Orthorhombic Nb$_{12}$O$_{29}$ Structure: A12B29_oC164_63_6f_3c13f-001
| Prototype | Nb$_{12}$O$_{29}$ |
| AFLOW prototype label | A12B29_oC164_63_6f_3c13f-001 |
| ICSD | 24089 |
| Pearson symbol | oC164 |
| Space group number | 63 |
| Space group symbol | $Cmcm$ |
| AFLOW prototype command |
aflow --proto=A12B29_oC164_63_6f_3c13f-001
--params=$a, \allowbreak b/a, \allowbreak c/a, \allowbreak y_{1}, \allowbreak y_{2}, \allowbreak y_{3}, \allowbreak y_{4}, \allowbreak z_{4}, \allowbreak y_{5}, \allowbreak z_{5}, \allowbreak y_{6}, \allowbreak z_{6}, \allowbreak y_{7}, \allowbreak z_{7}, \allowbreak y_{8}, \allowbreak z_{8}, \allowbreak y_{9}, \allowbreak z_{9}, \allowbreak y_{10}, \allowbreak z_{10}, \allowbreak y_{11}, \allowbreak z_{11}, \allowbreak y_{12}, \allowbreak z_{12}, \allowbreak y_{13}, \allowbreak z_{13}, \allowbreak y_{14}, \allowbreak z_{14}, \allowbreak y_{15}, \allowbreak z_{15}, \allowbreak y_{16}, \allowbreak z_{16}, \allowbreak y_{17}, \allowbreak z_{17}, \allowbreak y_{18}, \allowbreak z_{18}, \allowbreak y_{19}, \allowbreak z_{19}, \allowbreak y_{20}, \allowbreak z_{20}, \allowbreak y_{21}, \allowbreak z_{21}, \allowbreak y_{22}, \allowbreak z_{22}$ |
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 and
- an orthorhombic phase (this structure).
- (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, 1963) gives the structure of orthorhombic Nb$_{12}$O$_{29}$ in the $Amma$ setting of space group #63. We used FINDSYM to transform it to the standard $Cmcm$ setting.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{1}{2}b \,\mathbf{\hat{y}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}b \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $- y_{1} \, \mathbf{a}_{1}+y_{1} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $b y_{1} \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (4c) | O I |
| $\mathbf{B_{2}}$ | = | $y_{1} \, \mathbf{a}_{1}- y_{1} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $- b y_{1} \,\mathbf{\hat{y}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ | (4c) | O I |
| $\mathbf{B_{3}}$ | = | $- y_{2} \, \mathbf{a}_{1}+y_{2} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $b y_{2} \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (4c) | O II |
| $\mathbf{B_{4}}$ | = | $y_{2} \, \mathbf{a}_{1}- y_{2} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $- b y_{2} \,\mathbf{\hat{y}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ | (4c) | O II |
| $\mathbf{B_{5}}$ | = | $- y_{3} \, \mathbf{a}_{1}+y_{3} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $b y_{3} \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (4c) | O III |
| $\mathbf{B_{6}}$ | = | $y_{3} \, \mathbf{a}_{1}- y_{3} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $- b y_{3} \,\mathbf{\hat{y}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ | (4c) | O III |
