Monoclinic Nb$_{12}$O$_{29}$ Structure: A12B29_mC82_12_6i_a14i-001
| Prototype | Nb$_{12}$O$_{29}$ |
| AFLOW prototype label | A12B29_mC82_12_6i_a14i-001 |
| ICSD | 24111 |
| Pearson symbol | mC82 |
| Space group number | 12 |
| Space group symbol | $C2/m$ |
| AFLOW prototype command |
aflow --proto=A12B29_mC82_12_6i_a14i-001
--params=$a, \allowbreak b/a, \allowbreak c/a, \allowbreak \beta, \allowbreak x_{2}, \allowbreak z_{2}, \allowbreak x_{3}, \allowbreak z_{3}, \allowbreak x_{4}, \allowbreak z_{4}, \allowbreak x_{5}, \allowbreak z_{5}, \allowbreak x_{6}, \allowbreak z_{6}, \allowbreak x_{7}, \allowbreak z_{7}, \allowbreak x_{8}, \allowbreak z_{8}, \allowbreak x_{9}, \allowbreak z_{9}, \allowbreak x_{10}, \allowbreak z_{10}, \allowbreak x_{11}, \allowbreak z_{11}, \allowbreak x_{12}, \allowbreak z_{12}, \allowbreak x_{13}, \allowbreak z_{13}, \allowbreak x_{14}, \allowbreak z_{14}, \allowbreak x_{15}, \allowbreak z_{15}, \allowbreak x_{16}, \allowbreak z_{16}, \allowbreak x_{17}, \allowbreak z_{17}, \allowbreak x_{18}, \allowbreak z_{18}, \allowbreak x_{19}, \allowbreak z_{19}, \allowbreak x_{20}, \allowbreak z_{20}, \allowbreak x_{21}, \allowbreak z_{21}$ |
Other compounds with this structure
Ti$_{2}$Nb$_{10}$O$_{29}$
- Nb$_{12}$O$_{29}$ is known to exist in a least two phases (Norin, 1963; Norin, 1966):
- a monoclinic phase (this structure) and
- an orthorhombic phase.
- (Wadsley, 1961) earlier found that both known phases of Ti$_{2}$Nb$_{12}$O$_{29}$ are isostructural with the corresponding Nb$_{12}$O$_{29}$ phase, but as the titanium and niobium atoms are alloyed on the same site we use the binary Nb$_{12}$O$_{29}$ as the prototype.
- (Norin, 1966) gives the structure of orthorhombic Nb$_{12}$O$_{29}$ in the $A2/a$ setting of space group #15, with the origin at -1 on the $a$-glide plane. We when we checked this with FINDSYM we found that the structure could be placed in space group $C2/m$ #12 with a unit cell half that found by (Norin, 1966), and close to the dimensions of the cell found in (Wadsley, 1961) and (Norin, 1963).
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{1}{2}b \,\mathbf{\hat{y}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}b \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \cos{\beta} \,\mathbf{\hat{x}}+c \sin{\beta} \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $0$ | = | $0$ | (2a) | O I |
| $\mathbf{B_{2}}$ | = | $x_{2} \, \mathbf{a}_{1}+x_{2} \, \mathbf{a}_{2}+z_{2} \, \mathbf{a}_{3}$ | = | $\left(a x_{2} + c z_{2} \cos{\beta}\right) \,\mathbf{\hat{x}}+c z_{2} \sin{\beta} \,\mathbf{\hat{z}}$ | (4i) | Nb I |
| $\mathbf{B_{3}}$ | = | $- x_{2} \, \mathbf{a}_{1}- x_{2} \, \mathbf{a}_{2}- z_{2} \, \mathbf{a}_{3}$ | = | $- \left(a x_{2} + c z_{2} \cos{\beta}\right) \,\mathbf{\hat{x}}- c z_{2} \sin{\beta} \,\mathbf{\hat{z}}$ | (4i) | Nb I |
| $\mathbf{B_{4}}$ | = | $x_{3} \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{2}+z_{3} \, \mathbf{a}_{3}$ | = | $\left(a x_{3} + c z_{3} \cos{\beta}\right) \,\mathbf{\hat{x}}+c z_{3} \sin{\beta} \,\mathbf{\hat{z}}$ | (4i) | Nb II |
| $\mathbf{B_{5}}$ | = | $- x_{3} \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}- z_{3} \, \mathbf{a}_{3}$ | = | $- \left(a x_{3} + c z_{3} \cos{\beta}\right) \,\mathbf{\hat{x}}- c z_{3} \sin{\beta} \,\mathbf{\hat{z}}$ | (4i) | Nb II |
| $\mathbf{B_{6}}$ | = | $x_{4} \, \mathbf{a}_{1}+x_{4} \, \mathbf{a}_{2}+z_{4} \, \mathbf{a}_{3}$ | = | $\left(a x_{4} + c z_{4} \cos{\beta}\right) \,\mathbf{\hat{x}}+c z_{4} \sin{\beta} \,\mathbf{\hat{z}}$ | (4i) | Nb III |
| $\mathbf{B_{7}}$ | = | $- x_{4} \, \mathbf{a}_{1}- x_{4} \, \mathbf{a}_{2}- z_{4} \, \mathbf{a}_{3}$ | = | $- \left(a x_{4} + c z_{4} \cos{\beta}\right) \,\mathbf{\hat{x}}- c z_{4} \sin{\beta} \,\mathbf{\hat{z}}$ | (4i) | Nb III |
| $\mathbf{B_{8}}$ | = | $x_{5} \, \mathbf{a}_{1}+x_{5} \, \mathbf{a}_{2}+z_{5} \, \mathbf{a}_{3}$ | = | $\left(a x_{5} + c z_{5} \cos{\beta}\right) \,\mathbf{\hat{x}}+c z_{5} \sin{\beta} \,\mathbf{\hat{z}}$ | (4i) | Nb IV |
| $\mathbf{B_{9}}$ | = | $- x_{5} \, \mathbf{a}_{1}- x_{5} \, \mathbf{a}_{2}- z_{5} \, \mathbf{a}_{3}$ | = | $- \left(a x_{5} + c z_{5} \cos{\beta}\right) \,\mathbf{\hat{x}}- c z_{5} \sin{\beta} \,\mathbf{\hat{z}}$ | (4i) | Nb IV |
| $\mathbf{B_{10}}$ | = | $x_{6} \, \mathbf{a}_{1}+x_{6} \, \mathbf{a}_{2}+z_{6} \, \mathbf{a}_{3}$ | = | $\left(a x_{6} + c z_{6} \cos{\beta}\right) \,\mathbf{\hat{x}}+c z_{6} \sin{\beta} \,\mathbf{\hat{z}}$ | (4i) | Nb V |
| $\mathbf{B_{11}}$ | = | $- x_{6} \, \mathbf{a}_{1}- x_{6} \, \mathbf{a}_{2}- z_{6} \, \mathbf{a}_{3}$ | = | $- \left(a x_{6} + c z_{6} \cos{\beta}\right) \,\mathbf{\hat{x}}- c z_{6} \sin{\beta} \,\mathbf{\hat{z}}$ | (4i) | Nb V |
| $\mathbf{B_{12}}$ | = | $x_{7} \, \mathbf{a}_{1}+x_{7} \, \mathbf{a}_{2}+z_{7} \, \mathbf{a}_{3}$ | = | $\left(a x_{7} + c z_{7} \cos{\beta}\right) \,\mathbf{\hat{x}}+c z_{7} \sin{\beta} \,\mathbf{\hat{z}}$ | (4i) | Nb VI |
| $\mathbf{B_{13}}$ | = | $- x_{7} \, \mathbf{a}_{1}- x_{7} \, \mathbf{a}_{2}- z_{7} \, \mathbf{a}_{3}$ | = | $- \left(a x_{7} + c z_{7} \cos{\beta}\right) \,\mathbf{\hat{x}}- c z_{7} \sin{\beta} \,\mathbf{\hat{z}}$ | (4i) | Nb VI |
| $\mathbf{B_{14}}$ | = | $x_{8} \, \mathbf{a}_{1}+x_{8} \, \mathbf{a}_{2}+z_{8} \, \mathbf{a}_{3}$ | = | $\left(a x_{8} + c z_{8} \cos{\beta}\right) \,\mathbf{\hat{x}}+c z_{8} \sin{\beta} \,\mathbf{\hat{z}}$ | (4i) | O II |
| $\mathbf{B_{15}}$ | = | $- x_{8} \, \mathbf{a}_{1}- x_{8} \, \mathbf{a}_{2}- z_{8} \, \mathbf{a}_{3}$ | = | $- \left(a x_{8} + c z_{8} \cos{\beta}\right) \,\mathbf{\hat{x}}- c z_{8} \sin{\beta} \,\mathbf{\hat{z}}$ | (4i) | O II |
| $\mathbf{B_{16}}$ | = | $x_{9} \, \mathbf{a}_{1}+x_{9} \, \mathbf{a}_{2}+z_{9} \, \mathbf{a}_{3}$ | = | $\left(a x_{9} + c z_{9} \cos{\beta}\right) \,\mathbf{\hat{x}}+c z_{9} \sin{\beta} \,\mathbf{\hat{z}}$ | (4i) | O III |
| $\mathbf{B_{17}}$ | = | $- x_{9} \, \mathbf{a}_{1}- x_{9} \, \mathbf{a}_{2}- z_{9} \, \mathbf{a}_{3}$ | = | $- \left(a x_{9} + c z_{9} \cos{\beta}\right) \,\mathbf{\hat{x}}- c z_{9} \sin{\beta} \,\mathbf{\hat{z}}$ | (4i) | O III |
| $\mathbf{B_{18}}$ | = | $x_{10} \, \mathbf{a}_{1}+x_{10} \, \mathbf{a}_{2}+z_{10} \, \mathbf{a}_{3}$ | = | $\left(a x_{10} + c z_{10} \cos{\beta}\right) \,\mathbf{\hat{x}}+c z_{10} \sin{\beta} \,\mathbf{\hat{z}}$ | (4i) | O IV |
| $\mathbf{B_{19}}$ | = | $- x_{10} \, \mathbf{a}_{1}- x_{10} \, \mathbf{a}_{2}- z_{10} \, \mathbf{a}_{3}$ | = | $- \left(a x_{10} + c z_{10} \cos{\beta}\right) \,\mathbf{\hat{x}}- c z_{10} \sin{\beta} \,\mathbf{\hat{z}}$ | (4i) | O IV |
| $\mathbf{B_{20}}$ | = | $x_{11} \, \mathbf{a}_{1}+x_{11} \, \mathbf{a}_{2}+z_{11} \, \mathbf{a}_{3}$ | = | $\left(a x_{11} + c z_{11} \cos{\beta}\right) \,\mathbf{\hat{x}}+c z_{11} \sin{\beta} \,\mathbf{\hat{z}}$ | (4i) | O V |
| $\mathbf{B_{21}}$ | = | $- x_{11} \, \mathbf{a}_{1}- x_{11} \, \mathbf{a}_{2}- z_{11} \, \mathbf{a}_{3}$ | = | $- \left(a x_{11} + c z_{11} \cos{\beta}\right) \,\mathbf{\hat{x}}- c z_{11} \sin{\beta} \,\mathbf{\hat{z}}$ | (4i) | O V |
| $\mathbf{B_{22}}$ | = | $x_{12} \, \mathbf{a}_{1}+x_{12} \, \mathbf{a}_{2}+z_{12} \, \mathbf{a}_{3}$ | = | $\left(a x_{12} + c z_{12} \cos{\beta}\right) \,\mathbf{\hat{x}}+c z_{12} \sin{\beta} \,\mathbf{\hat{z}}$ | (4i) | O VI |
| $\mathbf{B_{23}}$ | = | $- x_{12} \, \mathbf{a}_{1}- x_{12} \, \mathbf{a}_{2}- z_{12} \, \mathbf{a}_{3}$ | = | $- \left(a x_{12} + c z_{12} \cos{\beta}\right) \,\mathbf{\hat{x}}- c z_{12} \sin{\beta} \,\mathbf{\hat{z}}$ | (4i) | O VI |
| $\mathbf{B_{24}}$ | = | $x_{13} \, \mathbf{a}_{1}+x_{13} \, \mathbf{a}_{2}+z_{13} \, \mathbf{a}_{3}$ | = | $\left(a x_{13} + c z_{13} \cos{\beta}\right) \,\mathbf{\hat{x}}+c z_{13} \sin{\beta} \,\mathbf{\hat{z}}$ | (4i) | O VII |
| $\mathbf{B_{25}}$ | = | $- x_{13} \, \mathbf{a}_{1}- x_{13} \, \mathbf{a}_{2}- z_{13} \, \mathbf{a}_{3}$ | = | $- \left(a x_{13} + c z_{13} \cos{\beta}\right) \,\mathbf{\hat{x}}- c z_{13} \sin{\beta} \,\mathbf{\hat{z}}$ | (4i) | O VII |
| $\mathbf{B_{26}}$ | = | $x_{14} \, \mathbf{a}_{1}+x_{14} \, \mathbf{a}_{2}+z_{14} \, \mathbf{a}_{3}$ | = | $\left(a x_{14} + c z_{14} \cos{\beta}\right) \,\mathbf{\hat{x}}+c z_{14} \sin{\beta} \,\mathbf{\hat{z}}$ | (4i) | O VIII |
| $\mathbf{B_{27}}$ | = | $- x_{14} \, \mathbf{a}_{1}- x_{14} \, \mathbf{a}_{2}- z_{14} \, \mathbf{a}_{3}$ | = | $- \left(a x_{14} + c z_{14} \cos{\beta}\right) \,\mathbf{\hat{x}}- c z_{14} \sin{\beta} \,\mathbf{\hat{z}}$ | (4i) | O VIII |
| $\mathbf{B_{28}}$ | = | $x_{15} \, \mathbf{a}_{1}+x_{15} \, \mathbf{a}_{2}+z_{15} \, \mathbf{a}_{3}$ | = | $\left(a x_{15} + c z_{15} \cos{\beta}\right) \,\mathbf{\hat{x}}+c z_{15} \sin{\beta} \,\mathbf{\hat{z}}$ | (4i) | O IX |
| $\mathbf{B_{29}}$ | = | $- x_{15} \, \mathbf{a}_{1}- x_{15} \, \mathbf{a}_{2}- z_{15} \, \mathbf{a}_{3}$ | = | $- \left(a x_{15} + c z_{15} \cos{\beta}\right) \,\mathbf{\hat{x}}- c z_{15} \sin{\beta} \,\mathbf{\hat{z}}$ | (4i) | O IX |
| $\mathbf{B_{30}}$ | = | $x_{16} \, \mathbf{a}_{1}+x_{16} \, \mathbf{a}_{2}+z_{16} \, \mathbf{a}_{3}$ | = | $\left(a x_{16} + c z_{16} \cos{\beta}\right) \,\mathbf{\hat{x}}+c z_{16} \sin{\beta} \,\mathbf{\hat{z}}$ | (4i) | O X |
| $\mathbf{B_{31}}$ | = | $- x_{16} \, \mathbf{a}_{1}- x_{16} \, \mathbf{a}_{2}- z_{16} \, \mathbf{a}_{3}$ | = | $- \left(a x_{16} + c z_{16} \cos{\beta}\right) \,\mathbf{\hat{x}}- c z_{16} \sin{\beta} \,\mathbf{\hat{z}}$ | (4i) | O X |
| $\mathbf{B_{32}}$ | = | $x_{17} \, \mathbf{a}_{1}+x_{17} \, \mathbf{a}_{2}+z_{17} \, \mathbf{a}_{3}$ | = | $\left(a x_{17} + c z_{17} \cos{\beta}\right) \,\mathbf{\hat{x}}+c z_{17} \sin{\beta} \,\mathbf{\hat{z}}$ | (4i) | O XI |
| $\mathbf{B_{33}}$ | = | $- x_{17} \, \mathbf{a}_{1}- x_{17} \, \mathbf{a}_{2}- z_{17} \, \mathbf{a}_{3}$ | = | $- \left(a x_{17} + c z_{17} \cos{\beta}\right) \,\mathbf{\hat{x}}- c z_{17} \sin{\beta} \,\mathbf{\hat{z}}$ | (4i) | O XI |
| $\mathbf{B_{34}}$ | = | $x_{18} \, \mathbf{a}_{1}+x_{18} \, \mathbf{a}_{2}+z_{18} \, \mathbf{a}_{3}$ | = | $\left(a x_{18} + c z_{18} \cos{\beta}\right) \,\mathbf{\hat{x}}+c z_{18} \sin{\beta} \,\mathbf{\hat{z}}$ | (4i) | O XII |
