Cu2Mg Cubic Laves Structure ($C15$): A2B_cF24_227_d_a

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Prototype : Cu2Mg
AFLOW prototype label : A2B_cF24_227_d_a
Strukturbericht designation : $C15$
Pearson symbol : cF24
Space group number : 227
Space group symbol : $\mbox{Fd}\bar{3}\mbox{m}$
AFLOW prototype command : aflow --proto=A2B_cF24_227_d_a
--params=
$a$


Other compounds with this structure

  • CsBi2, RbBi2

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:

\[ \begin{array}{ccccccc} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{Atom Type} \\ \mathbf{B}_{1} & = &\frac18 \, \mathbf{a}_{1}+ \frac18 \, \mathbf{a}_{2}+ \frac18 \, \mathbf{a}_{3}& = &\frac18 \, a \, \mathbf{\hat{x}}+ \frac18 \, a \, \mathbf{\hat{y}}+ \frac18 \, a \, \mathbf{\hat{z}}& \left(8a\right) & \mbox{Mg} \\ \mathbf{B}_{2} & = &\frac78 \, \mathbf{a}_{1}+ \frac78 \, \mathbf{a}_{2}+ \frac78 \, \mathbf{a}_{3}& = &\frac78 \, a \, \mathbf{\hat{x}}+ \frac78 \, a \, \mathbf{\hat{y}}+ \frac78 \, a \, \mathbf{\hat{z}}& \left(8a\right) & \mbox{Mg} \\ \mathbf{B}_{3} & = &\frac12 \, \mathbf{a}_{1}+ \frac12 \, \mathbf{a}_{2}+ \frac12 \, \mathbf{a}_{3}& = &\frac12 \, a \, \mathbf{\hat{x}}+ \frac12 \, a \, \mathbf{\hat{y}}+ \frac12 \, a \, \mathbf{\hat{z}}& \left(16d\right) & \mbox{Cu} \\ \mathbf{B}_{4} & = &\frac12 \, \mathbf{a}_{1}+ \frac12 \, \mathbf{a}_{2}& = &\frac14 \, a \, \mathbf{\hat{x}}+ \frac14 \, a \, \mathbf{\hat{y}}+ \frac12 \, a \, \mathbf{\hat{z}}& \left(16d\right) & \mbox{Cu} \\ \mathbf{B}_{5} & = &\frac12 \, \mathbf{a}_{1}+ \frac12 \, \mathbf{a}_{3}& = &\frac14 \, a \, \mathbf{\hat{x}}+ \frac12 \, a \, \mathbf{\hat{y}}+ \frac14 \, a \, \mathbf{\hat{z}}& \left(16d\right) & \mbox{Cu} \\ \mathbf{B}_{6} & = &\frac12 \, \mathbf{a}_{2}+ \frac12 \, \mathbf{a}_{3}& = &\frac12 \, a \, \mathbf{\hat{x}}+ \frac14 \, a \, \mathbf{\hat{y}}+ \frac14 \, a \, \mathbf{\hat{z}}& \left(16d\right) & \mbox{Cu} \\ \end{array} \]

References

  • J. B. Friauf, The Crystal Structures of Two Intermetallic Compounds, J. Am. Chem. Soc. 49, 3107–3114 (1927), doi:10.1021/ja01411a017.

Found in

  • R. W. G. Wyckoff, Crystal Structures Vol. 1 (Wiley, 1963), 2nd edn., pp. 365-367.

Geometry files


Prototype Generator

aflow --proto=A2B_cF24_227_d_a --params=

Species:

Running:

Output: