Sr$_{4}$Ti$_{3}$O$_{10}$ Structure: A10B4C3_tI34_139_c2eg_2e_ae-001
| Prototype | O$_{10}$Sr$_{4}$Ti$_{3}$ |
| AFLOW prototype label | A10B4C3_tI34_139_c2eg_2e_ae-001 |
| ICSD | 34630 |
| Pearson symbol | tI34 |
| Space group number | 139 |
| Space group symbol | $I4/mmm$ |
| AFLOW prototype command |
aflow --proto=A10B4C3_tI34_139_c2eg_2e_ae-001
--params=$a, \allowbreak c/a, \allowbreak z_{3}, \allowbreak z_{4}, \allowbreak z_{5}, \allowbreak z_{6}, \allowbreak z_{7}, \allowbreak z_{8}$ |
Other compounds with this structure
La$_{4}$Ni$_{3}$O$_{10}$, Sr$_{4}$V$_{3}$O$_{10}$, K$_{2}$La$_{2}$Ti$_{3}$O$_{10}$, Li$_{2}$Eu$_{2}$Ti$_{3}$O$_{10}$, Na$_{2}$Eu$_{2}$Ti$_{3}$O$_{10}$, Na$_{2}$Sr$_{2}$Nb$_{2}$MnO$_{10}$
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&- \frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}- \frac{1}{2}c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $0$ | = | $0$ | (2a) | Ti I |
| $\mathbf{B_{2}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{y}}$ | (4c) | O I |
| $\mathbf{B_{3}}$ | = | $\frac{1}{2} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}$ | (4c) | O I |
| $\mathbf{B_{4}}$ | = | $z_{3} \, \mathbf{a}_{1}+z_{3} \, \mathbf{a}_{2}$ | = | $c z_{3} \,\mathbf{\hat{z}}$ | (4e) | O II |
| $\mathbf{B_{5}}$ | = | $- z_{3} \, \mathbf{a}_{1}- z_{3} \, \mathbf{a}_{2}$ | = | $- c z_{3} \,\mathbf{\hat{z}}$ | (4e) | O II |
| $\mathbf{B_{6}}$ | = | $z_{4} \, \mathbf{a}_{1}+z_{4} \, \mathbf{a}_{2}$ | = | $c z_{4} \,\mathbf{\hat{z}}$ | (4e) | O III |
| $\mathbf{B_{7}}$ | = | $- z_{4} \, \mathbf{a}_{1}- z_{4} \, \mathbf{a}_{2}$ | = | $- c z_{4} \,\mathbf{\hat{z}}$ | (4e) | O III |
| $\mathbf{B_{8}}$ | = | $z_{5} \, \mathbf{a}_{1}+z_{5} \, \mathbf{a}_{2}$ | = | $c z_{5} \,\mathbf{\hat{z}}$ | (4e) | Sr I |
| $\mathbf{B_{9}}$ | = | $- z_{5} \, \mathbf{a}_{1}- z_{5} \, \mathbf{a}_{2}$ | = | $- c z_{5} \,\mathbf{\hat{z}}$ | (4e) | Sr I |
| $\mathbf{B_{10}}$ | = | $z_{6} \, \mathbf{a}_{1}+z_{6} \, \mathbf{a}_{2}$ | = | $c z_{6} \,\mathbf{\hat{z}}$ | (4e) | Sr II |
| $\mathbf{B_{11}}$ | = | $- z_{6} \, \mathbf{a}_{1}- z_{6} \, \mathbf{a}_{2}$ | = | $- c z_{6} \,\mathbf{\hat{z}}$ | (4e) | Sr II |
| $\mathbf{B_{12}}$ | = | $z_{7} \, \mathbf{a}_{1}+z_{7} \, \mathbf{a}_{2}$ | = | $c z_{7} \,\mathbf{\hat{z}}$ | (4e) | Ti II |
| $\mathbf{B_{13}}$ | = | $- z_{7} \, \mathbf{a}_{1}- z_{7} \, \mathbf{a}_{2}$ | = | $- c z_{7} \,\mathbf{\hat{z}}$ | (4e) | Ti II |
| $\mathbf{B_{14}}$ | = | $\left(z_{8} + \frac{1}{2}\right) \, \mathbf{a}_{1}+z_{8} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{y}}+c z_{8} \,\mathbf{\hat{z}}$ | (8g) | O IV |
| $\mathbf{B_{15}}$ | = | $z_{8} \, \mathbf{a}_{1}+\left(z_{8} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+c z_{8} \,\mathbf{\hat{z}}$ | (8g) | O IV |
| $\mathbf{B_{16}}$ | = | $- \left(z_{8} - \frac{1}{2}\right) \, \mathbf{a}_{1}- z_{8} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{y}}- c z_{8} \,\mathbf{\hat{z}}$ | (8g) | O IV |
| $\mathbf{B_{17}}$ | = | $- z_{8} \, \mathbf{a}_{1}- \left(z_{8} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- c z_{8} \,\mathbf{\hat{z}}$ | (8g) | O IV |
References
- S. N. Ruddlesden and P. Popper, The compound Sr$_{3}$Ti$_{2}$O$_{7}$ and its structure, Acta Cryst. 11, 54–55 (1958), doi:10.1107/S0365110X58000128.
Found in
- Wikipedia, Ruddlesden-Popper phase. A$_3$B$_2$X$_7$ series.
Prototype Generator
aflow --proto=A10B4C3_tI34_139_c2eg_2e_ae --params=$a,c/a,z_{3},z_{4},z_{5},z_{6},z_{7},z_{8}$