Sr$_{2}$IrO$_{4}$ Structure: AB4C2_tI56_142_a_df_d-001
| Prototype | IrO$_{4}$Sr$_{2}$ |
| AFLOW prototype label | AB4C2_tI56_142_a_df_d-001 |
| ICSD | 78260 |
| Pearson symbol | tI56 |
| Space group number | 142 |
| Space group symbol | $I4_1/acd$ |
| AFLOW prototype command |
aflow --proto=AB4C2_tI56_142_a_df_d-001
--params=$a, \allowbreak c/a, \allowbreak z_{2}, \allowbreak z_{3}, \allowbreak x_{4}$ |
Other compounds with this structure
Ca$_{2}$MnO$_{4}$, Sr$_{2}$HfO$_{4}$, Sr$_{2}$RhO$_{4}$
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&- \frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}- \frac{1}{2}c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $\frac{5}{8} \, \mathbf{a}_{1}+\frac{3}{8} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{y}}+\frac{3}{8}c \,\mathbf{\hat{z}}$ | (8a) | Ir I |
| $\mathbf{B_{2}}$ | = | $\frac{3}{8} \, \mathbf{a}_{1}+\frac{5}{8} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+\frac{1}{8}c \,\mathbf{\hat{z}}$ | (8a) | Ir I |
| $\mathbf{B_{3}}$ | = | $\frac{7}{8} \, \mathbf{a}_{1}+\frac{1}{8} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{3}{4}a \,\mathbf{\hat{y}}+\frac{1}{8}c \,\mathbf{\hat{z}}$ | (8a) | Ir I |
| $\mathbf{B_{4}}$ | = | $\frac{1}{8} \, \mathbf{a}_{1}+\frac{7}{8} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{1}{4}a \,\mathbf{\hat{y}}+\frac{3}{8}c \,\mathbf{\hat{z}}$ | (8a) | Ir I |
| $\mathbf{B_{5}}$ | = | $\left(z_{2} + \frac{1}{4}\right) \, \mathbf{a}_{1}+z_{2} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{y}}+c z_{2} \,\mathbf{\hat{z}}$ | (16d) | O I |
| $\mathbf{B_{6}}$ | = | $z_{2} \, \mathbf{a}_{1}+\left(z_{2} + \frac{1}{4}\right) \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+c \left(z_{2} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16d) | O I |
| $\mathbf{B_{7}}$ | = | $- \left(z_{2} - \frac{1}{4}\right) \, \mathbf{a}_{1}- \left(z_{2} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}- c z_{2} \,\mathbf{\hat{z}}$ | (16d) | O I |
| $\mathbf{B_{8}}$ | = | $- \left(z_{2} - \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(z_{2} - \frac{1}{4}\right) \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{y}}- c \left(z_{2} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16d) | O I |
| $\mathbf{B_{9}}$ | = | $- \left(z_{2} - \frac{3}{4}\right) \, \mathbf{a}_{1}- z_{2} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{3}{4}a \,\mathbf{\hat{y}}- c z_{2} \,\mathbf{\hat{z}}$ | (16d) | O I |
| $\mathbf{B_{10}}$ | = | $- z_{2} \, \mathbf{a}_{1}- \left(z_{2} - \frac{3}{4}\right) \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{1}{4}a \,\mathbf{\hat{y}}- c \left(z_{2} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16d) | O I |
| $\mathbf{B_{11}}$ | = | $\left(z_{2} + \frac{3}{4}\right) \, \mathbf{a}_{1}+\left(z_{2} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{y}}+c \left(z_{2} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (16d) | O I |
| $\mathbf{B_{12}}$ | = | $\left(z_{2} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(z_{2} + \frac{3}{4}\right) \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+c \left(z_{2} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16d) | O I |
| $\mathbf{B_{13}}$ | = | $\left(z_{3} + \frac{1}{4}\right) \, \mathbf{a}_{1}+z_{3} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{y}}+c z_{3} \,\mathbf{\hat{z}}$ | (16d) | Sr I |
| $\mathbf{B_{14}}$ | = | $z_{3} \, \mathbf{a}_{1}+\left(z_{3} + \frac{1}{4}\right) \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+c \left(z_{3} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16d) | Sr I |
| $\mathbf{B_{15}}$ | = | $- \left(z_{3} - \frac{1}{4}\right) \, \mathbf{a}_{1}- \left(z_{3} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}- c z_{3} \,\mathbf{\hat{z}}$ | (16d) | Sr I |
| $\mathbf{B_{16}}$ | = | $- \left(z_{3} - \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(z_{3} - \frac{1}{4}\right) \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{y}}- c \left(z_{3} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16d) | Sr I |
