Mg2Cu ($C_{b}$) Structure : AB2_oF48_70_g_fg

Picture of Structure; Click for Big Picture
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=
$a$,$b/a$,$c/a$,$y_{1}$,$z_{2}$,$z_{3}$


Other compounds with this structure

  • In2Ir, NbSn2, TiBi2, FeGaGe, and SbSnTi

Face-centered Orthorhombic primitive vectors:

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

Basis vectors:

\[ \begin{array}{ccccccc} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{Atom Type} \\ \mathbf{B}_{1} & = & 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) & \mbox{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) & \mbox{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) & \mbox{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) & \mbox{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) & \mbox{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) & \mbox{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) & \mbox{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) & \mbox{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) & \mbox{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) & \mbox{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) & \mbox{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) & \mbox{Mg II} \\ \end{array} \]

References

  • F. Gingl, P. Selvam, and K. Yvon, Structure refinement of Mg2Cu and a comparison of the Mg2Cu, Mg2Ni and Al2Cu structure types, Acta Crystallogr. Sect. B Struct. Sci. 49, 201–203 (1993), doi:10.1107/S0108768192008723.

Found in

Geometry files


Prototype Generator

aflow --proto=AB2_oF48_70_g_fg --params=

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