Murataite [(Y,Na)$_{6}$(Zn,Fe)$_{5}$Ti$_{12}$O$_{29}$(O,F)$_{10}$F$_{4}$] Structure: A16B40C12D6E5_cF316_216_eh_e2g2h_h_f_ae-001
| Prototype | F$_{16}$O$_{40}$Ti$_{12}$Y$_{6}$Zn$_{5}$ |
| AFLOW prototype label | A16B40C12D6E5_cF316_216_eh_e2g2h_h_f_ae-001 |
| Mineral name | murataite |
| ICSD | 81595 |
| Pearson symbol | cF316 |
| Space group number | 216 |
| Space group symbol | $F\overline{4}3m$ |
| AFLOW prototype command |
aflow --proto=A16B40C12D6E5_cF316_216_eh_e2g2h_h_f_ae-001
--params=$a, \allowbreak x_{2}, \allowbreak x_{3}, \allowbreak x_{4}, \allowbreak x_{5}, \allowbreak x_{6}, \allowbreak x_{7}, \allowbreak x_{8}, \allowbreak z_{8}, \allowbreak x_{9}, \allowbreak z_{9}, \allowbreak x_{10}, \allowbreak z_{10}, \allowbreak x_{11}, \allowbreak z_{11}$ |
- Most of the sites in this structure are somewhat disordered. The
nominal
composition is given as F$_{16}$O$_{40}$Ti$_{12}$Y$_{6}$Zn$_{5}$ by (Ercit, 1995), but as the CIF in (Downs, 2003) shows, even these labels are not quite correct. In our listing we label each Wyckoff position by the type of atom that has the largest concentration on that site. Following (Downs, 2003):- Site Zn-I has the composition Zn$_{0.89}$Si$_{0.11}$.
- Site F-I has the composition F$_{0.55}$O$_{0.45}$.
- Site O-I is pure oxygen.
- Site Zn-II has the composition Zn$_{0.48}$Fe$_{0.25}$Na$_{0.16}$Ti$_{0.11}$.
- Site Y has the composition Y$_{0.37}$Na$_{0.35}$Mn$_{0.03}$HREE$_{0.25}$, where
HREE
is a mixture of heavy Rare Earth elements. - Site O-II is pure oxygen, but only 8.3333% of the sites are occupied.
- Site O-III has the composition O$_{0.7}$F$_{0.3}$.
- Site O-IV is pure oxygen.
- Site O-V is pure oxygen, but only 87% of the sites are occupied.
- Site F-II is pure fluorine, but only 33.333% of the sites are occupied.
- Site Ti has the composition Ti$_{0.76}$Nb$_{0.13}$Na$_{0.11}$.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $0$ | = | $0$ | (4a) | Zn I |
| $\mathbf{B_{2}}$ | = | $x_{2} \, \mathbf{a}_{1}+x_{2} \, \mathbf{a}_{2}+x_{2} \, \mathbf{a}_{3}$ | = | $a x_{2} \,\mathbf{\hat{x}}+a x_{2} \,\mathbf{\hat{y}}+a x_{2} \,\mathbf{\hat{z}}$ | (16e) | F I |
| $\mathbf{B_{3}}$ | = | $x_{2} \, \mathbf{a}_{1}+x_{2} \, \mathbf{a}_{2}- 3 x_{2} \, \mathbf{a}_{3}$ | = | $- a x_{2} \,\mathbf{\hat{x}}- a x_{2} \,\mathbf{\hat{y}}+a x_{2} \,\mathbf{\hat{z}}$ | (16e) | F I |
| $\mathbf{B_{4}}$ | = | $x_{2} \, \mathbf{a}_{1}- 3 x_{2} \, \mathbf{a}_{2}+x_{2} \, \mathbf{a}_{3}$ | = | $- a x_{2} \,\mathbf{\hat{x}}+a x_{2} \,\mathbf{\hat{y}}- a x_{2} \,\mathbf{\hat{z}}$ | (16e) | F I |