| $\mathbf{B_{7}}$ | = | $- y_{4} \, \mathbf{a}_{1}+y_{4} \, \mathbf{a}_{2}+z_{4} \, \mathbf{a}_{3}$ | = | $b y_{4} \,\mathbf{\hat{y}}+c z_{4} \,\mathbf{\hat{z}}$ | (8f) | Nb I |
| $\mathbf{B_{8}}$ | = | $y_{4} \, \mathbf{a}_{1}- y_{4} \, \mathbf{a}_{2}+\left(z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- b y_{4} \,\mathbf{\hat{y}}+c \left(z_{4} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8f) | Nb I |
| $\mathbf{B_{9}}$ | = | $- y_{4} \, \mathbf{a}_{1}+y_{4} \, \mathbf{a}_{2}- \left(z_{4} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $b y_{4} \,\mathbf{\hat{y}}- c \left(z_{4} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8f) | Nb I |
| $\mathbf{B_{10}}$ | = | $y_{4} \, \mathbf{a}_{1}- y_{4} \, \mathbf{a}_{2}- z_{4} \, \mathbf{a}_{3}$ | = | $- b y_{4} \,\mathbf{\hat{y}}- c z_{4} \,\mathbf{\hat{z}}$ | (8f) | Nb I |
| $\mathbf{B_{11}}$ | = | $- y_{5} \, \mathbf{a}_{1}+y_{5} \, \mathbf{a}_{2}+z_{5} \, \mathbf{a}_{3}$ | = | $b y_{5} \,\mathbf{\hat{y}}+c z_{5} \,\mathbf{\hat{z}}$ | (8f) | Nb II |
| $\mathbf{B_{12}}$ | = | $y_{5} \, \mathbf{a}_{1}- y_{5} \, \mathbf{a}_{2}+\left(z_{5} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- b y_{5} \,\mathbf{\hat{y}}+c \left(z_{5} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8f) | Nb II |
| $\mathbf{B_{13}}$ | = | $- y_{5} \, \mathbf{a}_{1}+y_{5} \, \mathbf{a}_{2}- \left(z_{5} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $b y_{5} \,\mathbf{\hat{y}}- c \left(z_{5} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8f) | Nb II |
| $\mathbf{B_{14}}$ | = | $y_{5} \, \mathbf{a}_{1}- y_{5} \, \mathbf{a}_{2}- z_{5} \, \mathbf{a}_{3}$ | = | $- b y_{5} \,\mathbf{\hat{y}}- c z_{5} \,\mathbf{\hat{z}}$ | (8f) | Nb II |
| $\mathbf{B_{15}}$ | = | $- y_{6} \, \mathbf{a}_{1}+y_{6} \, \mathbf{a}_{2}+z_{6} \, \mathbf{a}_{3}$ | = | $b y_{6} \,\mathbf{\hat{y}}+c z_{6} \,\mathbf{\hat{z}}$ | (8f) | Nb III |
| $\mathbf{B_{16}}$ | = | $y_{6} \, \mathbf{a}_{1}- y_{6} \, \mathbf{a}_{2}+\left(z_{6} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- b y_{6} \,\mathbf{\hat{y}}+c \left(z_{6} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8f) | Nb III |
| $\mathbf{B_{17}}$ | = | $- y_{6} \, \mathbf{a}_{1}+y_{6} \, \mathbf{a}_{2}- \left(z_{6} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $b y_{6} \,\mathbf{\hat{y}}- c \left(z_{6} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8f) | Nb III |
| $\mathbf{B_{18}}$ | = | $y_{6} \, \mathbf{a}_{1}- y_{6} \, \mathbf{a}_{2}- z_{6} \, \mathbf{a}_{3}$ | = | $- b y_{6} \,\mathbf{\hat{y}}- c z_{6} \,\mathbf{\hat{z}}$ | (8f) | Nb III |
| $\mathbf{B_{19}}$ | = | $- y_{7} \, \mathbf{a}_{1}+y_{7} \, \mathbf{a}_{2}+z_{7} \, \mathbf{a}_{3}$ | = | $b y_{7} \,\mathbf{\hat{y}}+c z_{7} \,\mathbf{\hat{z}}$ | (8f) | Nb IV |
