MgZn2 Hexagonal Laves ($C14$) Structure: AB2_hP12_194_f_ah

Picture of Structure; Click for Big Picture
Prototype : MgZn2
AFLOW prototype label : AB2_hP12_194_f_ah
Strukturbericht designation : $C14$
Pearson symbol : hP12
Space group number : 194
Space group symbol : $\mbox{P6}_{3}\mbox{/mmc}$
AFLOW prototype command : aflow --proto=AB2_hP12_194_f_ah
--params=
$a$,$c/a$,$z_{2}$,$x_{3}$


Other compounds with this structure

  • CaMg2, ZrRe2, KNa2, TaFe2, NbMn2, UNi2

Hexagonal primitive vectors:

\[ \begin{array}{ccc} \mathbf{a}_1 & = & \frac12 \, a \, \mathbf{\hat{x}} - \frac{\sqrt3}2 \, a \, \mathbf{\hat{y}} \\ \mathbf{a}_2 & = & \frac12 \, a \, \mathbf{\hat{x}} + \frac{\sqrt3}2 \, a \, \mathbf{\hat{y}} \\ \mathbf{a}_3 & = & c \, \mathbf{\hat{z}}\\ \end{array} \]

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{Zn I} \\ \mathbf{B}_{2}& = &\frac12 \, \mathbf{a}_{3}& = &\frac12 \, c \, \mathbf{\hat{z}}& \left(2a\right) & \mbox{Zn I} \\ \mathbf{B}_{3}& = &\frac13 \, \mathbf{a}_{1}+ \frac23 \, \mathbf{a}_{2}+ z_{2} \, \mathbf{a}_{3}& = &\frac12 \, a \, \mathbf{\hat{x}}+\frac{1}{2\sqrt{3}} \, a \, \mathbf{\hat{y}}+ z_{2} \, c \, \mathbf{\hat{z}}& \left(4f\right) & \mbox{Mg} \\ \mathbf{B}_{4}& = &\frac23 \, \mathbf{a}_{1}+ \frac13 \, \mathbf{a}_{2}+ \left(\frac12 + z_{2}\right) \, \mathbf{a}_{3}& = &\frac12 \, a \, \mathbf{\hat{x}}- \frac{1}{2\sqrt{3}} \, a \, \mathbf{\hat{y}}+ \left(\frac12 + z_{2}\right) \, c \, \mathbf{\hat{z}}& \left(4f\right) & \mbox{Mg} \\ \mathbf{B}_{5}& = &\frac23 \, \mathbf{a}_{1}+ \frac13 \, \mathbf{a}_{2}- z_{2} \, \mathbf{a}_{3}& = &\frac12 \, a \, \mathbf{\hat{x}}- \frac{1}{2\sqrt{3}} \, a \, \mathbf{\hat{y}}- z_{2} \, c \, \mathbf{\hat{z}}& \left(4f\right) & \mbox{Mg} \\ \mathbf{B}_{6}& = &\frac13 \, \mathbf{a}_{1}+ \frac23 \, \mathbf{a}_{2}+ \left(\frac12 - z_{2}\right) \, \mathbf{a}_{3}& = &\frac12 \, a \, \mathbf{\hat{x}}+ \frac{1}{2\sqrt{3}} \, a \, \mathbf{\hat{y}}+ \left(\frac12 - z_{2}\right) \, c \, \mathbf{\hat{z}}& \left(4f\right) & \mbox{Mg} \\ \mathbf{B}_{7}& = &x_{3} \, \mathbf{a}_{1}+ 2 \, x_{3} \, \mathbf{a}_{2}+ \frac14 \, \mathbf{a}_{3}& = &\frac32 \, x_{3} \, a \, \mathbf{\hat{x}}+ \frac{\sqrt3}{2} \, x_{3} \, a \, \mathbf{\hat{y}}+ \frac14 \, c \, \mathbf{\hat{z}}& \left(6h\right) & \mbox{Zn II} \\ \mathbf{B}_{8}& = &- 2 \, x_{3} \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}+ \frac14 \, \mathbf{a}_{3}& = &- \frac32 \, x_{3} \, a \, \mathbf{\hat{x}}+ \frac{\sqrt3}{2} \, x_{3} \, a \, \mathbf{\hat{y}}+ \frac14 \, c \, \mathbf{\hat{z}}& \left(6h\right) & \mbox{Zn II} \\ \mathbf{B}_{9}& = &x_{3} \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}+ \frac14 \, \mathbf{a}_{3}& = &- \sqrt3 \, x_{3} \, a \, \mathbf{\hat{y}}+ \frac14 \, c \, \mathbf{\hat{z}}& \left(6h\right) & \mbox{Zn II} \\ \mathbf{B}_{10}& = &- x_{3} \, \mathbf{a}_{1}- 2 \, x_{3} \, \mathbf{a}_{2}+ \frac34 \, \mathbf{a}_{3}& = &- \frac32 \, x_{3} \, a \, \mathbf{\hat{x}}- \frac{\sqrt3}{2} \, x_{3} \, a \, \mathbf{\hat{y}}+ \frac34 \, c \, \mathbf{\hat{z}}& \left(6h\right) & \mbox{Zn II} \\ \mathbf{B}_{11}& = &2 \, x_{3} \, \mathbf{a}_{1}+ x_{3} \, \mathbf{a}_{2}+ \frac34 \, \mathbf{a}_{3}& = &\frac32 \, x_{3} \, a \, \mathbf{\hat{x}}- \frac{\sqrt3}{2} \, x_{3} \, a \, \mathbf{\hat{y}}+ \frac34 \, c \, \mathbf{\hat{z}}& \left(6h\right) & \mbox{Zn II} \\ \mathbf{B}_{12}& = &- x_{3} \, \mathbf{a}_{1}+ x_{3} \, \mathbf{a}_{2}+ \frac34 \, \mathbf{a}_{3}& = &+ \sqrt3 \, x_{3} \, a \, \mathbf{\hat{y}}+ \frac34 \, c \, \mathbf{\hat{z}}& \left(6h\right) & \mbox{Zn II} \\ \end{array} \]

References

  • T. Ohba, Y. Kitano, and Y. Komura, The charge–density study of the Laves phases, MgZn2 and MgCu2, Acta Crystallographic C 40, 1–5 (1984), doi:10.1107/S0108270184002791.

Geometry files


Prototype Generator

aflow --proto=AB2_hP12_194_f_ah --params=

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