$\beta$–TiCu3 ($D0_{a}$) Structure: A3B_oP8_59_bf_a

Picture of Structure; Click for Big Picture
Prototype : $\beta$–TiCu3
AFLOW prototype label : A3B_oP8_59_bf_a
Strukturbericht designation : $D0_{a}$
Pearson symbol : oP8
Space group number : 59
Space group symbol : $\mbox{Pmmn}$
AFLOW prototype command : aflow --proto=A3B_oP8_59_bf_a
--params=
$a$,$b/a$,$c/a$,$z_{1}$,$z_{2}$,$x_{3}$,$z_{3}$


  • We have been so far unable to obtain the original reference (Karlsson, 1951), and Pearson does not give the exact atomic coordinates. Wyckoff positions have been deduced from the structure of Cu3Sb, which Villars (1991) lists as having the TiCu3 structure. Atomic positions are set to give the approximate nearest-neighbor distances listed in Pearson. (Giessen, 1971) says that (Karlsson, 1951) structure of $\beta$–TiCu3 is mistaken. They do find a metastable $\beta$–TiCu3 phase which has the same space group and Wyckoff positions, but substantially different lattice constants than the original determination for $\beta$–TiCu3.

Simple Orthorhombic primitive vectors:

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

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 \, b \, \mathbf{\hat{y}}+ z_{1} \, c \, \mathbf{\hat{z}}& \left(2a\right) & \mbox{Ti} \\ \mathbf{B}_{2} & =&\frac34 \, \mathbf{a}_{1}+ \frac34 \, \mathbf{a}_{2}- z_{1} \, \mathbf{a}_{3}& =&\frac34 \, a \, \mathbf{\hat{x}}+ \frac34 \, b \, \mathbf{\hat{y}}- z_{1} \, c \, \mathbf{\hat{z}}& \left(2a\right) & \mbox{Ti} \\ \mathbf{B}_{3} & =&\frac14 \, \mathbf{a}_{1}+ \frac34 \, \mathbf{a}_{2}+ z_{2} \, \mathbf{a}_{3}& =&\frac14 \, a \, \mathbf{\hat{x}}+ \frac34 \, b \, \mathbf{\hat{y}}+ z_{2} \, c \, \mathbf{\hat{z}}& \left(2b\right) & \mbox{Cu I} \\ \mathbf{B}_{4} & =&\frac34 \, \mathbf{a}_{1}+ \frac14 \, \mathbf{a}_{2}- z_{2} \, \mathbf{a}_{3}& =&\frac34 \, a \, \mathbf{\hat{x}}+ \frac14 \, b \, \mathbf{\hat{y}}- z_{2} \, c \, \mathbf{\hat{z}}& \left(2b\right) & \mbox{Cu I} \\ \mathbf{B}_{5} & =&x_{3} \, \mathbf{a}_{1}+ \frac14 \, \mathbf{a}_{2}+ z_{3} \, \mathbf{a}_{3}& =&x_{3} \, a \, \mathbf{\hat{x}}+ \frac14 \, b \, \mathbf{\hat{y}}+ z_{3} \, c \, \mathbf{\hat{z}}& \left(4f\right) & \mbox{Cu II} \\ \mathbf{B}_{6} & =&\left(\frac12 - x_{3}\right) \, \mathbf{a}_{1}+ \frac14 \, \mathbf{a}_{2}+ z_{3} \, \mathbf{a}_{3}& =&\left(\frac12 - x_{3}\right) \, a \, \mathbf{\hat{x}}+ \frac14 \, b \, \mathbf{\hat{y}}+ z_{3} \, c \, \mathbf{\hat{z}}& \left(4f\right) & \mbox{Cu II} \\ \mathbf{B}_{7} & =&- x_{3} \, \mathbf{a}_{1}+ \frac34 \, \mathbf{a}_{2}- z_{3} \, \mathbf{a}_{3}& =&- x_{3} \, a \, \mathbf{\hat{x}}+ \frac34 \, b \, \mathbf{\hat{y}}- z_{3} \, c \, \mathbf{\hat{z}}& \left(4f\right) & \mbox{Cu II} \\ \mathbf{B}_{8} & =&\left(\frac12 + x_{3}\right) \, \mathbf{a}_{1}+ \frac34 \, \mathbf{a}_{2}- z_{3} \, \mathbf{a}_{3}& =&\left(\frac12 + x_{3}\right) \, a \, \mathbf{\hat{x}}+ \frac34 \, b \, \mathbf{\hat{y}}- z_{3} \, c \, \mathbf{\hat{z}}& \left(4f\right) & \mbox{Cu II} \\ \end{array} \]

References

  • N. Karlsson, , J. Inst. Met. 79, 391 (1951).

Found in

  • W. B. Pearson, The Crystal Chemistry and Physics of Metals and Alloys (Wiley– Interscience, New York, London, Sydney, Toronto, 1972)., pp. 329-331.

Geometry files


Prototype Generator

aflow --proto=A3B_oP8_59_bf_a --params=

Species:

Running:

Output: