Al3Ti ($D0_{22}$) Structure: A3B_tI8_139_bd_a

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Prototype : Al3Ti
AFLOW prototype label : A3B_tI8_139_bd_a
Strukturbericht designation : $D0_{22}$
Pearson symbol : tI8
Space group number : 139
Space group symbol : $\mbox{I4/mmm}$
AFLOW prototype command : aflow --proto=A3B_tI8_139_bd_a
--params=
$a$,$c/a$


  • When $c = 2a$ the atoms are on the sites of a face-centered cubic lattice. When $c/a = 1/\sqrt2$, this becomes the cubic D03 structure.

Body-centered Tetragonal primitive vectors:

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

Basis vectors:

\[ \begin{array}{ccccccc} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{Atom Type} \\ \mathbf{B}_{1} & =&0 \, \mathbf{a}_{1} + 0 \, \mathbf{a}_{2} + 0 \, \mathbf{a}_{3} & =&0 \mathbf{\hat{x}} + 0 \mathbf{\hat{y}} + 0 \mathbf{\hat{z}} & \left(2a\right) & \mbox{Ti} \\ \mathbf{B}_{2} & =&\frac12 \, \mathbf{a}_{1}+ \frac12 \, \mathbf{a}_{2}& =&\frac12 \, c \, \mathbf{\hat{z}}& \left(2b\right) & \mbox{Al I} \\ \mathbf{B}_{3} & =&\frac34 \, \mathbf{a}_{1}+ \frac14 \, \mathbf{a}_{2}+ \frac12 \, \mathbf{a}_{3}& =&\frac12 \, a \, \mathbf{\hat{y}}+ \frac14 \, c \, \mathbf{\hat{z}}& \left(4d\right) & \mbox{Al II} \\ \mathbf{B}_{4} & =&\frac14 \, \mathbf{a}_{1}+ \frac34 \, \mathbf{a}_{2}+ \frac12 \, \mathbf{a}_{3}& =&\frac12 \, a \, \mathbf{\hat{x}}+ \frac14 \, c \, \mathbf{\hat{z}}& \left(4d\right) & \mbox{Al II} \\ \end{array} \]

References

  • J. P. Nic, S. Zhang, and D. E. Mikkola, Observations on the systematic alloying of Al3Ti with fourth period elements to yield cubic phases, Scripta Metallurgica et Materialia 24, 1099–1104 (1990), doi:10.1016/0956-716X(90)90306-2.

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. 1023.

Geometry files


Prototype Generator

aflow --proto=A3B_tI8_139_bd_a --params=

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