Pyrochlore Iridate (Eu$_{2}$Ir$_{2}$O$_{7}$, $E8_{1}$) Structure: A2B2C7_cF88_227_c_d_af-001
| Prototype | Eu$_{2}$Ir$_{2}$O$_{7}$ |
| AFLOW prototype label | A2B2C7_cF88_227_c_d_af-001 |
| Strukturbericht designation | $E8_{1}$ |
| Mineral name | pyrochlore iridate |
| ICSD | 135031 |
| Pearson symbol | cF88 |
| Space group number | 227 |
| Space group symbol | $Fd\overline{3}m$ |
| AFLOW prototype command |
aflow --proto=A2B2C7_cF88_227_c_d_af-001
--params=$a, \allowbreak x_{4}$ |
Other compounds with this structure
FNb$_{2}$(Nb, Ca)$_{2}$O$_{6}$ (''synthetic'' pyrochlore), (Nb, Ta, Ti)$_{2}$(Ca, Ce, Na, K)$_{2}$(F, O)$_{7}$ (``natural'' pyrhochlore), (F, O, OH)(Nb, Fe)$_{2}$(Ca, Ce, Na, K)$_{2}$O$_{6}$ (Koppit), (F, OH)Sb$_{2}$(Ca, Mn, Na)$_{2}$O$_{6}$ (Rom\'{e}ite), (OH)Sb$_{2}$(Ca, Fe, Na)$_{2}$O$_{6}$ (Scheebergite), (Sb, Ti)$_{2}$(Ca, Fe, Mn, Na)$_{2}$(O, OH)$_{6}$ (Lewisite), (OH, F)(Nb, Ta, Ti)$_{2}$(Ca, Fe, Na)$_{2}$O$_{6}$ (Pyrrhite), (OH, F)(Nb, Ta)$_{2}$(Ca, Fe, Na)$_{2}$O$_{6}$ (Mikrolith), Sb$_{2}$Pb$_{2}$O$_{7}$ (Bindheimite), (H$_{2}$O)$_{0.875}$(Al$_{0.8125}$Mg$_{0.1875}$)$_{2}$Na$_{0.375}$[F$_{0.65}$(OH)$_{0.35}$]$_{6}$ (Ralstonite), Sb$_{3}$O$_{6}$OH, BiTa$_{2}$O$_{6}$F, Sn$_{2}$Nb$_{2}$O$_{7}$, Sn$_{2}$Nd$_{2}$O$_{7}$, Sn$_{2}$Ta$_{2}$O$_{7}$, Ca$_{2}$Nb$_{2}$O$_{7}$, Ca$_{2}$Ru$_{2}$O$_{7}$, Dy$_{2}$GaSbO$_{7}$, In$_{2}$Ge$_{2}$O$_{7}$, Pr$_{3}$IrO$_{7}$, Y$_{2}$Mn$_{2}$O$_{7}$, Yb$_{2}$Ir$_{2}$O$_{7}$
- (Herrmann, 1943) uses Strukturbericht $E8_{1}$ to describe the cubic pyrochlore structures. These have the general formula R$_{2}$Q$_{2}$X$_{7}$, where the X atoms or radicals occupy the (4a) and (48f) sites, and the R and Q atoms occupy the (16c) and(16d) sites. In many cases the sites are only partially filled and/or have mixed chemistry. We use Eu$_{2}$Ir$_{2}$O$_{7}$ as our prototype because it represents a fully filled system.
- We take our data from (Sagayama, 2013), but the ICSD entry is from the later work of (Nenoff, 2021).
