Hexagonal Close Packed (Mg, $A3$, hcp) Structure: A_hP2_194_c
| Prototype | : | Mg |
| AFLOW prototype label | : | A_hP2_194_c |
| Strukturbericht designation | : | $A3$ |
| Pearson symbol | : | hP2 |
| Space group number | : | 194 |
| Space group symbol | : | $\text{P6}_{3}\text{/mmc}$ |
| AFLOW prototype command | : | aflow --proto=A_hP2_194_c --params=$a$,$c/a$ |
Other elements with this structure
- Be, Sc, Ti, Co, Zn, Y, Zr, Tc, Ru, Cd, Gd, Tb, Dy, Ho, Er, Tm, Lu, Hf, Re, Os, Tl
Hexagonal primitive vectors:
\[ \begin{array}{ccc} \mathbf{a}_1 & = & \frac12 \, a \, \mathbf{\hat{x}} - \frac{\sqrt3}2 \, a \, \mathbf{\hat{y}} \\ \mathbf{a}_2 & = & \frac12 \, a \, \mathbf{\hat{x}} + \frac{\sqrt3}2 \, a \, \mathbf{\hat{y}} \\ \mathbf{a}_3 & = & c \, \mathbf{\hat{z}}\\ \end{array} \]
Basis vectors:
\[ \begin{array}{ccccccc} & & \text{Lattice Coordinates} & & \text{Cartesian Coordinates} &\text{Wyckoff Position} & \text{Atom Type} \\ \mathbf{B}_{1}& = &\frac13 \, \mathbf{a}_{1}+ \frac23 \, \mathbf{a}_{2}+ \frac14 \, \mathbf{a}_{3}& = &\frac12 \, a \, \mathbf{\hat{x}}+ \frac{1}{2\sqrt{3}} \, a \, \mathbf{\hat{y}}+ \frac14 \, c \, \mathbf{\hat{z}}& \left(2c\right) & \text{Mg} \\ \mathbf{B}_{2}& = &\frac23 \, \mathbf{a}_{1}+ \frac13 \, \mathbf{a}_{2}+ \frac34 \, \mathbf{a}_{3}& = &\frac12 \, a \, \mathbf{\hat{x}}- \frac{1}{2\sqrt{3}} \, a \, \mathbf{\hat{y}}+ \frac34 \, c \, \mathbf{\hat{z}}& \left(2c\right) & \text{Mg} \\ \end{array} \]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
- J. Donohue, The Structure of the Elements (Robert E. Krieger Publishing Company, Malabar, Florida, 1982)., pp. 39-40.