Rb$_{2}$Mo$_{2}$O$_{7}$ Structure: A2B7C2_oC88_40_abc_2b6c_a3b-001
| Prototype | Mo$_{2}$O$_{7}$Rb$_{2}$ |
| AFLOW prototype label | A2B7C2_oC88_40_abc_2b6c_a3b-001 |
| ICSD | 249126 |
| Pearson symbol | oC88 |
| Space group number | 40 |
| Space group symbol | $Ama2$ |
| AFLOW prototype command |
aflow --proto=A2B7C2_oC88_40_abc_2b6c_a3b-001
--params=$a, \allowbreak b/a, \allowbreak c/a, \allowbreak z_{1}, \allowbreak z_{2}, \allowbreak y_{3}, \allowbreak z_{3}, \allowbreak y_{4}, \allowbreak z_{4}, \allowbreak y_{5}, \allowbreak z_{5}, \allowbreak y_{6}, \allowbreak z_{6}, \allowbreak y_{7}, \allowbreak z_{7}, \allowbreak y_{8}, \allowbreak z_{8}, \allowbreak x_{9}, \allowbreak y_{9}, \allowbreak z_{9}, \allowbreak x_{10}, \allowbreak y_{10}, \allowbreak z_{10}, \allowbreak x_{11}, \allowbreak y_{11}, \allowbreak z_{11}, \allowbreak x_{12}, \allowbreak y_{12}, \allowbreak z_{12}, \allowbreak x_{13}, \allowbreak y_{13}, \allowbreak z_{13}, \allowbreak x_{14}, \allowbreak y_{14}, \allowbreak z_{14}, \allowbreak x_{15}, \allowbreak y_{15}, \allowbreak z_{15}$ |
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&a \,\mathbf{\hat{x}}\\\mathbf{a_{2}}&=&\frac{1}{2}b \,\mathbf{\hat{y}}- \frac{1}{2}c \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&\frac{1}{2}b \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $- z_{1} \, \mathbf{a}_{2}+z_{1} \, \mathbf{a}_{3}$ | = | $c z_{1} \,\mathbf{\hat{z}}$ | (4a) | Mo I |
| $\mathbf{B_{2}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}- z_{1} \, \mathbf{a}_{2}+z_{1} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+c z_{1} \,\mathbf{\hat{z}}$ | (4a) | Mo I |
| $\mathbf{B_{3}}$ | = | $- z_{2} \, \mathbf{a}_{2}+z_{2} \, \mathbf{a}_{3}$ | = | $c z_{2} \,\mathbf{\hat{z}}$ | (4a) | Rb I |
| $\mathbf{B_{4}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}- z_{2} \, \mathbf{a}_{2}+z_{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+c z_{2} \,\mathbf{\hat{z}}$ | (4a) | Rb I |
| $\mathbf{B_{5}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+\left(y_{3} - z_{3}\right) \, \mathbf{a}_{2}+\left(y_{3} + z_{3}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+b y_{3} \,\mathbf{\hat{y}}+c z_{3} \,\mathbf{\hat{z}}$ | (4b) | Mo II |
| $\mathbf{B_{6}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}- \left(y_{3} + z_{3}\right) \, \mathbf{a}_{2}- \left(y_{3} - z_{3}\right) \, \mathbf{a}_{3}$ | = | $\frac{3}{4}a \,\mathbf{\hat{x}}- b y_{3} \,\mathbf{\hat{y}}+c z_{3} \,\mathbf{\hat{z}}$ | (4b) | Mo II |
| $\mathbf{B_{7}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+\left(y_{4} - z_{4}\right) \, \mathbf{a}_{2}+\left(y_{4} + z_{4}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+b y_{4} \,\mathbf{\hat{y}}+c z_{4} \,\mathbf{\hat{z}}$ | (4b) | O I |
