$\alpha$–Pa (Aa) Structure: A_tI2_139_a
| 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
- W. H. Zachariasen, On the crystal structure of protactinium metal, Acta Cryst. 12, 698–700 (1959), doi:10.1107/S0365110X59002043.
Found in
- J. Donohue, The Structure of the Elements (Robert E. Krieger Publishing Company, Malabar, Florida, 1982)., pp. 125-127.