Hexagonal Close Packed (Mg, $A3$, hcp) Structure: A_hP2_194_c-001
| Prototype | Mg |
| AFLOW prototype label | A_hP2_194_c-001 |
| Strukturbericht designation | $A3$ |
| ICSD | 608404 |
| Pearson symbol | hP2 |
| Space group number | 194 |
| Space group symbol | $P6_3/mmc$ |
| AFLOW prototype command |
aflow --proto=A_hP2_194_c-001
--params=$a, \allowbreak c/a$ |
Other compounds with this structure
Be, Cd, Co, Dy, Er, $\epsilon$-Fe, Gd, Hf, Ho, Lu, Os, Re, Ru, Sc, Tb, Tc, Ti, Tl, Tm, Y, Zn, Zr
- We use the `pure magnesium' lattice constants from (Batchelder, 1957), but the ICSD entry uses the data for Mg$_{0.976}$Al$_{0.024}$.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \,\mathbf{\hat{y}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $\frac{1}{3} \, \mathbf{a}_{1}+\frac{2}{3} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (2c) | Mg I |
| $\mathbf{B_{2}}$ | = | $\frac{2}{3} \, \mathbf{a}_{1}+\frac{1}{3} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ | (2c) | Mg I |
References
- F. W. von Batchelder and R. F. Raeuchle, Lattice Constants and Brillouin Zone Overlap in Dilute Magnesium Alloys, Phys. Rev. 105, 59–61 (1957), doi:10.1103/PhysRev.105.59.
Found in
- R. T. Downs and M. Hall-Wallace, The American Mineralogist Crystal Structure Database, Am. Mineral. 88, 247–250 (2003).
Prototype Generator
aflow --proto=A_hP2_194_c --params=$a,c/a$