| $\mathbf{B_{8}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}- \left(y_{4} + z_{4}\right) \, \mathbf{a}_{2}- \left(y_{4} - z_{4}\right) \, \mathbf{a}_{3}$ | = | $\frac{3}{4}a \,\mathbf{\hat{x}}- b y_{4} \,\mathbf{\hat{y}}+c z_{4} \,\mathbf{\hat{z}}$ | (4b) | O I |
| $\mathbf{B_{9}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+\left(y_{5} - z_{5}\right) \, \mathbf{a}_{2}+\left(y_{5} + z_{5}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+b y_{5} \,\mathbf{\hat{y}}+c z_{5} \,\mathbf{\hat{z}}$ | (4b) | O II |
| $\mathbf{B_{10}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}- \left(y_{5} + z_{5}\right) \, \mathbf{a}_{2}- \left(y_{5} - z_{5}\right) \, \mathbf{a}_{3}$ | = | $\frac{3}{4}a \,\mathbf{\hat{x}}- b y_{5} \,\mathbf{\hat{y}}+c z_{5} \,\mathbf{\hat{z}}$ | (4b) | O II |
| $\mathbf{B_{11}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+\left(y_{6} - z_{6}\right) \, \mathbf{a}_{2}+\left(y_{6} + z_{6}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+b y_{6} \,\mathbf{\hat{y}}+c z_{6} \,\mathbf{\hat{z}}$ | (4b) | Rb II |
| $\mathbf{B_{12}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}- \left(y_{6} + z_{6}\right) \, \mathbf{a}_{2}- \left(y_{6} - z_{6}\right) \, \mathbf{a}_{3}$ | = | $\frac{3}{4}a \,\mathbf{\hat{x}}- b y_{6} \,\mathbf{\hat{y}}+c z_{6} \,\mathbf{\hat{z}}$ | (4b) | Rb II |
| $\mathbf{B_{13}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+\left(y_{7} - z_{7}\right) \, \mathbf{a}_{2}+\left(y_{7} + z_{7}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+b y_{7} \,\mathbf{\hat{y}}+c z_{7} \,\mathbf{\hat{z}}$ | (4b) | Rb III |
| $\mathbf{B_{14}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}- \left(y_{7} + z_{7}\right) \, \mathbf{a}_{2}- \left(y_{7} - z_{7}\right) \, \mathbf{a}_{3}$ | = | $\frac{3}{4}a \,\mathbf{\hat{x}}- b y_{7} \,\mathbf{\hat{y}}+c z_{7} \,\mathbf{\hat{z}}$ | (4b) | Rb III |
| $\mathbf{B_{15}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+\left(y_{8} - z_{8}\right) \, \mathbf{a}_{2}+\left(y_{8} + z_{8}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+b y_{8} \,\mathbf{\hat{y}}+c z_{8} \,\mathbf{\hat{z}}$ | (4b) | Rb IV |
| $\mathbf{B_{16}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}- \left(y_{8} + z_{8}\right) \, \mathbf{a}_{2}- \left(y_{8} - z_{8}\right) \, \mathbf{a}_{3}$ | = | $\frac{3}{4}a \,\mathbf{\hat{x}}- b y_{8} \,\mathbf{\hat{y}}+c z_{8} \,\mathbf{\hat{z}}$ | (4b) | Rb IV |
| $\mathbf{B_{17}}$ | = | $x_{9} \, \mathbf{a}_{1}+\left(y_{9} - z_{9}\right) \, \mathbf{a}_{2}+\left(y_{9} + z_{9}\right) \, \mathbf{a}_{3}$ | = | $a x_{9} \,\mathbf{\hat{x}}+b y_{9} \,\mathbf{\hat{y}}+c z_{9} \,\mathbf{\hat{z}}$ | (8c) | Mo III |
| $\mathbf{B_{18}}$ | = | $- x_{9} \, \mathbf{a}_{1}- \left(y_{9} + z_{9}\right) \, \mathbf{a}_{2}- \left(y_{9} - z_{9}\right) \, \mathbf{a}_{3}$ | = | $- a x_{9} \,\mathbf{\hat{x}}- b y_{9} \,\mathbf{\hat{y}}+c z_{9} \,\mathbf{\hat{z}}$ | (8c) | Mo III |
