Cubic Perovskite (CaTiO$_{3}$, $E2_{1}$) Structure: AB3C_cP5_221_a_c_b-001
| Prototype | CaTiO$_{3}$ |
| AFLOW prototype label | AB3C_cP5_221_a_c_b-001 |
| Strukturbericht designation | $E2_1$ |
| Mineral name | perovskite |
| ICSD | 31865 |
| Pearson symbol | cP5 |
| Space group number | 221 |
| Space group symbol | $Pm\overline{3}m$ |
| AFLOW prototype command |
aflow --proto=AB3C_cP5_221_a_c_b-001
--params=$a$ |
Other compounds with this structure
AlCFe$_{3}$, AlCMn$_{3}$, AlCTi$_{3}$, AlNMn$_{3}$, AuOCs$_{3}$, BaCeO$_{3}$, BaCrO$_{3}$, BaLiH$_{3}$, BaPuO$_{3}$, BaSnO$_{3}$, BaTiO$_{3}$, BaZrO$_{3}$, BiFeO$_{3}$, CeCRu$_{3}$, CeCrO$_{3}$, CuNMn$_{3}$, EuTiO$_{3}$, GaCMn$_{3}$, GaNMn$_{3}$, GeCMn$_{3}$, InCTi$_{3}$, InNTi$_{3}$, KMgF$_{3}$, KTaO$_{3}$, LaAlO$_{3}$, LaGaO$_{3}$, MgCNi$_{3}$, MgNaF$_{3}$, NiNFe$_{3}$, NiNMn$_{3}$, PbTiO$_{3}$, PbZrO$_{3}$, PdNFe$_{3}$, PrCoO$_{3}$, PtNFe$_{3}$, RbFeF$_{3}$, SmCoO$_{3}$, SmCrO$_{3}$, SnCFe$_{3}$, SnNFe$_{3}$, SrLiH$_{3}$, SrRuO$_{3}$, SrTiO$_{3}$, SrTlO$_{3}$, TlCTi$_{3}$, TlNTi$_{3}$, YAlO$_{3}$, ZnCMn$_{3}$, Ba$_{3}$N$_{2}$, Ba$_{3}$P$_{2}$, Ba$_{3}$Sb$_{2}$
- Cubic perovskite is actually the high-temperature phase of the compounds listed here. The ground states of these compounds are distored perovskite structures. Many of these substances are ferroelectric.
- By removing one atom type we get various structures, all with space group $Pm\overline{3}m$ #221:
- Removing the calcium atoms leads to the $\alpha$–ReO$_{3}$ ($D0_{9}$) structure;
- removing the titanium atoms leads to the Cu$_{3}$Au ($L1_{2}$) structure;
- removing the oxygen atoms leads to the CsCl ($B2$) structure;
- removing the calcium or titanium and the oxygen atoms leads to the simple cubic ($A_h$) structure.
- (Ewald, 1931) originally gave this compound the Strukturbericht Designation $G4$, but this was changed by (Gottfried, 1937) to $E2_{1}$.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&a \,\mathbf{\hat{x}}\\\mathbf{a_{2}}&=&a \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&a \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $0$ | = | $0$ | (1a) | Ca I |
| $\mathbf{B_{2}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}$ | (1b) | Ti I |
| $\mathbf{B_{3}}$ | = | $\frac{1}{2} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}$ | (3c) | O I |
| $\mathbf{B_{4}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{z}}$ | (3c) | O I |
| $\mathbf{B_{5}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}$ | (3c) | O I |
References
- T. Barth, Die Kristallstruktur von Perowskit und verwandter Verbindungen, Norsk. Geol. Tidssk. 8, 201–216 (1925).
- P. P. Ewald and C. Hermann, eds., Strukturbericht 1913-1928 (Akademische Verlagsgesellschaft M. B. H., Leipzig, 1931).
- C. Gottfried and F. Schossberger, eds., Strukturbericht Band III 1933-1935 (Akademische Verlagsgesellschaft M. B. H., Leipzig, 1937).
Found in
- R. T. Downs and M. Hall-Wallace, The American Mineralogist Crystal Structure Database, Am. Mineral. 88, 247–250 (2003).
Prototype Generator
aflow --proto=AB3C_cP5_221_a_c_b --params=$a$