| $\mathbf{B_{5}}$ | = | $- 3 x_{2} \, \mathbf{a}_{1}+x_{2} \, \mathbf{a}_{2}+x_{2} \, \mathbf{a}_{3}$ | = | $a x_{2} \,\mathbf{\hat{x}}- a x_{2} \,\mathbf{\hat{y}}- a x_{2} \,\mathbf{\hat{z}}$ | (16e) | F I |
| $\mathbf{B_{6}}$ | = | $x_{3} \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{2}+x_{3} \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{x}}+a x_{3} \,\mathbf{\hat{y}}+a x_{3} \,\mathbf{\hat{z}}$ | (16e) | O I |
| $\mathbf{B_{7}}$ | = | $x_{3} \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{2}- 3 x_{3} \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}- a x_{3} \,\mathbf{\hat{y}}+a x_{3} \,\mathbf{\hat{z}}$ | (16e) | O I |
| $\mathbf{B_{8}}$ | = | $x_{3} \, \mathbf{a}_{1}- 3 x_{3} \, \mathbf{a}_{2}+x_{3} \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}+a x_{3} \,\mathbf{\hat{y}}- a x_{3} \,\mathbf{\hat{z}}$ | (16e) | O I |
| $\mathbf{B_{9}}$ | = | $- 3 x_{3} \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{2}+x_{3} \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{x}}- a x_{3} \,\mathbf{\hat{y}}- a x_{3} \,\mathbf{\hat{z}}$ | (16e) | O I |
| $\mathbf{B_{10}}$ | = | $x_{4} \, \mathbf{a}_{1}+x_{4} \, \mathbf{a}_{2}+x_{4} \, \mathbf{a}_{3}$ | = | $a x_{4} \,\mathbf{\hat{x}}+a x_{4} \,\mathbf{\hat{y}}+a x_{4} \,\mathbf{\hat{z}}$ | (16e) | Zn II |
| $\mathbf{B_{11}}$ | = | $x_{4} \, \mathbf{a}_{1}+x_{4} \, \mathbf{a}_{2}- 3 x_{4} \, \mathbf{a}_{3}$ | = | $- a x_{4} \,\mathbf{\hat{x}}- a x_{4} \,\mathbf{\hat{y}}+a x_{4} \,\mathbf{\hat{z}}$ | (16e) | Zn II |
| $\mathbf{B_{12}}$ | = | $x_{4} \, \mathbf{a}_{1}- 3 x_{4} \, \mathbf{a}_{2}+x_{4} \, \mathbf{a}_{3}$ | = | $- a x_{4} \,\mathbf{\hat{x}}+a x_{4} \,\mathbf{\hat{y}}- a x_{4} \,\mathbf{\hat{z}}$ | (16e) | Zn II |
| $\mathbf{B_{13}}$ | = | $- 3 x_{4} \, \mathbf{a}_{1}+x_{4} \, \mathbf{a}_{2}+x_{4} \, \mathbf{a}_{3}$ | = | $a x_{4} \,\mathbf{\hat{x}}- a x_{4} \,\mathbf{\hat{y}}- a x_{4} \,\mathbf{\hat{z}}$ | (16e) | Zn II |
| $\mathbf{B_{14}}$ | = | $- x_{5} \, \mathbf{a}_{1}+x_{5} \, \mathbf{a}_{2}+x_{5} \, \mathbf{a}_{3}$ | = | $a x_{5} \,\mathbf{\hat{x}}$ | (24f) | Y I |
| $\mathbf{B_{15}}$ | = | $x_{5} \, \mathbf{a}_{1}- x_{5} \, \mathbf{a}_{2}- x_{5} \, \mathbf{a}_{3}$ | = | $- a x_{5} \,\mathbf{\hat{x}}$ | (24f) | Y I |
| $\mathbf{B_{16}}$ | = | $x_{5} \, \mathbf{a}_{1}- x_{5} \, \mathbf{a}_{2}+x_{5} \, \mathbf{a}_{3}$ | = | $a x_{5} \,\mathbf{\hat{y}}$ | (24f) | Y I |
| $\mathbf{B_{17}}$ | = | $- x_{5} \, \mathbf{a}_{1}+x_{5} \, \mathbf{a}_{2}- x_{5} \, \mathbf{a}_{3}$ | = | $- a x_{5} \,\mathbf{\hat{y}}$ | (24f) | Y I |
