Au5Mn2 Structure: A5B2_mC14_12_a2i_i

Picture of Structure; Click for Big Picture
Prototype : Au5Mn2
AFLOW prototype label : A5B2_mC14_12_a2i_i
Strukturbericht designation : None
Pearson symbol : mC14
Space group number : 12
Space group symbol : $\mbox{C2/m}$
AFLOW prototype command : aflow --proto=A5B2_mC14_12_a2i_i
--params=
$a$,$b/a$,$c/a$,$\beta$,$x_{2}$,$z_{2}$,$x_{3}$,$z_{3}$,$x_{4}$,$z_{4}$


  • As noted by (Pearson, 1972), this structure is very nearly cubic close-packed. As such, it is frequently used for cluster expansion models.

Base-centered Monoclinic primitive vectors:

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

Basis vectors:

\[ \begin{array}{ccccccc} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{Atom Type} \\ \mathbf{B}_{1} & = & 0 \, \mathbf{a}_{1} + 0 \, \mathbf{a}_{2} + 0 \, \mathbf{a}_{3} & = & 0 \mathbf{\hat{x}} + 0 \mathbf{\hat{y}} + 0 \mathbf{\hat{z}} & \left(2a\right) & \mbox{Au I} \\ \mathbf{B}_{2} & =& x_{2} \, \mathbf{a}_{1} + x_{2} \, \mathbf{a}_{2} + z_{2} \, \mathbf{a}_{3}& =& \left(x_{2} \, a \, + \, z_{2} \, c \, \cos\beta\right) \, \mathbf{\hat{x}}+ z_{2} \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(4i\right) & \mbox{Au II} \\ \mathbf{B}_{3} & =& - x_{2} \, \mathbf{a}_{1} - x_{2} \, \mathbf{a}_{2} - z_{2} \, \mathbf{a}_{3}& =& - \left(x_{2} \, a \, + \, z_{2} \, c \, \cos\beta\right) \, \mathbf{\hat{x}}- z_{2} \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(4i\right) & \mbox{Au II} \\ \mathbf{B}_{4} & =& x_{3} \, \mathbf{a}_{1} + x_{3} \, \mathbf{a}_{2} + z_{3} \, \mathbf{a}_{3}& =& \left(x_{3} \, a \, + \, z_{3} \, c \, \cos\beta\right) \, \mathbf{\hat{x}}+ z_{3} \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(4i\right) & \mbox{Au III} \\ \mathbf{B}_{5} & =& - x_{3} \, \mathbf{a}_{1} - x_{3} \, \mathbf{a}_{2} - z_{3} \, \mathbf{a}_{3}& =& - \left(x_{3} \, a \, + \, z_{3} \, c \, \cos\beta\right) \, \mathbf{\hat{x}}- z_{3} \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(4i\right) & \mbox{Au III} \\ \mathbf{B}_{6} & =& x_{4} \, \mathbf{a}_{1} + x_{4} \, \mathbf{a}_{2} + z_{4} \, \mathbf{a}_{3}& =& \left(x_{4} \, a \, + \, z_{4} \, c \, \cos\beta\right) \, \mathbf{\hat{x}}+ z_{4} \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(4i\right) & \mbox{Mn} \\ \mathbf{B}_{7} & =& - x_{4} \, \mathbf{a}_{1} - x_{4} \, \mathbf{a}_{2} - z_{4} \, \mathbf{a}_{3}& =& - \left(x_{4} \, a \, + \, z_{4} \, c \, \cos\beta\right) \, \mathbf{\hat{x}}- z_{4} \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(4i\right) & \mbox{Mn} \\ \end{array} \]

References

  • S. G. Humble, Establishment of an ordered phase of composition Au5Mn2 in the gold–manganese system, Acta Cryst. 17, 1485–1486 (1964), doi:10.1107/S0365110X64003723.

Found in

  • W. B. Pearson, The Crystal Chemistry and Physics of Metals and Alloys (Wiley– Interscience, New York, London, Sydney, Toronto, 1972)., pp. 346-348.

Geometry files


Prototype Generator

aflow --proto=A5B2_mC14_12_a2i_i --params=

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