| $\mathbf{B_{19}}$ | = | $\left(x_{9} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{9} + z_{9}\right) \, \mathbf{a}_{2}- \left(y_{9} - z_{9}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{9} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- b y_{9} \,\mathbf{\hat{y}}+c z_{9} \,\mathbf{\hat{z}}$ | (8c) | Mo III |
| $\mathbf{B_{20}}$ | = | $- \left(x_{9} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{9} - z_{9}\right) \, \mathbf{a}_{2}+\left(y_{9} + z_{9}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{9} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+b y_{9} \,\mathbf{\hat{y}}+c z_{9} \,\mathbf{\hat{z}}$ | (8c) | Mo III |
| $\mathbf{B_{21}}$ | = | $x_{10} \, \mathbf{a}_{1}+\left(y_{10} - z_{10}\right) \, \mathbf{a}_{2}+\left(y_{10} + z_{10}\right) \, \mathbf{a}_{3}$ | = | $a x_{10} \,\mathbf{\hat{x}}+b y_{10} \,\mathbf{\hat{y}}+c z_{10} \,\mathbf{\hat{z}}$ | (8c) | O III |
| $\mathbf{B_{22}}$ | = | $- x_{10} \, \mathbf{a}_{1}- \left(y_{10} + z_{10}\right) \, \mathbf{a}_{2}- \left(y_{10} - z_{10}\right) \, \mathbf{a}_{3}$ | = | $- a x_{10} \,\mathbf{\hat{x}}- b y_{10} \,\mathbf{\hat{y}}+c z_{10} \,\mathbf{\hat{z}}$ | (8c) | O III |
| $\mathbf{B_{23}}$ | = | $\left(x_{10} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{10} + z_{10}\right) \, \mathbf{a}_{2}- \left(y_{10} - z_{10}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{10} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- b y_{10} \,\mathbf{\hat{y}}+c z_{10} \,\mathbf{\hat{z}}$ | (8c) | O III |
| $\mathbf{B_{24}}$ | = | $- \left(x_{10} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{10} - z_{10}\right) \, \mathbf{a}_{2}+\left(y_{10} + z_{10}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{10} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+b y_{10} \,\mathbf{\hat{y}}+c z_{10} \,\mathbf{\hat{z}}$ | (8c) | O III |
| $\mathbf{B_{25}}$ | = | $x_{11} \, \mathbf{a}_{1}+\left(y_{11} - z_{11}\right) \, \mathbf{a}_{2}+\left(y_{11} + z_{11}\right) \, \mathbf{a}_{3}$ | = | $a x_{11} \,\mathbf{\hat{x}}+b y_{11} \,\mathbf{\hat{y}}+c z_{11} \,\mathbf{\hat{z}}$ | (8c) | O IV |
| $\mathbf{B_{26}}$ | = | $- x_{11} \, \mathbf{a}_{1}- \left(y_{11} + z_{11}\right) \, \mathbf{a}_{2}- \left(y_{11} - z_{11}\right) \, \mathbf{a}_{3}$ | = | $- a x_{11} \,\mathbf{\hat{x}}- b y_{11} \,\mathbf{\hat{y}}+c z_{11} \,\mathbf{\hat{z}}$ | (8c) | O IV |
| $\mathbf{B_{27}}$ | = | $\left(x_{11} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{11} + z_{11}\right) \, \mathbf{a}_{2}- \left(y_{11} - z_{11}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{11} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- b y_{11} \,\mathbf{\hat{y}}+c z_{11} \,\mathbf{\hat{z}}$ | (8c) | O IV |
