LaLi$_{3}$Sb$_{2}$ Structure: AB3C2_hP6_164_a_bd_d-001
| Prototype | LaLi$_{3}$Sb$_{2}$ |
| AFLOW prototype label | AB3C2_hP6_164_a_bd_d-001 |
| ICSD | 49625 |
| CCDC | 1614794 |
| Pearson symbol | hP6 |
| Space group number | 164 |
| Space group symbol | $P\overline{3}m1$ |
| AFLOW prototype command |
aflow --proto=AB3C2_hP6_164_a_bd_d-001
--params=$a, \allowbreak c/a, \allowbreak z_{3}, \allowbreak z_{4}$ |
Other compounds with this structure
CeLi$_{3}$Bi$_{2}$, CeLi$_{3}$Sb$_{2}$, DyLi$_{3}$Sb$_{2}$, GdLi$_{3}$Bi$_{2}$, HoLi$_{3}$Sb$_{2}$, LaLi$_{3}$As$_{2}$, LaLi$_{3}$Bi$_{2}$, LaLi$_{3}$P$_{2}$, NdLi$_{3}$As$_{2}$, NdLi$_{3}$Bi$_{2}$, NdLi$_{3}$Sb$_{2}$, PrLi$_{3}$Bi$_{2}$, PrLi$_{3}$Sb$_{2}$, SmLi$_{3}$Bi$_{2}$, SmLi$_{3}$Sb$_{2}$, TbLi$_{3}$Bi$_{2}$, YLi$_{3}$Bi$_{2}$, YLi$_{3}$Sb$_{2}$
- (Grund, 1984) refer to this as a
filled
LiAl$_{2}$Si$_{2}$ structure. That compound is isostructural with Ce$_{2}$O$_{2}$S. Removing the (1b) atom reduces this structure to the Ce$_{2}$O$_{2}$S prototype. - The quaternary form of this structure, with the (1b) site containing a different species, is TbLiCu$_{2}$P$_{2}$.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \,\mathbf{\hat{y}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $0$ | = | $0$ | (1a) | La I |
| $\mathbf{B_{2}}$ | = | $\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}c \,\mathbf{\hat{z}}$ | (1b) | Li I |
| $\mathbf{B_{3}}$ | = | $\frac{1}{3} \, \mathbf{a}_{1}+\frac{2}{3} \, \mathbf{a}_{2}+z_{3} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+c z_{3} \,\mathbf{\hat{z}}$ | (2d) | Li II |
| $\mathbf{B_{4}}$ | = | $\frac{2}{3} \, \mathbf{a}_{1}+\frac{1}{3} \, \mathbf{a}_{2}- z_{3} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}- c z_{3} \,\mathbf{\hat{z}}$ | (2d) | Li II |
| $\mathbf{B_{5}}$ | = | $\frac{1}{3} \, \mathbf{a}_{1}+\frac{2}{3} \, \mathbf{a}_{2}+z_{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+c z_{4} \,\mathbf{\hat{z}}$ | (2d) | Sb I |
| $\mathbf{B_{6}}$ | = | $\frac{2}{3} \, \mathbf{a}_{1}+\frac{1}{3} \, \mathbf{a}_{2}- z_{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}- c z_{4} \,\mathbf{\hat{z}}$ | (2d) | Sb I |
References
- I. Grund, H.-U. Schuster, and P. Müller, Ternäre Verbindungen von Lithium mit Yttrium, Lanthan bzw. Neodym und 5b-Elementen im
aufgefüllten
CaAl$_{2}$Si$_{2}$-Typ, Z. Anorganische und Allgemeine Chemie 515, 151–158 (1984), doi:10.1107/S2053229615016393.
Found in
- J. Prakash, M. C. Schäfer, and S. Bobev, Synthesis and structure determination of seven ternary bismuthides: crystal chemistry of the RELi$_{3}$Bi$_{2}$ family (RE = La-Nd, Sm, Gd, and Tb), Acta Crystallogr. Sect. C 71, 894–899 (2015), doi:10.1107/S2053229615016393.
First cited in
- N. Anderson, M. J. Mehl, H. Eckert, S. Divilov, X. Campilongo, S. Curtarolo, The AFLOW Library of Crystallographic Prototypes: Part 5. Submitted to Computational Materials Science (2026).
Geometry files
Prototype Generator
aflow --proto=AB3C2_hP6_164_a_bd_d --params=$a,c/a,z_{3},z_{4}$