β-SrIrO$_{3}$ Perovskite Structure: A2B6C7_cI90_204_e_dg_ac2f-001
| Prototype | IrSrO$_{3}$ |
| AFLOW prototype label | A2B6C7_cI90_204_e_dg_ac2f-001 |
| ICSD | 33738 |
| CCDC | 1606480 |
| Pearson symbol | cI90 |
| Space group number | 204 |
| Space group symbol | $Im\overline{3}$ |
| AFLOW prototype command |
aflow --proto=A2B6C7_cI90_204_e_dg_ac2f-001
--params=$a, \allowbreak x_{3}, \allowbreak x_{4}, \allowbreak x_{5}, \allowbreak x_{6}, \allowbreak y_{7}, \allowbreak z_{7}$ |
- The structural transitions in SrIrO$_{3}$ are less certain than for other perovskites.
- The ground state is usually believed to be monoclinic with space group $C2/c$ #15, however
- (Schmalle, 1990) found a somewhat disordered room temperature cubic phase (this structure).
- (Longo, 1971) found that to the right of a line from (700$^\circ$C, 5GPa) to (1650$^\circ$, 2GPa) there is a transformation to the orthorhombic CaTiO$_{3}$ structure, but
- (Wang, 2024) found a tetragonal double perovskite structure formed at 1400$^\circ$C and 6GPa, well into the range where (Longo, 1971) found the orthorhombic structure. This structure is very close to cubic perovskite ($E2_{1}$), which may well be the structure found at higher pressures and temperatures.
- The Greek letters used to designate the phase are arbitrarily assigned in the order of the first publication describing the phases.
- All of the strontium sites in this structure are sparsely populated. The occupation numbers from (Schmalle, 1990) do not give the correct stoichiometry, so we use the values from the ICSD entry. The occupations are:
- Sr I 33.6%
- Sr II 12.0%
- Sr III 23.4%
- Sr IV 30.0%
- These values give a stoichiometry of Sr$_{0.848}$IrO$_{3}$.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&- \frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}- \frac{1}{2}a \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $0$ | = | $0$ | (2a) | Sr I |
| $\mathbf{B_{2}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (8c) | Sr II |
| $\mathbf{B_{3}}$ | = | $\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}- \frac{1}{4}a \,\mathbf{\hat{z}}$ | (8c) | Sr II |
| $\mathbf{B_{4}}$ | = | $\frac{1}{2} \, \mathbf{a}_{2}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}- \frac{1}{4}a \,\mathbf{\hat{y}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (8c) | Sr II |
| $\mathbf{B_{5}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}$ | = | $- \frac{1}{4}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (8c) | Sr II |
| $\mathbf{B_{6}}$ | = | $x_{3} \, \mathbf{a}_{2}+x_{3} \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{x}}$ | (12d) | O I |
