Bergman [Mg32(Al,Zn)49, $D8_{e}$] Structure: AB32C48_cI162_204_a_2efg_2gh

Picture of Structure; Click for Big Picture
Prototype : Mg32(Al,Zn)49
AFLOW prototype label : AB32C48_cI162_204_a_2efg_2gh
Strukturbericht designation : $D8_{e}$
Pearson symbol : cI162
Space group number : 204
Space group symbol : $\mbox{Im}\bar{3}$
AFLOW prototype command : aflow --proto=AB32C48_cI162_204_a_2efg_2gh
--params=
$a$,$x_2$,$x_3$,$x_4$,$y_5$,$z_5$,$y_6$,$z_6$,$y_7$,$z_7$,$x_8$,$y_8$,$z_8$


Other compounds with this structure

  • Li20Mg6Cu13Al42

  • Most of the sites in this lattice have random occupancy. In particular, according to (Bergman, 1957): The Al–I (2a) site is only occupied 80% of the time, the Zn–I (24g) site is occupied by Al 19% of the time, the Zn–II (24g) site is occupied by Al 43% of the time, and the Zn–III (48h) site is occupied by Al 36% of the time. The Li20Mg6Cu13Al42 structure found by (Pavlyuk, 2019) has all sites fully occupied.

Body-centered Cubic primitive vectors:

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

Basis vectors:

\[ \begin{array}{ccccccc} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{Atom Type} \\ \mathbf{B_1} & = & 0 \, \mathbf{a}_{1} + 0 \, \mathbf{a}_{2} + 0 \, \mathbf{a}_{3} & = & 0 \mathbf{\hat{x}} + 0 \mathbf{\hat{y}} + 0 \mathbf{\hat{z}} & \left(2a\right) & \mbox{Al} \\ \mathbf{B_2} & =& \frac12 \, \mathbf{a}_{1}+ \left(\frac12 + x_2\right)\, \mathbf{a}_{2}+ x_2 \, \mathbf{a}_{3}& =& x_2 \, a \, \mathbf{\hat{x}}+ \frac12 \, a \, \mathbf{\hat{z}}& \left(12e\right) & \mbox{Mg I} \\ \mathbf{B_3} & =& \frac12 \, \mathbf{a}_{1}+ \left(\frac12 - x_2\right)\, \mathbf{a}_{2}- x_2 \, \mathbf{a}_{3}& =& - x_2 \, a \, \mathbf{\hat{x}}+ \frac12 \, a \, \mathbf{\hat{z}}& \left(12e\right) & \mbox{Mg I} \\ \mathbf{B_4} & =& x_2 \, \mathbf{a}_{1}+ \frac12 \, \mathbf{a}_{2}+ \left(\frac12 + x_2\right)\, \mathbf{a}_{3}& =& \frac12 \, a \, \mathbf{\hat{x}}+ x_2 \, a \, \mathbf{\hat{y}}& \left(12e\right) & \mbox{Mg I} \\ \mathbf{B_5} & =& - x_2 \, \mathbf{a}_{1}+ \frac12 \, \mathbf{a}_{2}+ \left(\frac12 - x_2\right)\, \mathbf{a}_{3}& =& \frac12 \, a \, \mathbf{\hat{x}}- x_2 \, a \, \mathbf{\hat{y}}& \left(12e\right) & \mbox{Mg I} \\ \mathbf{B_6} & =& \left(\frac12 + x_2\right) \, \mathbf{a}_{1}+ x_2 \, \mathbf{a}_{2}+ \frac12 \, \mathbf{a}_{3}& =& \frac12 \, a \, \mathbf{\hat{y}}+ x_2 \, a \, \mathbf{\hat{z}}& \left(12e\right) & \mbox{Mg I} \\ \mathbf{B_7} & =& \left(\frac12 - x_2\right) \, \mathbf{a}_{1}- x_2 \, \mathbf{a}_{2}+ \frac12 \, \mathbf{a}_{3}& =& \frac12 \, a \, \mathbf{\hat{y}}- x_2 \, a \, \mathbf{\hat{z}}& \left(12e\right) & \mbox{Mg I} \\ \mathbf{B_8} & =& \frac12 \, \mathbf{a}_{1}+ \left(\frac12 + x_3\right)\, \mathbf{a}_{2}+ x_3 \, \mathbf{a}_{3}& =& x_3 \, a \, \mathbf{\hat{x}}+ \frac12 \, a \, \mathbf{\hat{z}}& \left(12e\right) & \mbox{Mg II} \\ \mathbf{B_9} & =& \frac12 \, \mathbf{a}_{1}+ \left(\frac12 - x_3\right)\, \mathbf{a}_{2}- x_3 \, \mathbf{a}_{3}& =& - x_3 \, a \, \mathbf{\hat{x}}+ \frac12 \, a \, \mathbf{\hat{z}}& \left(12e\right) & \mbox{Mg II} \\ \mathbf{B}_{10} & =& x_3 \, \mathbf{a}_{1}+ \frac12 \, \mathbf{a}_{2}+ \left(\frac12 + x_3\right)\, \mathbf{a}_{3}& =& \frac12 \, a \, \mathbf{\hat{x}}+ x_3 \, a \, \mathbf{\hat{y}}& \left(12e\right) & \mbox{Mg II} \\ \mathbf{B}_{11} & =& - x_3 \, \mathbf{a}_{1}+ \frac12 \, \mathbf{a}_{2}+ \left(\frac12 - x_3\right)\, \mathbf{a}_{3}& =& \frac12 \, a \, \mathbf{\hat{x}}- x_3 \, a \, \mathbf{\hat{y}}& \left(12e\right) & \mbox{Mg II} \\ \mathbf{B}_{12} & =& \left(\frac12 + x_3\right) \, \mathbf{a}_{1}+ x_3 \, \mathbf{a}_{2}+ \frac12 \, \mathbf{a}_{3}& =& \frac12 \, a \, \mathbf{\hat{y}}+ x_3 \, a \, \mathbf{\hat{z}}& \left(12e\right) & \mbox{Mg II} \\ \mathbf{B}_{13} & =& \left(\frac12 - x_3\right) \, \mathbf{a}_{1}- x_3 \, \mathbf{a}_{2}+ \frac12 \, \mathbf{a}_{3}& =& \frac12 \, a \, \mathbf{\hat{y}}- x_3 \, a \, \mathbf{\hat{z}}& \left(12e\right) & \mbox{Mg II} \\ \mathbf{B}_{14} & =& 2 x_4 \, \mathbf{a}_{1}+ 2 x_4 \, \mathbf{a}_{2}+ 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(16f\right) & \mbox{Mg III} \\ \mathbf{B}_{15} & =& 2 x_4 \, \mathbf{a}_{1}& =& - x_4 \, a \, \mathbf{\hat{x}}+ x_4 \, a \, \mathbf{\hat{y}}+ x_4 \, a \, \mathbf{\hat{z}}& \left(16f\right) & \mbox{Mg III} \\ \mathbf{B}_{16} & =& 2 x_4 \, \mathbf{a}_{2}& =& x_4 \, a \, \mathbf{\hat{x}}- x_4 \, a \, \mathbf{\hat{y}}+ x_4 \, a \, \mathbf{\hat{z}}& \left(16f\right) & \mbox{Mg III} \\ \mathbf{B}_{17} & =& 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(16f\right) & \mbox{Mg III} \\ \mathbf{B}_{18} & =& - 2 x_4 \, \mathbf{a}_{1}- 2 x_4 \, \mathbf{a}_{2}- 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(16f\right) & \mbox{Mg III} \\ \mathbf{B}_{19} & =& - 2 x_4 \, \mathbf{a}_{1}& =& x_4 \, a \, \mathbf{\hat{x}}- x_4 \, a \, \mathbf{\hat{y}}- x_4 \, a \, \mathbf{\hat{z}}& \left(16f\right) & \mbox{Mg III} \\ \mathbf{B}_{20} & =& - 2 x_4 \, \mathbf{a}_{2}& =& - x_4 \, a \, \mathbf{\hat{x}}+ x_4 \, a \, \mathbf{\hat{y}}- x_4 \, a \, \mathbf{\hat{z}}& \left(16f\right) & \mbox{Mg III} \\ \mathbf{B}_{21} & =& - 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(16f\right) & \mbox{Mg III} \\ \mathbf{B}_{22} & =& \left(y_5 + z_5\right) \, \mathbf{a}_{1}+ z_5 \, \mathbf{a}_{2}+ y_5 \, \mathbf{a}_{3}& =& y_5 \, a \, \mathbf{\hat{y}}+ z_5 \, a \, \mathbf{\hat{z}}& \left(24g\right) & \mbox{Mg IV} \\ \mathbf{B}_{23} & =& \left(z_5 - y_5\right) \, \mathbf{a}_{1}+ z_5 \, \mathbf{a}_{2}- y_5 \, \mathbf{a}_{3}& =& - y_5 \, a \, \mathbf{\hat{y}}+ z_5 \, a \, \mathbf{\hat{z}}& \left(24g\right) & \mbox{Mg IV} \\ \mathbf{B}_{24} & =& \left(y_5 - z_5\right) \, \mathbf{a}_{1}- z_5 \, \mathbf{a}_{2}+ y_5 \, \mathbf{a}_{3}& =& y_5 \, a \, \mathbf{\hat{y}}- z_5 \, a \, \mathbf{\hat{z}}& \left(24g\right) & \mbox{Mg IV} \\ \mathbf{B}_{25} & =& - \left(y_5 + z_5\right) \, \mathbf{a}_{1}- z_5 \, \mathbf{a}_{2}- y_5 \, \mathbf{a}_{3}& =& - y_5 \, a \, \mathbf{\hat{y}}- z_5 \, a \, \mathbf{\hat{z}}& \left(24g\right) & \mbox{Mg IV} \\ \mathbf{B}_{26} & =& y_5 \, \mathbf{a}_{1}+ \left(y_5 + z_5\right) \, \mathbf{a}_{2}+ z_5 \, \mathbf{a}_{3}& =& z_5 \, a \, \mathbf{\hat{x}}+ y_5 \, a \, \mathbf{\hat{z}}& \left(24g\right) & \mbox{Mg IV} \\ \mathbf{B}_{27} & =& y_5 \, \mathbf{a}_{1}+ \left(y_5 - z_5\right) \, \mathbf{a}_{2}- z_5 \, \mathbf{a}_{3}& =& - z_5 \, a \, \mathbf{\hat{x}}+ y_5 \, a \, \mathbf{\hat{z}}& \left(24g\right) & \mbox{Mg