LiZn$_{2}$ ($C_{k}$) Structure: AB_hP4_194_a_c-003
| Prototype | LiZn$_{2}$ |
| AFLOW prototype label | AB_hP4_194_a_c-003 |
| Strukturbericht designation | $C_{k}$ |
| ICSD | 104793 |
| Pearson symbol | hP4 |
| Space group number | 194 |
| Space group symbol | $P6_3/mmc$ |
| AFLOW prototype command |
aflow --proto=AB_hP4_194_a_c-003
--params=$a, \allowbreak c/a$ |
- The actual stoichiometry of this compounds is Li$_{0.8}$Zn$_{2}$, so each (2a) site is only filled 40% of the time. This means that the short (1.26Å) distance between the lithium atoms shown here is illusionary.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \,\mathbf{\hat{y}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $0$ | = | $0$ | (2a) | Li I |
| $\mathbf{B_{2}}$ | = | $\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}c \,\mathbf{\hat{z}}$ | (2a) | Li I |
| $\mathbf{B_{3}}$ | = | $\frac{1}{3} \, \mathbf{a}_{1}+\frac{2}{3} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (2c) | Zn I |
| $\mathbf{B_{4}}$ | = | $\frac{2}{3} \, \mathbf{a}_{1}+\frac{1}{3} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ | (2c) | Zn I |
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
- C. J. Smithells, Metals Reference Book (Butterworths Scientific, London, 1955), second edn.
Prototype Generator
aflow --proto=AB_hP4_194_a_c --params=$a,c/a$