| $\mathbf{B_{7}}$ | = | $- x_{3} \, \mathbf{a}_{2}- x_{3} \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}$ | (12d) | O I |
| $\mathbf{B_{8}}$ | = | $x_{3} \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{y}}$ | (12d) | O I |
| $\mathbf{B_{9}}$ | = | $- x_{3} \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{y}}$ | (12d) | O I |
| $\mathbf{B_{10}}$ | = | $x_{3} \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{2}$ | = | $a x_{3} \,\mathbf{\hat{z}}$ | (12d) | O I |
| $\mathbf{B_{11}}$ | = | $- x_{3} \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}$ | = | $- a x_{3} \,\mathbf{\hat{z}}$ | (12d) | O I |
| $\mathbf{B_{12}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\left(x_{4} + \frac{1}{2}\right) \, \mathbf{a}_{2}+x_{4} \, \mathbf{a}_{3}$ | = | $a x_{4} \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{z}}$ | (12e) | Ir I |
| $\mathbf{B_{13}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}- \left(x_{4} - \frac{1}{2}\right) \, \mathbf{a}_{2}- x_{4} \, \mathbf{a}_{3}$ | = | $- a x_{4} \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{z}}$ | (12e) | Ir I |
| $\mathbf{B_{14}}$ | = | $x_{4} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+\left(x_{4} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+a x_{4} \,\mathbf{\hat{y}}$ | (12e) | Ir I |
| $\mathbf{B_{15}}$ | = | $- x_{4} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}- \left(x_{4} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- a x_{4} \,\mathbf{\hat{y}}$ | (12e) | Ir I |
| $\mathbf{B_{16}}$ | = | $\left(x_{4} + \frac{1}{2}\right) \, \mathbf{a}_{1}+x_{4} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{y}}+a x_{4} \,\mathbf{\hat{z}}$ | (12e) | Ir I |
| $\mathbf{B_{17}}$ | = | $- \left(x_{4} - \frac{1}{2}\right) \, \mathbf{a}_{1}- x_{4} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{y}}- a x_{4} \,\mathbf{\hat{z}}$ | (12e) | Ir I |
| $\mathbf{B_{18}}$ | = | $2 x_{5} \, \mathbf{a}_{1}+2 x_{5} \, \mathbf{a}_{2}+2 x_{5} \, \mathbf{a}_{3}$ | = | $a x_{5} \,\mathbf{\hat{x}}+a x_{5} \,\mathbf{\hat{y}}+a x_{5} \,\mathbf{\hat{z}}$ | (16f) | Sr III |
| $\mathbf{B_{19}}$ | = | $- 2 x_{5} \, \mathbf{a}_{3}$ | = | $- a x_{5} \,\mathbf{\hat{x}}- a x_{5} \,\mathbf{\hat{y}}+a x_{5} \,\mathbf{\hat{z}}$ | (16f) | Sr III |
| $\mathbf{B_{20}}$ | = | $- 2 x_{5} \, \mathbf{a}_{2}$ | = | $- a x_{5} \,\mathbf{\hat{x}}+a x_{5} \,\mathbf{\hat{y}}- a x_{5} \,\mathbf{\hat{z}}$ | (16f) | Sr III |
| $\mathbf{B_{21}}$ | = | $- 2 x_{5} \, \mathbf{a}_{1}$ | = | $a x_{5} \,\mathbf{\hat{x}}- a x_{5} \,\mathbf{\hat{y}}- a x_{5} \,\mathbf{\hat{z}}$ | (16f) | Sr III |
| $\mathbf{B_{22}}$ | = | $- 2 x_{5} \, \mathbf{a}_{1}- 2 x_{5} \, \mathbf{a}_{2}- 2 x_{5} \, \mathbf{a}_{3}$ | = | $- a x_{5} \,\mathbf{\hat{x}}- a x_{5} \,\mathbf{\hat{y}}- a x_{5} \,\mathbf{\hat{z}}$ | (16f) | Sr III |
| $\mathbf{B_{23}}$ | = | $2 x_{5} \, \mathbf{a}_{3}$ | = | $a x_{5} \,\mathbf{\hat{x}}+a x_{5} \,\mathbf{\hat{y}}- a x_{5} \,\mathbf{\hat{z}}$ | (16f) | Sr III |
| $\mathbf{B_{24}}$ | = | $2 x_{5} \, \mathbf{a}_{2}$ | = | $a x_{5} \,\mathbf{\hat{x}}- a x_{5} \,\mathbf{\hat{y}}+a x_{5} \,\mathbf{\hat{z}}$ | (16f) | Sr III |
| $\mathbf{B_{25}}$ | = | $2 x_{5} \, \mathbf{a}_{1}$ | = | $- a x_{5} \,\mathbf{\hat{x}}+a x_{5} \,\mathbf{\hat{y}}+a x_{5} \,\mathbf{\hat{z}}$ | (16f) | Sr III |
| $\mathbf{B_{26}}$ | = | $2 x_{6} \, \mathbf{a}_{1}+2 x_{6} \, \mathbf{a}_{2}+2 x_{6} \, \mathbf{a}_{3}$ | = | $a x_{6} \,\mathbf{\hat{x}}+a x_{6} \,\mathbf{\hat{y}}+a x_{6} \,\mathbf{\hat{z}}$ | (16f) | Sr IV |
| $\mathbf{B_{27}}$ | = | $- 2 x_{6} \, \mathbf{a}_{3}$ | = | $- a x_{6} \,\mathbf{\hat{x}}- a x_{6} \,\mathbf{\hat{y}}+a x_{6} \,\mathbf{\hat{z}}$ | (16f) | Sr IV |
| $\mathbf{B_{28}}$ | = | $- 2 x_{6} \, \mathbf{a}_{2}$ | = | $- a x_{6} \,\mathbf{\hat{x}}+a x_{6} \,\mathbf{\hat{y}}- a x_{6} \,\mathbf{\hat{z}}$ | (16f) | Sr IV |
| $\mathbf{B_{29}}$ | = | $- 2 x_{6} \, \mathbf{a}_{1}$ | = | $a x_{6} \,\mathbf{\hat{x}}- a x_{6} \,\mathbf{\hat{y}}- a x_{6} \,\mathbf{\hat{z}}$ | (16f) | Sr IV |
| $\mathbf{B_{30}}$ | = | $- 2 x_{6} \, \mathbf{a}_{1}- 2 x_{6} \, \mathbf{a}_{2}- 2 x_{6} \, \mathbf{a}_{3}$ | = | $- a x_{6} \,\mathbf{\hat{x}}- a x_{6} \,\mathbf{\hat{y}}- a x_{6} \,\mathbf{\hat{z}}$ | (16f) | Sr IV |
| $\mathbf{B_{31}}$ | = | $2 x_{6} \, \mathbf{a}_{3}$ | = | $a x_{6} \,\mathbf{\hat{x}}+a x_{6} \,\mathbf{\hat{y}}- a x_{6} \,\mathbf{\hat{z}}$ | (16f) | Sr IV |
| $\mathbf{B_{32}}$ | = | $2 x_{6} \, \mathbf{a}_{2}$ | = | $a x_{6} \,\mathbf{\hat{x}}- a x_{6} \,\mathbf{\hat{y}}+a x_{6} \,\mathbf{\hat{z}}$ | (16f) | Sr IV |
| $\mathbf{B_{33}}$ | = | $2 x_{6} \, \mathbf{a}_{1}$ | = | $- a x_{6} \,\mathbf{\hat{x}}+a x_{6} \,\mathbf{\hat{y}}+a x_{6} \,\mathbf{\hat{z}}$ | (16f) | Sr IV |
| $\mathbf{B_{34}}$ | = | $\left(y_{7} + z_{7}\right) \, \mathbf{a}_{1}+z_{7} \, \mathbf{a}_{2}+y_{7} \, \mathbf{a}_{3}$ | = | $a y_{7} \,\mathbf{\hat{y}}+a z_{7} \,\mathbf{\hat{z}}$ | (24g) | O II |
| $\mathbf{B_{35}}$ | = | $- \left(y_{7} - z_{7}\right) \, \mathbf{a}_{1}+z_{7} \, \mathbf{a}_{2}- y_{7} \, \mathbf{a}_{3}$ | = | $- a y_{7} \,\mathbf{\hat{y}}+a z_{7} \,\mathbf{\hat{z}}$ | (24g) | O II |
| $\mathbf{B_{36}}$ | = | $\left(y_{7} - z_{7}\right) \, \mathbf{a}_{1}- z_{7} \, \mathbf{a}_{2}+y_{7} \, \mathbf{a}_{3}$ | = | $a y_{7} \,\mathbf{\hat{y}}- a z_{7} \,\mathbf{\hat{z}}$ | (24g) | O II |
