NaNbO$_{3}$ Structure: ABC3_oP40_17_abcd_2e_abcd4e-001
| Prototype | NaNbO$_{3}$ |
| AFLOW prototype label | ABC3_oP40_17_abcd_2e_abcd4e-001 |
| ICSD | 76432 |
| Pearson symbol | oP40 |
| Space group number | 17 |
| Space group symbol | $P222_1$ |
| AFLOW prototype command |
aflow --proto=ABC3_oP40_17_abcd_2e_abcd4e-001
--params=$a, \allowbreak b/a, \allowbreak c/a, \allowbreak x_{1}, \allowbreak x_{2}, \allowbreak x_{3}, \allowbreak x_{4}, \allowbreak y_{5}, \allowbreak y_{6}, \allowbreak y_{7}, \allowbreak y_{8}, \allowbreak x_{9}, \allowbreak y_{9}, \allowbreak z_{9}, \allowbreak x_{10}, \allowbreak y_{10}, \allowbreak z_{10}, \allowbreak x_{11}, \allowbreak y_{11}, \allowbreak z_{11}, \allowbreak x_{12}, \allowbreak y_{12}, \allowbreak z_{12}, \allowbreak x_{13}, \allowbreak y_{13}, \allowbreak z_{13}, \allowbreak x_{14}, \allowbreak y_{14}, \allowbreak z_{14}$ |
- (Downs, 2003) identifies this as a
possible polymorph of lueshite.
- If the aflow parameters are set to
--params$=a,1,\sqrt{8},1/2,0,0,1/2,1/2,0,0,1/2,0,0,3/8,1/2,1/2,3/8,1/4,1/4,3/8,3/4,1/4,3/8,1/4,3/4,3/8,3/4,3/4,3/8$ then the structure is equivalent to cubic perovskite $E2_{1}$.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&a \,\mathbf{\hat{x}}\\\mathbf{a_{2}}&=&b \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $x_{1} \, \mathbf{a}_{1}$ | = | $a x_{1} \,\mathbf{\hat{x}}$ | (2a) | Na I |
| $\mathbf{B_{2}}$ | = | $- x_{1} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- a x_{1} \,\mathbf{\hat{x}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (2a) | Na I |
| $\mathbf{B_{3}}$ | = | $x_{2} \, \mathbf{a}_{1}$ | = | $a x_{2} \,\mathbf{\hat{x}}$ | (2a) | O I |
| $\mathbf{B_{4}}$ | = | $- x_{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- a x_{2} \,\mathbf{\hat{x}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (2a) | O I |
| $\mathbf{B_{5}}$ | = | $x_{3} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}$ | = | $a x_{3} \,\mathbf{\hat{x}}+\frac{1}{2}b \,\mathbf{\hat{y}}$ | (2b) | Na II |
| $\mathbf{B_{6}}$ | = | $- x_{3} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}+\frac{1}{2}b \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (2b) | Na II |
| $\mathbf{B_{7}}$ | = | $x_{4} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}$ | = | $a x_{4} \,\mathbf{\hat{x}}+\frac{1}{2}b \,\mathbf{\hat{y}}$ | (2b) | O II |
| $\mathbf{B_{8}}$ | = | $- x_{4} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- a x_{4} \,\mathbf{\hat{x}}+\frac{1}{2}b \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (2b) | O II |
| $\mathbf{B_{9}}$ | = | $y_{5} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $b y_{5} \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (2c) | Na III |
| $\mathbf{B_{10}}$ | = | $- y_{5} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $- b y_{5} \,\mathbf{\hat{y}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ | (2c) | Na III |
| $\mathbf{B_{11}}$ | = | $y_{6} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $b y_{6} \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (2c) | O III |
| $\mathbf{B_{12}}$ | = | $- y_{6} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $- b y_{6} \,\mathbf{\hat{y}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ | (2c) | O III |
| $\mathbf{B_{13}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+y_{7} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+b y_{7} \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (2d) | Na IV |
| $\mathbf{B_{14}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}- y_{7} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- b y_{7} \,\mathbf{\hat{y}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ | (2d) | Na IV |
| $\mathbf{B_{15}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+y_{8} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+b y_{8} \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (2d) | O IV |
| $\mathbf{B_{16}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}- y_{8} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- b y_{8} \,\mathbf{\hat{y}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ | (2d) | O IV |
| $\mathbf{B_{17}}$ | = | $x_{9} \, \mathbf{a}_{1}+y_{9} \, \mathbf{a}_{2}+z_{9} \, \mathbf{a}_{3}$ | = | $a x_{9} \,\mathbf{\hat{x}}+b y_{9} \,\mathbf{\hat{y}}+c z_{9} \,\mathbf{\hat{z}}$ | (4e) | Nb I |
| $\mathbf{B_{18}}$ | = | $- x_{9} \, \mathbf{a}_{1}- y_{9} \, \mathbf{a}_{2}+\left(z_{9} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{9} \,\mathbf{\hat{x}}- b y_{9} \,\mathbf{\hat{y}}+c \left(z_{9} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4e) | Nb I |
| $\mathbf{B_{19}}$ | = | $- x_{9} \, \mathbf{a}_{1}+y_{9} \, \mathbf{a}_{2}- \left(z_{9} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{9} \,\mathbf{\hat{x}}+b y_{9} \,\mathbf{\hat{y}}- c \left(z_{9} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4e) | Nb I |
| $\mathbf{B_{20}}$ | = | $x_{9} \, \mathbf{a}_{1}- y_{9} \, \mathbf{a}_{2}- z_{9} \, \mathbf{a}_{3}$ | = | $a x_{9} \,\mathbf{\hat{x}}- b y_{9} \,\mathbf{\hat{y}}- c z_{9} \,\mathbf{\hat{z}}$ | (4e) | Nb I |
| $\mathbf{B_{21}}$ | = | $x_{10} \, \mathbf{a}_{1}+y_{10} \, \mathbf{a}_{2}+z_{10} \, \mathbf{a}_{3}$ | = | $a x_{10} \,\mathbf{\hat{x}}+b y_{10} \,\mathbf{\hat{y}}+c z_{10} \,\mathbf{\hat{z}}$ | (4e) | Nb II |
| $\mathbf{B_{22}}$ | = | $- x_{10} \, \mathbf{a}_{1}- y_{10} \, \mathbf{a}_{2}+\left(z_{10} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{10} \,\mathbf{\hat{x}}- b y_{10} \,\mathbf{\hat{y}}+c \left(z_{10} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4e) | Nb II |
| $\mathbf{B_{23}}$ | = | $- x_{10} \, \mathbf{a}_{1}+y_{10} \, \mathbf{a}_{2}- \left(z_{10} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{10} \,\mathbf{\hat{x}}+b y_{10} \,\mathbf{\hat{y}}- c \left(z_{10} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4e) | Nb II |
| $\mathbf{B_{24}}$ | = | $x_{10} \, \mathbf{a}_{1}- y_{10} \, \mathbf{a}_{2}- z_{10} \, \mathbf{a}_{3}$ | = | $a x_{10} \,\mathbf{\hat{x}}- b y_{10} \,\mathbf{\hat{y}}- c z_{10} \,\mathbf{\hat{z}}$ | (4e) | Nb II |
| $\mathbf{B_{25}}$ | = | $x_{11} \, \mathbf{a}_{1}+y_{11} \, \mathbf{a}_{2}+z_{11} \, \mathbf{a}_{3}$ | = | $a x_{11} \,\mathbf{\hat{x}}+b y_{11} \,\mathbf{\hat{y}}+c z_{11} \,\mathbf{\hat{z}}$ | (4e) | O V |
| $\mathbf{B_{26}}$ | = | $- x_{11} \, \mathbf{a}_{1}- y_{11} \, \mathbf{a}_{2}+\left(z_{11} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{11} \,\mathbf{\hat{x}}- b y_{11} \,\mathbf{\hat{y}}+c \left(z_{11} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4e) | O V |
| $\mathbf{B_{27}}$ | = | $- x_{11} \, \mathbf{a}_{1}+y_{11} \, \mathbf{a}_{2}- \left(z_{11} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{11} \,\mathbf{\hat{x}}+b y_{11} \,\mathbf{\hat{y}}- c \left(z_{11} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4e) | O V |
| $\mathbf{B_{28}}$ | = | $x_{11} \, \mathbf{a}_{1}- y_{11} \, \mathbf{a}_{2}- z_{11} \, \mathbf{a}_{3}$ | = | $a x_{11} \,\mathbf{\hat{x}}- b y_{11} \,\mathbf{\hat{y}}- c z_{11} \,\mathbf{\hat{z}}$ | (4e) | O V |