| $\mathbf{B_{18}}$ | = | $x_{5} \, \mathbf{a}_{1}+x_{5} \, \mathbf{a}_{2}- x_{5} \, \mathbf{a}_{3}$ | = | $a x_{5} \,\mathbf{\hat{z}}$ | (24f) | Y I |
| $\mathbf{B_{19}}$ | = | $- x_{5} \, \mathbf{a}_{1}- x_{5} \, \mathbf{a}_{2}+x_{5} \, \mathbf{a}_{3}$ | = | $- a x_{5} \,\mathbf{\hat{z}}$ | (24f) | Y I |
| $\mathbf{B_{20}}$ | = | $- \left(x_{6} - \frac{1}{2}\right) \, \mathbf{a}_{1}+x_{6} \, \mathbf{a}_{2}+x_{6} \, \mathbf{a}_{3}$ | = | $a x_{6} \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (24g) | O II |
| $\mathbf{B_{21}}$ | = | $x_{6} \, \mathbf{a}_{1}- \left(x_{6} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{6} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{6} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (24g) | O II |
| $\mathbf{B_{22}}$ | = | $x_{6} \, \mathbf{a}_{1}- \left(x_{6} - \frac{1}{2}\right) \, \mathbf{a}_{2}+x_{6} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+a x_{6} \,\mathbf{\hat{y}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (24g) | O II |
| $\mathbf{B_{23}}$ | = | $- \left(x_{6} - \frac{1}{2}\right) \, \mathbf{a}_{1}+x_{6} \, \mathbf{a}_{2}- \left(x_{6} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}- a \left(x_{6} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (24g) | O II |
| $\mathbf{B_{24}}$ | = | $x_{6} \, \mathbf{a}_{1}+x_{6} \, \mathbf{a}_{2}- \left(x_{6} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+a x_{6} \,\mathbf{\hat{z}}$ | (24g) | O II |
| $\mathbf{B_{25}}$ | = | $- \left(x_{6} - \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{6} - \frac{1}{2}\right) \, \mathbf{a}_{2}+x_{6} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}- a \left(x_{6} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24g) | O II |
| $\mathbf{B_{26}}$ | = | $- \left(x_{7} - \frac{1}{2}\right) \, \mathbf{a}_{1}+x_{7} \, \mathbf{a}_{2}+x_{7} \, \mathbf{a}_{3}$ | = | $a x_{7} \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (24g) | O III |
| $\mathbf{B_{27}}$ | = | $x_{7} \, \mathbf{a}_{1}- \left(x_{7} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{7} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{7} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (24g) | O III |
| $\mathbf{B_{28}}$ | = | $x_{7} \, \mathbf{a}_{1}- \left(x_{7} - \frac{1}{2}\right) \, \mathbf{a}_{2}+x_{7} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+a x_{7} \,\mathbf{\hat{y}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (24g) | O III |
| $\mathbf{B_{29}}$ | = | $- \left(x_{7} - \frac{1}{2}\right) \, \mathbf{a}_{1}+x_{7} \, \mathbf{a}_{2}- \left(x_{7} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}- a \left(x_{7} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (24g) | O III |
| $\mathbf{B_{30}}$ | = | $x_{7} \, \mathbf{a}_{1}+x_{7} \, \mathbf{a}_{2}- \left(x_{7} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+a x_{7} \,\mathbf{\hat{z}}$ | (24g) | O III |
| $\mathbf{B_{31}}$ | = | $- \left(x_{7} - \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{7} - \frac{1}{2}\right) \, \mathbf{a}_{2}+x_{7} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}- a \left(x_{7} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24g) | O III |
| $\mathbf{B_{32}}$ | = | $z_{8} \, \mathbf{a}_{1}+z_{8} \, \mathbf{a}_{2}+\left(2 x_{8} - z_{8}\right) \, \mathbf{a}_{3}$ | = | $a x_{8} \,\mathbf{\hat{x}}+a x_{8} \,\mathbf{\hat{y}}+a z_{8} \,\mathbf{\hat{z}}$ | (48h) | F II |
| $\mathbf{B_{33}}$ | = | $z_{8} \, \mathbf{a}_{1}+z_{8} \, \mathbf{a}_{2}- \left(2 x_{8} + z_{8}\right) \, \mathbf{a}_{3}$ | = | $- a x_{8} \,\mathbf{\hat{x}}- a x_{8} \,\mathbf{\hat{y}}+a z_{8} \,\mathbf{\hat{z}}$ | (48h) | F II |
| $\mathbf{B_{34}}$ | = | $\left(2 x_{8} - z_{8}\right) \, \mathbf{a}_{1}- \left(2 x_{8} + z_{8}\right) \, \mathbf{a}_{2}+z_{8} \, \mathbf{a}_{3}$ | = | $- a x_{8} \,\mathbf{\hat{x}}+a x_{8} \,\mathbf{\hat{y}}- a z_{8} \,\mathbf{\hat{z}}$ | (48h) | F II |
| $\mathbf{B_{35}}$ | = | $- \left(2 x_{8} + z_{8}\right) \, \mathbf{a}_{1}+\left(2 x_{8} - z_{8}\right) \, \mathbf{a}_{2}+z_{8} \, \mathbf{a}_{3}$ | = | $a x_{8} \,\mathbf{\hat{x}}- a x_{8} \,\mathbf{\hat{y}}- a z_{8} \,\mathbf{\hat{z}}$ | (48h) | F II |
| $\mathbf{B_{36}}$ | = | $\left(2 x_{8} - z_{8}\right) \, \mathbf{a}_{1}+z_{8} \, \mathbf{a}_{2}+z_{8} \, \mathbf{a}_{3}$ | = | $a z_{8} \,\mathbf{\hat{x}}+a x_{8} \,\mathbf{\hat{y}}+a x_{8} \,\mathbf{\hat{z}}$ | (48h) | F II |
| $\mathbf{B_{37}}$ | = | $- \left(2 x_{8} + z_{8}\right) \, \mathbf{a}_{1}+z_{8} \, \mathbf{a}_{2}+z_{8} \, \mathbf{a}_{3}$ | = | $a z_{8} \,\mathbf{\hat{x}}- a x_{8} \,\mathbf{\hat{y}}- a x_{8} \,\mathbf{\hat{z}}$ | (48h) | F II |
| $\mathbf{B_{38}}$ | = | $z_{8} \, \mathbf{a}_{1}+\left(2 x_{8} - z_{8}\right) \, \mathbf{a}_{2}- \left(2 x_{8} + z_{8}\right) \, \mathbf{a}_{3}$ | = | $- a z_{8} \,\mathbf{\hat{x}}- a x_{8} \,\mathbf{\hat{y}}+a x_{8} \,\mathbf{\hat{z}}$ | (48h) | F II |
| $\mathbf{B_{39}}$ | = | $z_{8} \, \mathbf{a}_{1}- \left(2 x_{8} + z_{8}\right) \, \mathbf{a}_{2}+\left(2 x_{8} - z_{8}\right) \, \mathbf{a}_{3}$ | = | $- a z_{8} \,\mathbf{\hat{x}}+a x_{8} \,\mathbf{\hat{y}}- a x_{8} \,\mathbf{\hat{z}}$ | (48h) | F II |
| $\mathbf{B_{40}}$ | = | $z_{8} \, \mathbf{a}_{1}+\left(2 x_{8} - z_{8}\right) \, \mathbf{a}_{2}+z_{8} \, \mathbf{a}_{3}$ | = | $a x_{8} \,\mathbf{\hat{x}}+a z_{8} \,\mathbf{\hat{y}}+a x_{8} \,\mathbf{\hat{z}}$ | (48h) | F II |
| $\mathbf{B_{41}}$ | = | $z_{8} \, \mathbf{a}_{1}- \left(2 x_{8} + z_{8}\right) \, \mathbf{a}_{2}+z_{8} \, \mathbf{a}_{3}$ | = | $- a x_{8} \,\mathbf{\hat{x}}+a z_{8} \,\mathbf{\hat{y}}- a x_{8} \,\mathbf{\hat{z}}$ | (48h) | F II |
| $\mathbf{B_{42}}$ | = | $- \left(2 x_{8} + z_{8}\right) \, \mathbf{a}_{1}+z_{8} \, \mathbf{a}_{2}+\left(2 x_{8} - z_{8}\right) \, \mathbf{a}_{3}$ | = | $a x_{8} \,\mathbf{\hat{x}}- a z_{8} \,\mathbf{\hat{y}}- a x_{8} \,\mathbf{\hat{z}}$ | (48h) | F II |
| $\mathbf{B_{43}}$ | = | $\left(2 x_{8} - z_{8}\right) \, \mathbf{a}_{1}+z_{8} \, \mathbf{a}_{2}- \left(2 x_{8} + z_{8}\right) \, \mathbf{a}_{3}$ | = | $- a x_{8} \,\mathbf{\hat{x}}- a z_{8} \,\mathbf{\hat{y}}+a x_{8} \,\mathbf{\hat{z}}$ | (48h) | F II |
| $\mathbf{B_{44}}$ | = | $z_{9} \, \mathbf{a}_{1}+z_{9} \, \mathbf{a}_{2}+\left(2 x_{9} - z_{9}\right) \, \mathbf{a}_{3}$ | = | $a x_{9} \,\mathbf{\hat{x}}+a x_{9} \,\mathbf{\hat{y}}+a z_{9} \,\mathbf{\hat{z}}$ | (48h) | O IV |
| $\mathbf{B_{45}}$ | = | $z_{9} \, \mathbf{a}_{1}+z_{9} \, \mathbf{a}_{2}- \left(2 x_{9} + z_{9}\right) \, \mathbf{a}_{3}$ | = | $- a x_{9} \,\mathbf{\hat{x}}- a x_{9} \,\mathbf{\hat{y}}+a z_{9} \,\mathbf{\hat{z}}$ | (48h) | O IV |
| $\mathbf{B_{46}}$ | = | $\left(2 x_{9} - z_{9}\right) \, \mathbf{a}_{1}- \left(2 x_{9} + z_{9}\right) \, \mathbf{a}_{2}+z_{9} \, \mathbf{a}_{3}$ | = | $- a x_{9} \,\mathbf{\hat{x}}+a x_{9} \,\mathbf{\hat{y}}- a z_{9} \,\mathbf{\hat{z}}$ | (48h) | O IV |
| $\mathbf{B_{47}}$ | = | $- \left(2 x_{9} + z_{9}\right) \, \mathbf{a}_{1}+\left(2 x_{9} - z_{9}\right) \, \mathbf{a}_{2}+z_{9} \, \mathbf{a}_{3}$ | = | $a x_{9} \,\mathbf{\hat{x}}- a x_{9} \,\mathbf{\hat{y}}- a z_{9} \,\mathbf{\hat{z}}$ | (48h) | O IV |
| $\mathbf{B_{48}}$ | = | $\left(2 x_{9} - z_{9}\right) \, \mathbf{a}_{1}+z_{9} \, \mathbf{a}_{2}+z_{9} \, \mathbf{a}_{3}$ | = | $a z_{9} \,\mathbf{\hat{x}}+a x_{9} \,\mathbf{\hat{y}}+a x_{9} \,\mathbf{\hat{z}}$ | (48h) | O IV |
| $\mathbf{B_{49}}$ | = | $- \left(2 x_{9} + z_{9}\right) \, \mathbf{a}_{1}+z_{9} \, \mathbf{a}_{2}+z_{9} \, \mathbf{a}_{3}$ | = | $a z_{9} \,\mathbf{\hat{x}}- a x_{9} \,\mathbf{\hat{y}}- a x_{9} \,\mathbf{\hat{z}}$ | (48h) | O IV |
| $\mathbf{B_{50}}$ | = | $z_{9} \, \mathbf{a}_{1}+\left(2 x_{9} - z_{9}\right) \, \mathbf{a}_{2}- \left(2 x_{9} + z_{9}\right) \, \mathbf{a}_{3}$ | = | $- a z_{9} \,\mathbf{\hat{x}}- a x_{9} \,\mathbf{\hat{y}}+a x_{9} \,\mathbf{\hat{z}}$ | (48h) | O IV |
| $\mathbf{B_{51}}$ | = | $z_{9} \, \mathbf{a}_{1}- \left(2 x_{9} + z_{9}\right) \, \mathbf{a}_{2}+\left(2 x_{9} - z_{9}\right) \, \mathbf{a}_{3}$ | = | $- a z_{9} \,\mathbf{\hat{x}}+a x_{9} \,\mathbf{\hat{y}}- a x_{9} \,\mathbf{\hat{z}}$ | (48h) | O IV |
| $\mathbf{B_{52}}$ | = | $z_{9} \, \mathbf{a}_{1}+\left(2 x_{9} - z_{9}\right) \, \mathbf{a}_{2}+z_{9} \, \mathbf{a}_{3}$ | = | $a x_{9} \,\mathbf{\hat{x}}+a z_{9} \,\mathbf{\hat{y}}+a x_{9} \,\mathbf{\hat{z}}$ | (48h) | O IV |
| $\mathbf{B_{53}}$ | = | $z_{9} \, \mathbf{a}_{1}- \left(2 x_{9} + z_{9}\right) \, \mathbf{a}_{2}+z_{9} \, \mathbf{a}_{3}$ | = | $- a x_{9} \,\mathbf{\hat{x}}+a z_{9} \,\mathbf{\hat{y}}- a x_{9} \,\mathbf{\hat{z}}$ | (48h) | O IV |
| $\mathbf{B_{54}}$ | = | $- \left(2 x_{9} + z_{9}\right) \, \mathbf{a}_{1}+z_{9} \, \mathbf{a}_{2}+\left(2 x_{9} - z_{9}\right) \, \mathbf{a}_{3}$ | = | $a x_{9} \,\mathbf{\hat{x}}- a z_{9} \,\mathbf{\hat{y}}- a x_{9} \,\mathbf{\hat{z}}$ | (48h) | O IV |
| $\mathbf{B_{55}}$ | = | $\left(2 x_{9} - z_{9}\right) \, \mathbf{a}_{1}+z_{9} \, \mathbf{a}_{2}- \left(2 x_{9} + z_{9}\right) \, \mathbf{a}_{3}$ | = | $- a x_{9} \,\mathbf{\hat{x}}- a z_{9} \,\mathbf{\hat{y}}+a x_{9} \,\mathbf{\hat{z}}$ | (48h) | O IV |
| $\mathbf{B_{56}}$ | = | $z_{10} \, \mathbf{a}_{1}+z_{10} \, \mathbf{a}_{2}+\left(2 x_{10} - z_{10}\right) \, \mathbf{a}_{3}$ | = | $a x_{10} \,\mathbf{\hat{x}}+a x_{10} \,\mathbf{\hat{y}}+a z_{10} \,\mathbf{\hat{z}}$ | (48h) | O V |
| $\mathbf{B_{57}}$ | = | $z_{10} \, \mathbf{a}_{1}+z_{10} \, \mathbf{a}_{2}- \left(2 x_{10} + z_{10}\right) \, \mathbf{a}_{3}$ | = | $- a x_{10} \,\mathbf{\hat{x}}- a x_{10} \,\mathbf{\hat{y}}+a z_{10} \,\mathbf{\hat{z}}$ | (48h) | O V |
| $\mathbf{B_{58}}$ | = | $\left(2 x_{10} - z_{10}\right) \, \mathbf{a}_{1}- \left(2 x_{10} + z_{10}\right) \, \mathbf{a}_{2}+z_{10} \, \mathbf{a}_{3}$ | = | $- a x_{10} \,\mathbf{\hat{x}}+a x_{10} \,\mathbf{\hat{y}}- a z_{10} \,\mathbf{\hat{z}}$ | (48h) | O V |
| $\mathbf{B_{59}}$ | = | $- \left(2 x_{10} + z_{10}\right) \, \mathbf{a}_{1}+\left(2 x_{10} - z_{10}\right) \, \mathbf{a}_{2}+z_{10} \, \mathbf{a}_{3}$ | = | $a x_{10} \,\mathbf{\hat{x}}- a x_{10} \,\mathbf{\hat{y}}- a z_{10} \,\mathbf{\hat{z}}$ | (48h) | O V |
| $\mathbf{B_{60}}$ | = | $\left(2 x_{10} - z_{10}\right) \, \mathbf{a}_{1}+z_{10} \, \mathbf{a}_{2}+z_{10} \, \mathbf{a}_{3}$ | = | $a z_{10} \,\mathbf{\hat{x}}+a x_{10} \,\mathbf{\hat{y}}+a x_{10} \,\mathbf{\hat{z}}$ | (48h) | O V |
