Os4Al13 Structure : A13B4_mC34_12_b6i_2i

Picture of Structure; Click for Big Picture
Prototype : Al13Os4
AFLOW prototype label : A13B4_mC34_12_b6i_2i
Strukturbericht designation : None
Pearson symbol : mC34
Space group number : 12
Space group symbol : $C2/m$
AFLOW prototype command : aflow --proto=A13B4_mC34_12_b6i_2i
--params=
$a$,$b/a$,$c/a$,$\beta$,$x_{2}$,$z_{2}$,$x_{3}$,$z_{3}$,$x_{4}$,$z_{4}$,$x_{5}$,$z_{5}$,$x_{6}$,$z_{6}$,$x_{7}$,$z_{7}$,$x_{8}$,$z_{8}$,$x_{9}$,$z_{9}$


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} & = & \frac{1}{2} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{2} & = & \frac{1}{2}a \, \mathbf{\hat{x}} & \left(2b\right) & \mbox{Al 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{Al 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{Al 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{Al 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{Al 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{Al IV} \\ \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{Al IV} \\ \mathbf{B}_{8} & = & x_{5} \, \mathbf{a}_{1} + x_{5} \, \mathbf{a}_{2} + z_{5} \, \mathbf{a}_{3} & = & \left(x_{5}a+z_{5}c\cos\beta\right) \, \mathbf{\hat{x}} + z_{5}c\sin\beta \, \mathbf{\hat{z}} & \left(4i\right) & \mbox{Al V} \\ \mathbf{B}_{9} & = & -x_{5} \, \mathbf{a}_{1}-x_{5} \, \mathbf{a}_{2}-z_{5} \, \mathbf{a}_{3} & = & \left(-x_{5}a-z_{5}c\cos\beta\right) \, \mathbf{\hat{x}}-z_{5}c\sin\beta \, \mathbf{\hat{z}} & \left(4i\right) & \mbox{Al V} \\ \mathbf{B}_{10} & = & x_{6} \, \mathbf{a}_{1} + x_{6} \, \mathbf{a}_{2} + z_{6} \, \mathbf{a}_{3} & = & \left(x_{6}a+z_{6}c\cos\beta\right) \, \mathbf{\hat{x}} + z_{6}c\sin\beta \, \mathbf{\hat{z}} & \left(4i\right) & \mbox{Al VI} \\ \mathbf{B}_{11} & = & -x_{6} \, \mathbf{a}_{1}-x_{6} \, \mathbf{a}_{2}-z_{6} \, \mathbf{a}_{3} & = & \left(-x_{6}a-z_{6}c\cos\beta\right) \, \mathbf{\hat{x}}-z_{6}c\sin\beta \, \mathbf{\hat{z}} & \left(4i\right) & \mbox{Al VI} \\ \mathbf{B}_{12} & = & x_{7} \, \mathbf{a}_{1} + x_{7} \, \mathbf{a}_{2} + z_{7} \, \mathbf{a}_{3} & = & \left(x_{7}a+z_{7}c\cos\beta\right) \, \mathbf{\hat{x}} + z_{7}c\sin\beta \, \mathbf{\hat{z}} & \left(4i\right) & \mbox{Al VII} \\ \mathbf{B}_{13} & = & -x_{7} \, \mathbf{a}_{1}-x_{7} \, \mathbf{a}_{2}-z_{7} \, \mathbf{a}_{3} & = & \left(-x_{7}a-z_{7}c\cos\beta\right) \, \mathbf{\hat{x}}-z_{7}c\sin\beta \, \mathbf{\hat{z}} & \left(4i\right) & \mbox{Al VII} \\ \mathbf{B}_{14} & = & x_{8} \, \mathbf{a}_{1} + x_{8} \, \mathbf{a}_{2} + z_{8} \, \mathbf{a}_{3} & = & \left(x_{8}a+z_{8}c\cos\beta\right) \, \mathbf{\hat{x}} + z_{8}c\sin\beta \, \mathbf{\hat{z}} & \left(4i\right) & \mbox{Os I} \\ \mathbf{B}_{15} & = & -x_{8} \, \mathbf{a}_{1}-x_{8} \, \mathbf{a}_{2}-z_{8} \, \mathbf{a}_{3} & = & \left(-x_{8}a-z_{8}c\cos\beta\right) \, \mathbf{\hat{x}}-z_{8}c\sin\beta \, \mathbf{\hat{z}} & \left(4i\right) & \mbox{Os I} \\ \mathbf{B}_{16} & = & x_{9} \, \mathbf{a}_{1} + x_{9} \, \mathbf{a}_{2} + z_{9} \, \mathbf{a}_{3} & = & \left(x_{9}a+z_{9}c\cos\beta\right) \, \mathbf{\hat{x}} + z_{9}c\sin\beta \, \mathbf{\hat{z}} & \left(4i\right) & \mbox{Os II} \\ \mathbf{B}_{17} & = & -x_{9} \, \mathbf{a}_{1}-x_{9} \, \mathbf{a}_{2}-z_{9} \, \mathbf{a}_{3} & = & \left(-x_{9}a-z_{9}c\cos\beta\right) \, \mathbf{\hat{x}}-z_{9}c\sin\beta \, \mathbf{\hat{z}} & \left(4i\right) & \mbox{Os II} \\ \end{array} \]

References

Geometry files


Prototype Generator

aflow --proto=A13B4_mC34_12_b6i_2i --params=

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