Hexagonal Close Packed (Mg, $A3$, hcp) Structure: A_hP2_194_c

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Prototype : Mg
AFLOW prototype label : A_hP2_194_c
Strukturbericht designation : $A3$
Pearson symbol : hP2
Space group number : 194
Space group symbol : $\mbox{P6}_{3}\mbox{/mmc}$
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:

\[ \begin{array}{ccccccc} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{Atom Type} \\ \mathbf{B}_{1}& = &\frac13 \, \mathbf{a}_{1}+ \frac23 \, \mathbf{a}_{2}+ \frac14 \, \mathbf{a}_{3}& = &\frac12 \, a \, \mathbf{\hat{x}}+ \frac{1}{2\sqrt{3}} \, a \, \mathbf{\hat{y}}+ \frac14 \, c \, \mathbf{\hat{z}}& \left(2c\right) & \mbox{Mg} \\ \mathbf{B}_{2}& = &\frac23 \, \mathbf{a}_{1}+ \frac13 \, \mathbf{a}_{2}+ \frac34 \, \mathbf{a}_{3}& = &\frac12 \, a \, \mathbf{\hat{x}}- \frac{1}{2\sqrt{3}} \, a \, \mathbf{\hat{y}}+ \frac34 \, c \, \mathbf{\hat{z}}& \left(2c\right) & \mbox{Mg} \\ \end{array} \]

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.

Geometry files


Prototype Generator

aflow --proto=A_hP2_194_c --params=

Species:

Running:

Output: