$\alpha$–Sm (C19) Structure: A_hR3_166_ac
| Prototype | : | $\alpha$–Sm |
| AFLOW prototype label | : | A_hR3_166_ac |
| Strukturbericht designation | : | $C19$ |
| Pearson symbol | : | hR3 |
| Space group number | : | 166 |
| Space group symbol | : | $\mbox{R}\bar{3}\mbox{m}$ |
| AFLOW prototype command | : | aflow --proto=A_hR3_166_ac [--hex] --params=$a,c/a,x_{2}$ |
Other elements with this structure
- Li (Overhauser, 1984).
- Note that 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 of this structure can be obtained with the option ––hex.
Rhombohedral primitive vectors:
\[
\begin{array}{ccc}
\mathbf{a}_1 & = & ~ \frac12 \, a \, \mathbf{\hat{x}} - \frac{1}{2\sqrt{3}} \, a \, \mathbf{\hat{y}} + \frac13
\, c \, \mathbf{\hat{z}} \\
\mathbf{a}_2 & = & \frac{1}{\sqrt{3}} \, a \, \mathbf{\hat{y}} + \frac13 \, c \, \mathbf{\hat{z}} \\
\mathbf{a}_3 & = & - \frac12 \, a \, \mathbf{\hat{x}} - \frac{1}{2\sqrt{3}} \, a \, \mathbf{\hat{y}} + \frac13
\, c \, \mathbf{\hat{z}} \\
\end{array}
\]
Basis vectors:
\[ \begin{array}{ccccccc} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{Atom Type} \\ \mathbf{B}_{1} & =&0 \, \mathbf{a}_{1} + 0 \, \mathbf{a}_{2} + 0 \, \mathbf{a}_{3} & =&0 \mathbf{\hat{x}} + 0 \mathbf{\hat{y}} + 0 \mathbf{\hat{z}} & \left(1a\right) & \mbox{Sm I} \\ \mathbf{B}_{2} & =&x_{2} \, \mathbf{a}_{1}+ x_{2} \, \mathbf{a}_{2}+ x_{2} \, \mathbf{a}_{3}& =&x_{2} \, c \, \mathbf{\hat{z}}& \left(2c\right) & \mbox{Sm II} \\ \mathbf{B}_{3} & =&- x_{2} \, \mathbf{a}_{1}- x_{2} \, \mathbf{a}_{2}- x_{2} \, \mathbf{a}_{3}& =&- x_{2} \, c \, \mathbf{\hat{z}}& \left(2c\right) & \mbox{Sm II} \\ \end{array} \]References
- A. W. Overhauser, Crystal Structure of Lithium at 4.2 K, Phys. Rev. Lett. 53, 64–65 (1984), doi:10.1103/PhysRevLett.53.64.
- 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.