Simple Hexagonal Lattice ($A_{f}$): A_hP1_191_a

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Prototype : $\gamma$–HgSn6–10
AFLOW prototype label : A_hP1_191_a
Strukturbericht designation : $A_{f}$
Pearson symbol : hP1
Space group number : 191
Space group symbol : $P6/mmm$
AFLOW prototype command : aflow --proto=A_hP1_191_a
--params=
$a$,$c/a$


Other compounds with this structure

  • Si (metastable) disordered phases of BiIn, CdSn19, In7Sb3, InSb

  • Unlike the simple cubic lattice, there are no elements which take this structure as the ground state. There is a metastable silicon phase with this structure. The prototype state is a mercury-tin alloy. Thus the atom type M represents an average of Hg and Sn atoms.

Hexagonal primitive vectors:

\[ \begin{array}{ccc} \mathbf{a}_1 & = & \frac12 \, a \, \mathbf{\hat{x}} - \frac{\sqrt{3}}{2} \, a \, \mathbf{\hat{y}} \\ \mathbf{a}_2 & = & \frac12 \, a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2} \, a \, \mathbf{\hat{y}} \\ \mathbf{a}_3 & = & c \, \mathbf{\hat{z}}\\ \end{array} \]

Basis vectors:

\[ \begin{array}{ccccccc} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{Atom Type} \\ \mathbf{B}_{1}& = &0 \, \mathbf{a}_{1} + 0 \, \mathbf{a}_{2} + 0 \, \mathbf{a}_{3} & = &0 \mathbf{\hat{x}} + 0 \mathbf{\hat{y}} + 0 \mathbf{\hat{z}} & \left(1a\right) & \mbox{M} \\ \end{array} \]

References

  • G. V. Raynor and J. A. Lee, The tin–rich intermediate phases in the alloys of tin with cadmium, indium and mercury, Acta Metallurgica 2, 616–620 (1954), doi:10.1016/0001-6160(54)90197-2.

Found in

  • P. Villars and L. Calvert, Pearson's Handbook of Crystallographic Data for Intermetallic Phases (ASM International, Materials Park, OH, 1991), 2nd edn., pp. 3947.

Geometry files


Prototype Generator

aflow --proto=A_hP1_191_a --params=

Species:

Running:

Output: