Li$_{7}$Pb$_{2}$ Structure: A7B2_hP9_164_ac2d_d-001
| Prototype | Li$_{7}$Pb$_{2}$ |
| AFLOW prototype label | A7B2_hP9_164_ac2d_d-001 |
| ICSD | 104765 |
| Pearson symbol | hP9 |
| Space group number | 164 |
| Space group symbol | $P\overline{3}m1$ |
| AFLOW prototype command |
aflow --proto=A7B2_hP9_164_ac2d_d-001
--params=$a, \allowbreak c/a, \allowbreak z_{2}, \allowbreak z_{3}, \allowbreak z_{4}, \allowbreak z_{5}$ |
- (Zalkin, 1956) put this structure in space group $P321$ #150, however the occupied Wyckoff positions are duplicated in the higher symmetry space group $P\overline{3}m1$ #164. Accordingly we use the higher symmetry space group.
- (Cenzual, 1991) note that the coordinate $z_{3}$ of the Li-III atom should be -1/12 rather than -1/2 as given in (Zalkin, 1956). This agrees with the figures in the original reference so we use that value.
- The ICSD entry is from (Zalkin, 1956).
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \,\mathbf{\hat{y}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $0$ | = | $0$ | (1a) | Li I |
| $\mathbf{B_{2}}$ | = | $z_{2} \, \mathbf{a}_{3}$ | = | $c z_{2} \,\mathbf{\hat{z}}$ | (2c) | Li II |
| $\mathbf{B_{3}}$ | = | $- z_{2} \, \mathbf{a}_{3}$ | = | $- c z_{2} \,\mathbf{\hat{z}}$ | (2c) | Li II |
| $\mathbf{B_{4}}$ | = | $\frac{1}{3} \, \mathbf{a}_{1}+\frac{2}{3} \, \mathbf{a}_{2}+z_{3} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+c z_{3} \,\mathbf{\hat{z}}$ | (2d) | Li III |
| $\mathbf{B_{5}}$ | = | $\frac{2}{3} \, \mathbf{a}_{1}+\frac{1}{3} \, \mathbf{a}_{2}- z_{3} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}- c z_{3} \,\mathbf{\hat{z}}$ | (2d) | Li III |
| $\mathbf{B_{6}}$ | = | $\frac{1}{3} \, \mathbf{a}_{1}+\frac{2}{3} \, \mathbf{a}_{2}+z_{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+c z_{4} \,\mathbf{\hat{z}}$ | (2d) | Li IV |
| $\mathbf{B_{7}}$ | = | $\frac{2}{3} \, \mathbf{a}_{1}+\frac{1}{3} \, \mathbf{a}_{2}- z_{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}- c z_{4} \,\mathbf{\hat{z}}$ | (2d) | Li IV |
| $\mathbf{B_{8}}$ | = | $\frac{1}{3} \, \mathbf{a}_{1}+\frac{2}{3} \, \mathbf{a}_{2}+z_{5} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+c z_{5} \,\mathbf{\hat{z}}$ | (2d) | Pb I |
| $\mathbf{B_{9}}$ | = | $\frac{2}{3} \, \mathbf{a}_{1}+\frac{1}{3} \, \mathbf{a}_{2}- z_{5} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}- c z_{5} \,\mathbf{\hat{z}}$ | (2d) | Pb I |
References
- A. Zalkin and W. J. Ramsey, Intermetallic Compounds between Lithium and Lead. I. The Structures of Li$_{3}$Pb and Li$_{7}$Pb$_{2}$, J. Phys. Chem. 60, 234–236 (1956), doi:10.1021/j150536a022.
- K. Cenzual, L. M. Gelato, M. Penzo, and E. Parthé, Inorganic structure types with revised space groups. I, Acta Crystallogr. Sect. B 47, 433–439 (1991), doi:10.1107/S0108768191000903.
Found in
- J. Hauck and K. Mika, Architecture of crystal structures from square planes, Acta Crystallogr. Sect. B 56, 750–765 (2000), doi:10.1107/S0108768100006480.
Prototype Generator
aflow --proto=A7B2_hP9_164_ac2d_d --params=$a,c/a,z_{2},z_{3},z_{4},z_{5}$