In ($A6$) Structure: A_tI2_139_a

Picture of Structure; Click for Big Picture
Prototype : In
AFLOW prototype label : A_tI2_139_a
Strukturbericht designation : $A6$
Pearson symbol : tI2
Space group number : 139
Space group symbol : $\mbox{I4/mmm}$
AFLOW prototype command : aflow --proto=A_tI2_139_a
--params=
$a$,$c/a$


  • This is an example of a face-centered tetragonal (fct) lattice, a distortion of the fcc lattice. Note that this structure is actually a body-centered tetragonal lattice, since in the tetragonal system there is no distinction between face- and body-centered structures. In the A6 structure, $c/a$ is near the fcc ratio of $\sqrt2$, while in the Aa structure, $c/a$ is near the bcc ratio of $1$. Note that In (A_tI2_139_a, In) and $\alpha$–Pa (A_tI2_139_a, $\alpha$–Pa) have the same AFLOW prototype label. They are generated by the same symmetry operations with different sets of parameters (––params) specified in their corresponding CIF files. (Deshpande, 1969) give the lattice constants for indium using the fct description of the lattice. We have changed this to the bct description, dividing their lattice constant a by $\sqrt{2}$.

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:

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

References

  • V. T. Deshpande and R. R. Pawar, Anisotropic Thermal Expansion of Indium, Acta Crystallogr. Sect. A 25, 415–416 (1969), doi:10.1107/S0567739469000830.

Found in

  • J. Donohue, The Structure of the Elements (Robert E. Krieger Publishing Company, Malabar, Florida, 1982)., pp. 244-246.

Geometry files


Prototype Generator

aflow --proto=A_tI2_139_a --params=

Species:

Running:

Output: