α-Sm ($C19$) Structure: A_hR3_166_ac-001
| Prototype | Sm |
| AFLOW prototype label | A_hR3_166_ac-001 |
| Strukturbericht designation | $C19$ |
| ICSD | 76031 |
| CCDC | 1636669 |
| Pearson symbol | hR3 |
| Space group number | 166 |
| Space group symbol | $R\overline{3}m$ |
| AFLOW prototype command |
aflow --proto=A_hR3_166_ac-001
--params=$a, \allowbreak c/a, \allowbreak x_{2}$ |
Other compounds with this structure
Li, Gd
- This is also the proposed ground state of lithium as described in (Overhauser, 1984).
- Binary compounds with this structure are listed using CdCl$_{2}$ as the prototype.
- This is a close-packed system, with stacking ABCBCACAB, in contrast to the ABAB stacking of the hexagonal close-packed structure and the ABCABC stacking of the face-centered cubic structure.
- Hexagonal settings for rhombohedral structures can be obtained with the option
--hex.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+\frac{1}{3}c \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{\sqrt{3}}a \,\mathbf{\hat{y}}+\frac{1}{3}c \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&- \frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+\frac{1}{3}c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $0$ | = | $0$ | (1a) | Sm I |
| $\mathbf{B_{2}}$ | = | $x_{2} \, \mathbf{a}_{1}+x_{2} \, \mathbf{a}_{2}+x_{2} \, \mathbf{a}_{3}$ | = | $c x_{2} \,\mathbf{\hat{z}}$ | (2c) | Sm II |
| $\mathbf{B_{3}}$ | = | $- x_{2} \, \mathbf{a}_{1}- x_{2} \, \mathbf{a}_{2}- x_{2} \, \mathbf{a}_{3}$ | = | $- c x_{2} \,\mathbf{\hat{z}}$ | (2c) | Sm II |
References
- A. H. Daane, R. E. Rundle, H. G. Smith, and F. H. Spedding, The crystal structure of samarium, Acta Cryst. 7, 532–535 (1954), doi:10.1107/S0365110X54001818.
- A. W. Overhauser, Crystal Structure of Lithium at 4.2 K, Phys. Rev. Lett. 53, 64–65 (1984), doi:10.1103/PhysRevLett.53.64.
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_hR3_166_ac --params=$a,c/a,x_{2}$