| $\mathbf{B_{28}}$ | = | $- \left(x_{11} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{11} - z_{11}\right) \, \mathbf{a}_{2}+\left(y_{11} + z_{11}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{11} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+b y_{11} \,\mathbf{\hat{y}}+c z_{11} \,\mathbf{\hat{z}}$ | (8c) | O IV |
| $\mathbf{B_{29}}$ | = | $x_{12} \, \mathbf{a}_{1}+\left(y_{12} - z_{12}\right) \, \mathbf{a}_{2}+\left(y_{12} + z_{12}\right) \, \mathbf{a}_{3}$ | = | $a x_{12} \,\mathbf{\hat{x}}+b y_{12} \,\mathbf{\hat{y}}+c z_{12} \,\mathbf{\hat{z}}$ | (8c) | O V |
| $\mathbf{B_{30}}$ | = | $- x_{12} \, \mathbf{a}_{1}- \left(y_{12} + z_{12}\right) \, \mathbf{a}_{2}- \left(y_{12} - z_{12}\right) \, \mathbf{a}_{3}$ | = | $- a x_{12} \,\mathbf{\hat{x}}- b y_{12} \,\mathbf{\hat{y}}+c z_{12} \,\mathbf{\hat{z}}$ | (8c) | O V |
| $\mathbf{B_{31}}$ | = | $\left(x_{12} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{12} + z_{12}\right) \, \mathbf{a}_{2}- \left(y_{12} - z_{12}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{12} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- b y_{12} \,\mathbf{\hat{y}}+c z_{12} \,\mathbf{\hat{z}}$ | (8c) | O V |
| $\mathbf{B_{32}}$ | = | $- \left(x_{12} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{12} - z_{12}\right) \, \mathbf{a}_{2}+\left(y_{12} + z_{12}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{12} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+b y_{12} \,\mathbf{\hat{y}}+c z_{12} \,\mathbf{\hat{z}}$ | (8c) | O V |
| $\mathbf{B_{33}}$ | = | $x_{13} \, \mathbf{a}_{1}+\left(y_{13} - z_{13}\right) \, \mathbf{a}_{2}+\left(y_{13} + z_{13}\right) \, \mathbf{a}_{3}$ | = | $a x_{13} \,\mathbf{\hat{x}}+b y_{13} \,\mathbf{\hat{y}}+c z_{13} \,\mathbf{\hat{z}}$ | (8c) | O VI |
| $\mathbf{B_{34}}$ | = | $- x_{13} \, \mathbf{a}_{1}- \left(y_{13} + z_{13}\right) \, \mathbf{a}_{2}- \left(y_{13} - z_{13}\right) \, \mathbf{a}_{3}$ | = | $- a x_{13} \,\mathbf{\hat{x}}- b y_{13} \,\mathbf{\hat{y}}+c z_{13} \,\mathbf{\hat{z}}$ | (8c) | O VI |
| $\mathbf{B_{35}}$ | = | $\left(x_{13} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{13} + z_{13}\right) \, \mathbf{a}_{2}- \left(y_{13} - z_{13}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{13} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- b y_{13} \,\mathbf{\hat{y}}+c z_{13} \,\mathbf{\hat{z}}$ | (8c) | O VI |
| $\mathbf{B_{36}}$ | = | $- \left(x_{13} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{13} - z_{13}\right) \, \mathbf{a}_{2}+\left(y_{13} + z_{13}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{13} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+b y_{13} \,\mathbf{\hat{y}}+c z_{13} \,\mathbf{\hat{z}}$ | (8c) | O VI |
