$\alpha$–Pa ($A_{a}$) Structure: A_tI2_139_a

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Prototype : $\alpha$–Pa
AFLOW prototype label : A_tI2_139_a
Strukturbericht designation : $A_{a}$
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 body-centered tetragonal (bct) lattice, a distortion of the bcc lattice. 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. 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. When $c/a = \sqrt{2/3} \approx 0.816$ the coordination number of this system is 10. In Pa the c/a ratio is 0.827.

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:

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

References

Found in

  • J. Donohue, The Structure of the Elements (Robert E. Krieger Publishing Company, Malabar, Florida, 1982)., pp. 125-127.

Geometry files


Prototype Generator

aflow --proto=A_tI2_139_a --params=

Species:

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