| $\mathbf{B_{20}}$ | = | $y_{7} \, \mathbf{a}_{1}- y_{7} \, \mathbf{a}_{2}+\left(z_{7} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- b y_{7} \,\mathbf{\hat{y}}+c \left(z_{7} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8f) | Nb IV |
| $\mathbf{B_{21}}$ | = | $- y_{7} \, \mathbf{a}_{1}+y_{7} \, \mathbf{a}_{2}- \left(z_{7} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $b y_{7} \,\mathbf{\hat{y}}- c \left(z_{7} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8f) | Nb IV |
| $\mathbf{B_{22}}$ | = | $y_{7} \, \mathbf{a}_{1}- y_{7} \, \mathbf{a}_{2}- z_{7} \, \mathbf{a}_{3}$ | = | $- b y_{7} \,\mathbf{\hat{y}}- c z_{7} \,\mathbf{\hat{z}}$ | (8f) | Nb IV |
| $\mathbf{B_{23}}$ | = | $- y_{8} \, \mathbf{a}_{1}+y_{8} \, \mathbf{a}_{2}+z_{8} \, \mathbf{a}_{3}$ | = | $b y_{8} \,\mathbf{\hat{y}}+c z_{8} \,\mathbf{\hat{z}}$ | (8f) | Nb V |
| $\mathbf{B_{24}}$ | = | $y_{8} \, \mathbf{a}_{1}- y_{8} \, \mathbf{a}_{2}+\left(z_{8} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- b y_{8} \,\mathbf{\hat{y}}+c \left(z_{8} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8f) | Nb V |
| $\mathbf{B_{25}}$ | = | $- y_{8} \, \mathbf{a}_{1}+y_{8} \, \mathbf{a}_{2}- \left(z_{8} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $b y_{8} \,\mathbf{\hat{y}}- c \left(z_{8} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8f) | Nb V |
| $\mathbf{B_{26}}$ | = | $y_{8} \, \mathbf{a}_{1}- y_{8} \, \mathbf{a}_{2}- z_{8} \, \mathbf{a}_{3}$ | = | $- b y_{8} \,\mathbf{\hat{y}}- c z_{8} \,\mathbf{\hat{z}}$ | (8f) | Nb V |
| $\mathbf{B_{27}}$ | = | $- y_{9} \, \mathbf{a}_{1}+y_{9} \, \mathbf{a}_{2}+z_{9} \, \mathbf{a}_{3}$ | = | $b y_{9} \,\mathbf{\hat{y}}+c z_{9} \,\mathbf{\hat{z}}$ | (8f) | Nb VI |
| $\mathbf{B_{28}}$ | = | $y_{9} \, \mathbf{a}_{1}- y_{9} \, \mathbf{a}_{2}+\left(z_{9} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- b y_{9} \,\mathbf{\hat{y}}+c \left(z_{9} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8f) | Nb VI |
| $\mathbf{B_{29}}$ | = | $- y_{9} \, \mathbf{a}_{1}+y_{9} \, \mathbf{a}_{2}- \left(z_{9} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $b y_{9} \,\mathbf{\hat{y}}- c \left(z_{9} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8f) | Nb VI |
| $\mathbf{B_{30}}$ | = | $y_{9} \, \mathbf{a}_{1}- y_{9} \, \mathbf{a}_{2}- z_{9} \, \mathbf{a}_{3}$ | = | $- b y_{9} \,\mathbf{\hat{y}}- c z_{9} \,\mathbf{\hat{z}}$ | (8f) | Nb VI |
| $\mathbf{B_{31}}$ | = | $- y_{10} \, \mathbf{a}_{1}+y_{10} \, \mathbf{a}_{2}+z_{10} \, \mathbf{a}_{3}$ | = | $b y_{10} \,\mathbf{\hat{y}}+c z_{10} \,\mathbf{\hat{z}}$ | (8f) | O IV |
| $\mathbf{B_{32}}$ | = | $y_{10} \, \mathbf{a}_{1}- y_{10} \, \mathbf{a}_{2}+\left(z_{10} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- b y_{10} \,\mathbf{\hat{y}}+c \left(z_{10} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8f) | O IV |
| $\mathbf{B_{33}}$ | = | $- y_{10} \, \mathbf{a}_{1}+y_{10} \, \mathbf{a}_{2}- \left(z_{10} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $b y_{10} \,\mathbf{\hat{y}}- c \left(z_{10} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8f) | O IV |
| $\mathbf{B_{34}}$ | = | $y_{10} \, \mathbf{a}_{1}- y_{10} \, \mathbf{a}_{2}- z_{10} \, \mathbf{a}_{3}$ | = | $- b y_{10} \,\mathbf{\hat{y}}- c z_{10} \,\mathbf{\hat{z}}$ | (8f) | O IV |
| $\mathbf{B_{35}}$ | = | $- y_{11} \, \mathbf{a}_{1}+y_{11} \, \mathbf{a}_{2}+z_{11} \, \mathbf{a}_{3}$ | = | $b y_{11} \,\mathbf{\hat{y}}+c z_{11} \,\mathbf{\hat{z}}$ | (8f) | O V |
| $\mathbf{B_{36}}$ | = | $y_{11} \, \mathbf{a}_{1}- y_{11} \, \mathbf{a}_{2}+\left(z_{11} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- b y_{11} \,\mathbf{\hat{y}}+c \left(z_{11} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8f) | O V |
| $\mathbf{B_{37}}$ | = | $- y_{11} \, \mathbf{a}_{1}+y_{11} \, \mathbf{a}_{2}- \left(z_{11} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $b y_{11} \,\mathbf{\hat{y}}- c \left(z_{11} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8f) | O V |
| $\mathbf{B_{38}}$ | = | $y_{11} \, \mathbf{a}_{1}- y_{11} \, \mathbf{a}_{2}- z_{11} \, \mathbf{a}_{3}$ | = | $- b y_{11} \,\mathbf{\hat{y}}- c z_{11} \,\mathbf{\hat{z}}$ | (8f) | O V |
| $\mathbf{B_{39}}$ | = | $- y_{12} \, \mathbf{a}_{1}+y_{12} \, \mathbf{a}_{2}+z_{12} \, \mathbf{a}_{3}$ | = | $b y_{12} \,\mathbf{\hat{y}}+c z_{12} \,\mathbf{\hat{z}}$ | (8f) | O VI |
| $\mathbf{B_{40}}$ | = | $y_{12} \, \mathbf{a}_{1}- y_{12} \, \mathbf{a}_{2}+\left(z_{12} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- b y_{12} \,\mathbf{\hat{y}}+c \left(z_{12} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8f) | O VI |
| $\mathbf{B_{41}}$ | = | $- y_{12} \, \mathbf{a}_{1}+y_{12} \, \mathbf{a}_{2}- \left(z_{12} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $b y_{12} \,\mathbf{\hat{y}}- c \left(z_{12} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8f) | O VI |
| $\mathbf{B_{42}}$ | = | $y_{12} \, \mathbf{a}_{1}- y_{12} \, \mathbf{a}_{2}- z_{12} \, \mathbf{a}_{3}$ | = | $- b y_{12} \,\mathbf{\hat{y}}- c z_{12} \,\mathbf{\hat{z}}$ | (8f) | O VI |
| $\mathbf{B_{43}}$ | = | $- y_{13} \, \mathbf{a}_{1}+y_{13} \, \mathbf{a}_{2}+z_{13} \, \mathbf{a}_{3}$ | = | $b y_{13} \,\mathbf{\hat{y}}+c z_{13} \,\mathbf{\hat{z}}$ | (8f) | O VII |
| $\mathbf{B_{44}}$ | = | $y_{13} \, \mathbf{a}_{1}- y_{13} \, \mathbf{a}_{2}+\left(z_{13} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- b y_{13} \,\mathbf{\hat{y}}+c \left(z_{13} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8f) | O VII |
| $\mathbf{B_{45}}$ | = | $- y_{13} \, \mathbf{a}_{1}+y_{13} \, \mathbf{a}_{2}- \left(z_{13} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $b y_{13} \,\mathbf{\hat{y}}- c \left(z_{13} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8f) | O VII |
| $\mathbf{B_{46}}$ | = | $y_{13} \, \mathbf{a}_{1}- y_{13} \, \mathbf{a}_{2}- z_{13} \, \mathbf{a}_{3}$ | = | $- b y_{13} \,\mathbf{\hat{y}}- c z_{13} \,\mathbf{\hat{z}}$ | (8f) | O VII |
| $\mathbf{B_{47}}$ | = | $- y_{14} \, \mathbf{a}_{1}+y_{14} \, \mathbf{a}_{2}+z_{14} \, \mathbf{a}_{3}$ | = | $b y_{14} \,\mathbf{\hat{y}}+c z_{14} \,\mathbf{\hat{z}}$ | (8f) | O VIII |
| $\mathbf{B_{48}}$ | = | $y_{14} \, \mathbf{a}_{1}- y_{14} \, \mathbf{a}_{2}+\left(z_{14} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- b y_{14} \,\mathbf{\hat{y}}+c \left(z_{14} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8f) | O VIII |
| $\mathbf{B_{49}}$ | = | $- y_{14} \, \mathbf{a}_{1}+y_{14} \, \mathbf{a}_{2}- \left(z_{14} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $b y_{14} \,\mathbf{\hat{y}}- c \left(z_{14} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8f) | O VIII |
| $\mathbf{B_{50}}$ | = | $y_{14} \, \mathbf{a}_{1}- y_{14} \, \mathbf{a}_{2}- z_{14} \, \mathbf{a}_{3}$ | = | $- b y_{14} \,\mathbf{\hat{y}}- c z_{14} \,\mathbf{\hat{z}}$ | (8f) | O VIII |
| $\mathbf{B_{51}}$ | = | $- y_{15} \, \mathbf{a}_{1}+y_{15} \, \mathbf{a}_{2}+z_{15} \, \mathbf{a}_{3}$ | = | $b y_{15} \,\mathbf{\hat{y}}+c z_{15} \,\mathbf{\hat{z}}$ | (8f) | O IX |
| $\mathbf{B_{52}}$ | = | $y_{15} \, \mathbf{a}_{1}- y_{15} \, \mathbf{a}_{2}+\left(z_{15} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- b y_{15} \,\mathbf{\hat{y}}+c \left(z_{15} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8f) | O IX |
| $\mathbf{B_{53}}$ | = | $- y_{15} \, \mathbf{a}_{1}+y_{15} \, \mathbf{a}_{2}- \left(z_{15} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $b y_{15} \,\mathbf{\hat{y}}- c \left(z_{15} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8f) | O IX |
| $\mathbf{B_{54}}$ | = | $y_{15} \, \mathbf{a}_{1}- y_{15} \, \mathbf{a}_{2}- z_{15} \, \mathbf{a}_{3}$ | = | $- b y_{15} \,\mathbf{\hat{y}}- c z_{15} \,\mathbf{\hat{z}}$ | (8f) | O IX |
| $\mathbf{B_{55}}$ | = | $- y_{16} \, \mathbf{a}_{1}+y_{16} \, \mathbf{a}_{2}+z_{16} \, \mathbf{a}_{3}$ | = | $b y_{16} \,\mathbf{\hat{y}}+c z_{16} \,\mathbf{\hat{z}}$ | (8f) | O X |
| $\mathbf{B_{56}}$ | = | $y_{16} \, \mathbf{a}_{1}- y_{16} \, \mathbf{a}_{2}+\left(z_{16} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- b y_{16} \,\mathbf{\hat{y}}+c \left(z_{16} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8f) | O X |
| $\mathbf{B_{57}}$ | = | $- y_{16} \, \mathbf{a}_{1}+y_{16} \, \mathbf{a}_{2}- \left(z_{16} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $b y_{16} \,\mathbf{\hat{y}}- c \left(z_{16} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8f) | O X |
| $\mathbf{B_{58}}$ | = | $y_{16} \, \mathbf{a}_{1}- y_{16} \, \mathbf{a}_{2}- z_{16} \, \mathbf{a}_{3}$ | = | $- b y_{16} \,\mathbf{\hat{y}}- c z_{16} \,\mathbf{\hat{z}}$ | (8f) | O X |
