BaPb$_{3}$ Structure: AB3_hR12_166_ac_eh-001
| Prototype | BaPb$_{3}$ |
| AFLOW prototype label | AB3_hR12_166_ac_eh-001 |
| ICSD | 58665 |
| Pearson symbol | hR12 |
| Space group number | 166 |
| Space group symbol | $R\overline{3}m$ |
| AFLOW prototype command |
aflow --proto=AB3_hR12_166_ac_eh-001
--params=$a, \allowbreak c/a, \allowbreak x_{2}, \allowbreak x_{4}, \allowbreak z_{4}$ |
Other compounds with this structure
GdAl$_{3}$, PuAl$_{3}$, TbAl$_{3}$, YAl$_{3}$
- Hexagonal settings of this structure can be obtained with the option
--hex.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+\frac{1}{3}c \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{\sqrt{3}}a \,\mathbf{\hat{y}}+\frac{1}{3}c \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&- \frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+\frac{1}{3}c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $0$ | = | $0$ | (1a) | Ba I |
| $\mathbf{B_{2}}$ | = | $x_{2} \, \mathbf{a}_{1}+x_{2} \, \mathbf{a}_{2}+x_{2} \, \mathbf{a}_{3}$ | = | $c x_{2} \,\mathbf{\hat{z}}$ | (2c) | Ba II |
| $\mathbf{B_{3}}$ | = | $- x_{2} \, \mathbf{a}_{1}- x_{2} \, \mathbf{a}_{2}- x_{2} \, \mathbf{a}_{3}$ | = | $- c x_{2} \,\mathbf{\hat{z}}$ | (2c) | Ba II |
| $\mathbf{B_{4}}$ | = | $\frac{1}{2} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- \frac{1}{4}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{12}a \,\mathbf{\hat{y}}+\frac{1}{3}c \,\mathbf{\hat{z}}$ | (3e) | Pb I |
| $\mathbf{B_{5}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+\frac{1}{3}c \,\mathbf{\hat{z}}$ | (3e) | Pb I |
| $\mathbf{B_{6}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{12}a \,\mathbf{\hat{y}}+\frac{1}{3}c \,\mathbf{\hat{z}}$ | (3e) | Pb I |
| $\mathbf{B_{7}}$ | = | $x_{4} \, \mathbf{a}_{1}+x_{4} \, \mathbf{a}_{2}+z_{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{4} - z_{4}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(x_{4} - z_{4}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(2 x_{4} + z_{4}\right) \,\mathbf{\hat{z}}$ | (6h) | Pb II |
| $\mathbf{B_{8}}$ | = | $z_{4} \, \mathbf{a}_{1}+x_{4} \, \mathbf{a}_{2}+x_{4} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{4} - z_{4}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(x_{4} - z_{4}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(2 x_{4} + z_{4}\right) \,\mathbf{\hat{z}}$ | (6h) | Pb II |
| $\mathbf{B_{9}}$ | = | $x_{4} \, \mathbf{a}_{1}+z_{4} \, \mathbf{a}_{2}+x_{4} \, \mathbf{a}_{3}$ | = | $- \frac{1}{\sqrt{3}}a \left(x_{4} - z_{4}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(2 x_{4} + z_{4}\right) \,\mathbf{\hat{z}}$ | (6h) | Pb II |
| $\mathbf{B_{10}}$ | = | $- z_{4} \, \mathbf{a}_{1}- x_{4} \, \mathbf{a}_{2}- x_{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{4} - z_{4}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(x_{4} - z_{4}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(2 x_{4} + z_{4}\right) \,\mathbf{\hat{z}}$ | (6h) | Pb II |
| $\mathbf{B_{11}}$ | = | $- x_{4} \, \mathbf{a}_{1}- x_{4} \, \mathbf{a}_{2}- z_{4} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{4} - z_{4}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(x_{4} - z_{4}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(2 x_{4} + z_{4}\right) \,\mathbf{\hat{z}}$ | (6h) | Pb II |
| $\mathbf{B_{12}}$ | = | $- x_{4} \, \mathbf{a}_{1}- z_{4} \, \mathbf{a}_{2}- x_{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{\sqrt{3}}a \left(x_{4} - z_{4}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(2 x_{4} + z_{4}\right) \,\mathbf{\hat{z}}$ | (6h) | Pb II |
References
- D. E. Sands, D. H. Wood, and W. J. Ramsey, The structures of Ba$_{5}$Pb$_{3}$, BaPb and BaPb$_{3}$, Acta Cryst. 17, 986–989 (1964), doi:10.1107/S0365110X64002547.
Found in
- M. Langenmaier, M. Jehle, and C. Röhr, Mixed Sr and Ba Tri-Stannides/Plumbides A$^{II}$(Sn$_{1−x}$Pb$_{x}$)$_{3}$, Crystals 8, 204 (2018), doi:10.3390/cryst8050204.
Prototype Generator
aflow --proto=AB3_hR12_166_ac_eh --params=$a,c/a,x_{2},x_{4},z_{4}$