LiZn2 ($C_{k}$) Structure : AB_hP4_194_a_c

Picture of Structure; Click for Big Picture
Prototype : LiZn2
AFLOW prototype label : AB_hP4_194_a_c
Strukturbericht designation : $C_{k}$
Pearson symbol : hP4
Space group number : 194
Space group symbol : $P6_{3}/mmc$
AFLOW prototype command : aflow --proto=AB_hP4_194_a_c
--params=
$a$,$c/a$


  • The actual stoichiometry of this compounds is Li0.8Zn2, so each ($2a$) site is only filled 40% of the time. This means that the short (1.26 Å) distance between the lithium atoms shown here is illusionary.

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:

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

References

  • E. Zintl and A. Schneider, Röntgenanalyse der Lithium–Zink–Legierungen (15. Mitteilung über Metalle und Legierungen), Z. Elektrochem. 41, 764–767 (1935), doi:10.1002/bbpc.19350411103.

Found in

  • W. B. Pearson, A Handbook of Lattice Spacings and Structures of Metals and Alloys, International Series of Monographs on Metal Physics and Physical Metallurgy, vol. 4 (Pergamon Press, Oxford, London, Edinburgh, New York, Paris, Frankfort, 1958), 1964 reprint with corrections edn. N. R. C. No. 4303.

Geometry files


Prototype Generator

aflow --proto=AB_hP4_194_a_c --params=

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