| $\mathbf{B_{59}}$ | = | $- y_{17} \, \mathbf{a}_{1}+y_{17} \, \mathbf{a}_{2}+z_{17} \, \mathbf{a}_{3}$ | = | $b y_{17} \,\mathbf{\hat{y}}+c z_{17} \,\mathbf{\hat{z}}$ | (8f) | O XI |
| $\mathbf{B_{60}}$ | = | $y_{17} \, \mathbf{a}_{1}- y_{17} \, \mathbf{a}_{2}+\left(z_{17} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- b y_{17} \,\mathbf{\hat{y}}+c \left(z_{17} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8f) | O XI |
| $\mathbf{B_{61}}$ | = | $- y_{17} \, \mathbf{a}_{1}+y_{17} \, \mathbf{a}_{2}- \left(z_{17} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $b y_{17} \,\mathbf{\hat{y}}- c \left(z_{17} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8f) | O XI |
| $\mathbf{B_{62}}$ | = | $y_{17} \, \mathbf{a}_{1}- y_{17} \, \mathbf{a}_{2}- z_{17} \, \mathbf{a}_{3}$ | = | $- b y_{17} \,\mathbf{\hat{y}}- c z_{17} \,\mathbf{\hat{z}}$ | (8f) | O XI |
| $\mathbf{B_{63}}$ | = | $- y_{18} \, \mathbf{a}_{1}+y_{18} \, \mathbf{a}_{2}+z_{18} \, \mathbf{a}_{3}$ | = | $b y_{18} \,\mathbf{\hat{y}}+c z_{18} \,\mathbf{\hat{z}}$ | (8f) | O XII |
| $\mathbf{B_{64}}$ | = | $y_{18} \, \mathbf{a}_{1}- y_{18} \, \mathbf{a}_{2}+\left(z_{18} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- b y_{18} \,\mathbf{\hat{y}}+c \left(z_{18} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8f) | O XII |
| $\mathbf{B_{65}}$ | = | $- y_{18} \, \mathbf{a}_{1}+y_{18} \, \mathbf{a}_{2}- \left(z_{18} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $b y_{18} \,\mathbf{\hat{y}}- c \left(z_{18} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8f) | O XII |
| $\mathbf{B_{66}}$ | = | $y_{18} \, \mathbf{a}_{1}- y_{18} \, \mathbf{a}_{2}- z_{18} \, \mathbf{a}_{3}$ | = | $- b y_{18} \,\mathbf{\hat{y}}- c z_{18} \,\mathbf{\hat{z}}$ | (8f) | O XII |
| $\mathbf{B_{67}}$ | = | $- y_{19} \, \mathbf{a}_{1}+y_{19} \, \mathbf{a}_{2}+z_{19} \, \mathbf{a}_{3}$ | = | $b y_{19} \,\mathbf{\hat{y}}+c z_{19} \,\mathbf{\hat{z}}$ | (8f) | O XIII |
| $\mathbf{B_{68}}$ | = | $y_{19} \, \mathbf{a}_{1}- y_{19} \, \mathbf{a}_{2}+\left(z_{19} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- b y_{19} \,\mathbf{\hat{y}}+c \left(z_{19} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8f) | O XIII |
| $\mathbf{B_{69}}$ | = | $- y_{19} \, \mathbf{a}_{1}+y_{19} \, \mathbf{a}_{2}- \left(z_{19} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $b y_{19} \,\mathbf{\hat{y}}- c \left(z_{19} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8f) | O XIII |
| $\mathbf{B_{70}}$ | = | $y_{19} \, \mathbf{a}_{1}- y_{19} \, \mathbf{a}_{2}- z_{19} \, \mathbf{a}_{3}$ | = | $- b y_{19} \,\mathbf{\hat{y}}- c z_{19} \,\mathbf{\hat{z}}$ | (8f) | O XIII |
| $\mathbf{B_{71}}$ | = | $- y_{20} \, \mathbf{a}_{1}+y_{20} \, \mathbf{a}_{2}+z_{20} \, \mathbf{a}_{3}$ | = | $b y_{20} \,\mathbf{\hat{y}}+c z_{20} \,\mathbf{\hat{z}}$ | (8f) | O XIV |
