AFLOW Prototype: A16B2C_cF152_227_eg_d_a
Prototype | : | H16Li2Mg |
AFLOW prototype label | : | A16B2C_cF152_227_eg_d_a |
Strukturbericht designation | : | None |
Pearson symbol | : | cF152 |
Space group number | : | 227 |
Space group symbol | : | $Fd\bar{3}m$ |
AFLOW prototype command | : | aflow --proto=A16B2C_cF152_227_eg_d_a --params=$a$,$x_{3}$,$x_{4}$,$z_{4}$ |
Basis vectors:
\[ \begin{array}{ccccccc} & & \text{Lattice Coordinates} & & \text{Cartesian Coordinates} &\text{Wyckoff Position} & \text{Atom Type} \\ \mathbf{B}_{1} & = & \frac{1}{8} \, \mathbf{a}_{1} + \frac{1}{8} \, \mathbf{a}_{2} + \frac{1}{8} \, \mathbf{a}_{3} & = & \frac{1}{8}a \, \mathbf{\hat{x}} + \frac{1}{8}a \, \mathbf{\hat{y}} + \frac{1}{8}a \, \mathbf{\hat{z}} & \left(8a\right) & \text{Mg} \\ \mathbf{B}_{2} & = & \frac{7}{8} \, \mathbf{a}_{1} + \frac{7}{8} \, \mathbf{a}_{2} + \frac{7}{8} \, \mathbf{a}_{3} & = & \frac{7}{8}a \, \mathbf{\hat{x}} + \frac{7}{8}a \, \mathbf{\hat{y}} + \frac{7}{8}a \, \mathbf{\hat{z}} & \left(8a\right) & \text{Mg} \\ \mathbf{B}_{3} & = & \frac{1}{2} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + \frac{1}{2}a \, \mathbf{\hat{y}} + \frac{1}{2}a \, \mathbf{\hat{z}} & \left(16d\right) & \text{Li} \\ \mathbf{B}_{4} & = & \frac{1}{2} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{2} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + \frac{1}{4}a \, \mathbf{\hat{y}} + \frac{1}{2}a \, \mathbf{\hat{z}} & \left(16d\right) & \text{Li} \\ \mathbf{B}_{5} & = & \frac{1}{2} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + \frac{1}{2}a \, \mathbf{\hat{y}} + \frac{1}{4}a \, \mathbf{\hat{z}} & \left(16d\right) & \text{Li} \\ \mathbf{B}_{6} & = & \frac{1}{2} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + \frac{1}{4}a \, \mathbf{\hat{y}} + \frac{1}{4}a \, \mathbf{\hat{z}} & \left(16d\right) & \text{Li} \\ \mathbf{B}_{7} & = & 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(32e\right) & \text{H I} \\ \mathbf{B}_{8} & = & x_{3} \, \mathbf{a}_{1} + x_{3} \, \mathbf{a}_{2} + \left(\frac{1}{2} - 3x_{3}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4}-x_{3}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4}-x_{3}\right)a \, \mathbf{\hat{y}} + x_{3}a \, \mathbf{\hat{z}} & \left(32e\right) & \text{H I} \\ \mathbf{B}_{9} & = & x_{3} \, \mathbf{a}_{1} + \left(\frac{1}{2} - 3x_{3}\right) \, \mathbf{a}_{2} + x_{3} \, \mathbf{a}_{3} & = & \left(\frac{1}{4}-x_{3}\right)a \, \mathbf{\hat{x}} + x_{3}a \, \mathbf{\hat{y}} + \left(\frac{1}{4}-x_{3}\right)a \, \mathbf{\hat{z}} & \left(32e\right) & \text{H I} \\ \mathbf{B}_{10} & = & \left(\frac{1}{2} - 3x_{3}\right) \, \mathbf{a}_{1} + x_{3} \, \mathbf{a}_{2} + x_{3} \, \mathbf{a}_{3} & = & x_{3}a \, \mathbf{\hat{x}} + \left(\frac{1}{4}-x_{3}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4}-x_{3}\right)a \, \mathbf{\hat{z}} & \left(32e\right) & \text{H I} \\ \mathbf{B}_{11} & = & -x_{3} \, \mathbf{a}_{1}-x_{3} \, \mathbf{a}_{2} + \left(\frac{1}{2} +3x_{3}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4} +x_{3}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4} +x_{3}\right)a \, \mathbf{\hat{y}}-x_{3}a \, \mathbf{\hat{z}} & \left(32e\right) & \text{H I} \\ \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(32e\right) & \text{H I} \\ \mathbf{B}_{13} & = & -x_{3} \, \mathbf{a}_{1} + \left(\frac{1}{2} +3x_{3}\right) \, \mathbf{a}_{2}-x_{3} \, \mathbf{a}_{3} & = & \left(\frac{1}{4} +x_{3}\right)a \, \mathbf{\hat{x}}-x_{3}a \, \mathbf{\hat{y}} + \left(\frac{1}{4} +x_{3}\right)a \, \mathbf{\hat{z}} & \left(32e\right) & \text{H I} \\ \mathbf{B}_{14} & = & \left(\frac{1}{2} +3x_{3}\right) \, \mathbf{a}_{1}-x_{3} \, \mathbf{a}_{2}-x_{3} \, \mathbf{a}_{3} & = & -x_{3}a \, \mathbf{\hat{x}} + \left(\frac{1}{4} +x_{3}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4} +x_{3}\right)a \, \mathbf{\hat{z}} & \left(32e\right) & \text{H I} \\ \mathbf{B}_{15} & = & z_{4} \, \mathbf{a}_{1} + z_{4} \, \mathbf{a}_{2} + \left(2x_{4}-z_{4}\right) \, \mathbf{a}_{3} & = & x_{4}a \, \mathbf{\hat{x}} + x_{4}a \, \mathbf{\hat{y}} + z_{4}a \, \mathbf{\hat{z}} & \left(96g\right) & \text{H II} \\ \mathbf{B}_{16} & = & z_{4} \, \mathbf{a}_{1} + z_{4} \, \mathbf{a}_{2} + \left(\frac{1}{2} - 2x_{4} - z_{4}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4}-x_{4}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4}-x_{4}\right)a \, \mathbf{\hat{y}} + z_{4}a \, \mathbf{\hat{z}} & \left(96g\right) & \text{H II} \\ \mathbf{B}_{17} & = & \left(2x_{4}-z_{4}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - 2x_{4} - z_{4}\right) \, \mathbf{a}_{2} + z_{4} \, \mathbf{a}_{3} & = & \left(\frac{1}{4}-x_{4}\right)a \, \mathbf{\hat{x}} + x_{4}a \, \mathbf{\hat{y}} + \left(\frac{1}{4}-z_{4}\right)a \, \mathbf{\hat{z}} & \left(96g\right) & \text{H II} \\ \mathbf{B}_{18} & = & \left(\frac{1}{2} - 2x_{4} - z_{4}\right) \, \mathbf{a}_{1} + \left(2x_{4}-z_{4}\right) \, \mathbf{a}_{2} + z_{4} \, \mathbf{a}_{3} & = & x_{4}a \, \mathbf{\hat{x}} + \left(\frac{1}{4}-x_{4}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4}-z_{4}\right)a \, \mathbf{\hat{z}} & \left(96g\right) & \text{H II} \\ \mathbf{B}_{19} & = & \left(2x_{4}-z_{4}\right) \, \mathbf{a}_{1} + z_{4} \, \mathbf{a}_{2} + z_{4} \, \mathbf{a}_{3} & = & z_{4}a \, \mathbf{\hat{x}} + x_{4}a \, \mathbf{\hat{y}} + x_{4}a \, \mathbf{\hat{z}} & \left(96g\right) & \text{H II} \\ \mathbf{B}_{20} & = & \left(\frac{1}{2} - 2x_{4} - z_{4}\right) \, \mathbf{a}_{1} + z_{4} \, \mathbf{a}_{2} + z_{4} \, \mathbf{a}_{3} & = & z_{4}a \, \mathbf{\hat{x}} + \left(\frac{1}{4}-x_{4}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4}-x_{4}\right)a \, \mathbf{\hat{z}} & \left(96g\right) & \text{H