$\delta$–CuTi ($L2_{a}$) Structure : AB_tP2_123_a_d

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Prototype : CuTi
AFLOW prototype label : AB_tP2_123_a_d
Strukturbericht designation : $L2_{a}$
Pearson symbol : tP2
Space group number : 123
Space group symbol : $P4/mmm$
AFLOW prototype command : aflow --proto=AB_tP2_123_a_d
--params=
$a$,$c/a$


Other compounds with this structure

  • HgMn

  • This structure has the same AFLOW designation, AB_tP2_123_a_d, as CuAu ($L1_{0}$). The only difference in the structures is the $c/a$ ratio. $L1_{0}$ has $c/a$ ≈ $\sqrt{2}$, characteristitic of face–centered cubic ordering, while $L2_{a}$ has $c/a$ ≈ $0.6$.

Simple Tetragonal primitive vectors:

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

Basis vectors:

\[ \begin{array}{ccccccc} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{Atom Type} \\ \mathbf{B}_{1} & = & 0 \, \mathbf{a}_{1} + 0 \, \mathbf{a}_{2} + 0 \, \mathbf{a}_{3} & = & 0 \, \mathbf{\hat{x}} + 0 \, \mathbf{\hat{y}} + 0 \, \mathbf{\hat{z}} & \left(1a\right) & \mbox{Cu} \\ \mathbf{B}_{2} & = & \frac{1}{2} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + \frac{1}{2}a \, \mathbf{\hat{y}} + \frac{1}{2}c \, \mathbf{\hat{z}} & \left(1d\right) & \mbox{Ti} \\ \end{array} \]

References

  • N. Karlsson, An X–Ray Study of the Phases in the Copper–Titanium System, J. Inst. Met. 79, 391–405 (1951).

Found in

  • W. B. Pearson, A Handbook of Lattice Spacings and Structures of Metals and Alloys, International Series of Monographs on Metal Physics and Physical Metallurgy, vol. 4 (Pergamon Press, Oxford, London, Edinburgh, New York, Paris, Frankfort, 1958), 1964 reprint with corrections edn. N. R. C. No. 4303.

Geometry files


Prototype Generator

aflow --proto=AB_tP2_123_a_d --params=

Species:

Running:

Output: