β-NbO$_{2}$ Structure: AB2_tI48_80_2b_4b-001
| Prototype | NbO$_{2}$ |
| AFLOW prototype label | AB2_tI48_80_2b_4b-001 |
| ICSD | 35181 |
| Pearson symbol | tI48 |
| Space group number | 80 |
| Space group symbol | $I4_1$ |
| AFLOW prototype command |
aflow --proto=AB2_tI48_80_2b_4b-001
--params=$a, \allowbreak c/a, \allowbreak x_{1}, \allowbreak y_{1}, \allowbreak z_{1}, \allowbreak x_{2}, \allowbreak y_{2}, \allowbreak z_{2}, \allowbreak x_{3}, \allowbreak y_{3}, \allowbreak z_{3}, \allowbreak x_{4}, \allowbreak y_{4}, \allowbreak z_{4}, \allowbreak x_{5}, \allowbreak y_{5}, \allowbreak z_{5}, \allowbreak x_{6}, \allowbreak y_{6}, \allowbreak z_{6}$ |
- The actual composition is Nb$_{2-x}$O$_{2}$, with $0.002 < x < 0.1$.
- NbO$_{2}$ can also be found in the $\alpha$–NbO$_{2}$ structure.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&- \frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}- \frac{1}{2}c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $\left(y_{1} + z_{1}\right) \, \mathbf{a}_{1}+\left(x_{1} + z_{1}\right) \, \mathbf{a}_{2}+\left(x_{1} + y_{1}\right) \, \mathbf{a}_{3}$ | = | $a x_{1} \,\mathbf{\hat{x}}+a y_{1} \,\mathbf{\hat{y}}+c z_{1} \,\mathbf{\hat{z}}$ | (8b) | Nb I |
| $\mathbf{B_{2}}$ | = | $- \left(y_{1} - z_{1}\right) \, \mathbf{a}_{1}- \left(x_{1} - z_{1}\right) \, \mathbf{a}_{2}- \left(x_{1} + y_{1}\right) \, \mathbf{a}_{3}$ | = | $- a x_{1} \,\mathbf{\hat{x}}- a y_{1} \,\mathbf{\hat{y}}+c z_{1} \,\mathbf{\hat{z}}$ | (8b) | Nb I |
| $\mathbf{B_{3}}$ | = | $\left(x_{1} + z_{1} + \frac{3}{4}\right) \, \mathbf{a}_{1}+\left(- y_{1} + z_{1} + \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(x_{1} - y_{1} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a y_{1} \,\mathbf{\hat{x}}+a \left(x_{1} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{1} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | Nb I |
| $\mathbf{B_{4}}$ | = | $\left(- x_{1} + z_{1} + \frac{3}{4}\right) \, \mathbf{a}_{1}+\left(y_{1} + z_{1} + \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(- x_{1} + y_{1} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a y_{1} \,\mathbf{\hat{x}}- a \left(x_{1} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{1} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | Nb I |
| $\mathbf{B_{5}}$ | = | $\left(y_{2} + z_{2}\right) \, \mathbf{a}_{1}+\left(x_{2} + z_{2}\right) \, \mathbf{a}_{2}+\left(x_{2} + y_{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{2} \,\mathbf{\hat{x}}+a y_{2} \,\mathbf{\hat{y}}+c z_{2} \,\mathbf{\hat{z}}$ | (8b) | Nb II |
| $\mathbf{B_{6}}$ | = | $- \left(y_{2} - z_{2}\right) \, \mathbf{a}_{1}- \left(x_{2} - z_{2}\right) \, \mathbf{a}_{2}- \left(x_{2} + y_{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{2} \,\mathbf{\hat{x}}- a y_{2} \,\mathbf{\hat{y}}+c z_{2} \,\mathbf{\hat{z}}$ | (8b) | Nb II |
| $\mathbf{B_{7}}$ | = | $\left(x_{2} + z_{2} + \frac{3}{4}\right) \, \mathbf{a}_{1}+\left(- y_{2} + z_{2} + \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(x_{2} - y_{2} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a y_{2} \,\mathbf{\hat{x}}+a \left(x_{2} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{2} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | Nb II |
