Pa ($A_{a}$) Structure: A_tI2_139_a-002
- This is an example of a body-centered tetragonal (bct) lattice, a distortion of the bcc lattice.
- $A6$ and $A_{a}$ structures have the same AFLOW prototype label, A_tI2_139_a. They are generated by the same symmetry operations with different sets of parameters (
--params) specified in their corresponding CIF files. When $c/a=\sqrt{2/3}≈ 0.861$ the coordination number of this system is 10. In Pa the $c/a$ ratio is 0.823. - We take our data from (Zachariasen, 1959), but the ICSD entry is from the later work of (Benedict, 1982).
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&- \frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}- \frac{1}{2}c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $0$ | = | $0$ | (2a) | Pa I |
References
- W. H. Zachariasen, On the crystal structure of protactinium metal, Acta Cryst. 12, 698–700 (1959), doi:10.1107/S0365110X59002043.
- U. Benedict, J. C. Spirlet, C. Doufour, I. Birkel, W. B. Holzapfle, and J. R. Petersen, X-ray diffraction study of protactinium metal to 53 GPa, J. Magn. Magn. Mater. 29, 287–290 (1982), doi:10.1016/0304-8853(82)90252-9.
Found in
- J. Donohue, The Structures of the Elements (Robert E. Krieger Publishing Company, New York, 1974).
First cited in
- M. J. Mehl, D. Hicks, C. Toher, O. Levy, R. M. Hanson, G. L. W. Hart, and S. Curtarolo, The AFLOW Library of Crystallographic Prototypes: Part 1, Comp. Mat. Sci. 136, S1-S828 (2017). (doi=10.1016/j.commatsci.2017.01.017)
Geometry files
Prototype Generator
aflow --proto=A_tI2_139_a --params=$a,c/a$