| $\mathbf{B_{37}}$ | = | $- \left(y_{7} + z_{7}\right) \, \mathbf{a}_{1}- z_{7} \, \mathbf{a}_{2}- y_{7} \, \mathbf{a}_{3}$ | = | $- a y_{7} \,\mathbf{\hat{y}}- a z_{7} \,\mathbf{\hat{z}}$ | (24g) | O II |
| $\mathbf{B_{38}}$ | = | $y_{7} \, \mathbf{a}_{1}+\left(y_{7} + z_{7}\right) \, \mathbf{a}_{2}+z_{7} \, \mathbf{a}_{3}$ | = | $a z_{7} \,\mathbf{\hat{x}}+a y_{7} \,\mathbf{\hat{z}}$ | (24g) | O II |
| $\mathbf{B_{39}}$ | = | $- y_{7} \, \mathbf{a}_{1}- \left(y_{7} - z_{7}\right) \, \mathbf{a}_{2}+z_{7} \, \mathbf{a}_{3}$ | = | $a z_{7} \,\mathbf{\hat{x}}- a y_{7} \,\mathbf{\hat{z}}$ | (24g) | O II |
| $\mathbf{B_{40}}$ | = | $y_{7} \, \mathbf{a}_{1}+\left(y_{7} - z_{7}\right) \, \mathbf{a}_{2}- z_{7} \, \mathbf{a}_{3}$ | = | $- a z_{7} \,\mathbf{\hat{x}}+a y_{7} \,\mathbf{\hat{z}}$ | (24g) | O II |
| $\mathbf{B_{41}}$ | = | $- y_{7} \, \mathbf{a}_{1}- \left(y_{7} + z_{7}\right) \, \mathbf{a}_{2}- z_{7} \, \mathbf{a}_{3}$ | = | $- a z_{7} \,\mathbf{\hat{x}}- a y_{7} \,\mathbf{\hat{z}}$ | (24g) | O II |
| $\mathbf{B_{42}}$ | = | $z_{7} \, \mathbf{a}_{1}+y_{7} \, \mathbf{a}_{2}+\left(y_{7} + z_{7}\right) \, \mathbf{a}_{3}$ | = | $a y_{7} \,\mathbf{\hat{x}}+a z_{7} \,\mathbf{\hat{y}}$ | (24g) | O II |
| $\mathbf{B_{43}}$ | = | $z_{7} \, \mathbf{a}_{1}- y_{7} \, \mathbf{a}_{2}- \left(y_{7} - z_{7}\right) \, \mathbf{a}_{3}$ | = | $- a y_{7} \,\mathbf{\hat{x}}+a z_{7} \,\mathbf{\hat{y}}$ | (24g) | O II |
| $\mathbf{B_{44}}$ | = | $- z_{7} \, \mathbf{a}_{1}+y_{7} \, \mathbf{a}_{2}+\left(y_{7} - z_{7}\right) \, \mathbf{a}_{3}$ | = | $a y_{7} \,\mathbf{\hat{x}}- a z_{7} \,\mathbf{\hat{y}}$ | (24g) | O II |
| $\mathbf{B_{45}}$ | = | $- z_{7} \, \mathbf{a}_{1}- y_{7} \, \mathbf{a}_{2}- \left(y_{7} + z_{7}\right) \, \mathbf{a}_{3}$ | = | $- a y_{7} \,\mathbf{\hat{x}}- a z_{7} \,\mathbf{\hat{y}}$ | (24g) | O II |
References
- H. Schmalle, C. Gurtner, H. R. Oswald, and A. Reller, The crystal structure of SrIrO$_{3}$, Z. Krystallogr. 191, 239–247 (1990), doi:10.1524/zkri.1990.191.14.239.
- J. M. Longo, J. A. Kafalas, and R. Arnott, Structure and properties of the high and low pressure forms of SrIrO$_{3}$, J. Solid State Chem. 3, 174–179 (1971), doi:10.1016/0022-4596(71)90022-3.
- H. Wang, A. de la Torre, J. T. Race, Q. Wang, J. P. C. Ruff, P. M. Woodward, K. W. Plumb, D. Walker, and W. Xie, Pseudosymmetry in Tetragonal Perovskite SrIrO$_{3}$ Synthesized under High Pressure, ACS App. Electron. Mater. 6, 6820–6825 (2024), doi:10.1021/acsaelm.4c01214.
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=A2B6C7_cI90_204_e_dg_ac2f --params=$a,x_{3},x_{4},x_{5},x_{6},y_{7},z_{7}$