| $\mathbf{B_{37}}$ | = | $x_{14} \, \mathbf{a}_{1}+\left(y_{14} - z_{14}\right) \, \mathbf{a}_{2}+\left(y_{14} + z_{14}\right) \, \mathbf{a}_{3}$ | = | $a x_{14} \,\mathbf{\hat{x}}+b y_{14} \,\mathbf{\hat{y}}+c z_{14} \,\mathbf{\hat{z}}$ | (8c) | O VII |
| $\mathbf{B_{38}}$ | = | $- x_{14} \, \mathbf{a}_{1}- \left(y_{14} + z_{14}\right) \, \mathbf{a}_{2}- \left(y_{14} - z_{14}\right) \, \mathbf{a}_{3}$ | = | $- a x_{14} \,\mathbf{\hat{x}}- b y_{14} \,\mathbf{\hat{y}}+c z_{14} \,\mathbf{\hat{z}}$ | (8c) | O VII |
| $\mathbf{B_{39}}$ | = | $\left(x_{14} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{14} + z_{14}\right) \, \mathbf{a}_{2}- \left(y_{14} - z_{14}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{14} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- b y_{14} \,\mathbf{\hat{y}}+c z_{14} \,\mathbf{\hat{z}}$ | (8c) | O VII |
| $\mathbf{B_{40}}$ | = | $- \left(x_{14} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{14} - z_{14}\right) \, \mathbf{a}_{2}+\left(y_{14} + z_{14}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{14} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+b y_{14} \,\mathbf{\hat{y}}+c z_{14} \,\mathbf{\hat{z}}$ | (8c) | O VII |
| $\mathbf{B_{41}}$ | = | $x_{15} \, \mathbf{a}_{1}+\left(y_{15} - z_{15}\right) \, \mathbf{a}_{2}+\left(y_{15} + z_{15}\right) \, \mathbf{a}_{3}$ | = | $a x_{15} \,\mathbf{\hat{x}}+b y_{15} \,\mathbf{\hat{y}}+c z_{15} \,\mathbf{\hat{z}}$ | (8c) | O VIII |
| $\mathbf{B_{42}}$ | = | $- x_{15} \, \mathbf{a}_{1}- \left(y_{15} + z_{15}\right) \, \mathbf{a}_{2}- \left(y_{15} - z_{15}\right) \, \mathbf{a}_{3}$ | = | $- a x_{15} \,\mathbf{\hat{x}}- b y_{15} \,\mathbf{\hat{y}}+c z_{15} \,\mathbf{\hat{z}}$ | (8c) | O VIII |
| $\mathbf{B_{43}}$ | = | $\left(x_{15} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{15} + z_{15}\right) \, \mathbf{a}_{2}- \left(y_{15} - z_{15}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{15} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- b y_{15} \,\mathbf{\hat{y}}+c z_{15} \,\mathbf{\hat{z}}$ | (8c) | O VIII |
| $\mathbf{B_{44}}$ | = | $- \left(x_{15} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{15} - z_{15}\right) \, \mathbf{a}_{2}+\left(y_{15} + z_{15}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{15} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+b y_{15} \,\mathbf{\hat{y}}+c z_{15} \,\mathbf{\hat{z}}$ | (8c) | O VIII |
References
- Z. A. Solodovnikova and S. F. Solodovnikov, Rubidium dimolybdate, Rb$_{2}$Mo$_{2}$O$_{7}$, and caesium dimolybdate, Cs$_{2}$Mo$_{2}$O$_{7}$, Acta Crystallogr. Sect. C 62, i53–i56 (2006), doi:10.1107/S0108270106014880.
Prototype Generator
aflow --proto=A2B7C2_oC88_40_abc_2b6c_a3b --params=$a,b/a,c/a,z_{1},z_{2},y_{3},z_{3},y_{4},z_{4},y_{5},z_{5},y_{6},z_{6},y_{7},z_{7},y_{8},z_{8},x_{9},y_{9},z_{9},x_{10},y_{10},z_{10},x_{11},y_{11},z_{11},x_{12},y_{12},z_{12},x_{13},y_{13},z_{13},x_{14},y_{14},z_{14},x_{15},y_{15},z_{15}$