| $\mathbf{B_{61}}$ | = | $- \left(2 x_{10} + z_{10}\right) \, \mathbf{a}_{1}+z_{10} \, \mathbf{a}_{2}+z_{10} \, \mathbf{a}_{3}$ | = | $a z_{10} \,\mathbf{\hat{x}}- a x_{10} \,\mathbf{\hat{y}}- a x_{10} \,\mathbf{\hat{z}}$ | (48h) | O V |
| $\mathbf{B_{62}}$ | = | $z_{10} \, \mathbf{a}_{1}+\left(2 x_{10} - z_{10}\right) \, \mathbf{a}_{2}- \left(2 x_{10} + z_{10}\right) \, \mathbf{a}_{3}$ | = | $- a z_{10} \,\mathbf{\hat{x}}- a x_{10} \,\mathbf{\hat{y}}+a x_{10} \,\mathbf{\hat{z}}$ | (48h) | O V |
| $\mathbf{B_{63}}$ | = | $z_{10} \, \mathbf{a}_{1}- \left(2 x_{10} + z_{10}\right) \, \mathbf{a}_{2}+\left(2 x_{10} - z_{10}\right) \, \mathbf{a}_{3}$ | = | $- a z_{10} \,\mathbf{\hat{x}}+a x_{10} \,\mathbf{\hat{y}}- a x_{10} \,\mathbf{\hat{z}}$ | (48h) | O V |
| $\mathbf{B_{64}}$ | = | $z_{10} \, \mathbf{a}_{1}+\left(2 x_{10} - z_{10}\right) \, \mathbf{a}_{2}+z_{10} \, \mathbf{a}_{3}$ | = | $a x_{10} \,\mathbf{\hat{x}}+a z_{10} \,\mathbf{\hat{y}}+a x_{10} \,\mathbf{\hat{z}}$ | (48h) | O V |
| $\mathbf{B_{65}}$ | = | $z_{10} \, \mathbf{a}_{1}- \left(2 x_{10} + z_{10}\right) \, \mathbf{a}_{2}+z_{10} \, \mathbf{a}_{3}$ | = | $- a x_{10} \,\mathbf{\hat{x}}+a z_{10} \,\mathbf{\hat{y}}- a x_{10} \,\mathbf{\hat{z}}$ | (48h) | O V |
| $\mathbf{B_{66}}$ | = | $- \left(2 x_{10} + z_{10}\right) \, \mathbf{a}_{1}+z_{10} \, \mathbf{a}_{2}+\left(2 x_{10} - z_{10}\right) \, \mathbf{a}_{3}$ | = | $a x_{10} \,\mathbf{\hat{x}}- a z_{10} \,\mathbf{\hat{y}}- a x_{10} \,\mathbf{\hat{z}}$ | (48h) | O V |
| $\mathbf{B_{67}}$ | = | $\left(2 x_{10} - z_{10}\right) \, \mathbf{a}_{1}+z_{10} \, \mathbf{a}_{2}- \left(2 x_{10} + z_{10}\right) \, \mathbf{a}_{3}$ | = | $- a x_{10} \,\mathbf{\hat{x}}- a z_{10} \,\mathbf{\hat{y}}+a x_{10} \,\mathbf{\hat{z}}$ | (48h) | O V |
| $\mathbf{B_{68}}$ | = | $z_{11} \, \mathbf{a}_{1}+z_{11} \, \mathbf{a}_{2}+\left(2 x_{11} - z_{11}\right) \, \mathbf{a}_{3}$ | = | $a x_{11} \,\mathbf{\hat{x}}+a x_{11} \,\mathbf{\hat{y}}+a z_{11} \,\mathbf{\hat{z}}$ | (48h) | Ti I |
| $\mathbf{B_{69}}$ | = | $z_{11} \, \mathbf{a}_{1}+z_{11} \, \mathbf{a}_{2}- \left(2 x_{11} + z_{11}\right) \, \mathbf{a}_{3}$ | = | $- a x_{11} \,\mathbf{\hat{x}}- a x_{11} \,\mathbf{\hat{y}}+a z_{11} \,\mathbf{\hat{z}}$ | (48h) | Ti I |
| $\mathbf{B_{70}}$ | = | $\left(2 x_{11} - z_{11}\right) \, \mathbf{a}_{1}- \left(2 x_{11} + z_{11}\right) \, \mathbf{a}_{2}+z_{11} \, \mathbf{a}_{3}$ | = | $- a x_{11} \,\mathbf{\hat{x}}+a x_{11} \,\mathbf{\hat{y}}- a z_{11} \,\mathbf{\hat{z}}$ | (48h) | Ti I |
| $\mathbf{B_{71}}$ | = | $- \left(2 x_{11} + z_{11}\right) \, \mathbf{a}_{1}+\left(2 x_{11} - z_{11}\right) \, \mathbf{a}_{2}+z_{11} \, \mathbf{a}_{3}$ | = | $a x_{11} \,\mathbf{\hat{x}}- a x_{11} \,\mathbf{\hat{y}}- a z_{11} \,\mathbf{\hat{z}}$ | (48h) | Ti I |
