AFLOW Prototype: AB2_oF48_70_g_fg
Prototype | : | CuMg2 |
AFLOW prototype label | : | AB2_oF48_70_g_fg |
Strukturbericht designation | : | $C_{b}$ |
Pearson symbol | : | oF48 |
Space group number | : | 70 |
Space group symbol | : | $Fddd$ |
AFLOW prototype command | : | aflow --proto=AB2_oF48_70_g_fg --params=$a$,$b/a$,$c/a$,$y_{1}$,$z_{2}$,$z_{3}$ |
Basis vectors:
\[ \begin{array}{ccccccc} & & \text{Lattice Coordinates} & & \text{Cartesian Coordinates} &\text{Wyckoff Position} & \text{Atom Type} \\ \mathbf{B}_{1} & = & y_{1} \, \mathbf{a}_{1} + \left(\frac{1}{4} - y_{1}\right) \, \mathbf{a}_{2} + y_{1} \, \mathbf{a}_{3} & = & \frac{1}{8}a \, \mathbf{\hat{x}} + y_{1}b \, \mathbf{\hat{y}} + \frac{1}{8}c \, \mathbf{\hat{z}} & \left(16f\right) & \text{Mg I} \\ \mathbf{B}_{2} & = & \left(\frac{1}{4} - y_{1}\right) \, \mathbf{a}_{1} + y_{1} \, \mathbf{a}_{2} + \left(\frac{1}{4} - y_{1}\right) \, \mathbf{a}_{3} & = & \frac{1}{8}a \, \mathbf{\hat{x}} + \left(\frac{1}{4}-y_{1}\right)b \, \mathbf{\hat{y}} + \frac{1}{8}c \, \mathbf{\hat{z}} & \left(16f\right) & \text{Mg I} \\ \mathbf{B}_{3} & = & -y_{1} \, \mathbf{a}_{1} + \left(\frac{3}{4} +y_{1}\right) \, \mathbf{a}_{2}-y_{1} \, \mathbf{a}_{3} & = & \frac{3}{8}a \, \mathbf{\hat{x}}-y_{1}b \, \mathbf{\hat{y}} + \frac{3}{8}c \, \mathbf{\hat{z}} & \left(16f\right) & \text{Mg I} \\ \mathbf{B}_{4} & = & \left(\frac{3}{4} +y_{1}\right) \, \mathbf{a}_{1}-y_{1} \, \mathbf{a}_{2} + \left(\frac{3}{4} +y_{1}\right) \, \mathbf{a}_{3} & = & \frac{3}{8}a \, \mathbf{\hat{x}} + \left(\frac{3}{4} +y_{1}\right)b \, \mathbf{\hat{y}} + \frac{3}{8}c \, \mathbf{\hat{z}} & \left(16f\right) & \text{Mg I} \\ \mathbf{B}_{5} & = & z_{2} \, \mathbf{a}_{1} + z_{2} \, \mathbf{a}_{2} + \left(\frac{1}{4} - z_{2}\right) \, \mathbf{a}_{3} & = & \frac{1}{8}a \, \mathbf{\hat{x}} + \frac{1}{8}b \, \mathbf{\hat{y}} + z_{2}c \, \mathbf{\hat{z}} & \left(16g\right) & \text{Cu} \\ \mathbf{B}_{6} & = & \left(\frac{1}{4} - z_{2}\right) \, \mathbf{a}_{1} + \left(\frac{1}{4} - z_{2}\right) \, \mathbf{a}_{2} + z_{2} \, \mathbf{a}_{3} & = & \frac{1}{8}a \, \mathbf{\hat{x}} + \frac{1}{8}b \, \mathbf{\hat{y}} + \left(\frac{1}{4}-z_{2}\right)c \, \mathbf{\hat{z}} & \left(16g\right) & \text{Cu} \\ \mathbf{B}_{7} & = & -z_{2} \, \mathbf{a}_{1}-z_{2} \, \mathbf{a}_{2} + \left(\frac{3}{4} +z_{2}\right) \, \mathbf{a}_{3} & = & \frac{3}{8}a \, \mathbf{\hat{x}} + \frac{3}{8}b \, \mathbf{\hat{y}}-z_{2}c \, \mathbf{\hat{z}} & \left(16g\right) & \text{Cu} \\ \mathbf{B}_{8} & = & \left(\frac{3}{4} +z_{2}\right) \, \mathbf{a}_{1} + \left(\frac{3}{4} +z_{2}\right) \, \mathbf{a}_{2}-z_{2} \, \mathbf{a}_{3} & = & \frac{3}{8}a \, \mathbf{\hat{x}} + \frac{3}{8}b \, \mathbf{\hat{y}} + \left(\frac{3}{4} +z_{2}\right)c \, \mathbf{\hat{z}} & \left(16g\right) & \text{Cu} \\ \mathbf{B}_{9} & = & z_{3} \, \mathbf{a}_{1} + z_{3} \, \mathbf{a}_{2} + \left(\frac{1}{4} - z_{3}\right) \, \mathbf{a}_{3} & = & \frac{1}{8}a \, \mathbf{\hat{x}} + \frac{1}{8}b \, \mathbf{\hat{y}} + z_{3}c \, \mathbf{\hat{z}} & \left(16g\right) & \text{Mg II} \\ \mathbf{B}_{10} & = & \left(\frac{1}{4} - z_{3}\right) \, \mathbf{a}_{1} + \left(\frac{1}{4} - z_{3}\right) \, \mathbf{a}_{2} + z_{3} \, \mathbf{a}_{3} & = & \frac{1}{8}a \, \mathbf{\hat{x}} + \frac{1}{8}b \, \mathbf{\hat{y}} + \left(\frac{1}{4}-z_{3}\right)c \, \mathbf{\hat{z}} & \left(16g\right) & \text{Mg II} \\ \mathbf{B}_{11} & = & -z_{3} \, \mathbf{a}_{1}-z_{3} \, \mathbf{a}_{2} + \left(\frac{3}{4} +z_{3}\right) \, \mathbf{a}_{3} & = & \frac{3}{8}a \, \mathbf{\hat{x}} + \frac{3}{8}b \, \mathbf{\hat{y}}-z_{3}c \, \mathbf{\hat{z}} & \left(16g\right) & \text{Mg II} \\ \mathbf{B}_{12} & = & \left(\frac{3}{4} +z_{3}\right) \, \mathbf{a}_{1} + \left(\frac{3}{4} +z_{3}\right) \, \mathbf{a}_{2}-z_{3} \, \mathbf{a}_{3} & = & \frac{3}{8}a \, \mathbf{\hat{x}} + \frac{3}{8}b \, \mathbf{\hat{y}} + \left(\frac{3}{4} +z_{3}\right)c \, \mathbf{\hat{z}} & \left(16g\right) & \text{Mg II} \\ \end{array} \]