β-BaPbO$_{3}$ Perovskite Structure: AB3C_oI20_74_e_eg_a-001
| Prototype | BaO$_{3}$Pb |
| AFLOW prototype label | AB3C_oI20_74_e_eg_a-001 |
| ICSD | 78681 |
| CCDC | 1638954 |
| Pearson symbol | oI20 |
| Space group number | 74 |
| Space group symbol | $Imma$ |
| AFLOW prototype command |
aflow --proto=AB3C_oI20_74_e_eg_a-001
--params=$a, \allowbreak b/a, \allowbreak c/a, \allowbreak z_{2}, \allowbreak z_{3}, \allowbreak y_{4}$ |
Other compounds with this structure
AlCeO$_{3}$, BaCeO$_{3}$, BaPrO$_{3}$, BaTbO$_{3}$, BaThO$_{3}$, EuNbO$_{3}$, PuAlO$_{3}$, SrMoO$_{3}$, SrSnO$_{3}$, SrTcO$_{3}$, SrZrO$_{3}$, Ba(Ce$_{1-x}$In$_{x}$)O$_{3}$, Ba(Ce$_{1-x}$Zr$_{x}$)O$_{3}$, Ba(Pb$_{1-x}$Bi$_{x}$)O$_{3}$, Ba(Pb$_{1-x}$Tl$_{x}$)O$_{3}$, Ba(Sb$_{1-x}$Tl$_{x}$)O$_{3}$, (Ba$_{1-x}$K$_{x}$)BiO$_{3}$, (Bi$_{1-x}$La$_{x}$)FeO$_{3}$, (La$_{1-x}$Ba$_{x}$)MnO$_{3}$, (Na$_{1-x}$Pr$_{x}$)TiO$_{3}$, (Nd$_{1-x}$Sr$_{x}$)MnO$_{3}$, (Pr$_{1-x}$Ba$_{x}$)MnO$_{3}$, (Sr$_{1-x}$Ba$_{x}$)SnO$_{3}$
- 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$_{3}$.
- At some point above 26\,K (Ritter, 1989) we find orthorhombic $\beta$–BaPbO$_{3}$ (this structure).
- 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.
- All of the metallic sites may be alloyed, we have only listed a small number of possibilities. The oxygen sites may be partially filled, or partially replaced by nitrogen or fluorine.
- (Fu, 1995) gave the structural information in the $Ibmm$ setting of space group #74. We used AFLOW to transform this to the standard $Imma$ setting. This requires change of the axes so that $(x y z) \rightarrow (y z x)$.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&- \frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}b \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{1}{2}b \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}b \,\mathbf{\hat{y}}- \frac{1}{2}c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $0$ | = | $0$ | (4a) | Pb I |
| $\mathbf{B_{2}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}b \,\mathbf{\hat{y}}$ | (4a) | Pb I |
| $\mathbf{B_{3}}$ | = | $\left(z_{2} + \frac{1}{4}\right) \, \mathbf{a}_{1}+z_{2} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}b \,\mathbf{\hat{y}}+c z_{2} \,\mathbf{\hat{z}}$ | (4e) | Ba I |
| $\mathbf{B_{4}}$ | = | $- \left(z_{2} - \frac{3}{4}\right) \, \mathbf{a}_{1}- z_{2} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{3}{4}b \,\mathbf{\hat{y}}- c z_{2} \,\mathbf{\hat{z}}$ | (4e) | Ba I |
| $\mathbf{B_{5}}$ | = | $\left(z_{3} + \frac{1}{4}\right) \, \mathbf{a}_{1}+z_{3} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}b \,\mathbf{\hat{y}}+c z_{3} \,\mathbf{\hat{z}}$ | (4e) | O I |
| $\mathbf{B_{6}}$ | = | $- \left(z_{3} - \frac{3}{4}\right) \, \mathbf{a}_{1}- z_{3} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{3}{4}b \,\mathbf{\hat{y}}- c z_{3} \,\mathbf{\hat{z}}$ | (4e) | O I |
| $\mathbf{B_{7}}$ | = | $\left(y_{4} + \frac{1}{4}\right) \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+\left(y_{4} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+b y_{4} \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (8g) | O II |
| $\mathbf{B_{8}}$ | = | $- \left(y_{4} - \frac{3}{4}\right) \, \mathbf{a}_{1}- \left(y_{4} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{4}a \,\mathbf{\hat{x}}- b \left(y_{4} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (8g) | O II |
| $\mathbf{B_{9}}$ | = | $- \left(y_{4} - \frac{3}{4}\right) \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}- \left(y_{4} - \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}- b \left(y_{4} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (8g) | O II |
| $\mathbf{B_{10}}$ | = | $\left(y_{4} + \frac{1}{4}\right) \, \mathbf{a}_{1}+\left(y_{4} + \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+b \left(y_{4} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- \frac{1}{4}c \,\mathbf{\hat{z}}$ | (8g) | O II |
References
- 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.
- 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.
- 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
- 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.
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_oI20_74_e_eg_a --params=$a,b/a,c/a,z_{2},z_{3},y_{4}$