TaTi7 (BCC SQS–16) Structure : AB7_hR16_166_c_c2h

Picture of Structure; Click for Big Picture
Prototype : TaTi7
AFLOW prototype label : AB7_hR16_166_c_c2h
Strukturbericht designation : None
Pearson symbol : hR16
Space group number : 166
Space group symbol : $R\bar{3}m$
AFLOW prototype command : aflow --proto=AB7_hR16_166_c_c2h
--params=
$a$,$c/a$,$x_{1}$,$x_{2}$,$x_{3}$,$z_{3}$,$x_{4}$,$z_{4}$



Rhombohedral primitive vectors:

\[ \begin{array}{ccc} \mathbf{a}_1 & = & ~ \frac12 \, a \, \mathbf{\hat{x}} - \frac{1}{2\sqrt{3}} \, a \, \mathbf{\hat{y}} + \frac13 \, c \, \mathbf{\hat{z}} \\ \mathbf{a}_2 & = & \frac{1}{\sqrt{3}} \, a \, \mathbf{\hat{y}} + \frac13 \, c \, \mathbf{\hat{z}} \\ \mathbf{a}_3 & = & - \frac12 \, a \, \mathbf{\hat{x}} - \frac{1}{2\sqrt{3}} \, a \, \mathbf{\hat{y}} + \frac13 \, c \, \mathbf{\hat{z}} \\ \end{array} \]

Basis vectors:

\[ \begin{array}{ccccccc} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{Atom Type} \\ \mathbf{B}_{1} & = & x_{1} \, \mathbf{a}_{1} + x_{1} \, \mathbf{a}_{2} + x_{1} \, \mathbf{a}_{3} & = & x_{1}c \, \mathbf{\hat{z}} & \left(2c\right) & \mbox{Ta} \\ \mathbf{B}_{2} & = & -x_{1} \, \mathbf{a}_{1}-x_{1} \, \mathbf{a}_{2}-x_{1} \, \mathbf{a}_{3} & = & -x_{1}c \, \mathbf{\hat{z}} & \left(2c\right) & \mbox{Ta} \\ \mathbf{B}_{3} & = & x_{2} \, \mathbf{a}_{1} + x_{2} \, \mathbf{a}_{2} + x_{2} \, \mathbf{a}_{3} & = & x_{2}c \, \mathbf{\hat{z}} & \left(2c\right) & \mbox{Ti I} \\ \mathbf{B}_{4} & = & -x_{2} \, \mathbf{a}_{1}-x_{2} \, \mathbf{a}_{2}-x_{2} \, \mathbf{a}_{3} & = & -x_{2}c \, \mathbf{\hat{z}} & \left(2c\right) & \mbox{Ti I} \\ \mathbf{B}_{5} & = & x_{3} \, \mathbf{a}_{1} + x_{3} \, \mathbf{a}_{2} + z_{3} \, \mathbf{a}_{3} & = & \frac{1}{2}\left(x_{3}-z_{3}\right)a \, \mathbf{\hat{x}} + \frac{1}{2\sqrt{3}}\left(x_{3}-z_{3}\right)a \, \mathbf{\hat{y}} + \left(\frac{2}{3}x_{3}+\frac{1}{3}z_{3}\right)c \, \mathbf{\hat{z}} & \left(6h\right) & \mbox{Ti II} \\ \mathbf{B}_{6} & = & z_{3} \, \mathbf{a}_{1} + x_{3} \, \mathbf{a}_{2} + x_{3} \, \mathbf{a}_{3} & = & \frac{1}{2}\left(-x_{3}+z_{3}\right)a \, \mathbf{\hat{x}} + \frac{1}{2\sqrt{3}}\left(x_{3}-z_{3}\right)a \, \mathbf{\hat{y}} + \left(\frac{2}{3}x_{3}+\frac{1}{3}z_{3}\right)c \, \mathbf{\hat{z}} & \left(6h\right) & \mbox{Ti II} \\ \mathbf{B}_{7} & = & x_{3} \, \mathbf{a}_{1} + z_{3} \, \mathbf{a}_{2} + x_{3} \, \mathbf{a}_{3} & = & \frac{1}{\sqrt{3}}\left(-x_{3}+z_{3}\right)a \, \mathbf{\hat{y}} + \left(\frac{2}{3}x_{3}+\frac{1}{3}z_{3}\right)c \, \mathbf{\hat{z}} & \left(6h\right) & \mbox{Ti II} \\ \mathbf{B}_{8} & = & -z_{3} \, \mathbf{a}_{1}-x_{3} \, \mathbf{a}_{2}-x_{3} \, \mathbf{a}_{3} & = & \frac{1}{2}\left(x_{3}-z_{3}\right)a \, \mathbf{\hat{x}} + \frac{1}{2\sqrt{3}}\left(-x_{3}+z_{3}\right)a \, \mathbf{\hat{y}}-\left(\frac{2}{3}x_{3}+\frac{1}{3}z_{3}\right)c \, \mathbf{\hat{z}} & \left(6h\right) & \mbox{Ti II} \\ \mathbf{B}_{9} & = & -x_{3} \, \mathbf{a}_{1}-x_{3} \, \mathbf{a}_{2}-z_{3} \, \mathbf{a}_{3} & = & \frac{1}{2}\left(-x_{3}+z_{3}\right)a \, \mathbf{\hat{x}} + \frac{1}{2\sqrt{3}}\left(-x_{3}+z_{3}\right)a \, \mathbf{\hat{y}}-\left(\frac{2}{3}x_{3}+\frac{1}{3}z_{3}\right)c \, \mathbf{\hat{z}} & \left(6h\right) & \mbox{Ti II} \\ \mathbf{B}_{10} & = & -x_{3} \, \mathbf{a}_{1}-z_{3} \, \mathbf{a}_{2}-x_{3} \, \mathbf{a}_{3} & = & \frac{1}{\sqrt{3}}\left(x_{3}-z_{3}\right)a \, \mathbf{\hat{y}}-\left(\frac{2}{3}x_{3}+\frac{1}{3}z_{3}\right)c \, \mathbf{\hat{z}} & \left(6h\right) & \mbox{Ti II} \\ \mathbf{B}_{11} & = & x_{4} \, \mathbf{a}_{1} + x_{4} \, \mathbf{a}_{2} + z_{4} \, \mathbf{a}_{3} & = & \frac{1}{2}\left(x_{4}-z_{4}\right)a \, \mathbf{\hat{x}} + \frac{1}{2\sqrt{3}}\left(x_{4}-z_{4}\right)a \, \mathbf{\hat{y}} + \left(\frac{2}{3}x_{4}+\frac{1}{3}z_{4}\right)c \, \mathbf{\hat{z}} & \left(6h\right) & \mbox{Ti III} \\ \mathbf{B}_{12} & = & z_{4} \, \mathbf{a}_{1} + x_{4} \, \mathbf{a}_{2} + x_{4} \, \mathbf{a}_{3} & = & \frac{1}{2}\left(-x_{4}+z_{4}\right)a \, \mathbf{\hat{x}} + \frac{1}{2\sqrt{3}}\left(x_{4}-z_{4}\right)a \, \mathbf{\hat{y}} + \left(\frac{2}{3}x_{4}+\frac{1}{3}z_{4}\right)c \, \mathbf{\hat{z}} & \left(6h\right) & \mbox{Ti III} \\ \mathbf{B}_{13} & = & x_{4} \, \mathbf{a}_{1} + z_{4} \, \mathbf{a}_{2} + x_{4} \, \mathbf{a}_{3} & = & \frac{1}{\sqrt{3}}\left(-x_{4}+z_{4}\right)a \, \mathbf{\hat{y}} + \left(\frac{2}{3}x_{4}+\frac{1}{3}z_{4}\right)c \, \mathbf{\hat{z}} & \left(6h\right) & \mbox{Ti III} \\ \mathbf{B}_{14} & = & -z_{4} \, \mathbf{a}_{1}-x_{4} \, \mathbf{a}_{2}-x_{4} \, \mathbf{a}_{3} & = & \frac{1}{2}\left(x_{4}-z_{4}\right)a \, \mathbf{\hat{x}} + \frac{1}{2\sqrt{3}}\left(-x_{4}+z_{4}\right)a \, \mathbf{\hat{y}}-\left(\frac{2}{3}x_{4}+\frac{1}{3}z_{4}\right)c \, \mathbf{\hat{z}} & \left(6h\right) & \mbox{Ti III} \\ \mathbf{B}_{15} & = & -x_{4} \, \mathbf{a}_{1}-x_{4} \, \mathbf{a}_{2}-z_{4} \, \mathbf{a}_{3} & = & \frac{1}{2}\left(-x_{4}+z_{4}\right)a \, \mathbf{\hat{x}} + \frac{1}{2\sqrt{3}}\left(-x_{4}+z_{4}\right)a \, \mathbf{\hat{y}}-\left(\frac{2}{3}x_{4}+\frac{1}{3}z_{4}\right)c \, \mathbf{\hat{z}} & \left(6h\right) & \mbox{Ti III} \\ \mathbf{B}_{16} & = & -x_{4} \, \mathbf{a}_{1}-z_{4} \, \mathbf{a}_{2}-x_{4} \, \mathbf{a}_{3} & = & \frac{1}{\sqrt{3}}\left(x_{4}-z_{4}\right)a \, \mathbf{\hat{y}}-\left(\frac{2}{3}x_{4}+\frac{1}{3}z_{4}\right)c \, \mathbf{\hat{z}} & \left(6h\right) & \mbox{Ti III} \\ \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=AB7_hR16_166_c_c2h --params=

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