α-BaPbO$_{3}$ Perovskite Structure: AB3C_mC20_12_i_ghi_e-001
| Prototype | BaO$_{3}$Pb |
| AFLOW prototype label | AB3C_mC20_12_i_ghi_e-001 |
| ICSD | 94313 |
| CCDC | 1653754 |
| Pearson symbol | mC20 |
| Space group number | 12 |
| Space group symbol | $C2/m$ |
| AFLOW prototype command |
aflow --proto=AB3C_mC20_12_i_ghi_e-001
--params=$a, \allowbreak b/a, \allowbreak c/a, \allowbreak \beta, \allowbreak y_{2}, \allowbreak y_{3}, \allowbreak x_{4}, \allowbreak z_{4}, \allowbreak x_{5}, \allowbreak z_{5}$ |
Other compounds with this structure
Al(Pr$_{1-x}$La$_{x}$)O$_{3}$, Ba(Ce$_{1-x}$Nd$_{x}$)O$_{3}$, Ba(Ce$_{1-x}$Y$_{x}$)O$_{3}$, Ba(Pb$_{1-x}$Bi$_{x}$)O$_{3}$, LaTa(O, N)$_{3}$, SrTa(O, N)$_{3}$
- As with most perovskites, BaPbO$_{3}$ has a number of phase transitions. The temperature-driven transitions are summarized in (Fu, 1995), (Moussa, 2001), and (Hestor, 2002). We will follow our usual convention and label the phases by Greek letters, increasing with temperature.
- The low temperature structure is monoclinic $\alpha$–BaPbO$_{3}$ (this structure).
- At some point above 26\,K (Ritter, 1989) we find orthorhombic $\beta$–BaPbO$_{3}$.
- At 548\,K it transforms into the tetragonal $\gamma$–BaPbO$_{3}$ in the $\gamma$–SrZrO$_{3}$ structure.
- Finally, above 723-725\,K $\delta$–BaPbO$_{3}$ is in the cubic perovskite ($E2_{1}$) structure.
- The oxygen atoms may be replaced by nitrogen in some systems.
- We use the data taken by (Moussa, 2001) at 15\,K.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{1}{2}b \,\mathbf{\hat{y}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}b \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \cos{\beta} \,\mathbf{\hat{x}}+c \sin{\beta} \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $\frac{1}{2} \, \mathbf{a}_{2}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{1}{4}b \,\mathbf{\hat{y}}$ | (4e) | Pb I |
| $\mathbf{B_{2}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}- \frac{1}{4}b \,\mathbf{\hat{y}}$ | (4e) | Pb I |
| $\mathbf{B_{3}}$ | = | $- y_{2} \, \mathbf{a}_{1}+y_{2} \, \mathbf{a}_{2}$ | = | $b y_{2} \,\mathbf{\hat{y}}$ | (4g) | O I |
| $\mathbf{B_{4}}$ | = | $y_{2} \, \mathbf{a}_{1}- y_{2} \, \mathbf{a}_{2}$ | = | $- b y_{2} \,\mathbf{\hat{y}}$ | (4g) | O I |
| $\mathbf{B_{5}}$ | = | $- y_{3} \, \mathbf{a}_{1}+y_{3} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}c \cos{\beta} \,\mathbf{\hat{x}}+b y_{3} \,\mathbf{\hat{y}}+\frac{1}{2}c \sin{\beta} \,\mathbf{\hat{z}}$ | (4h) | O II |
| $\mathbf{B_{6}}$ | = | $y_{3} \, \mathbf{a}_{1}- y_{3} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}c \cos{\beta} \,\mathbf{\hat{x}}- b y_{3} \,\mathbf{\hat{y}}+\frac{1}{2}c \sin{\beta} \,\mathbf{\hat{z}}$ | (4h) | O II |
| $\mathbf{B_{7}}$ | = | $x_{4} \, \mathbf{a}_{1}+x_{4} \, \mathbf{a}_{2}+z_{4} \, \mathbf{a}_{3}$ | = | $\left(a x_{4} + c z_{4} \cos{\beta}\right) \,\mathbf{\hat{x}}+c z_{4} \sin{\beta} \,\mathbf{\hat{z}}$ | (4i) | Ba I |
| $\mathbf{B_{8}}$ | = | $- x_{4} \, \mathbf{a}_{1}- x_{4} \, \mathbf{a}_{2}- z_{4} \, \mathbf{a}_{3}$ | = | $- \left(a x_{4} + c z_{4} \cos{\beta}\right) \,\mathbf{\hat{x}}- c z_{4} \sin{\beta} \,\mathbf{\hat{z}}$ | (4i) | Ba I |
| $\mathbf{B_{9}}$ | = | $x_{5} \, \mathbf{a}_{1}+x_{5} \, \mathbf{a}_{2}+z_{5} \, \mathbf{a}_{3}$ | = | $\left(a x_{5} + c z_{5} \cos{\beta}\right) \,\mathbf{\hat{x}}+c z_{5} \sin{\beta} \,\mathbf{\hat{z}}$ | (4i) | O III |
| $\mathbf{B_{10}}$ | = | $- x_{5} \, \mathbf{a}_{1}- x_{5} \, \mathbf{a}_{2}- z_{5} \, \mathbf{a}_{3}$ | = | $- \left(a x_{5} + c z_{5} \cos{\beta}\right) \,\mathbf{\hat{x}}- c z_{5} \sin{\beta} \,\mathbf{\hat{z}}$ | (4i) | O III |
References
- S. M. Moussa, B. J. Kennedy, and T. Vogt, Structural variants in ABO$_{3}$ type perovskite oxides. On the structure of BaPbO$_{3}$, Solid State Commun. 119, 549–552 (2001), doi:10.1016/S0038-1098(01)00265-4.
- W. T. Fu and D. J. W. Ijdo, A comparative study on the structure of APbO$_{3}$ (A=Ba,Sr), Solid State Commun. 95, 581–585 (1995), doi:10.1016/0038-1098(95)00334-7.
- J. R. Hester, C. J. Howard, B. J. Kennedy, and R. Macquart, High-Temperature Structural Studies of SrPbO$_{3}$ and BaPbO$_{3}$, Aust. J. Chem. 55, 543–545 (2008), doi:10.1071/CH02023.
- H. Ritter, J. Ihringer, J. K. Maichle, W. Prandl, A. Hoser, and A. W. Hewat, The crystal structure of the prototypic ceramic superconductor BaPbO$_{3}$: An X-ray and neutron diffraction study, Z. Phys. B: Condens. Matter 75, 297–302 (1989), doi:10.1007/BF01321817.
Found in
- AFLOW Database}, \href{https://aflow.org}{https://aflow.org}. BaPbO$_{3$, ICSD entry 94313.
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=AB3C_mC20_12_i_ghi_e --params=$a,b/a,c/a,\beta,y_{2},y_{3},x_{4},z_{4},x_{5},z_{5}$