CTi2 Structure: AB2_cF48_227_c_e

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Prototype : CTi2
AFLOW prototype label : AB2_cF48_227_c_e
Strukturbericht designation : None
Pearson symbol : cF48
Space group number : 227
Space group symbol : $\mbox{Fd}\bar{3}\mbox{m}$
AFLOW prototype command : aflow --proto=AB2_cF48_227_c_e
--params=
$a$,$x_{2}$


Other compounds with this structure

  • Ca33Ge

  • Some sources consider the real prototype of this system to be Ca33Ge, with the (32e) sites occupied by calcium atoms and the (16c) sites randomly occupied by calcium and germanium atoms.

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{C} \\ \mathbf{B}_{2} & = &\frac12 \mathbf{a}_{3}& = &\frac14 \, a \, \mathbf{\hat{x}}+ \frac14 \, a \, \mathbf{\hat{y}}& \left(16c\right) & \mbox{C} \\ \mathbf{B}_{3} & = &\frac12 \mathbf{a}_{2}& = &\frac14 \, a \, \mathbf{\hat{x}}+ \frac14 \, a \, \mathbf{\hat{z}}& \left(16c\right) & \mbox{C} \\ \mathbf{B}_{4} & = &\frac12 \mathbf{a}_{1}& = &\frac14 \, a \, \mathbf{\hat{y}}+ \frac14 \, a \, \mathbf{\hat{z}}& \left(16c\right) & \mbox{C} \\ \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{Ti} \\ \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{Ti} \\ \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{Ti} \\ \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{Ti} \\ \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{Ti} \\ \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{Ti} \\ \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{Ti} \\ \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{Ti} \\ \end{array} \]

References

  • H. Goretzki, Neutron Diffraction Studies on Titanium–Carbon and Zirconium–Carbon Alloys, Phys. Stat. Solidi B 20, K141–K143 (1967), doi:10.1002/pssb.19670200260.

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. 2022.

Geometry files


Prototype Generator

aflow --proto=AB2_cF48_227_c_e --params=

Species:

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