Ta3Ti5 (BCC SQS–16) Structure : A3B5_oC32_38_abce_abcdf

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Prototype : Ta3Ti5
AFLOW prototype label : A3B5_oC32_38_abce_abcdf
Strukturbericht designation : None
Pearson symbol : oC32
Space group number : 38
Space group symbol : $Amm2$
AFLOW prototype command : aflow --proto=A3B5_oC32_38_abce_abcdf
--params=
$a$,$b/a$,$c/a$,$z_{1}$,$z_{2}$,$z_{3}$,$z_{4}$,$x_{5}$,$z_{5}$,$x_{6}$,$z_{6}$,$y_{7}$,$z_{7}$,$y_{8}$,$z_{8}$,$x_{9}$,$y_{9}$,$z_{9}$



Base-centered Orthorhombic primitive vectors:

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

Basis vectors:

\[ \begin{array}{ccccccc} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{Atom Type} \\ \mathbf{B}_{1} & = & -z_{1} \, \mathbf{a}_{2} + z_{1} \, \mathbf{a}_{3} & = & z_{1}c \, \mathbf{\hat{z}} & \left(2a\right) & \mbox{Ta I} \\ \mathbf{B}_{2} & = & -z_{2} \, \mathbf{a}_{2} + z_{2} \, \mathbf{a}_{3} & = & z_{2}c \, \mathbf{\hat{z}} & \left(2a\right) & \mbox{Ti I} \\ \mathbf{B}_{3} & = & \frac{1}{2} \, \mathbf{a}_{1}-z_{3} \, \mathbf{a}_{2} + z_{3} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + z_{3}c \, \mathbf{\hat{z}} & \left(2b\right) & \mbox{Ta II} \\ \mathbf{B}_{4} & = & \frac{1}{2} \, \mathbf{a}_{1}-z_{4} \, \mathbf{a}_{2} + z_{4} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + z_{4}c \, \mathbf{\hat{z}} & \left(2b\right) & \mbox{Ti II} \\ \mathbf{B}_{5} & = & x_{5} \, \mathbf{a}_{1}-z_{5} \, \mathbf{a}_{2} + z_{5} \, \mathbf{a}_{3} & = & x_{5}a \, \mathbf{\hat{x}} + z_{5}c \, \mathbf{\hat{z}} & \left(4c\right) & \mbox{Ta III} \\ \mathbf{B}_{6} & = & -x_{5} \, \mathbf{a}_{1}-z_{5} \, \mathbf{a}_{2} + z_{5} \, \mathbf{a}_{3} & = & -x_{5}a \, \mathbf{\hat{x}} + z_{5}c \, \mathbf{\hat{z}} & \left(4c\right) & \mbox{Ta III} \\ \mathbf{B}_{7} & = & x_{6} \, \mathbf{a}_{1}-z_{6} \, \mathbf{a}_{2} + z_{6} \, \mathbf{a}_{3} & = & x_{6}a \, \mathbf{\hat{x}} + z_{6}c \, \mathbf{\hat{z}} & \left(4c\right) & \mbox{Ti III} \\ \mathbf{B}_{8} & = & -x_{6} \, \mathbf{a}_{1}-z_{6} \, \mathbf{a}_{2} + z_{6} \, \mathbf{a}_{3} & = & -x_{6}a \, \mathbf{\hat{x}} + z_{6}c \, \mathbf{\hat{z}} & \left(4c\right) & \mbox{Ti III} \\ \mathbf{B}_{9} & = & \left(y_{7}-z_{7}\right) \, \mathbf{a}_{2} + \left(y_{7}+z_{7}\right) \, \mathbf{a}_{3} & = & y_{7}b \, \mathbf{\hat{y}} + z_{7}c \, \mathbf{\hat{z}} & \left(4d\right) & \mbox{Ti IV} \\ \mathbf{B}_{10} & = & \left(-y_{7}-z_{7}\right) \, \mathbf{a}_{2} + \left(-y_{7}+z_{7}\right) \, \mathbf{a}_{3} & = & -y_{7}b \, \mathbf{\hat{y}} + z_{7}c \, \mathbf{\hat{z}} & \left(4d\right) & \mbox{Ti IV} \\ \mathbf{B}_{11} & = & \frac{1}{2} \, \mathbf{a}_{1} + \left(y_{8}-z_{8}\right) \, \mathbf{a}_{2} + \left(y_{8}+z_{8}\right) \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + y_{8}b \, \mathbf{\hat{y}} + z_{8}c \, \mathbf{\hat{z}} & \left(4e\right) & \mbox{Ta IV} \\ \mathbf{B}_{12} & = & \frac{1}{2} \, \mathbf{a}_{1} + \left(-y_{8}-z_{8}\right) \, \mathbf{a}_{2} + \left(-y_{8}+z_{8}\right) \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}}-y_{8}b \, \mathbf{\hat{y}} + z_{8}c \, \mathbf{\hat{z}} & \left(4e\right) & \mbox{Ta IV} \\ \mathbf{B}_{13} & = & x_{9} \, \mathbf{a}_{1} + \left(y_{9}-z_{9}\right) \, \mathbf{a}_{2} + \left(y_{9}+z_{9}\right) \, \mathbf{a}_{3} & = & x_{9}a \, \mathbf{\hat{x}} + y_{9}b \, \mathbf{\hat{y}} + z_{9}c \, \mathbf{\hat{z}} & \left(8f\right) & \mbox{Ti V} \\ \mathbf{B}_{14} & = & -x_{9} \, \mathbf{a}_{1} + \left(-y_{9}-z_{9}\right) \, \mathbf{a}_{2} + \left(-y_{9}+z_{9}\right) \, \mathbf{a}_{3} & = & -x_{9}a \, \mathbf{\hat{x}}-y_{9}b \, \mathbf{\hat{y}} + z_{9}c \, \mathbf{\hat{z}} & \left(8f\right) & \mbox{Ti V} \\ \mathbf{B}_{15} & = & x_{9} \, \mathbf{a}_{1} + \left(-y_{9}-z_{9}\right) \, \mathbf{a}_{2} + \left(-y_{9}+z_{9}\right) \, \mathbf{a}_{3} & = & x_{9}a \, \mathbf{\hat{x}}-y_{9}b \, \mathbf{\hat{y}} + z_{9}c \, \mathbf{\hat{z}} & \left(8f\right) & \mbox{Ti V} \\ \mathbf{B}_{16} & = & -x_{9} \, \mathbf{a}_{1} + \left(y_{9}-z_{9}\right) \, \mathbf{a}_{2} + \left(y_{9}+z_{9}\right) \, \mathbf{a}_{3} & = & -x_{9}a \, \mathbf{\hat{x}} + y_{9}b \, \mathbf{\hat{y}} + z_{9}c \, \mathbf{\hat{z}} & \left(8f\right) & \mbox{Ti V} \\ \end{array} \]

References

  • T. Chakraborty, J. Rogal, and R. Drautz, Unraveling the composition dependence of the martensitic transformation temperature: A first–principles study of Ti–Ta alloys, Phys. Rev. B 94, 224104 (2016), doi:10.1103/PhysRevB.94.224104.

Geometry files


Prototype Generator

aflow --proto=A3B5_oC32_38_abce_abcdf --params=

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