| $\mathbf{B_{17}}$ | = | $- \left(z_{3} - \frac{3}{4}\right) \, \mathbf{a}_{1}- z_{3} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{3}{4}a \,\mathbf{\hat{y}}- c z_{3} \,\mathbf{\hat{z}}$ | (16d) | Sr I |
| $\mathbf{B_{18}}$ | = | $- z_{3} \, \mathbf{a}_{1}- \left(z_{3} - \frac{3}{4}\right) \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{1}{4}a \,\mathbf{\hat{y}}- c \left(z_{3} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16d) | Sr I |
| $\mathbf{B_{19}}$ | = | $\left(z_{3} + \frac{3}{4}\right) \, \mathbf{a}_{1}+\left(z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{y}}+c \left(z_{3} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (16d) | Sr I |
| $\mathbf{B_{20}}$ | = | $\left(z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(z_{3} + \frac{3}{4}\right) \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+c \left(z_{3} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16d) | Sr I |
| $\mathbf{B_{21}}$ | = | $\left(x_{4} + \frac{3}{8}\right) \, \mathbf{a}_{1}+\left(x_{4} + \frac{1}{8}\right) \, \mathbf{a}_{2}+\left(2 x_{4} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $a x_{4} \,\mathbf{\hat{x}}+a \left(x_{4} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+\frac{1}{8}c \,\mathbf{\hat{z}}$ | (16f) | O II |
| $\mathbf{B_{22}}$ | = | $- \left(x_{4} - \frac{3}{8}\right) \, \mathbf{a}_{1}- \left(x_{4} - \frac{1}{8}\right) \, \mathbf{a}_{2}- \left(2 x_{4} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $- a x_{4} \,\mathbf{\hat{x}}- a \left(x_{4} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+\frac{1}{8}c \,\mathbf{\hat{z}}$ | (16f) | O II |
| $\mathbf{B_{23}}$ | = | $\left(x_{4} + \frac{1}{8}\right) \, \mathbf{a}_{1}- \left(x_{4} - \frac{3}{8}\right) \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $- a \left(x_{4} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(x_{4} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- \frac{1}{8}c \,\mathbf{\hat{z}}$ | (16f) | O II |
| $\mathbf{B_{24}}$ | = | $- \left(x_{4} - \frac{1}{8}\right) \, \mathbf{a}_{1}+\left(x_{4} + \frac{3}{8}\right) \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $a \left(x_{4} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(x_{4} - \frac{1}{4}\right) \,\mathbf{\hat{y}}- \frac{1}{8}c \,\mathbf{\hat{z}}$ | (16f) | O II |
| $\mathbf{B_{25}}$ | = | $- \left(x_{4} - \frac{5}{8}\right) \, \mathbf{a}_{1}- \left(x_{4} - \frac{7}{8}\right) \, \mathbf{a}_{2}- \left(2 x_{4} - \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{4} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(x_{4} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+\frac{3}{8}c \,\mathbf{\hat{z}}$ | (16f) | O II |
| $\mathbf{B_{26}}$ | = | $\left(x_{4} + \frac{5}{8}\right) \, \mathbf{a}_{1}+\left(x_{4} + \frac{7}{8}\right) \, \mathbf{a}_{2}+\left(2 x_{4} + \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{4} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(x_{4} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+\frac{3}{8}c \,\mathbf{\hat{z}}$ | (16f) | O II |
| $\mathbf{B_{27}}$ | = | $- \left(x_{4} - \frac{7}{8}\right) \, \mathbf{a}_{1}+\left(x_{4} + \frac{5}{8}\right) \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $a x_{4} \,\mathbf{\hat{x}}- a \left(x_{4} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+\frac{5}{8}c \,\mathbf{\hat{z}}$ | (16f) | O II |
| $\mathbf{B_{28}}$ | = | $\left(x_{4} + \frac{7}{8}\right) \, \mathbf{a}_{1}- \left(x_{4} - \frac{5}{8}\right) \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $- a x_{4} \,\mathbf{\hat{x}}+a \left(x_{4} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+\frac{5}{8}c \,\mathbf{\hat{z}}$ | (16f) | O II |
References
- M. K. Crawford, M. A. Subramanian, R. L. Harlow, J. A. Fernandez-Baca, Z. R. Wang, and D. C. Johnston, Structural and magnetic studies of Sr$_{2}$IrO$_{4}$, Phys. Rev. B 49, 9198–9201 (1994), doi:10.1103/PhysRevB.87.140406.
Found in
- F. Ye, S. Chi, B. C. Chakoumakos, J. A. Fernandez-Baca, T. Qi, and G. Cao, Magnetic and crystal structures of Sr$_{2}$IrO$_{4}$: A neutron diffraction study, Phys. Rev. B 87, 140406 (2013), doi:10.1103/PhysRevB.87.140406.
Prototype Generator
aflow --proto=AB4C2_tI56_142_a_df_d --params=$a,c/a,z_{2},z_{3},x_{4}$