| $\mathbf{B_{8}}$ | = | $\left(- x_{2} + z_{2} + \frac{3}{4}\right) \, \mathbf{a}_{1}+\left(y_{2} + z_{2} + \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(- x_{2} + y_{2} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a y_{2} \,\mathbf{\hat{x}}- a \left(x_{2} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{2} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | Nb II |
| $\mathbf{B_{9}}$ | = | $\left(y_{3} + z_{3}\right) \, \mathbf{a}_{1}+\left(x_{3} + z_{3}\right) \, \mathbf{a}_{2}+\left(x_{3} + y_{3}\right) \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{x}}+a y_{3} \,\mathbf{\hat{y}}+c z_{3} \,\mathbf{\hat{z}}$ | (8b) | O I |
| $\mathbf{B_{10}}$ | = | $- \left(y_{3} - z_{3}\right) \, \mathbf{a}_{1}- \left(x_{3} - z_{3}\right) \, \mathbf{a}_{2}- \left(x_{3} + y_{3}\right) \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}- a y_{3} \,\mathbf{\hat{y}}+c z_{3} \,\mathbf{\hat{z}}$ | (8b) | O I |
| $\mathbf{B_{11}}$ | = | $\left(x_{3} + z_{3} + \frac{3}{4}\right) \, \mathbf{a}_{1}+\left(- y_{3} + z_{3} + \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(x_{3} - y_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a y_{3} \,\mathbf{\hat{x}}+a \left(x_{3} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{3} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | O I |
| $\mathbf{B_{12}}$ | = | $\left(- x_{3} + z_{3} + \frac{3}{4}\right) \, \mathbf{a}_{1}+\left(y_{3} + z_{3} + \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(- x_{3} + y_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a y_{3} \,\mathbf{\hat{x}}- a \left(x_{3} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{3} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | O I |
| $\mathbf{B_{13}}$ | = | $\left(y_{4} + z_{4}\right) \, \mathbf{a}_{1}+\left(x_{4} + z_{4}\right) \, \mathbf{a}_{2}+\left(x_{4} + y_{4}\right) \, \mathbf{a}_{3}$ | = | $a x_{4} \,\mathbf{\hat{x}}+a y_{4} \,\mathbf{\hat{y}}+c z_{4} \,\mathbf{\hat{z}}$ | (8b) | O II |
| $\mathbf{B_{14}}$ | = | $- \left(y_{4} - z_{4}\right) \, \mathbf{a}_{1}- \left(x_{4} - z_{4}\right) \, \mathbf{a}_{2}- \left(x_{4} + y_{4}\right) \, \mathbf{a}_{3}$ | = | $- a x_{4} \,\mathbf{\hat{x}}- a y_{4} \,\mathbf{\hat{y}}+c z_{4} \,\mathbf{\hat{z}}$ | (8b) | O II |
| $\mathbf{B_{15}}$ | = | $\left(x_{4} + z_{4} + \frac{3}{4}\right) \, \mathbf{a}_{1}+\left(- y_{4} + z_{4} + \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(x_{4} - y_{4} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a y_{4} \,\mathbf{\hat{x}}+a \left(x_{4} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{4} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | O II |
| $\mathbf{B_{16}}$ | = | $\left(- x_{4} + z_{4} + \frac{3}{4}\right) \, \mathbf{a}_{1}+\left(y_{4} + z_{4} + \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(- x_{4} + y_{4} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a y_{4} \,\mathbf{\hat{x}}- a \left(x_{4} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{4} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | O II |
