NiTi2 Structure: AB2_cF96_227_e_cf

Picture of Structure; Click for Big Picture
Prototype : NiTi2
AFLOW prototype label : AB2_cF96_227_e_cf
Strukturbericht designation : None
Pearson symbol : cF96
Space group number : 227
Space group symbol : $\mbox{Fd}\bar{3}\mbox{m}$
AFLOW prototype command : aflow --proto=AB2_cF96_227_e_cf
--params=
$a$,$x_{2}$,$x_{3}$


Other compounds with this structure

  • CoTi2, CoZr2, Cr2Nb, FeTi2, FeZr2, Hf2Ir, Hf2Pt, IrZr2, NiSc2, PdSc2, many others.

  • We have used the fact that all vectors of the form $\left(0, \pm \, a/2, \pm \, a/2\right)$, $\left(\pm \, a/2, 0, \pm \, a/2\right)$, and $\left(\pm \, a/2, \pm \, a/2, 0 \right)$ are primitive vectors of the face-centered cubic lattice to simplify the positions of some atoms in both lattice and Cartesian coordinates

Face-centered Cubic primitive vectors:

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

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(16c\right) & \mbox{Ti I} \\ \mathbf{B}_{2} & = &\frac12 \mathbf{a}_{3}& = &\frac14 \, a \, \mathbf{\hat{x}}+ \frac14 \, a \, \mathbf{\hat{y}}& \left(16c\right) & \mbox{Ti I} \\ \mathbf{B}_{3} & = &\frac12 \mathbf{a}_{2}& = &\frac14 \, a \, \mathbf{\hat{x}}+ \frac14 \, a \, \mathbf{\hat{z}}& \left(16c\right) & \mbox{Ti I} \\ \mathbf{B}_{4} & = &\frac12 \mathbf{a}_{1}& = &\frac14 \, a \, \mathbf{\hat{y}}+ \frac14 \, a \, \mathbf{\hat{z}}& \left(16c\right) & \mbox{Ti I} \\ \mathbf{B}_{5} & = &x_{2} \mathbf{a}_{1}+ x_{2} \mathbf{a}_{2}+ x_{2} \mathbf{a}_{3}& = &x_{2} \, a \, \mathbf{\hat{x}}+ x_{2} \, a \, \mathbf{\hat{y}}+ x_{2} \, a \, \mathbf{\hat{z}}& \left(32e\right) & \mbox{Ni} \\ \mathbf{B}_{6} & = &x_{2} \mathbf{a}_{1}+ x_{2} \mathbf{a}_{2}+ \left(\frac12 - 3 \, x_{2}\right) \mathbf{a}_{3}& = &\left(\frac14 - x_{2}\right) \, a \, \mathbf{\hat{x}}+ \left(\frac14 - x_{2}\right) \, a \, \mathbf{\hat{y}}+ x_{2} \, a \, \mathbf{\hat{z}}& \left(32e\right) & \mbox{Ni} \\ \mathbf{B}_{7} & = &x_{2} \mathbf{a}_{1}+ \left(\frac12 - 3 \, x_{2}\right) \mathbf{a}_{2}+ x_{2} \mathbf{a}_{3}& = &\left(\frac14 - x_{2}\right) \, a \, \mathbf{\hat{x}}+ x_{2} \, a \, \mathbf{\hat{y}}+ \left(\frac14 - x_{2}\right) \, a \, \mathbf{\hat{z}}& \left(32e\right) & \mbox{Ni} \\ \mathbf{B}_{8} & = &\left(\frac12 - 3 \, x_{2}\right) \mathbf{a}_{1}+ x_{2} \mathbf{a}_{2}+ x_{2} \mathbf{a}_{3}& = &x_{2} \, a \, \mathbf{\hat{x}}+ \left(\frac14 - x_{2}\right) \, a \, \mathbf{\hat{y}}+ \left(\frac14 - x_{2}\right) \, a \, \mathbf{\hat{z}}& \left(32e\right) & \mbox{Ni} \\ \mathbf{B}_{9} & = &- x_{2} \mathbf{a}_{1}- x_{2} \mathbf{a}_{2}+ \left(\frac12 + 3 \, x_{2}\right) \mathbf{a}_{3}& = &\left(\frac14 + x_{2}\right) \, a \, \mathbf{\hat{x}}+ \left(\frac14 + x_{2}\right) \, a \, \mathbf{\hat{y}}- x_{2} \, a \, \mathbf{\hat{z}}& \left(32e\right) & \mbox{Ni} \\ \mathbf{B}_{10} & = &- x_{2} \mathbf{a}_{1}- x_{2} \mathbf{a}_{2}- x_{2} \mathbf{a}_{3}& = &- x_{2} \, a \, \mathbf{\hat{x}}- x_{2} \, a \, \mathbf{\hat{y}}- x_{2} \, a \, \mathbf{\hat{z}}& \left(32e\right) & \mbox{Ni} \\ \mathbf{B}_{11} & = &- x_{2} \mathbf{a}_{1}+ \left(\frac12 + 3 \, x_{2}\right) \mathbf{a}_{2}- x_{2} \mathbf{a}_{3}& = &\left(\frac14 + x_{2}\right) \, a \, \mathbf{\hat{x}}- x_{2} \, a \, \mathbf{\hat{y}}+ \left(\frac14 + x_{2}\right) \, a \, \mathbf{\hat{z}}& \left(32e\right) & \mbox{Ni} \\ \mathbf{B}_{12} & = &\left(\frac12 + 3 \, x_{2}\right) \mathbf{a}_{1}- x_{2} \mathbf{a}_{2}- x_{2} \mathbf{a}_{3}& = &- x_{2} \, a \, \mathbf{\hat{x}}+ \left(\frac14 + x_{2}\right) \, a \, \mathbf{\hat{y}}+ \left(\frac14 + x_{2}\right) \, a \, \mathbf{\hat{z}}& \left(32e\right) & \mbox{Ni} \\ \mathbf{B}_{13} & = &\left(\frac14 - x_{3}\right) \mathbf{a}_{1}+ x_{3} \mathbf{a}_{2}+ x_{3} \mathbf{a}_{3}& = &x_{3} \, a \, \mathbf{\hat{x}}+ \frac18 \, a \, \mathbf{\hat{y}}+ \frac18 \, a \, \mathbf{\hat{z}}& \left(48f\right) & \mbox{Ti II} \\ \mathbf{B}_{14} & = &x_{3} \mathbf{a}_{1}+ \left(\frac14 - x_{3}\right) \mathbf{a}_{2}+ \left(\frac14 - x_{3}\right) \mathbf{a}_{3}& = &\left(\frac14 - x_{3}\right) \, a \, \mathbf{\hat{x}}+ \frac18 \, a \, \mathbf{\hat{y}}+ \frac18 \, a \, \mathbf{\hat{z}}& \left(48f\right) & \mbox{Ti II} \\ \mathbf{B}_{15} & = &x_{3} \mathbf{a}_{1}+ \left(\frac14 - x_{3}\right) \mathbf{a}_{2}+ x_{3} \mathbf{a}_{3}& = &\frac18 \, a \, \mathbf{\hat{x}}+ x_{3} \, a \, \mathbf{\hat{y}}+ \frac18 \, a \, \mathbf{\hat{z}}& \left(48f\right) & \mbox{Ti II} \\ \mathbf{B}_{16} & = &\left(\frac14 - x_{3}\right) \mathbf{a}_{1}+ x_{3} \mathbf{a}_{2}+ \left(\frac14 - x_{3}\right) \mathbf{a}_{3}& = &\frac18 \, a \, \mathbf{\hat{x}}+ \left(\frac14 - x_{3}\right) \, a \, \mathbf{\hat{y}}+ \frac18 \, a \, \mathbf{\hat{z}}& \left(48f\right) & \mbox{Ti II} \\ \mathbf{B}_{17} & = &x_{3} \mathbf{a}_{1}+ x_{3} \mathbf{a}_{2}+ \left(\frac14 - x_{3}\right) \mathbf{a}_{3}& = &\frac18 \, a \, \mathbf{\hat{x}}+ \frac18 \, a \, \mathbf{\hat{y}}+ x_{3} \, a \, \mathbf{\hat{z}}& \left(48f\right) & \mbox{Ti II} \\ \mathbf{B}_{18} & = &\left(\frac14 - x_{3}\right) \mathbf{a}_{1}+ \left(\frac14 - x_{3}\right) \mathbf{a}_{2}+ x_{3} \mathbf{a}_{3}& = &\frac18 \, a \, \mathbf{\hat{x}}+ \frac18 \, a \, \mathbf{\hat{y}}+ \left(\frac14 - x_{3}\right) \, a \, \mathbf{\hat{z}}& \left(48f\right) & \mbox{Ti II} \\ \mathbf{B}_{19} & = &\left(x_{3} + \frac34\right) \mathbf{a}_{1}- x_{3} \mathbf{a}_{2}+ \left(x_{3} + \frac34\right) \mathbf{a}_{3}& = &\frac38 \, a \, \mathbf{\hat{x}}+ \left(x_{3} + \frac34\right) \, a \, \mathbf{\hat{y}}+ \frac38 \, a \, \mathbf{\hat{z}}& \left(48f\right) & \mbox{Ti II} \\ \mathbf{B}_{20} & = &- x_{3} \mathbf{a}_{1}+ \left(x_{3} + \frac34\right) \mathbf{a}_{2}- x_{3} \mathbf{a}_{3}& = &\frac38 \, a \, \mathbf{\hat{x}}- x_{3} \, a \, \mathbf{\hat{y}}+ \frac38 \, a \, \mathbf{\hat{z}}& \left(48f\right) & \mbox{Ti II} \\ \mathbf{B}_{21} & = &- x_{3} \mathbf{a}_{1}+ \left(x_{3} + \frac34\right) \mathbf{a}_{2}+ \left(x_{3} + \frac34\right) \mathbf{a}_{3}& = &\left(x_{3} + \frac34\right) \, a \, \mathbf{\hat{x}}+ \frac38 \, a \, \mathbf{\hat{y}}+ \frac38 \, a \, \mathbf{\hat{z}}& \left(48f\right) & \mbox{Ti II} \\ \mathbf{B}_{22} & = &\left(x_{3} + \frac34\right) \mathbf{a}_{1}- x_{3} \mathbf{a}_{2}- x_{3} \mathbf{a}_{3}& = &- x_{3} \, a \, \mathbf{\hat{x}}+ \frac38 \, a \, \mathbf{\hat{y}}+ \frac38 \, a \, \mathbf{\hat{z}}& \left(48f\right) & \mbox{Ti II} \\ \mathbf{B}_{23} & = &- x_{3} \mathbf{a}_{1}- x_{3} \mathbf{a}_{2}+ \left(x_{3} + \frac34\right) \mathbf{a}_{3}& = &\frac38 \, a \, \mathbf{\hat{x}}+ \frac38 \, a \, \mathbf{\hat{y}}- x_{3} \, a \, \mathbf{\hat{z}}& \left(48f\right) & \mbox{Ti II} \\ \mathbf{B}_{24} & = &+ \left(x_{3} + \frac34\right) \mathbf{a}_{1}+ \left(x_{3} + \frac34\right) \mathbf{a}_{2}- x_{3} \mathbf{a}_{3}& = &\frac38 \, a \, \mathbf{\hat{x}}+ \frac38 \, a \, \mathbf{\hat{y}}+ \left(x_{3} + \frac34\right) \, a \, \mathbf{\hat{z}}& \left(48f\right) & \mbox{Ti II} \\ \end{array} \]

References

Found in

  • P. Villars and L. Calvert, Pearson's Handbook of Crystallographic Data for Intermetallic Phases (ASM International, Materials Park, OH, 1991), 2nd edn., pp. 4715.

Geometry files


Prototype Generator

aflow --proto=AB2_cF96_227_e_cf --params=

Species:

Running:

Output: