Nd$_{4}$Ni$_{3}$O$_{8}$ Structure: A4B3C8_tI30_139_2e_ae_cdg-002
| Prototype | Nd$_{4}$Ni$_{3}$O$_{8}$ |
| AFLOW prototype label | A4B3C8_tI30_139_2e_ae_cdg-002 |
| ICSD | 173372 |
| Pearson symbol | tI30 |
| Space group number | 139 |
| Space group symbol | $I4/mmm$ |
| AFLOW prototype command |
aflow --proto=A4B3C8_tI30_139_2e_ae_cdg-002
--params=$a, \allowbreak c/a, \allowbreak z_{4}, \allowbreak z_{5}, \allowbreak z_{6}, \allowbreak z_{7}$ |
Other compounds with this structure
La$_{4}$Ni$_{3}$O$_{8}$, Pr$_{4}$Ni$_{3}$O$_{8}$
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&- \frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}- \frac{1}{2}c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $0$ | = | $0$ | (2a) | Ni 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 |
| $\mathbf{B_{4}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (4d) | O II |
| $\mathbf{B_{5}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (4d) | O II |
| $\mathbf{B_{6}}$ | = | $z_{4} \, \mathbf{a}_{1}+z_{4} \, \mathbf{a}_{2}$ | = | $c z_{4} \,\mathbf{\hat{z}}$ | (4e) | Nd I |
| $\mathbf{B_{7}}$ | = | $- z_{4} \, \mathbf{a}_{1}- z_{4} \, \mathbf{a}_{2}$ | = | $- c z_{4} \,\mathbf{\hat{z}}$ | (4e) | Nd I |
| $\mathbf{B_{8}}$ | = | $z_{5} \, \mathbf{a}_{1}+z_{5} \, \mathbf{a}_{2}$ | = | $c z_{5} \,\mathbf{\hat{z}}$ | (4e) | Nd II |
| $\mathbf{B_{9}}$ | = | $- z_{5} \, \mathbf{a}_{1}- z_{5} \, \mathbf{a}_{2}$ | = | $- c z_{5} \,\mathbf{\hat{z}}$ | (4e) | Nd II |
| $\mathbf{B_{10}}$ | = | $z_{6} \, \mathbf{a}_{1}+z_{6} \, \mathbf{a}_{2}$ | = | $c z_{6} \,\mathbf{\hat{z}}$ | (4e) | Ni II |
| $\mathbf{B_{11}}$ | = | $- z_{6} \, \mathbf{a}_{1}- z_{6} \, \mathbf{a}_{2}$ | = | $- c z_{6} \,\mathbf{\hat{z}}$ | (4e) | Ni II |
| $\mathbf{B_{12}}$ | = | $\left(z_{7} + \frac{1}{2}\right) \, \mathbf{a}_{1}+z_{7} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{y}}+c z_{7} \,\mathbf{\hat{z}}$ | (8g) | O III |
| $\mathbf{B_{13}}$ | = | $z_{7} \, \mathbf{a}_{1}+\left(z_{7} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+c z_{7} \,\mathbf{\hat{z}}$ | (8g) | O III |
| $\mathbf{B_{14}}$ | = | $- \left(z_{7} - \frac{1}{2}\right) \, \mathbf{a}_{1}- z_{7} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{y}}- c z_{7} \,\mathbf{\hat{z}}$ | (8g) | O III |
| $\mathbf{B_{15}}$ | = | $- z_{7} \, \mathbf{a}_{1}- \left(z_{7} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- c z_{7} \,\mathbf{\hat{z}}$ | (8g) | O III |
References
- V. V. Poltavets, K. A. Lokshin, M. Croft, T. K. Mandal, T. Egami, and M. Greenblatt, Crystal Structures of Ln$_{4}$Ni$_{3}$O$_{8}$ (Ln = La, Nd) Triple Layer T'-type Nickelates, Inorg. Chem. 46, 10887–10891 (2007), doi:10.1016/j.intermet.2008.04.018.
Prototype Generator
aflow --proto=A4B3C8_tI30_139_2e_ae_cdg --params=$a,c/a,z_{4},z_{5},z_{6},z_{7}$