II} \\ \mathbf{B}_{21} & = & z_{4} \, \mathbf{a}_{1} + \left(2x_{4}-z_{4}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - 2x_{4} - z_{4}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4}-z_{4}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4}-x_{4}\right)a \, \mathbf{\hat{y}} + x_{4}a \, \mathbf{\hat{z}} & \left(96g\right) & \text{H II} \\ \mathbf{B}_{22} & = & z_{4} \, \mathbf{a}_{1} + \left(\frac{1}{2} - 2x_{4} - z_{4}\right) \, \mathbf{a}_{2} + \left(2x_{4}-z_{4}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4}-z_{4}\right)a \, \mathbf{\hat{x}} + x_{4}a \, \mathbf{\hat{y}} + \left(\frac{1}{4}-x_{4}\right)a \, \mathbf{\hat{z}} & \left(96g\right) & \text{H II} \\ \mathbf{B}_{23} & = & z_{4} \, \mathbf{a}_{1} + \left(2x_{4}-z_{4}\right) \, \mathbf{a}_{2} + z_{4} \, \mathbf{a}_{3} & = & x_{4}a \, \mathbf{\hat{x}} + z_{4}a \, \mathbf{\hat{y}} + x_{4}a \, \mathbf{\hat{z}} & \left(96g\right) & \text{H II} \\ \mathbf{B}_{24} & = & z_{4} \, \mathbf{a}_{1} + \left(\frac{1}{2} - 2x_{4} - z_{4}\right) \, \mathbf{a}_{2} + z_{4} \, \mathbf{a}_{3} & = & \left(\frac{1}{4}-x_{4}\right)a \, \mathbf{\hat{x}} + z_{4}a \, \mathbf{\hat{y}} + \left(\frac{1}{4}-x_{4}\right)a \, \mathbf{\hat{z}} & \left(96g\right) & \text{H II} \\ \mathbf{B}_{25} & = & \left(\frac{1}{2} - 2x_{4} - z_{4}\right) \, \mathbf{a}_{1} + z_{4} \, \mathbf{a}_{2} + \left(2x_{4}-z_{4}\right) \, \mathbf{a}_{3} & = & x_{4}a \, \mathbf{\hat{x}} + \left(\frac{1}{4}-z_{4}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4}-x_{4}\right)a \, \mathbf{\hat{z}} & \left(96g\right) & \text{H II} \\ \mathbf{B}_{26} & = & \left(2x_{4}-z_{4}\right) \, \mathbf{a}_{1} + z_{4} \, \mathbf{a}_{2} + \left(\frac{1}{2} - 2x_{4} - z_{4}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4}-x_{4}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4}-z_{4}\right)a \, \mathbf{\hat{y}} + x_{4}a \, \mathbf{\hat{z}} & \left(96g\right) & \text{H II} \\ \mathbf{B}_{27} & = & -z_{4} \, \mathbf{a}_{1}-z_{4} \, \mathbf{a}_{2} + \left(\frac{1}{2} +2x_{4} + z_{4}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4} +x_{4}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4} +x_{4}\right)a \, \mathbf{\hat{y}}-z_{4}a \, \mathbf{\hat{z}} & \left(96g\right) & \text{H II} \\ \mathbf{B}_{28} & = & -z_{4} \, \mathbf{a}_{1}-z_{4} \, \mathbf{a}_{2} + \left(-2x_{4}+z_{4}\right) \, \mathbf{a}_{3} & = & -x_{4}a \, \mathbf{\hat{x}}-x_{4}a \, \mathbf{\hat{y}}-z_{4}a \, \mathbf{\hat{z}} & \left(96g\right) & \text{H II} \\ \mathbf{B}_{29} & = & \left(-2x_{4}+z_{4}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +2x_{4} + z_{4}\right) \, \mathbf{a}_{2}-z_{4} \, \mathbf{a}_{3} & = & \left(\frac{1}{4} +x_{4}\right)a \, \mathbf{\hat{x}}-x_{4}a \, \mathbf{\hat{y}} + \left(\frac{1}{4} +z_{4}\right)a \, \mathbf{\hat{z}} & \left(96g\right) & \text{H II} \\ \mathbf{B}_{30} & = & \left(\frac{1}{2} +2x_{4} + z_{4}\right) \, \mathbf{a}_{1} + \left(-2x_{4}+z_{4}\right) \, \mathbf{a}_{2}-z_{4} \, \mathbf{a}_{3} & = & -x_{4}a \, \mathbf{\hat{x}} + \left(\frac{1}{4} +x_{4}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4} +z_{4}\right)a \, \mathbf{\hat{z}} & \left(96g\right) & \text{H II} \\ \mathbf{B}_{31} & = & \left(-2x_{4}+z_{4}\right) \, \mathbf{a}_{1}-z_{4} \, \mathbf{a}_{2} + \left(\frac{1}{2} +2x_{4} + z_{4}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4} +x_{4}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4} +z_{4}\right)a \, \mathbf{\hat{y}}-x_{4}a \, \mathbf{\hat{z}} & \left(96g\right) & \text{H II} \\ \mathbf{B}_{32} & = & \left(\frac{1}{2} +2x_{4} + z_{4}\right) \, \mathbf{a}_{1}-z_{4} \, \mathbf{a}_{2} + \left(-2x_{4}+z_{4}\right) \, \mathbf{a}_{3} & = & -x_{4}a \, \mathbf{\hat{x}} + \left(\frac{1}{4} +z_{4}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4} +x_{4}\right)a \, \mathbf{\hat{z}} & \left(96g\right) & \text{H II} \\ \mathbf{B}_{33} & = & -z_{4} \, \mathbf{a}_{1} + \left(-2x_{4}+z_{4}\right) \, \mathbf{a}_{2}-z_{4} \, \mathbf{a}_{3} & = & -x_{4}a \, \mathbf{\hat{x}}-z_{4}a \, \mathbf{\hat{y}}-x_{4}a \, \mathbf{\hat{z}} & \left(96g\right) & \text{H II} \\ \mathbf{B}_{34} & = & -z_{4} \, \mathbf{a}_{1} + \left(\frac{1}{2} +2x_{4} + z_{4}\right) \, \mathbf{a}_{2}-z_{4} \, \mathbf{a}_{3} & = & \left(\frac{1}{4} +x_{4}\right)a \, \mathbf{\hat{x}}-z_{4}a \, \mathbf{\hat{y}} + \left(\frac{1}{4} +x_{4}\right)a \, \mathbf{\hat{z}} & \left(96g\right) & \text{H II} \\ \mathbf{B}_{35} & = & -z_{4} \, \mathbf{a}_{1} + \left(-2x_{4}+z_{4}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +2x_{4} + z_{4}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4} +z_{4}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4} +x_{4}\right)a \, \mathbf{\hat{y}}-x_{4}a \, \mathbf{\hat{z}} & \left(96g\right) & \text{H II} \\ \mathbf{B}_{36} & = & -z_{4} \, \mathbf{a}_{1} + \left(\frac{1}{2} +2x_{4} + z_{4}\right) \, \mathbf{a}_{2} + \left(-2x_{4}+z_{4}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4} +z_{4}\right)a \, \mathbf{\hat{x}}-x_{4}a \, \mathbf{\hat{y}} + \left(\frac{1}{4} +x_{4}\right)a \, \mathbf{\hat{z}} & \left(96g\right) & \text{H II} \\ \mathbf{B}_{37} & = & \left(\frac{1}{2} +2x_{4} + z_{4}\right) \, \mathbf{a}_{1}-z_{4} \, \mathbf{a}_{2}-z_{4} \, \mathbf{a}_{3} & = & -z_{4}a \, \mathbf{\hat{x}} + \left(\frac{1}{4} +x_{4}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4} +x_{4}\right)a \, \mathbf{\hat{z}} & \left(96g\right) & \text{H II} \\ \mathbf{B}_{38} & = & \left(-2x_{4}+z_{4}\right) \, \mathbf{a}_{1}-z_{4} \, \mathbf{a}_{2}-z_{4} \, \mathbf{a}_{3} & = & -z_{4}a \, \mathbf{\hat{x}}-x_{4}a \, \mathbf{\hat{y}}-x_{4}a \, \mathbf{\hat{z}} & \left(96g\right) & \text{H II} \\ \end{array} \]