In ($A6$) Structure: A_tI2_139_a-001
- This is an example of a
face
-centered tetragonal (fct) lattice, a distortion of the fcc lattice. 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 $c/a > 1$, while in the $A_{a}$ structure $c/a < 1$. - $A6$ 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. - (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 $\sqrt{2}$.
- The ICSD entry is from the earlier work of (Ridley, 1965).
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&- \frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}- \frac{1}{2}c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $0$ | = | $0$ | (2a) | In I |
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.
- N. Ridley, Densities of some indium solid solutions, J. Less-Common Met. 8, 354–358 (1965), doi:10.1016/0022-5088(65)90071-8.
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=$a,c/a$