$\alpha$–La ($A3'$) Structure: A_hP4_194_ac

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Prototype : $\alpha$–La
AFLOW prototype label : A_hP4_194_ac
Strukturbericht designation : $A3'$
Pearson symbol : hP4
Space group number : 194
Space group symbol : $\mbox{P6}_{3}\mbox{/mmc}$
AFLOW prototype command : aflow --proto=A_hP4_194_ac
--params=
$a$,$c/a$


Other elements with this structure

  • Pr, Nd, Pm, Ce, Am, Cm, Bk, Cf.

  • This crystal is close-packed, with stacking ABACABAC…, as opposed to ABAB… for the hcp (A3) lattice and ABCABC… for the fcc (A1) lattice. The (2a) crystallographic sites (the A's) form a simple hexagonal lattice. The (2c) sites (the B's and C's) form an hcp structure.

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:

\[ \begin{array}{ccccccc} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{Atom Type} \\ \mathbf{B}_{1}& = &0 \, \mathbf{a}_{1} + 0 \, \mathbf{a}_{2} + 0 \, \mathbf{a}_{3} & = &0 \mathbf{\hat{x}} + 0 \mathbf{\hat{y}} + 0 \mathbf{\hat{z}} & \left(2a\right) & \mbox{La I} \\ \mathbf{B}_{2}& = &\frac12 \, \mathbf{a}_{3}& = &\frac12 \, c \, \mathbf{\hat{z}}& \left(2a\right) & \mbox{La I} \\ \mathbf{B}_{3}& = &\frac13 \, \mathbf{a}_{1}+ \frac23 \, \mathbf{a}_{2}+ \frac14 \, \mathbf{a}_{3}& = &\frac12 \, a \, \mathbf{\hat{x}}+ \frac{1}{2\sqrt{3}} \, a \, \mathbf{\hat{y}}+ \frac14 \, c \, \mathbf{\hat{z}}& \left(2c\right) & \mbox{La II} \\ \mathbf{B}_{4}& = &\frac23 \, \mathbf{a}_{1}+ \frac13 \, \mathbf{a}_{2}+ \frac34 \, \mathbf{a}_{3}& = &\frac12 \, a \, \mathbf{\hat{x}}- \frac{1}{2\sqrt{3}} \, a \, \mathbf{\hat{y}}+ \frac34 \, c \, \mathbf{\hat{z}}& \left(2c\right) & \mbox{La II} \\ \end{array} \]

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 Structure of the Elements (Robert E. Krieger Publishing Company, Malabar, Florida, 1982)., pp. 83-86.

Geometry files


Prototype Generator

aflow --proto=A_hP4_194_ac --params=

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