| $\mathbf{B_{17}}$ | = | $\left(y_{5} + z_{5}\right) \, \mathbf{a}_{1}+\left(x_{5} + z_{5}\right) \, \mathbf{a}_{2}+\left(x_{5} + y_{5}\right) \, \mathbf{a}_{3}$ | = | $a x_{5} \,\mathbf{\hat{x}}+a y_{5} \,\mathbf{\hat{y}}+c z_{5} \,\mathbf{\hat{z}}$ | (8b) | O III |
| $\mathbf{B_{18}}$ | = | $- \left(y_{5} - z_{5}\right) \, \mathbf{a}_{1}- \left(x_{5} - z_{5}\right) \, \mathbf{a}_{2}- \left(x_{5} + y_{5}\right) \, \mathbf{a}_{3}$ | = | $- a x_{5} \,\mathbf{\hat{x}}- a y_{5} \,\mathbf{\hat{y}}+c z_{5} \,\mathbf{\hat{z}}$ | (8b) | O III |
| $\mathbf{B_{19}}$ | = | $\left(x_{5} + z_{5} + \frac{3}{4}\right) \, \mathbf{a}_{1}+\left(- y_{5} + z_{5} + \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(x_{5} - y_{5} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a y_{5} \,\mathbf{\hat{x}}+a \left(x_{5} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{5} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | O III |
| $\mathbf{B_{20}}$ | = | $\left(- x_{5} + z_{5} + \frac{3}{4}\right) \, \mathbf{a}_{1}+\left(y_{5} + z_{5} + \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(- x_{5} + y_{5} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a y_{5} \,\mathbf{\hat{x}}- a \left(x_{5} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{5} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | O III |
| $\mathbf{B_{21}}$ | = | $\left(y_{6} + z_{6}\right) \, \mathbf{a}_{1}+\left(x_{6} + z_{6}\right) \, \mathbf{a}_{2}+\left(x_{6} + y_{6}\right) \, \mathbf{a}_{3}$ | = | $a x_{6} \,\mathbf{\hat{x}}+a y_{6} \,\mathbf{\hat{y}}+c z_{6} \,\mathbf{\hat{z}}$ | (8b) | O IV |
| $\mathbf{B_{22}}$ | = | $- \left(y_{6} - z_{6}\right) \, \mathbf{a}_{1}- \left(x_{6} - z_{6}\right) \, \mathbf{a}_{2}- \left(x_{6} + y_{6}\right) \, \mathbf{a}_{3}$ | = | $- a x_{6} \,\mathbf{\hat{x}}- a y_{6} \,\mathbf{\hat{y}}+c z_{6} \,\mathbf{\hat{z}}$ | (8b) | O IV |
| $\mathbf{B_{23}}$ | = | $\left(x_{6} + z_{6} + \frac{3}{4}\right) \, \mathbf{a}_{1}+\left(- y_{6} + z_{6} + \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(x_{6} - y_{6} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a y_{6} \,\mathbf{\hat{x}}+a \left(x_{6} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{6} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | O IV |
| $\mathbf{B_{24}}$ | = | $\left(- x_{6} + z_{6} + \frac{3}{4}\right) \, \mathbf{a}_{1}+\left(y_{6} + z_{6} + \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(- x_{6} + y_{6} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a y_{6} \,\mathbf{\hat{x}}- a \left(x_{6} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{6} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | O IV |
References
- H.-J. Schweizer and R. Gruehn, Zur Darstellung und Kristallstruktur von β-NbO$_{2}$, Z. f. Naturf. B 37, 1361–1368 (1982), doi:10.1515/znb-1982-1101.
Found in
- P. Villars and L. D. Calvert, eds., Pearson's Handbook of Crystallographic Data (ASM International, Materials Park OH, 1991), vol. IV, chap. , p. 4535.
Prototype Generator
aflow --proto=AB2_tI48_80_2b_4b --params=$a,c/a,x_{1},y_{1},z_{1},x_{2},y_{2},z_{2},x_{3},y_{3},z_{3},x_{4},y_{4},z_{4},x_{5},y_{5},z_{5},x_{6},y_{6},z_{6}$