| $\mathbf{B_{29}}$ | = | $x_{12} \, \mathbf{a}_{1}+y_{12} \, \mathbf{a}_{2}+z_{12} \, \mathbf{a}_{3}$ | = | $a x_{12} \,\mathbf{\hat{x}}+b y_{12} \,\mathbf{\hat{y}}+c z_{12} \,\mathbf{\hat{z}}$ | (4e) | O VI |
| $\mathbf{B_{30}}$ | = | $- x_{12} \, \mathbf{a}_{1}- y_{12} \, \mathbf{a}_{2}+\left(z_{12} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{12} \,\mathbf{\hat{x}}- b y_{12} \,\mathbf{\hat{y}}+c \left(z_{12} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4e) | O VI |
| $\mathbf{B_{31}}$ | = | $- x_{12} \, \mathbf{a}_{1}+y_{12} \, \mathbf{a}_{2}- \left(z_{12} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{12} \,\mathbf{\hat{x}}+b y_{12} \,\mathbf{\hat{y}}- c \left(z_{12} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4e) | O VI |
| $\mathbf{B_{32}}$ | = | $x_{12} \, \mathbf{a}_{1}- y_{12} \, \mathbf{a}_{2}- z_{12} \, \mathbf{a}_{3}$ | = | $a x_{12} \,\mathbf{\hat{x}}- b y_{12} \,\mathbf{\hat{y}}- c z_{12} \,\mathbf{\hat{z}}$ | (4e) | O VI |
| $\mathbf{B_{33}}$ | = | $x_{13} \, \mathbf{a}_{1}+y_{13} \, \mathbf{a}_{2}+z_{13} \, \mathbf{a}_{3}$ | = | $a x_{13} \,\mathbf{\hat{x}}+b y_{13} \,\mathbf{\hat{y}}+c z_{13} \,\mathbf{\hat{z}}$ | (4e) | O VII |
| $\mathbf{B_{34}}$ | = | $- x_{13} \, \mathbf{a}_{1}- y_{13} \, \mathbf{a}_{2}+\left(z_{13} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{13} \,\mathbf{\hat{x}}- b y_{13} \,\mathbf{\hat{y}}+c \left(z_{13} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4e) | O VII |
| $\mathbf{B_{35}}$ | = | $- x_{13} \, \mathbf{a}_{1}+y_{13} \, \mathbf{a}_{2}- \left(z_{13} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{13} \,\mathbf{\hat{x}}+b y_{13} \,\mathbf{\hat{y}}- c \left(z_{13} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4e) | O VII |
| $\mathbf{B_{36}}$ | = | $x_{13} \, \mathbf{a}_{1}- y_{13} \, \mathbf{a}_{2}- z_{13} \, \mathbf{a}_{3}$ | = | $a x_{13} \,\mathbf{\hat{x}}- b y_{13} \,\mathbf{\hat{y}}- c z_{13} \,\mathbf{\hat{z}}$ | (4e) | O VII |
| $\mathbf{B_{37}}$ | = | $x_{14} \, \mathbf{a}_{1}+y_{14} \, \mathbf{a}_{2}+z_{14} \, \mathbf{a}_{3}$ | = | $a x_{14} \,\mathbf{\hat{x}}+b y_{14} \,\mathbf{\hat{y}}+c z_{14} \,\mathbf{\hat{z}}$ | (4e) | O VIII |
| $\mathbf{B_{38}}$ | = | $- x_{14} \, \mathbf{a}_{1}- y_{14} \, \mathbf{a}_{2}+\left(z_{14} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{14} \,\mathbf{\hat{x}}- b y_{14} \,\mathbf{\hat{y}}+c \left(z_{14} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4e) | O VIII |
| $\mathbf{B_{39}}$ | = | $- x_{14} \, \mathbf{a}_{1}+y_{14} \, \mathbf{a}_{2}- \left(z_{14} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{14} \,\mathbf{\hat{x}}+b y_{14} \,\mathbf{\hat{y}}- c \left(z_{14} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4e) | O VIII |
| $\mathbf{B_{40}}$ | = | $x_{14} \, \mathbf{a}_{1}- y_{14} \, \mathbf{a}_{2}- z_{14} \, \mathbf{a}_{3}$ | = | $a x_{14} \,\mathbf{\hat{x}}- b y_{14} \,\mathbf{\hat{y}}- c z_{14} \,\mathbf{\hat{z}}$ | (4e) | O VIII |
References
- P. Vousden, The Structure of Ferroelectric Sodium Niobate at Room Temperature, Acta Cryst. 4, 545–551 (1951), doi:10.1107/S0365110X51001768.
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=ABC3_oP40_17_abcd_2e_abcd4e --params=$a,b/a,c/a,x_{1},x_{2},x_{3},x_{4},y_{5},y_{6},y_{7},y_{8},x_{9},y_{9},z_{9},x_{10},y_{10},z_{10},x_{11},y_{11},z_{11},x_{12},y_{12},z_{12},x_{13},y_{13},z_{13},x_{14},y_{14},z_{14}$