LiZn2 ($C_{k}$) Structure : AB_hP4_194_a_c
| 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:
\[ \begin{array}{ccccccc} & & \text{Lattice Coordinates} & & \text{Cartesian Coordinates} &\text{Wyckoff Position} & \text{Atom Type} \\ \mathbf{B}_{1} & = & 0 \, \mathbf{a}_{1} + 0 \, \mathbf{a}_{2} + 0 \, \mathbf{a}_{3} & = & 0 \, \mathbf{\hat{x}} + 0 \, \mathbf{\hat{y}} + 0 \, \mathbf{\hat{z}} & \left(2a\right) & \text{Li} \\ \mathbf{B}_{2} & = & \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{1}{2}c \, \mathbf{\hat{z}} & \left(2a\right) & \text{Li} \\ \mathbf{B}_{3} & = & \frac{1}{3} \, \mathbf{a}_{1} + \frac{2}{3} \, \mathbf{a}_{2} + \frac{1}{4} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + \frac{1}{2\sqrt{3}}a \, \mathbf{\hat{y}} + \frac{1}{4}c \, \mathbf{\hat{z}} & \left(2c\right) & \text{Zn} \\ \mathbf{B}_{4} & = & \frac{2}{3} \, \mathbf{a}_{1} + \frac{1}{3} \, \mathbf{a}_{2} + \frac{3}{4} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}}- \frac{1}{2\sqrt{3}}a \, \mathbf{\hat{y}} + \frac{3}{4}c \, \mathbf{\hat{z}} & \left(2c\right) & \text{Zn} \\ \end{array} \]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.