| $\mathbf{B_{35}}$ | = | $- x_{18} \, \mathbf{a}_{1}- x_{18} \, \mathbf{a}_{2}- z_{18} \, \mathbf{a}_{3}$ | = | $- \left(a x_{18} + c z_{18} \cos{\beta}\right) \,\mathbf{\hat{x}}- c z_{18} \sin{\beta} \,\mathbf{\hat{z}}$ | (4i) | O XII |
| $\mathbf{B_{36}}$ | = | $x_{19} \, \mathbf{a}_{1}+x_{19} \, \mathbf{a}_{2}+z_{19} \, \mathbf{a}_{3}$ | = | $\left(a x_{19} + c z_{19} \cos{\beta}\right) \,\mathbf{\hat{x}}+c z_{19} \sin{\beta} \,\mathbf{\hat{z}}$ | (4i) | O XIII |
| $\mathbf{B_{37}}$ | = | $- x_{19} \, \mathbf{a}_{1}- x_{19} \, \mathbf{a}_{2}- z_{19} \, \mathbf{a}_{3}$ | = | $- \left(a x_{19} + c z_{19} \cos{\beta}\right) \,\mathbf{\hat{x}}- c z_{19} \sin{\beta} \,\mathbf{\hat{z}}$ | (4i) | O XIII |
| $\mathbf{B_{38}}$ | = | $x_{20} \, \mathbf{a}_{1}+x_{20} \, \mathbf{a}_{2}+z_{20} \, \mathbf{a}_{3}$ | = | $\left(a x_{20} + c z_{20} \cos{\beta}\right) \,\mathbf{\hat{x}}+c z_{20} \sin{\beta} \,\mathbf{\hat{z}}$ | (4i) | O XIV |
| $\mathbf{B_{39}}$ | = | $- x_{20} \, \mathbf{a}_{1}- x_{20} \, \mathbf{a}_{2}- z_{20} \, \mathbf{a}_{3}$ | = | $- \left(a x_{20} + c z_{20} \cos{\beta}\right) \,\mathbf{\hat{x}}- c z_{20} \sin{\beta} \,\mathbf{\hat{z}}$ | (4i) | O XIV |
| $\mathbf{B_{40}}$ | = | $x_{21} \, \mathbf{a}_{1}+x_{21} \, \mathbf{a}_{2}+z_{21} \, \mathbf{a}_{3}$ | = | $\left(a x_{21} + c z_{21} \cos{\beta}\right) \,\mathbf{\hat{x}}+c z_{21} \sin{\beta} \,\mathbf{\hat{z}}$ | (4i) | O XV |
| $\mathbf{B_{41}}$ | = | $- x_{21} \, \mathbf{a}_{1}- x_{21} \, \mathbf{a}_{2}- z_{21} \, \mathbf{a}_{3}$ | = | $- \left(a x_{21} + c z_{21} \cos{\beta}\right) \,\mathbf{\hat{x}}- c z_{21} \sin{\beta} \,\mathbf{\hat{z}}$ | (4i) | O XV |
References
- R. Norin, The Crystal Structure of Nb$_{12}$O$_{29}$ (o-rh), Acta Chem. Scand. 17, 1391–1404 (1963), doi:10.3891/acta.chem.scand.17-1391.
- R. Norin, The Crystal Structure of Nb$_{12}$O$_{29}$ (mon), Acta Chem. Scand. 20, 871–880 (1966), doi:10.3891/acta.chem.scand.20-0871.
- A. D. Wadsley, Mixed oxides of titanium and niobium. II. The crystal structures of the dimorphic forms Ti$_{2}$Nb$_{10}$O$_{29}$, Acta Cryst. 14, 664–670 (1961), doi:10.1107/S0365110X6100200X.
Prototype Generator
aflow --proto=A12B29_mC82_12_6i_a14i --params=$a,b/a,c/a,\beta,x_{2},z_{2},x_{3},z_{3},x_{4},z_{4},x_{5},z_{5},x_{6},z_{6},x_{7},z_{7},x_{8},z_{8},x_{9},z_{9},x_{10},z_{10},x_{11},z_{11},x_{12},z_{12},x_{13},z_{13},x_{14},z_{14},x_{15},z_{15},x_{16},z_{16},x_{17},z_{17},x_{18},z_{18},x_{19},z_{19},x_{20},z_{20},x_{21},z_{21}$