| $\mathbf{B_{72}}$ | = | $\left(2 x_{11} - z_{11}\right) \, \mathbf{a}_{1}+z_{11} \, \mathbf{a}_{2}+z_{11} \, \mathbf{a}_{3}$ | = | $a z_{11} \,\mathbf{\hat{x}}+a x_{11} \,\mathbf{\hat{y}}+a x_{11} \,\mathbf{\hat{z}}$ | (48h) | Ti I |
| $\mathbf{B_{73}}$ | = | $- \left(2 x_{11} + z_{11}\right) \, \mathbf{a}_{1}+z_{11} \, \mathbf{a}_{2}+z_{11} \, \mathbf{a}_{3}$ | = | $a z_{11} \,\mathbf{\hat{x}}- a x_{11} \,\mathbf{\hat{y}}- a x_{11} \,\mathbf{\hat{z}}$ | (48h) | Ti I |
| $\mathbf{B_{74}}$ | = | $z_{11} \, \mathbf{a}_{1}+\left(2 x_{11} - z_{11}\right) \, \mathbf{a}_{2}- \left(2 x_{11} + z_{11}\right) \, \mathbf{a}_{3}$ | = | $- a z_{11} \,\mathbf{\hat{x}}- a x_{11} \,\mathbf{\hat{y}}+a x_{11} \,\mathbf{\hat{z}}$ | (48h) | Ti I |
| $\mathbf{B_{75}}$ | = | $z_{11} \, \mathbf{a}_{1}- \left(2 x_{11} + z_{11}\right) \, \mathbf{a}_{2}+\left(2 x_{11} - z_{11}\right) \, \mathbf{a}_{3}$ | = | $- a z_{11} \,\mathbf{\hat{x}}+a x_{11} \,\mathbf{\hat{y}}- a x_{11} \,\mathbf{\hat{z}}$ | (48h) | Ti I |
| $\mathbf{B_{76}}$ | = | $z_{11} \, \mathbf{a}_{1}+\left(2 x_{11} - z_{11}\right) \, \mathbf{a}_{2}+z_{11} \, \mathbf{a}_{3}$ | = | $a x_{11} \,\mathbf{\hat{x}}+a z_{11} \,\mathbf{\hat{y}}+a x_{11} \,\mathbf{\hat{z}}$ | (48h) | Ti I |
| $\mathbf{B_{77}}$ | = | $z_{11} \, \mathbf{a}_{1}- \left(2 x_{11} + z_{11}\right) \, \mathbf{a}_{2}+z_{11} \, \mathbf{a}_{3}$ | = | $- a x_{11} \,\mathbf{\hat{x}}+a z_{11} \,\mathbf{\hat{y}}- a x_{11} \,\mathbf{\hat{z}}$ | (48h) | Ti I |
| $\mathbf{B_{78}}$ | = | $- \left(2 x_{11} + z_{11}\right) \, \mathbf{a}_{1}+z_{11} \, \mathbf{a}_{2}+\left(2 x_{11} - z_{11}\right) \, \mathbf{a}_{3}$ | = | $a x_{11} \,\mathbf{\hat{x}}- a z_{11} \,\mathbf{\hat{y}}- a x_{11} \,\mathbf{\hat{z}}$ | (48h) | Ti I |
| $\mathbf{B_{79}}$ | = | $\left(2 x_{11} - z_{11}\right) \, \mathbf{a}_{1}+z_{11} \, \mathbf{a}_{2}- \left(2 x_{11} + z_{11}\right) \, \mathbf{a}_{3}$ | = | $- a x_{11} \,\mathbf{\hat{x}}- a z_{11} \,\mathbf{\hat{y}}+a x_{11} \,\mathbf{\hat{z}}$ | (48h) | Ti I |
References
- T. S. Ercit and F. C. Hawthorne, Murataite, A UB$_{12}$ derivative structure with condensed Keggin molecules, Can. Mineral. 33, 1233–1229 (1995).
- R. T. Downs and M. Hall-Wallace, The American Mineralogist Crystal Structure Database, Am. Mineral. 88, 247–250 (2003).
Prototype Generator
aflow --proto=A16B40C12D6E5_cF316_216_eh_e2g2h_h_f_ae --params=$a,x_{2},x_{3},x_{4},x_{5},x_{6},x_{7},x_{8},z_{8},x_{9},z_{9},x_{10},z_{10},x_{11},z_{11}$