IV} \\ \mathbf{B}_{28} & =& - y_5 \, \mathbf{a}_{1}+ \left(z_5 - y_5\right) \, \mathbf{a}_{2}+ z_5 \, \mathbf{a}_{3}& =& z_5 \, a \, \mathbf{\hat{x}}- y_5 \, a \, \mathbf{\hat{z}}& \left(24g\right) & \mbox{Mg IV} \\ \mathbf{B}_{29} & =& - y_5 \, \mathbf{a}_{1}- \left(y_5 + z_5\right) \, \mathbf{a}_{2}- z_5 \, \mathbf{a}_{3}& =& - z_5 \, a \, \mathbf{\hat{x}}- y_5 \, a \, \mathbf{\hat{z}}& \left(24g\right) & \mbox{Mg IV} \\ \mathbf{B}_{30} & =& z_5 \, \mathbf{a}_{1}+ y_5 \, \mathbf{a}_{2}+ \left(y_5 + z_5\right) \, \mathbf{a}_{3}& =& y_5 \, a \, \mathbf{\hat{x}}+ z_5 \, a \, \mathbf{\hat{y}}& \left(24g\right) & \mbox{Mg IV} \\ \mathbf{B}_{31} & =& z_5 \, \mathbf{a}_{1}- y_5 \, \mathbf{a}_{2}+ \left(z_5 - y_5\right) \, \mathbf{a}_{3}& =& - y_5 \, a \, \mathbf{\hat{x}}+ z_5 \, a \, \mathbf{\hat{y}}& \left(24g\right) & \mbox{Mg IV} \\ \mathbf{B}_{32} & =& - z_5 \, \mathbf{a}_{1}+ y_5 \, \mathbf{a}_{2}+ \left(y_5 - z_5\right) \, \mathbf{a}_{3}& =& y_5 \, a \, \mathbf{\hat{x}}- z_5 \, a \, \mathbf{\hat{y}}& \left(24g\right) & \mbox{Mg IV} \\ \mathbf{B}_{33} & =& - z_5 \, \mathbf{a}_{1}- y_5 \, \mathbf{a}_{2}- \left(y_5 + z_5\right) \, \mathbf{a}_{3}& =& - y_5 \, a \, \mathbf{\hat{x}}- z_5 \, a \, \mathbf{\hat{y}}& \left(24g\right) & \mbox{Mg IV} \\ \mathbf{B}_{34} & =& \left(y_6 + z_6\right) \, \mathbf{a}_{1}+ z_6 \, \mathbf{a}_{2}+ y_6 \, \mathbf{a}_{3}& =& y_6 \, a \, \mathbf{\hat{y}}+ z_6 \, a \, \mathbf{\hat{z}}& \left(24g\right) & \mbox{Zn I} \\ \mathbf{B}_{35} & =& \left(z_6 - y_6\right) \, \mathbf{a}_{1}+ z_6 \, \mathbf{a}_{2}- y_6 \, \mathbf{a}_{3}& =& - y_6 \, a \, \mathbf{\hat{y}}+ z_6 \, a \, \mathbf{\hat{z}}& \left(24g\right) & \mbox{Zn I} \\ \mathbf{B}_{36} & =& \left(y_6 - z_6\right) \, \mathbf{a}_{1}- z_6 \, \mathbf{a}_{2}+ y_6 \, \mathbf{a}_{3}& =& y_6 \, a \, \mathbf{\hat{y}}- z_6 \, a \, \mathbf{\hat{z}}& \left(24g\right) & \mbox{Zn I} \\ \mathbf{B}_{37} & =& - \left(y_6 + z_6\right) \, \mathbf{a}_{1}- z_6 \, \mathbf{a}_{2}- y_6 \, \mathbf{a}_{3}& =& - y_6 \, a \, \mathbf{\hat{y}}- z_6 \, a \, \mathbf{\hat{z}}& \left(24g\right) & \mbox{Zn I} \\ \mathbf{B}_{38} & =& y_6 \, \mathbf{a}_{1}+ \left(y_6 + z_6\right) \, \mathbf{a}_{2}+ z_6 \, \mathbf{a}_{3}& =& z_6 \, a \, \mathbf{\hat{x}}+ y_6 \, a \, \mathbf{\hat{z}}& \left(24g\right) & \mbox{Zn I} \\ \mathbf{B}_{39} & =& y_6 \, \mathbf{a}_{1}+ \left(y_6 - z_6\right) \, \mathbf{a}_{2}- z_6 \, \mathbf{a}_{3}& =& - z_6 \, a \, \mathbf{\hat{x}}+ y_6 \, a \, \mathbf{\hat{z}}& \left(24g\right) & \mbox{Zn I} \\ \mathbf{B}_{40} & =& - y_6 \, \mathbf{a}_{1}+ \left(z_6 - y_6\right) \, \mathbf{a}_{2}+ z_6 \, \mathbf{a}_{3}& =& z_6 \, a \, \mathbf{\hat{x}}- y_6 \, a \, \mathbf{\hat{z}}& \left(24g\right) & \mbox{Zn I} \\ \mathbf{B}_{41} & =& - y_6 \, \mathbf{a}_{1}- \left(y_6 + z_6\right) \, \mathbf{a}_{2}- z_6 \, \mathbf{a}_{3}& =& - z_6 \, a \, \mathbf{\hat{x}}- y_6 \, a \, \mathbf{\hat{z}}& \left(24g\right) & \mbox{Zn I} \\ \mathbf{B}_{42} & =& z_6 \, \mathbf{a}_{1}+ y_6 \, \mathbf{a}_{2}+ \left(y_6 + z_6\right) \, \mathbf{a}_{3}& =& y_6 \, a \, \mathbf{\hat{x}}+ z_6 \, a \, \mathbf{\hat{y}}& \left(24g\right) & \mbox{Zn I} \\ \mathbf{B}_{43} & =& z_6 \, \mathbf{a}_{1}- y_6 \, \mathbf{a}_{2}+ \left(z_6 - y_6\right) \, \mathbf{a}_{3}& =& - y_6 \, a \, \mathbf{\hat{x}}+ z_6 \, a \, \mathbf{\hat{y}}& \left(24g\right) & \mbox{Zn I} \\ \mathbf{B}_{44} & =& - z_6 \, \mathbf{a}_{1}+ y_6 \, \mathbf{a}_{2}+ \left(y_6 - z_6\right) \, \mathbf{a}_{3}& =& y_6 \, a \, \mathbf{\hat{x}}- z_6 \, a \, \mathbf{\hat{y}}& \left(24g\right) & \mbox{Zn I} \\ \mathbf{B}_{45} & =& - z_6 \, \mathbf{a}_{1}- y_6 \, \mathbf{a}_{2}- \left(y_6 + z_6\right) \, \mathbf{a}_{3}& =& - y_6 \, a \, \mathbf{\hat{x}}- z_6 \, a \, \mathbf{\hat{y}}& \left(24g\right) & \mbox{Zn I} \\ \mathbf{B}_{46} & =& \left(y_7 + z_7\right) \, \mathbf{a}_{1}+ z_7 \, \mathbf{a}_{2}+ y_7 \, \mathbf{a}_{3}& =& y_7 \, a \, \mathbf{\hat{y}}+ z_7 \, a \, \mathbf{\hat{z}}& \left(24g\right) & \mbox{Zn II} \\ \mathbf{B}_{47} & =& \left(z_7 - y_7\right) \, \mathbf{a}_{1}+ z_7 \, \mathbf{a}_{2}- y_7 \, \mathbf{a}_{3}& =& - y_7 \, a \, \mathbf{\hat{y}}+ z_7 \, a \, \mathbf{\hat{z}}& \left(24g\right) & \mbox{Zn II} \\ \mathbf{B}_{48} & =& \left(y_7 - z_7\right) \, \mathbf{a}_{1}- z_7 \, \mathbf{a}_{2}+ y_7 \, \mathbf{a}_{3}& =& y_7 \, a \, \mathbf{\hat{y}}- z_7 \, a \, \mathbf{\hat{z}}& \left(24g\right) & \mbox{Zn II} \\ \mathbf{B}_{49} & =& - \left(y_7 + z_7\right) \, \mathbf{a}_{1}- z_7 \, \mathbf{a}_{2}- y_7 \, \mathbf{a}_{3}& =& - y_7 \, a \, \mathbf{\hat{y}}- z_7 \, a \, \mathbf{\hat{z}}& \left(24g\right) & \mbox{Zn II} \\ \mathbf{B}_{50} & =& y_7 \, \mathbf{a}_{1}+ \left(y_7 + z_7\right) \, \mathbf{a}_{2}+ z_7 \, \mathbf{a}_{3}& =& z_7 \, a \, \mathbf{\hat{x}}+ y_7 \, a \, \mathbf{\hat{z}}& \left(24g\right) & \mbox{Zn II} \\ \mathbf{B}_{51} & =& y_7 \, \mathbf{a}_{1}+ \left(y_7 - z_7\right) \, \mathbf{a}_{2}- z_7 \, \mathbf{a}_{3}& =& - z_7 \, a \, \mathbf{\hat{x}}+ y_7 \, a \, \mathbf{\hat{z}}& \left(24g\right) & \mbox{Zn II} \\ \mathbf{B}_{52} & =& - y_7 \, \mathbf{a}_{1}+ \left(z_7 - y_7\right) \, \mathbf{a}_{2}+ z_7 \, \mathbf{a}_{3}& =& z_7 \, a \, \mathbf{\hat{x}}- y_7 \, a \, \mathbf{\hat{z}}& \left(24g\right) & \mbox{Zn II} \\ \mathbf{B}_{53} & =& - y_7 \, \mathbf{a}_{1}- \left(y_7 + z_7\right) \, \mathbf{a}_{2}- z_7 \, \mathbf{a}_{3}& =& - z_7 \, a \, \mathbf{\hat{x}}- y_7 \, a \, \mathbf{\hat{z}}& \left(24g\right) & \mbox{Zn II} \\ \mathbf{B}_{54} & =& z_7 \, \mathbf{a}_{1}+ y_7 \, \mathbf{a}_{2}+ \left(y_7 + z_7\right) \, \mathbf{a}_{3}& =& y_7 \, a \, \mathbf{\hat{x}}+ z_7 \, a \, \mathbf{\hat{y}}& \left(24g\right) & \mbox{Zn II} \\ \mathbf{B}_{55} & =& z_7 \, \mathbf{a}_{1}- y_7 \, \mathbf{a}_{2}+ \left(z_7 - y_7\right) \, \mathbf{a}_{3}& =& - y_7 \, a \, \mathbf{\hat{x}}+ z_7 \, a \, \mathbf{\hat{y}}& \left(24g\right) & \mbox{Zn II} \\ \mathbf{B}_{56} & =& - z_7 \, \mathbf{a}_{1}+ y_7 \, \mathbf{a}_{2}+ \left(y_7 - z_7\right) \, \mathbf{a}_{3}& =& y_7 \, a \, \mathbf{\hat{x}}- z_7 \, a \, \mathbf{\hat{y}}& \left(24g\right) & \mbox{Zn II} \\ \mathbf{B}_{57} & =& - z_7 \, \mathbf{a}_{1}- y_7 \, \mathbf{a}_{2}- \left(y_7 + z_7\right) \, \mathbf{a}_{3}& =& - y_7 \, a \, \mathbf{\hat{x}}- z_7 \, a \, \mathbf{\hat{y}}& \left(24g\right) & \mbox{Zn II} \\ \mathbf{B}_{58} & =& \left(y_8+z_8\right) \, \mathbf{a}_{1}+ \left(z_8+x_8\right) \, \mathbf{a}_{2}+ \left(x_8+y_8\right) \, \mathbf{a}_{3}& =& x_8 \, a \, \mathbf{\hat{x}}+ y_8 \, a \, \mathbf{\hat{y}}+ z_8 \, a \, \mathbf{\hat{z}}& \left(48h\right) & \mbox{Zn III} \\ \mathbf{B}_{59} & =& \left(z_8-y_8\right) \, \mathbf{a}_{1}+ \left(z_8-x_8\right) \, \mathbf{a}_{2}- \left(x_8+y_8\right) \, \mathbf{a}_{3}& =& - x_8 \, a \, \mathbf{\hat{x}}- y_8 \, a \, \mathbf{\hat{y}}+ z_8 \, a \, \mathbf{\hat{z}}& \left(48h\right) & \mbox{Zn III} \\ \mathbf{B}_{60} & =& \left(y_8-z_8\right) \, \mathbf{a}_{1}- \left(z_8+x_8\right) \, \mathbf{a}_{2}+ \left(y_8-x_8\right) \, \mathbf{a}_{3}& =& - x_8 \, a \, \mathbf{\hat{x}}+ y_8 \, a \, \mathbf{\hat{y}}- z_8 \, a \, \mathbf{\hat{z}}& \left(48h\right) & \mbox{Zn III} \\ \mathbf{B}_{61} & =& - \left(y_8+z_8\right) \, \mathbf{a}_{1}+ \left(x_8-z_8\right) \, \mathbf{a}_{2}+ \left(x_8-y_8\right) \, \mathbf{a}_{3}& =& x_8 \, a \, \mathbf{\hat{x}}- y_8 \, a \, \mathbf{\hat{y}}- z_8 \, a \, \mathbf{\hat{z}}& \left(48h\right) & \mbox{Zn III} \\ \mathbf{B}_{62} & =& - \left(y_8+z_8\right) \, \mathbf{a}_{1}- \left(z_8+x_8\right) \, \mathbf{a}_{2}- \left(x_8+y_8\right) \, \mathbf{a}_{3}& =& - x_8 \, a \, \mathbf{\hat{x}}- y_8 \, a \, \mathbf{\hat{y}}- z_8 \, a \, \mathbf{\hat{z}}& \left(48h\right) & \mbox{Zn III} \\ \mathbf{B}_{63} & =& \left(y_8-z_8\right) \, \mathbf{a}_{1}+ \left(x_8-z_8\right) \, \mathbf{a}_{2}+ \left(x_8+y_8\right) \, \mathbf{a}_{3}& =& + x_8 \, a \, \mathbf{\hat{x}}+ y_8 \, a \, \mathbf{\hat{y}}- z_8 \, a \, \mathbf{\hat{z}}& \left(48h\right) & \mbox{Zn III} \\ \mathbf{B}_{64} & =& \left(z_8-y_8\right) \, \mathbf{a}_{1}+ \left(z_8+x_8\right) \, \mathbf{a}_{2}+ \left(x_8-y_8\right) \, \mathbf{a}_{3}& =& + x_8 \, a \, \mathbf{\hat{x}}- y_8 \, a \, \mathbf{\hat{y}}+ z_8 \, a \, \mathbf{\hat{z}}& \left(48h\right) & \mbox{Zn III} \\ \mathbf{B}_{65} & =& \left(y_8+z_8\right) \, \mathbf{a}_{1}+ \left(z_8-x_8\right) \, \mathbf{a}_{2}+ \left(y_8-x_8\right) \, \mathbf{a}_{3}& =& - x_8 \, a \, \mathbf{\hat{x}}+ y_8 \, a \, \mathbf{\hat{y}}+ z_8 \, a \, \mathbf{\hat{z}}& \left(48h\right) & \mbox{Zn III} \\ \mathbf{B}_{66} & =& \left(x_8+y_8\right) \, \mathbf{a}_{1}+ \left(y_8+z_8\right) \, \mathbf{a}_{2}+ \left(z_8+x_8\right) \, \mathbf{a}_{3}& =& z_8 \, a \, \mathbf{\hat{x}}+ x_8 \, a \, \mathbf{\hat{y}}+ y_8 \, a \, \mathbf{\hat{z}}& \left(48h\right) & \mbox{Zn III} \\ \mathbf{B}_{67} & =& \left(y_8-x_8\right) \, \mathbf{a}_{1}+ \left(y_8-z_8\right) \, \mathbf{a}_{2}- \left(z_8+x_8\right) \, \mathbf{a}_{3}& =& - z_8 \, a \, \mathbf{\hat{x}}- x_8 \, a \, \mathbf{\hat{y}}+ y_8 \, a \, \mathbf{\hat{z}}& \left(48h\right) & \mbox{Zn III} \\ \mathbf{B}_{68} & =& \left(x_8-y_8\right) \, \mathbf{a}_{1}- \left(y_8+z_8\right) \, \mathbf{a}_{2}+ \left(x_8-z_8\right) \, \mathbf{a}_{3}& =& - z_8 \, a \, \mathbf{\hat{x}}+ x_8 \, a \, \mathbf{\hat{y}}- y_8 \, a \, \mathbf{\hat{z}}& \left(48h\right) & \mbox{Zn III} \\ \mathbf{B}_{69} & =& - \left(x_8+y_8\right) \, \mathbf{a}_{1}+ \left(z_8-y_8\right) \, \mathbf{a}_{2}+ \left(z_8-x_8\right) \, \mathbf{a}_{3}& =& z_8 \, a \, \mathbf{\hat{x}}- x_8 \, a \, \mathbf{\hat{y}}- y_8 \, a \, \mathbf{\hat{z}}& \left(48h\right) & \mbox{Zn III} \\ \mathbf{B}_{70} & =& - \left(x_8+y_8\right) \, \mathbf{a}_{1}- \left(y_8+z_8\right) \, \mathbf{a}_{2}- \left(z_8+x_8\right) \, \mathbf{a}_{3}& =& - z_8 \, a \, \mathbf{\hat{x}}- x_8 \, a \, \mathbf{\hat{y}}- y_8 \, a \, \mathbf{\hat{z}}& \left(48h\right) & \mbox{Zn III} \\ \mathbf{B}_{71} & =& \left(x_8-y_8\right) \, \mathbf{a}_{1}+ \left(z_8-y_8\right) \, \mathbf{a}_{2}+ \left(z_8+x_8\right) \, \mathbf{a}_{3}& =& + z_8 \, a \, \mathbf{\hat{x}}+ x_8 \, a \, \mathbf{\hat{y}}- y_8 \, a \, \mathbf{\hat{z}}& \left(48h\right) & \mbox{Zn III} \\ \mathbf{B}_{72} & =& \left(y_8-x_8\right) \, \mathbf{a}_{1}+ \left(y_8+z_8\right) \, \mathbf{a}_{2}+ \left(z_8-x_8\right) \, \mathbf{a}_{3}& =& + z_8 \, a \, \mathbf{\hat{x}}- x_8 \, a \, \mathbf{\hat{y}}+ y_8 \, a \, \mathbf{\hat{z}}& \left(48h\right) & \mbox{Zn III} \\ \mathbf{B}_{73} & =& \left(x_8+y_8\right) \, \mathbf{a}_{1}+ \left(y_8-z_8\right) \, \mathbf{a}_{2}+ \left(x_8-z_8\right) \, \mathbf{a}_{3}& =& - z_8 \, a \, \mathbf{\hat{x}}+ x_8 \, a \, \mathbf{\hat{y}}+ y_8 \, a \, \mathbf{\hat{z}}& \left(48h\right) & \mbox{Zn III} \\ \mathbf{B}_{74} & =& \left(z_8+x_8\right) \, \mathbf{a}_{1}+ \left(x_8+y_8\right) \, \mathbf{a}_{2}+ \left(y_8+z_8\right) \, \mathbf{a}_{3}& =& y_8 \, a \, \mathbf{\hat{x}}+ z_8 \, a \, \mathbf{\hat{y}}+ x_8 \, a \, \mathbf{\hat{z}}& \left(48h\right) & \mbox{Zn III} \\ \mathbf{B}_{75} & =& \left(x_8-z_8\right) \, \mathbf{a}_{1}+ \left(x_8-y_8\right) \, \mathbf{a}_{2}- \left(y_8+z_8\right) \, \mathbf{a}_{3}& =& - y_8 \, a \, \mathbf{\hat{x}}- z_8 \, a \, \mathbf{\hat{y}}+ x_8 \, a \, \mathbf{\hat{z}}& \left(48h\right) & \mbox{Zn III} \\ \mathbf{B}_{76} & =& \left(z_8-x_8\right) \, \mathbf{a}_{1}- \left(x_8+y_8\right) \, \mathbf{a}_{2}+ \left(z_8-y_8\right) \, \mathbf{a}_{3}& =& - y_8 \, a \, \mathbf{\hat{x}}+ z_8 \, a \, \mathbf{\hat{y}}- x_8 \, a \, \mathbf{\hat{z}}& \left(48h\right) & \mbox{Zn III} \\ \mathbf{B}_{77} & =& - \left(z_8+x_8\right) \, \mathbf{a}_{1}+ \left(y_8-x_8\right) \, \mathbf{a}_{2}+ \left(y_8-z_8\right) \, \mathbf{a}_{3}& =& y_8 \, a \, \mathbf{\hat{x}}- z_8 \, a \, \mathbf{\hat{y}}- x_8 \, a \, \mathbf{\hat{z}}& \left(48h\right) & \mbox{Zn III} \\ \mathbf{B}_{78} & =& - \left(z_8+x_8\right) \, \mathbf{a}_{1}- \left(x_8+y_8\right) \, \mathbf{a}_{2}- \left(y_8+z_8\right) \, \mathbf{a}_{3}& =& - y_8 \, a \, \mathbf{\hat{x}}- z_8 \, a \, \mathbf{\hat{y}}- x_8 \, a \, \mathbf{\hat{z}}& \left(48h\right) & \mbox{Zn III} \\ \mathbf{B}_{79} & =& \left(z_8-x_8\right) \, \mathbf{a}_{1}+ \left(y_8-x_8\right) \, \mathbf{a}_{2}+ \left(y_8+z_8\right) \, \mathbf{a}_{3}& =& + y_8 \, a \, \mathbf{\hat{x}}+ z_8 \, a \, \mathbf{\hat{y}}- x_8 \, a \, \mathbf{\hat{z}}& \left(48h\right) & \mbox{Zn III} \\ \mathbf{B}_{80} & =& \left(x_8-z_8\right) \, \mathbf{a}_{1}+ \left(x_8+y_8\right) \, \mathbf{a}_{2}+ \left(y_8-z_8\right) \, \mathbf{a}_{3}& =& + y_8 \, a \, \mathbf{\hat{x}}- z_8 \, a \, \mathbf{\hat{y}}+ x_8 \, a \, \mathbf{\hat{z}}& \left(48h\right) & \mbox{Zn III} \\ \mathbf{B}_{81} & =& \left(z_8+x_8\right) \, \mathbf{a}_{1}+ \left(x_8-y_8\right) \, \mathbf{a}_{2}+ \left(z_8-y_8\right) \, \mathbf{a}_{3}& =& - y_8 \, a \, \mathbf{\hat{x}}+ z_8 \, a \, \mathbf{\hat{y}}+ x_8 \, a \, \mathbf{\hat{z}}& \left(48h\right) & \mbox{Zn III} \\ \end{array} \]

References

  • G. Bergman, J. L. T. Waugh, and L. Pauling, The crystal structure of the metallic phase Mg32(Al, Zn)49, Acta Cryst. 10, 254–259 (1957), doi:10.1107/S0365110X57000808.
  • N. Pavlyuk and G. Dmytriv and V. Pavlyuk and H. Ehrenberg, Li20Mg6Cu13Al42: a new ordered quaternary superstructure to the icosahedral T-Mg32(Zn,Al)49 phase with fullerene-like Al60 cluster, Acta Cryst. B 75, 168–174 (2019), doi:10.1107/S2052520619000349.

Geometry files


Prototype Generator

aflow --proto=AB32C48_cI162_204_a_2efg_2gh --params=

Species:

Running:

Output: