PrNiO$_{3}$ Structure: AB3C_hR10_167_b_e_a-001
| Prototype | NiO$_{3}$Pr |
| AFLOW prototype label | AB3C_hR10_167_b_e_a-001 |
| ICSD | 69186 |
| Pearson symbol | hR10 |
| Space group number | 167 |
| Space group symbol | $R\overline{3}c$ |
| AFLOW prototype command |
aflow --proto=AB3C_hR10_167_b_e_a-001
--params=$a, \allowbreak c/a, \allowbreak x_{3}$ |
Other compounds with this structure
LaAlO$_{3}$, LaNiO$_{3}$
- This structure has the same crystal structure and occupies the same Wyckoff positions as Calcite (CaCO$_{3}$, $G0_{1}$, ABC3_hR10_167_a_b_e), but $c/a$ and $x_{3}$ are different enough to warrant calling this a new structure.
- This is the high-temperature form of PrNiO$_{3}$, and we present the data collected at 500°C, below which it transforms into the orthorhombic perovskite structure (AB3C_oP20_62_c_cd_a).
- Hexagonal settings of this structure can be obtained with the option
--hex.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+\frac{1}{3}c \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{\sqrt{3}}a \,\mathbf{\hat{y}}+\frac{1}{3}c \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&- \frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+\frac{1}{3}c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}c \,\mathbf{\hat{z}}$ | (2a) | Pr I |
| $\mathbf{B_{2}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{3}{4}c \,\mathbf{\hat{z}}$ | (2a) | Pr I |
| $\mathbf{B_{3}}$ | = | $0$ | = | $0$ | (2b) | Ni I |
| $\mathbf{B_{4}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}c \,\mathbf{\hat{z}}$ | (2b) | Ni I |
| $\mathbf{B_{5}}$ | = | $x_{3} \, \mathbf{a}_{1}- \left(x_{3} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{8}a \left(4 x_{3} - 1\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{8}a \left(4 x_{3} - 1\right) \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (6e) | O I |
| $\mathbf{B_{6}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{2}- \left(x_{3} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{8}a \left(4 x_{3} - 1\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{8}a \left(4 x_{3} - 1\right) \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (6e) | O I |
| $\mathbf{B_{7}}$ | = | $- \left(x_{3} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}+x_{3} \, \mathbf{a}_{3}$ | = | $- a \left(x_{3} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (6e) | O I |
| $\mathbf{B_{8}}$ | = | $- x_{3} \, \mathbf{a}_{1}+\left(x_{3} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $- \frac{1}{8}a \left(4 x_{3} + 3\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{24}a \left(12 x_{3} + 1\right) \,\mathbf{\hat{y}}+\frac{5}{12}c \,\mathbf{\hat{z}}$ | (6e) | O I |
| $\mathbf{B_{9}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}+\left(x_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{8}a \left(4 x_{3} - 1\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{24}a \left(12 x_{3} + 5\right) \,\mathbf{\hat{y}}+\frac{5}{12}c \,\mathbf{\hat{z}}$ | (6e) | O I |
| $\mathbf{B_{10}}$ | = | $\left(x_{3} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}- x_{3} \, \mathbf{a}_{3}$ | = | $a \left(x_{3} + \frac{1}{4}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+\frac{5}{12}c \,\mathbf{\hat{z}}$ | (6e) | O I |
References
- T. C. Huang, W. Parrish, H. Toraya, P. Lacorre, and J. B. Torrance, High-Temperature Crystal Structures of Orthorhombic and Rhombohedral PrNiO$_{3}$, Mater. Res. Bull. 25, 1091–1098 (1990), doi:10.1016/0025-5408(90)90138-R.
Found in
- R. T. Downs and M. Hall-Wallace, The American Mineralogist Crystal Structure Database, Am. Mineral. 88, 247–250 (2003).
Prototype Generator
aflow --proto=AB3C_hR10_167_b_e_a --params=$a,c/a,x_{3}$