TaTi3 (BCC SQS–16) Structure : AB3_mC32_8_4a_12a

Picture of Structure; Click for Big Picture
Prototype : TaTi3
AFLOW prototype label : AB3_mC32_8_4a_12a
Strukturbericht designation : None
Pearson symbol : mC32
Space group number : 8
Space group symbol : $Cm$
AFLOW prototype command : aflow --proto=AB3_mC32_8_4a_12a
--params=
$a$,$b/a$,$c/a$,$\beta$,$x_{1}$,$z_{1}$,$x_{2}$,$z_{2}$,$x_{3}$,$z_{3}$,$x_{4}$,$z_{4}$,$x_{5}$,$z_{5}$,$x_{6}$,$z_{6}$,$x_{7}$,$z_{7}$,$x_{8}$,$z_{8}$,$x_{9}$,$z_{9}$,$x_{10}$,$z_{10}$,$x_{11}$,$z_{11}$,$x_{12}$,$z_{12}$,$x_{13}$,$z_{13}$,$x_{14}$,$z_{14}$,$x_{15}$,$z_{15}$,$x_{16}$,$z_{16}$


  • This is a special quasirandom structure with 16 atoms per unit cell (SQS–16) for a bcc binary substitutional alloy $AxB1–x (Jiang, 2004). This prototype represents the $x=0.25$ and $x=0.75$ structures (change concentration by swapping elements). The $x=0.5$ structure is given by AB_aP16_2_4i_4i.

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} & = & x_{1} \, \mathbf{a}_{1} + x_{1} \, \mathbf{a}_{2} + z_{1} \, \mathbf{a}_{3} & = & \left(x_{1}a+z_{1}c\cos\beta\right) \, \mathbf{\hat{x}} + z_{1}c\sin\beta \, \mathbf{\hat{z}} & \left(2a\right) & \mbox{Ta 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(2a\right) & \mbox{Ta II} \\ \mathbf{B}_{3} & = & 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(2a\right) & \mbox{Ta III} \\ \mathbf{B}_{4} & = & 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(2a\right) & \mbox{Ta IV} \\ \mathbf{B}_{5} & = & 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(2a\right) & \mbox{Ti I} \\ \mathbf{B}_{6} & = & 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(2a\right) & \mbox{Ti II} \\ \mathbf{B}_{7} & = & 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(2a\right) & \mbox{Ti III} \\ \mathbf{B}_{8} & = & 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(2a\right) & \mbox{Ti IV} \\ \mathbf{B}_{9} & = & 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(2a\right) & \mbox{Ti V} \\ \mathbf{B}_{10} & = & x_{10} \, \mathbf{a}_{1} + x_{10} \, \mathbf{a}_{2} + z_{10} \, \mathbf{a}_{3} & = & \left(x_{10}a+z_{10}c\cos\beta\right) \, \mathbf{\hat{x}} + z_{10}c\sin\beta \, \mathbf{\hat{z}} & \left(2a\right) & \mbox{Ti VI} \\ \mathbf{B}_{11} & = & x_{11} \, \mathbf{a}_{1} + x_{11} \, \mathbf{a}_{2} + z_{11} \, \mathbf{a}_{3} & = & \left(x_{11}a+z_{11}c\cos\beta\right) \, \mathbf{\hat{x}} + z_{11}c\sin\beta \, \mathbf{\hat{z}} & \left(2a\right) & \mbox{Ti VII} \\ \mathbf{B}_{12} & = & x_{12} \, \mathbf{a}_{1} + x_{12} \, \mathbf{a}_{2} + z_{12} \, \mathbf{a}_{3} & = & \left(x_{12}a+z_{12}c\cos\beta\right) \, \mathbf{\hat{x}} + z_{12}c\sin\beta \, \mathbf{\hat{z}} & \left(2a\right) & \mbox{Ti VIII} \\ \mathbf{B}_{13} & = & x_{13} \, \mathbf{a}_{1} + x_{13} \, \mathbf{a}_{2} + z_{13} \, \mathbf{a}_{3} & = & \left(x_{13}a+z_{13}c\cos\beta\right) \, \mathbf{\hat{x}} + z_{13}c\sin\beta \, \mathbf{\hat{z}} & \left(2a\right) & \mbox{Ti IX} \\ \mathbf{B}_{14} & = & x_{14} \, \mathbf{a}_{1} + x_{14} \, \mathbf{a}_{2} + z_{14} \, \mathbf{a}_{3} & = & \left(x_{14}a+z_{14}c\cos\beta\right) \, \mathbf{\hat{x}} + z_{14}c\sin\beta \, \mathbf{\hat{z}} & \left(2a\right) & \mbox{Ti X} \\ \mathbf{B}_{15} & = & x_{15} \, \mathbf{a}_{1} + x_{15} \, \mathbf{a}_{2} + z_{15} \, \mathbf{a}_{3} & = & \left(x_{15}a+z_{15}c\cos\beta\right) \, \mathbf{\hat{x}} + z_{15}c\sin\beta \, \mathbf{\hat{z}} & \left(2a\right) & \mbox{Ti XI} \\ \mathbf{B}_{16} & = & x_{16} \, \mathbf{a}_{1} + x_{16} \, \mathbf{a}_{2} + z_{16} \, \mathbf{a}_{3} & = & \left(x_{16}a+z_{16}c\cos\beta\right) \, \mathbf{\hat{x}} + z_{16}c\sin\beta \, \mathbf{\hat{z}} & \left(2a\right) & \mbox{Ti XII} \\ \end{array} \]

References

  • C. Jiang, C. Wolverton, J. Sofo, L.–Q. Chen, and Z.–K. Liu, First–principles study of binary bcc alloys using special quasirandom structures, Phys. Rev. B 69, 214202 (2004), doi:10.1103/PhysRevB.69.214202.

Geometry files


Prototype Generator

aflow --proto=AB3_mC32_8_4a_12a --params=

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