Ca$_{5}$Ir$_{3}$O$_{12}$ Structure: A5B3C12_hP20_189_dg_f_2gj-001
| Prototype | Ca$_{5}$Ir$_{3}$O$_{12}$ |
| AFLOW prototype label | A5B3C12_hP20_189_dg_f_2gj-001 |
| ICSD | 120112 |
| Pearson symbol | hP20 |
| Space group number | 189 |
| Space group symbol | $P\overline{6}2m$ |
| AFLOW prototype command |
aflow --proto=A5B3C12_hP20_189_dg_f_2gj-001
--params=$a, \allowbreak c/a, \allowbreak x_{2}, \allowbreak x_{3}, \allowbreak x_{4}, \allowbreak x_{5}, \allowbreak x_{6}, \allowbreak y_{6}$ |
- The data for this structure was taken at 90K.
- There is no ICSD entry for (Wakeshima, 2003). We use the entry from (Cao, 2007), which the authors say is in agreement with the Wakeshima result.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \,\mathbf{\hat{y}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $\frac{1}{3} \, \mathbf{a}_{1}+\frac{2}{3} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (2d) | Ca I |
| $\mathbf{B_{2}}$ | = | $\frac{2}{3} \, \mathbf{a}_{1}+\frac{1}{3} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (2d) | Ca I |
| $\mathbf{B_{3}}$ | = | $x_{2} \, \mathbf{a}_{1}$ | = | $\frac{1}{2}a x_{2} \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{2} \,\mathbf{\hat{y}}$ | (3f) | Ir I |
| $\mathbf{B_{4}}$ | = | $x_{2} \, \mathbf{a}_{2}$ | = | $\frac{1}{2}a x_{2} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{2} \,\mathbf{\hat{y}}$ | (3f) | Ir I |
| $\mathbf{B_{5}}$ | = | $- x_{2} \, \mathbf{a}_{1}- x_{2} \, \mathbf{a}_{2}$ | = | $- a x_{2} \,\mathbf{\hat{x}}$ | (3f) | Ir I |
| $\mathbf{B_{6}}$ | = | $x_{3} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a x_{3} \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{3} \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (3g) | Ca II |
| $\mathbf{B_{7}}$ | = | $x_{3} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a x_{3} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{3} \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (3g) | Ca II |
| $\mathbf{B_{8}}$ | = | $- x_{3} \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (3g) | Ca II |
| $\mathbf{B_{9}}$ | = | $x_{4} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a x_{4} \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{4} \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (3g) | O I |
| $\mathbf{B_{10}}$ | = | $x_{4} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a x_{4} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{4} \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (3g) | O I |
| $\mathbf{B_{11}}$ | = | $- x_{4} \, \mathbf{a}_{1}- x_{4} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- a x_{4} \,\mathbf{\hat{x}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (3g) | O I |
| $\mathbf{B_{12}}$ | = | $x_{5} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a x_{5} \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{5} \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (3g) | O II |
| $\mathbf{B_{13}}$ | = | $x_{5} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a x_{5} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{5} \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (3g) | O II |
| $\mathbf{B_{14}}$ | = | $- x_{5} \, \mathbf{a}_{1}- x_{5} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- a x_{5} \,\mathbf{\hat{x}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (3g) | O II |
| $\mathbf{B_{15}}$ | = | $x_{6} \, \mathbf{a}_{1}+y_{6} \, \mathbf{a}_{2}$ | = | $\frac{1}{2}a \left(x_{6} + y_{6}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \left(x_{6} - y_{6}\right) \,\mathbf{\hat{y}}$ | (6j) | O III |
| $\mathbf{B_{16}}$ | = | $- y_{6} \, \mathbf{a}_{1}+\left(x_{6} - y_{6}\right) \, \mathbf{a}_{2}$ | = | $\frac{1}{2}a \left(x_{6} - 2 y_{6}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{6} \,\mathbf{\hat{y}}$ | (6j) | O III |
| $\mathbf{B_{17}}$ | = | $- \left(x_{6} - y_{6}\right) \, \mathbf{a}_{1}- x_{6} \, \mathbf{a}_{2}$ | = | $- \frac{1}{2}a \left(2 x_{6} - y_{6}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a y_{6} \,\mathbf{\hat{y}}$ | (6j) | O III |
| $\mathbf{B_{18}}$ | = | $y_{6} \, \mathbf{a}_{1}+x_{6} \, \mathbf{a}_{2}$ | = | $\frac{1}{2}a \left(x_{6} + y_{6}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \left(x_{6} - y_{6}\right) \,\mathbf{\hat{y}}$ | (6j) | O III |
| $\mathbf{B_{19}}$ | = | $\left(x_{6} - y_{6}\right) \, \mathbf{a}_{1}- y_{6} \, \mathbf{a}_{2}$ | = | $\frac{1}{2}a \left(x_{6} - 2 y_{6}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{6} \,\mathbf{\hat{y}}$ | (6j) | O III |
| $\mathbf{B_{20}}$ | = | $- x_{6} \, \mathbf{a}_{1}- \left(x_{6} - y_{6}\right) \, \mathbf{a}_{2}$ | = | $- \frac{1}{2}a \left(2 x_{6} - y_{6}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a y_{6} \,\mathbf{\hat{y}}$ | (6j) | O III |
References
- M. Wakeshima, N. Taira, Y. Hinatsu, and Y. Ishiib, Electrical and magnetic properties of pseudo-one-dimensional calcium iridium oxide Ca$_{5}$Ir$_{3}$O$_{12}$, Solid State Commun. 125, 311–315 (2003), doi:10.1016/S0038-1098(02)00823-2.
- G. Cao, V. Durairaj, S. Chikara, S. Parkin, and P. Schlottmann, Partial antiferromagnetism in spin-chain Sr$_{5}$Rh$_{4}$O$_{12}$, Ca$_{5}$Ir$_{3}$O$_{12}$, and Ca4IrO6 single crystals, Phys. Rev. B 75, 075153 (2007), doi:10.1103/PhysRevB.75.134402.
Found in
- M. Charlebois, J.-B. Morée, K. Nakamura, Y. Nomura, T. Tadano, Y. Yoshimoto, Y. Yamaji, T. Hasegawa, K. Matsuhira, and M. Imada, {\em Ab initio} Derivation of Low-Energy Hamiltonians for Systems with Strong Spin-Orbit Interaction and Its Application to Ca$_{5}$Ir$_{3}$O$_{12}$, Phys. Rev. B 104, 075153 (2021), doi:10.1103/PhysRevB.104.075153.
Prototype Generator
aflow --proto=A5B3C12_hP20_189_dg_f_2gj --params=$a,c/a,x_{2},x_{3},x_{4},x_{5},x_{6},y_{6}$