{\hat{x}}-x_{7}a \, \mathbf{\hat{y}} + x_{7}a \, \mathbf{\hat{z}} & \left(12i\right) & \text{Al II} \\ \mathbf{B}_{36} & = & -z_{7} \, \mathbf{a}_{1} + x_{7} \, \mathbf{a}_{2}-x_{7} \, \mathbf{a}_{3} & = & -z_{7}a \, \mathbf{\hat{x}} + x_{7}a \, \mathbf{\hat{y}}-x_{7}a \, \mathbf{\hat{z}} & \left(12i\right) & \text{Al II} \\ \mathbf{B}_{37} & = & x_{7} \, \mathbf{a}_{1} + z_{7} \, \mathbf{a}_{2} + x_{7} \, \mathbf{a}_{3} & = & x_{7}a \, \mathbf{\hat{x}} + z_{7}a \, \mathbf{\hat{y}} + x_{7}a \, \mathbf{\hat{z}} & \left(12i\right) & \text{Al II} \\ \mathbf{B}_{38} & = & -x_{7} \, \mathbf{a}_{1} + z_{7} \, \mathbf{a}_{2}-x_{7} \, \mathbf{a}_{3} & = & -x_{7}a \, \mathbf{\hat{x}} + z_{7}a \, \mathbf{\hat{y}}-x_{7}a \, \mathbf{\hat{z}} & \left(12i\right) & \text{Al II} \\ \mathbf{B}_{39} & = & x_{7} \, \mathbf{a}_{1}-z_{7} \, \mathbf{a}_{2}-x_{7} \, \mathbf{a}_{3} & = & x_{7}a \, \mathbf{\hat{x}}-z_{7}a \, \mathbf{\hat{y}}-x_{7}a \, \mathbf{\hat{z}} & \left(12i\right) & \text{Al II} \\ \mathbf{B}_{40} & = & -x_{7} \, \mathbf{a}_{1}-z_{7} \, \mathbf{a}_{2} + x_{7} \, \mathbf{a}_{3} & = & -x_{7}a \, \mathbf{\hat{x}}-z_{7}a \, \mathbf{\hat{y}} + x_{7}a \, \mathbf{\hat{z}} & \left(12i\right) & \text{Al II} \\ \mathbf{B}_{41} & = & x_{8} \, \mathbf{a}_{1} + x_{8} \, \mathbf{a}_{2} + z_{8} \, \mathbf{a}_{3} & = & x_{8}a \, \mathbf{\hat{x}} + x_{8}a \, \mathbf{\hat{y}} + z_{8}a \, \mathbf{\hat{z}} & \left(12i\right) & \text{Cu VI} \\ \mathbf{B}_{42} & = & -x_{8} \, \mathbf{a}_{1}-x_{8} \, \mathbf{a}_{2} + z_{8} \, \mathbf{a}_{3} & = & -x_{8}a \, \mathbf{\hat{x}}-x_{8}a \, \mathbf{\hat{y}} + z_{8}a \, \mathbf{\hat{z}} & \left(12i\right) & \text{Cu VI} \\ \mathbf{B}_{43} & = & -x_{8} \, \mathbf{a}_{1} + x_{8} \, \mathbf{a}_{2}-z_{8} \, \mathbf{a}_{3} & = & -x_{8}a \, \mathbf{\hat{x}} + x_{8}a \, \mathbf{\hat{y}}-z_{8}a \, \mathbf{\hat{z}} & \left(12i\right) & \text{Cu VI} \\ \mathbf{B}_{44} & = & x_{8} \, \mathbf{a}_{1}-x_{8} \, \mathbf{a}_{2}-z_{8} \, \mathbf{a}_{3} & = & x_{8}a \, \mathbf{\hat{x}}-x_{8}a \, \mathbf{\hat{y}}-z_{8}a \, \mathbf{\hat{z}} & \left(12i\right) & \text{Cu VI} \\ \mathbf{B}_{45} & = & z_{8} \, \mathbf{a}_{1} + x_{8} \, \mathbf{a}_{2} + x_{8} \, \mathbf{a}_{3} & = & z_{8}a \, \mathbf{\hat{x}} + x_{8}a \, \mathbf{\hat{y}} + x_{8}a \, \mathbf{\hat{z}} & \left(12i\right) & \text{Cu VI} \\ \mathbf{B}_{46} & = & z_{8} \, \mathbf{a}_{1}-x_{8} \, \mathbf{a}_{2}-x_{8} \, \mathbf{a}_{3} & = & z_{8}a \, \mathbf{\hat{x}}-x_{8}a \, \mathbf{\hat{y}}-x_{8}a \, \mathbf{\hat{z}} & \left(12i\right) & \text{Cu VI} \\ \mathbf{B}_{47} & = & -z_{8} \, \mathbf{a}_{1}-x_{8} \, \mathbf{a}_{2} + x_{8} \, \mathbf{a}_{3} & = & -z_{8}a \, \mathbf{\hat{x}}-x_{8}a \, \mathbf{\hat{y}} + x_{8}a \, \mathbf{\hat{z}} & \left(12i\right) & \text{Cu VI} \\ \mathbf{B}_{48} & = & -z_{8} \, \mathbf{a}_{1} + x_{8} \, \mathbf{a}_{2}-x_{8} \, \mathbf{a}_{3} & = & -z_{8}a \, \mathbf{\hat{x}} + x_{8}a \, \mathbf{\hat{y}}-x_{8}a \, \mathbf{\hat{z}} & \left(12i\right) & \text{Cu VI} \\ \mathbf{B}_{49} & = & x_{8} \, \mathbf{a}_{1} + z_{8} \, \mathbf{a}_{2} + x_{8} \, \mathbf{a}_{3} & = & x_{8}a \, \mathbf{\hat{x}} + z_{8}a \, \mathbf{\hat{y}} + x_{8}a \, \mathbf{\hat{z}} & \left(12i\right) & \text{Cu VI} \\ \mathbf{B}_{50} & = & -x_{8} \, \mathbf{a}_{1} + z_{8} \, \mathbf{a}_{2}-x_{8} \, \mathbf{a}_{3} & = & -x_{8}a \, \mathbf{\hat{x}} + z_{8}a \, \mathbf{\hat{y}}-x_{8}a \, \mathbf{\hat{z}} & \left(12i\right) & \text{Cu VI} \\ \mathbf{B}_{51} & = & x_{8} \, \mathbf{a}_{1}-z_{8} \, \mathbf{a}_{2}-x_{8} \, \mathbf{a}_{3} & = & x_{8}a \, \mathbf{\hat{x}}-z_{8}a \, \mathbf{\hat{y}}-x_{8}a \, \mathbf{\hat{z}} & \left(12i\right) & \text{Cu VI} \\ \mathbf{B}_{52} & = & -x_{8} \, \mathbf{a}_{1}-z_{8} \, \mathbf{a}_{2} + x_{8} \, \mathbf{a}_{3} & = & -x_{8}a \, \mathbf{\hat{x}}-z_{8}a \, \mathbf{\hat{y}} + x_{8}a \, \mathbf{\hat{z}} & \left(12i\right) & \text{Cu VI} \\ \end{array} \]