Spinel (Al2MgO4, $H1_{1}$) Structure: A2BC4_cF56_227_d_a_e

Picture of Structure; Click for Big Picture
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 : $\mbox{Fd}\bar{3}\mbox{m}$
AFLOW prototype command : aflow --proto=A2BC4_cF56_227_d_a_e
--params=
$a$,$x_3$


Other compounds with this structure

  • Al2Se4Zn, Al2CrS4, CaIn2S4, Al2CdS4, Cr2Se4Zr, Mn2Te4Zn, many others.

  • An inverse spinel has four Al atoms on the (8a) sites and (Al,Mg) alloyed on the (16d) sites.

Face-centered Cubic primitive vectors:

\[ \begin{array}{ccc} \mathbf{a}_1 & = & \frac12 \, a \, \mathbf{\hat{y}} + \frac12 \, a \, \mathbf{\hat{z}} \\ \mathbf{a}_2 & = & \frac12 \, a \, \mathbf{\hat{x}} + \frac12 \, a \, \mathbf{\hat{z}} \\ \mathbf{a}_3 & = & \frac12 \, a \, \mathbf{\hat{x}} + \frac12 \, a \, \mathbf{\hat{y}} \\ \end{array} \]

Basis vectors:

\[ \begin{array}{ccccccc} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{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) & \mbox{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) & \mbox{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) & \mbox{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) & \mbox{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) & \mbox{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) & \mbox{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) & \mbox{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) & \mbox{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) & \mbox{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) & \mbox{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) & \mbox{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) & \mbox{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) & \mbox{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) & \mbox{O} \\ \end{array} \]

References

  • R. J. Hill, J. R. Craig, and G. V. Gibbs, Systematics of the Spinel Structure Type, Phys. Chem. Miner. 4, 317–339 (1979).

Geometry files


Prototype Generator

aflow --proto=A2BC4_cF56_227_d_a_e --params=

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