$\gamma$–CuTi ($B11$) Structure: AB_tP4_129_c_c

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Prototype : $\gamma$–CuTi
AFLOW prototype label : AB_tP4_129_c_c
Strukturbericht designation : $B11$
Pearson symbol : tP4
Space group number : 129
Space group symbol : $\mbox{P4/nmm}$
AFLOW prototype command : aflow --proto=AB_tP4_129_c_c
--params=
$a$,$c/a$,$z_{1}$,$z_{2}$


Other compounds with this structure

  • AuCu, AlRe, TlF–I (high–temperature)

  • When $c = 2 a$, $z_{1} = 1/8$, and $z_{2} = 5/8$, the atoms are on the sites of a body-centered cubic lattice. If, on the other hand, $c = 2\sqrt{2} a$, with the same $x_{i}$, the atoms are on the site of a face-centered cubic lattice. This is the phase that Lu et al. refer to as Z2.

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:

\[ \begin{array}{ccccccc} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{Atom Type} \\ \mathbf{B}_{1} & =&\frac14 \, \mathbf{a}_{1}+ \frac14 \, \mathbf{a}_{2}+ z_{1} \, \mathbf{a}_{3}& =&\frac14 \, a \, \mathbf{\hat{x}}+ \frac14 \, a \, \mathbf{\hat{y}}+ z_{1} \, c \, \mathbf{\hat{z}}& \left(2c\right) & \mbox{Cu} \\ \mathbf{B}_{2} & =&\frac34 \, \mathbf{a}_{1}+ \frac34 \, \mathbf{a}_{2}- z_{1} \, \mathbf{a}_{3}& =&\frac34 \, a \, \mathbf{\hat{x}}+ \frac34 \, a \, \mathbf{\hat{y}}- z_{1} \, c \, \mathbf{\hat{z}}& \left(2c\right) & \mbox{Cu} \\ \mathbf{B}_{3} & =&\frac14 \, \mathbf{a}_{1}+ \frac14 \, \mathbf{a}_{2}+ z_{2} \, \mathbf{a}_{3}& =&\frac14 \, a \, \mathbf{\hat{x}}+ \frac14 \, a \, \mathbf{\hat{y}}+ z_{2} \, c \, \mathbf{\hat{z}}& \left(2c\right) & \mbox{Ti} \\ \mathbf{B}_{4} & =&\frac34 \, \mathbf{a}_{1}+ \frac34 \, \mathbf{a}_{2}- z_{2} \, \mathbf{a}_{3}& =&\frac34 \, a \, \mathbf{\hat{x}}+ \frac34 \, a \, \mathbf{\hat{y}}- z_{2} \, c \, \mathbf{\hat{z}}& \left(2c\right) & \mbox{Ti} \\ \end{array} \]

References

  • V. N. Eremenko, Y. I. Buyanov, and S. B. Prima, Phase diagram of the system titanium–copper, Soviet Powder Metallurgy and Metal Ceramics 5, 494–502 (1966), doi:10.1007/BF00775543.
  • Z. W. Lu., S.–H. Wei, and A. Zunger, Long–range order in binary late–transition–metal alloys, Phys. Rev. Lett. 66, 1753 (1991), doi:10.1103/PhysRevLett.66.1753.

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. 3021.

Geometry files


Prototype Generator

aflow --proto=AB_tP4_129_c_c --params=

Species:

Running:

Output: