AFLOW Prototype: A2BC4_cF56_227_d_a_e
Prototype | : | Al2MgO4 |
AFLOW prototype label | : | A2BC4_cF56_227_d_a_e |
Strukturbericht designation | : | $H1_{1}$ |
Pearson symbol | : | cF56 |
Space group number | : | 227 |
Space group symbol | : | $\text{Fd}\bar{3}\text{m}$ |
AFLOW prototype command | : | aflow --proto=A2BC4_cF56_227_d_a_e --params=$a$,$x_3$ |
Basis vectors:
\[ \begin{array}{ccccccc} & & \text{Lattice Coordinates} & & \text{Cartesian Coordinates} &\text{Wyckoff Position} & \text{Atom Type} \\ \mathbf{B_1} & =& \frac18 \mathbf{a}_{1} + \frac18 \mathbf{a}_{2} + \frac18\mathbf{a}_{3}& =& \frac18 \, a \, \mathbf{\hat{x}} + \frac18 \, a \, \mathbf{\hat{y}} + \frac18 \, a \, \mathbf{\hat{z}}& \left(8a\right) & \text{Mg} \\ \mathbf{B_2} & =& \frac78 \mathbf{a}_{1} + \frac78 \mathbf{a}_{2} + \frac78\mathbf{a}_{3}& =& \frac78 \, a \, \mathbf{\hat{x}} + \frac78 \, a \, \mathbf{\hat{y}} + \frac78 \, a \, \mathbf{\hat{z}}& \left(8a\right) & \text{Mg} \\ \mathbf{B_3} & =& \frac12 \mathbf{a}_{1} + \frac12 \mathbf{a}_{2} + \frac12\mathbf{a}_{3}& =& \frac12 \, a \, \mathbf{\hat{x}} + \frac12 \, a \, \mathbf{\hat{y}} + \frac12 \, a \, \mathbf{\hat{z}}& \left(16d\right) & \text{Al} \\ \mathbf{B_4} & =& \frac12 \mathbf{a}_{1} + \frac12 \mathbf{a}_{2}& =& \frac14 \, a \, \mathbf{\hat{x}} + \frac14 \, a \, \mathbf{\hat{y}} + \frac12 \, a \, \mathbf{\hat{z}}& \left(16d\right) & \text{Al} \\ \mathbf{B_5} & =& \frac12 \mathbf{a}_{1} + \frac12 \mathbf{a}_{3}& =& \frac14 \, a \, \mathbf{\hat{x}} + \frac12 \, a \, \mathbf{\hat{y}} + \frac14 \, a \, \mathbf{\hat{z}}& \left(16d\right) & \text{Al} \\ \mathbf{B_6} & =& \frac12 \mathbf{a}_{2} + \frac12 \mathbf{a}_{3}& =& \frac12 \, a \, \mathbf{\hat{x}} + \frac14 \, a \, \mathbf{\hat{y}} + \frac14 \, a \, \mathbf{\hat{z}}& \left(16d\right) & \text{Al} \\ \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{O} \\ \mathbf{B_8} & =& x_3 \, \mathbf{a}_{1}+ \left(1 + x_3\right) \, \mathbf{a}_{2}+ \left(\frac12 - 3 x_3\right) \, \mathbf{a}_{3}& =& \left(\frac34 - x_3\right) \, a \, \mathbf{\hat{x}}+ \left(\frac14 - x_3\right) \, a \, \mathbf{\hat{y}}+ \left(\frac12 + x_3\right) \, a \, \mathbf{\hat{z}}& \left(32e\right) & \text{O} \\ \mathbf{B_9} & =& \left(1 + x_3\right) \, \mathbf{a}_{1}+ \left(\frac12 - 3 x_3\right) \, \mathbf{a}_{2}+ x_3 \, \mathbf{a}_{3}& =& \left(\frac14 - x_3\right) \, a \, \mathbf{\hat{x}}+ \left(\frac12 + x_3\right) \, a \, \mathbf{\hat{y}}+ \left(\frac34 - x_3\right) \, a \, \mathbf{\hat{z}}& \left(32e\right) & \text{O} \\ \mathbf{B}_{10} & =& \left(\frac12 - 3 x_3\right) \, \mathbf{a}_{1}+ x_3 \, \mathbf{a}_{2}+ \left(1 + x_3\right) \, \mathbf{a}_{3}& =& \left(\frac12 + x_3\right) \, a \, \mathbf{\hat{x}}+ \left(\frac34 - x_3\right) \, a \, \mathbf{\hat{y}}+ \left(\frac14 - x_3\right) \, a \, \mathbf{\hat{z}}& \left(32e\right) & \text{O} \\ \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(32e\right) & \text{O} \\ \mathbf{B}_{12} & =& - x_3 \, \mathbf{a}_{1}+ \left(1 - x_3\right) \, \mathbf{a}_{2}+ \left(\frac12 + 3 x_3\right) \, \mathbf{a}_{3}& =& \left(\frac34 + x_3\right) \, a \, \mathbf{\hat{x}}+ \left(\frac14 + x_3\right) \, a \, \mathbf{\hat{y}}+ \left(\frac12 - x_3\right) \, a \, \mathbf{\hat{z}}& \left(32e\right) & \text{O} \\ \mathbf{B}_{13} & =& \left(1 - x_3\right) \, \mathbf{a}_{1}+ \left(\frac12 + 3 x_3\right) \, \mathbf{a}_{2}- x_3 \, \mathbf{a}_{3}& =& \left(\frac14 + x_3\right) \, a \, \mathbf{\hat{x}}+ \left(\frac12 - x_3\right) \, a \, \mathbf{\hat{y}}+ \left(\frac34 + x_3\right) \, a \, \mathbf{\hat{z}}& \left(32e\right) & \text{O} \\ \mathbf{B}_{14} & =& \left(\frac12 + 3 x_3\right) \, \mathbf{a}_{1}- x_3 \, \mathbf{a}_{2}+ \left(1 - x_3\right) \, \mathbf{a}_{3}& =& \left(\frac12 - x_3\right) \, a \, \mathbf{\hat{x}}+ \left(\frac34 + x_3\right) \, a \, \mathbf{\hat{y}}+ \left(\frac14 + x_3\right) \, a \, \mathbf{\hat{z}}& \left(32e\right) & \text{O} \\ \end{array} \]