α-La ($A3'$) Structure: A_hP4_194_ac-001
| Prototype | La |
| AFLOW prototype label | A_hP4_194_ac-001 |
| Strukturbericht designation | $A3'$ |
| ICSD | 43573 |
| Pearson symbol | hP4 |
| Space group number | 194 |
| Space group symbol | $P6_3/mmc$ |
| AFLOW prototype command |
aflow --proto=A_hP4_194_ac-001
--params=$a, \allowbreak c/a$ |
Other compounds with this structure
Am, Bk, Ce, Cf, Cm, Nd, Pm, Pr
- This crystal is close-packed, with stacking ABACABAC$…$, as opposed to ABAB$…$ for the hcp ($A3$) structure and ABCABC$…$ for the fcc ($A1$) lattice. The (2a) crystallographic sites (the A layer) form a simple hexagonal lattice. The (2c) sites (the B and C layers) form an hcp structure.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \,\mathbf{\hat{y}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $0$ | = | $0$ | (2a) | La I |
| $\mathbf{B_{2}}$ | = | $\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}c \,\mathbf{\hat{z}}$ | (2a) | La I |
| $\mathbf{B_{3}}$ | = | $\frac{1}{3} \, \mathbf{a}_{1}+\frac{2}{3} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (2c) | La II |
| $\mathbf{B_{4}}$ | = | $\frac{2}{3} \, \mathbf{a}_{1}+\frac{1}{3} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ | (2c) | La II |
References
- F. H. Spedding, J. J. Hanak, and A. H. Daane, High temperature allotropy and thermal expansion of the rare-earth metals, J. Less-Common Met. 3, 110–124 (1961), doi:10.1016/0022-5088(61)90003-0.
Found in
- J. Donohue, The Structures of the Elements (Robert E. Krieger Publishing Company, New York, 1974).
Prototype Generator
aflow --proto=A_hP4_194_ac --params=$a,c/a$