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $\frac{1}{8} \, \mathbf{a}_{1}+\frac{1}{8} \, \mathbf{a}_{2}+\frac{1}{8} \, \mathbf{a}_{3}$ | = | $\frac{1}{8}a \,\mathbf{\hat{x}}+\frac{1}{8}a \,\mathbf{\hat{y}}+\frac{1}{8}a \,\mathbf{\hat{z}}$ | (8a) | O I |
| $\mathbf{B_{2}}$ | = | $\frac{7}{8} \, \mathbf{a}_{1}+\frac{7}{8} \, \mathbf{a}_{2}+\frac{7}{8} \, \mathbf{a}_{3}$ | = | $\frac{7}{8}a \,\mathbf{\hat{x}}+\frac{7}{8}a \,\mathbf{\hat{y}}+\frac{7}{8}a \,\mathbf{\hat{z}}$ | (8a) | O I |
| $\mathbf{B_{3}}$ | = | $0$ | = | $0$ | (16c) | Eu I |
| $\mathbf{B_{4}}$ | = | $\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}$ | (16c) | Eu I |
| $\mathbf{B_{5}}$ | = | $\frac{1}{2} \, \mathbf{a}_{2}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (16c) | Eu I |
| $\mathbf{B_{6}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}$ | = | $\frac{1}{4}a \,\mathbf{\hat{y}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (16c) | Eu I |
| $\mathbf{B_{7}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}$ | (16d) | Ir I |
| $\mathbf{B_{8}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}$ | (16d) | Ir I |
| $\mathbf{B_{9}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (16d) | Ir I |
| $\mathbf{B_{10}}$ | = | $\frac{1}{2} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (16d) | Ir I |
| $\mathbf{B_{11}}$ | = | $- \left(x_{4} - \frac{1}{4}\right) \, \mathbf{a}_{1}+x_{4} \, \mathbf{a}_{2}+x_{4} \, \mathbf{a}_{3}$ | = | $a x_{4} \,\mathbf{\hat{x}}+\frac{1}{8}a \,\mathbf{\hat{y}}+\frac{1}{8}a \,\mathbf{\hat{z}}$ | (48f) | O II |
| $\mathbf{B_{12}}$ | = | $x_{4} \, \mathbf{a}_{1}- \left(x_{4} - \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(x_{4} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{4} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+\frac{1}{8}a \,\mathbf{\hat{y}}+\frac{1}{8}a \,\mathbf{\hat{z}}$ | (48f) | O II |
| $\mathbf{B_{13}}$ | = | $x_{4} \, \mathbf{a}_{1}- \left(x_{4} - \frac{1}{4}\right) \, \mathbf{a}_{2}+x_{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{8}a \,\mathbf{\hat{x}}+a x_{4} \,\mathbf{\hat{y}}+\frac{1}{8}a \,\mathbf{\hat{z}}$ | (48f) | O II |
| $\mathbf{B_{14}}$ | = | $- \left(x_{4} - \frac{1}{4}\right) \, \mathbf{a}_{1}+x_{4} \, \mathbf{a}_{2}- \left(x_{4} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{8}a \,\mathbf{\hat{x}}- a \left(x_{4} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+\frac{1}{8}a \,\mathbf{\hat{z}}$ | (48f) | O II |
| $\mathbf{B_{15}}$ | = | $x_{4} \, \mathbf{a}_{1}+x_{4} \, \mathbf{a}_{2}- \left(x_{4} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{8}a \,\mathbf{\hat{x}}+\frac{1}{8}a \,\mathbf{\hat{y}}+a x_{4} \,\mathbf{\hat{z}}$ | (48f) | O II |
| $\mathbf{B_{16}}$ | = | $- \left(x_{4} - \frac{1}{4}\right) \, \mathbf{a}_{1}- \left(x_{4} - \frac{1}{4}\right) \, \mathbf{a}_{2}+x_{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{8}a \,\mathbf{\hat{x}}+\frac{1}{8}a \,\mathbf{\hat{y}}- a \left(x_{4} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (48f) | O II |
| $\mathbf{B_{17}}$ | = | $\left(x_{4} + \frac{3}{4}\right) \, \mathbf{a}_{1}- x_{4} \, \mathbf{a}_{2}+\left(x_{4} + \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $\frac{3}{8}a \,\mathbf{\hat{x}}+a \left(x_{4} + \frac{3}{4}\right) \,\mathbf{\hat{y}}+\frac{3}{8}a \,\mathbf{\hat{z}}$ | (48f) | O II |
| $\mathbf{B_{18}}$ | = | $- x_{4} \, \mathbf{a}_{1}+\left(x_{4} + \frac{3}{4}\right) \, \mathbf{a}_{2}- x_{4} \, \mathbf{a}_{3}$ | = | $\frac{3}{8}a \,\mathbf{\hat{x}}- a x_{4} \,\mathbf{\hat{y}}+\frac{3}{8}a \,\mathbf{\hat{z}}$ | (48f) | O II |
| $\mathbf{B_{19}}$ | = | $- x_{4} \, \mathbf{a}_{1}+\left(x_{4} + \frac{3}{4}\right) \, \mathbf{a}_{2}+\left(x_{4} + \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{4} + \frac{3}{4}\right) \,\mathbf{\hat{x}}+\frac{3}{8}a \,\mathbf{\hat{y}}+\frac{3}{8}a \,\mathbf{\hat{z}}$ | (48f) | O II |
| $\mathbf{B_{20}}$ | = | $\left(x_{4} + \frac{3}{4}\right) \, \mathbf{a}_{1}- x_{4} \, \mathbf{a}_{2}- x_{4} \, \mathbf{a}_{3}$ | = | $- a x_{4} \,\mathbf{\hat{x}}+\frac{3}{8}a \,\mathbf{\hat{y}}+\frac{3}{8}a \,\mathbf{\hat{z}}$ | (48f) | O II |
| $\mathbf{B_{21}}$ | = | $- x_{4} \, \mathbf{a}_{1}- x_{4} \, \mathbf{a}_{2}+\left(x_{4} + \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $\frac{3}{8}a \,\mathbf{\hat{x}}+\frac{3}{8}a \,\mathbf{\hat{y}}- a x_{4} \,\mathbf{\hat{z}}$ | (48f) | O II |
| $\mathbf{B_{22}}$ | = | $\left(x_{4} + \frac{3}{4}\right) \, \mathbf{a}_{1}+\left(x_{4} + \frac{3}{4}\right) \, \mathbf{a}_{2}- x_{4} \, \mathbf{a}_{3}$ | = | $\frac{3}{8}a \,\mathbf{\hat{x}}+\frac{3}{8}a \,\mathbf{\hat{y}}+a \left(x_{4} + \frac{3}{4}\right) \,\mathbf{\hat{z}}$ | (48f) | O II |
References
- H. Sagayama, D. Uematsu, T. Arima, K. Sugimoto, J. J. Ishikawa, E. O’Farrell, and S. Nakatsuji, Determination of long-range all-in-all-out ordering of Ir$^{4+}$ moments in a pyrochlore iridate Eu$_{2}$Ir$_{2}$O$_{7}$ by resonant x-ray diffraction, Phys. Rev. B 87, 100403 (2013), doi:10.1103/PhysRevB.87.100403.
- C. Hermann, O. Lohrmann, and H. Philipp, eds., Strukturbericht Band II 1928-1932 (Akademische Verlagsgesellschaft M. B. H., Leipzig, 1937).
- K. Herrmann, ed., Strukturbericht Band VII 1939 (Akademische Verlagsgesellschaft M. B. H., Leipzig, 1943).
- T. M. Nenoff, D. X. Rademacher, M. A. Rodriguez, T. J. Garino, T. Subramani, and A. Navrotsky, Structure-Property and Thermodynamic Relationships in Rare Earth (Y, Eu, Pr) Iridate Pyrochlores, J. Solid State Chem. 299, 122163 (2021), doi:10.1016/j.jssc.2021.122163.
Found in
- S. H. Chun, B. Yuan, D. Casa, J. Kim, C.-Y. Kim, Z. Tian, Y. Qiu, S. Nakatsuji, and Y.-J. Kim, Magnetic Excitations across the Metal-Insulator Transition in the Pyrochlore Iridate Eu$_{2}$Ir$_{2}$O$_{7}$, Phys. Rev. Lett. 120, 177203 (2018), doi:10.1103/PhysRevLett.120.177203.
Prototype Generator
aflow --proto=A2B2C7_cF88_227_c_d_af --params=$a,x_{4}$