| $\mathbf{B_{72}}$ | = | $y_{20} \, \mathbf{a}_{1}- y_{20} \, \mathbf{a}_{2}+\left(z_{20} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- b y_{20} \,\mathbf{\hat{y}}+c \left(z_{20} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8f) | O XIV |
| $\mathbf{B_{73}}$ | = | $- y_{20} \, \mathbf{a}_{1}+y_{20} \, \mathbf{a}_{2}- \left(z_{20} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $b y_{20} \,\mathbf{\hat{y}}- c \left(z_{20} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8f) | O XIV |
| $\mathbf{B_{74}}$ | = | $y_{20} \, \mathbf{a}_{1}- y_{20} \, \mathbf{a}_{2}- z_{20} \, \mathbf{a}_{3}$ | = | $- b y_{20} \,\mathbf{\hat{y}}- c z_{20} \,\mathbf{\hat{z}}$ | (8f) | O XIV |
| $\mathbf{B_{75}}$ | = | $- y_{21} \, \mathbf{a}_{1}+y_{21} \, \mathbf{a}_{2}+z_{21} \, \mathbf{a}_{3}$ | = | $b y_{21} \,\mathbf{\hat{y}}+c z_{21} \,\mathbf{\hat{z}}$ | (8f) | O XV |
| $\mathbf{B_{76}}$ | = | $y_{21} \, \mathbf{a}_{1}- y_{21} \, \mathbf{a}_{2}+\left(z_{21} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- b y_{21} \,\mathbf{\hat{y}}+c \left(z_{21} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8f) | O XV |
| $\mathbf{B_{77}}$ | = | $- y_{21} \, \mathbf{a}_{1}+y_{21} \, \mathbf{a}_{2}- \left(z_{21} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $b y_{21} \,\mathbf{\hat{y}}- c \left(z_{21} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8f) | O XV |
| $\mathbf{B_{78}}$ | = | $y_{21} \, \mathbf{a}_{1}- y_{21} \, \mathbf{a}_{2}- z_{21} \, \mathbf{a}_{3}$ | = | $- b y_{21} \,\mathbf{\hat{y}}- c z_{21} \,\mathbf{\hat{z}}$ | (8f) | O XV |
| $\mathbf{B_{79}}$ | = | $- y_{22} \, \mathbf{a}_{1}+y_{22} \, \mathbf{a}_{2}+z_{22} \, \mathbf{a}_{3}$ | = | $b y_{22} \,\mathbf{\hat{y}}+c z_{22} \,\mathbf{\hat{z}}$ | (8f) | O XVI |
| $\mathbf{B_{80}}$ | = | $y_{22} \, \mathbf{a}_{1}- y_{22} \, \mathbf{a}_{2}+\left(z_{22} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- b y_{22} \,\mathbf{\hat{y}}+c \left(z_{22} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8f) | O XVI |
| $\mathbf{B_{81}}$ | = | $- y_{22} \, \mathbf{a}_{1}+y_{22} \, \mathbf{a}_{2}- \left(z_{22} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $b y_{22} \,\mathbf{\hat{y}}- c \left(z_{22} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8f) | O XVI |
| $\mathbf{B_{82}}$ | = | $y_{22} \, \mathbf{a}_{1}- y_{22} \, \mathbf{a}_{2}- z_{22} \, \mathbf{a}_{3}$ | = | $- b y_{22} \,\mathbf{\hat{y}}- c z_{22} \,\mathbf{\hat{z}}$ | (8f) | O XVI |
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_oC164_63_6f_3c13f --params=$a,b/a,c/a,y_{1},y_{2},y_{3},y_{4},z_{4},y_{5},z_{5},y_{6},z_{6},y_{7},z_{7},y_{8},z_{8},y_{9},z_{9},y_{10},z_{10},y_{11},z_{11},y_{12},z_{12},y_{13},z_{13},y_{14},z_{14},y_{15},z_{15},y_{16},z_{16},y_{17},z_{17},y_{18},z_{18},y_{19},z_{19},y_{20},z_{20},y_{21},z_{21},y_{22},z_{22}$