$H5_{6}$ [Tychite, Na$_{6}$Mg$_{2}$SO$_{4}$(CO$_{3}$)$_{4}$)] Structure (Obsolete): A4B2C6D16E_cF232_227_e_c_f_eg_b-001
| Prototype | C$_{4}$Mg$_{2}$Na$_{6}$O$_{16}$S |
| AFLOW prototype label | A4B2C6D16E_cF232_227_e_c_f_eg_b-001 |
| Strukturbericht designation | $H5_{6}$ |
| Mineral name | tychite |
| ICSD | 27792 |
| Pearson symbol | cF232 |
| Space group number | 227 |
| Space group symbol | $Fd\overline{3}m$ |
| AFLOW prototype command |
aflow --proto=A4B2C6D16E_cF232_227_e_c_f_eg_b-001
--params=$a, \allowbreak x_{3}, \allowbreak x_{4}, \allowbreak x_{5}, \allowbreak x_{6}, \allowbreak z_{6}$ |
- This is the original structure determined by (Shiba, 1931) and given the designation $H5_{6}$ in (Hermann, 1937). (Schmidt, 2006) showed that the true structure is in space group $Fd\overline{3}$ #203, however the two structures are very similar, and a displacement of the oxygen atoms by less than 1Å brings the two structures into agreement.
- (Hermann, 1937) gives the chemical formula as Na$_{6}$Mg$_{2}$SO$_{4}$(CO$_{3}$)$_{2}$, but the given Wyckoff positions are in agreement with the correct formula, Na$_{6}$Mg$_{2}$SO$_{4}$(CO$_{3}$)$_{4}$.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $\frac{3}{8} \, \mathbf{a}_{1}+\frac{3}{8} \, \mathbf{a}_{2}+\frac{3}{8} \, \mathbf{a}_{3}$ | = | $\frac{3}{8}a \,\mathbf{\hat{x}}+\frac{3}{8}a \,\mathbf{\hat{y}}+\frac{3}{8}a \,\mathbf{\hat{z}}$ | (8b) | S I |
| $\mathbf{B_{2}}$ | = | $\frac{5}{8} \, \mathbf{a}_{1}+\frac{5}{8} \, \mathbf{a}_{2}+\frac{5}{8} \, \mathbf{a}_{3}$ | = | $\frac{5}{8}a \,\mathbf{\hat{x}}+\frac{5}{8}a \,\mathbf{\hat{y}}+\frac{5}{8}a \,\mathbf{\hat{z}}$ | (8b) | S I |
| $\mathbf{B_{3}}$ | = | $0$ | = | $0$ | (16c) | Mg I |
| $\mathbf{B_{4}}$ | = | $\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}$ | (16c) | Mg I |
| $\mathbf{B_{5}}$ | = | $\frac{1}{2} \, \mathbf{a}_{2}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (16c) | Mg I |
| $\mathbf{B_{6}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}$ | = | $\frac{1}{4}a \,\mathbf{\hat{y}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (16c) | Mg I |
| $\mathbf{B_{7}}$ | = | $x_{3} \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{2}+x_{3} \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{x}}+a x_{3} \,\mathbf{\hat{y}}+a x_{3} \,\mathbf{\hat{z}}$ | (32e) | C I |
| $\mathbf{B_{8}}$ | = | $x_{3} \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{2}- \left(3 x_{3} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{3} - \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(x_{3} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a x_{3} \,\mathbf{\hat{z}}$ | (32e) | C I |
| $\mathbf{B_{9}}$ | = | $x_{3} \, \mathbf{a}_{1}- \left(3 x_{3} - \frac{1}{2}\right) \, \mathbf{a}_{2}+x_{3} \, \mathbf{a}_{3}$ | = | $- a \left(x_{3} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a x_{3} \,\mathbf{\hat{y}}- a \left(x_{3} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (32e) | C I |
| $\mathbf{B_{10}}$ | = | $- \left(3 x_{3} - \frac{1}{2}\right) \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{2}+x_{3} \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{x}}- a \left(x_{3} - \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(x_{3} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (32e) | C I |
| $\mathbf{B_{11}}$ | = | $- x_{3} \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}+\left(3 x_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{3} + \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(x_{3} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a x_{3} \,\mathbf{\hat{z}}$ | (32e) | C I |
| $\mathbf{B_{12}}$ | = | $- x_{3} \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}- x_{3} \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}- a x_{3} \,\mathbf{\hat{y}}- a x_{3} \,\mathbf{\hat{z}}$ | (32e) | C I |
| $\mathbf{B_{13}}$ | = | $- x_{3} \, \mathbf{a}_{1}+\left(3 x_{3} + \frac{1}{2}\right) \, \mathbf{a}_{2}- x_{3} \, \mathbf{a}_{3}$ | = | $a \left(x_{3} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a x_{3} \,\mathbf{\hat{y}}+a \left(x_{3} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (32e) | C I |
| $\mathbf{B_{14}}$ | = | $\left(3 x_{3} + \frac{1}{2}\right) \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}- x_{3} \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}+a \left(x_{3} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(x_{3} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (32e) | C I |
| $\mathbf{B_{15}}$ | = | $x_{4} \, \mathbf{a}_{1}+x_{4} \, \mathbf{a}_{2}+x_{4} \, \mathbf{a}_{3}$ | = | $a x_{4} \,\mathbf{\hat{x}}+a x_{4} \,\mathbf{\hat{y}}+a x_{4} \,\mathbf{\hat{z}}$ | (32e) | O I |
| $\mathbf{B_{16}}$ | = | $x_{4} \, \mathbf{a}_{1}+x_{4} \, \mathbf{a}_{2}- \left(3 x_{4} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{4} - \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(x_{4} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a x_{4} \,\mathbf{\hat{z}}$ | (32e) | O I |
| $\mathbf{B_{17}}$ | = | $x_{4} \, \mathbf{a}_{1}- \left(3 x_{4} - \frac{1}{2}\right) \, \mathbf{a}_{2}+x_{4} \, \mathbf{a}_{3}$ | = | $- a \left(x_{4} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a x_{4} \,\mathbf{\hat{y}}- a \left(x_{4} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (32e) | O I |
| $\mathbf{B_{18}}$ | = | $- \left(3 x_{4} - \frac{1}{2}\right) \, \mathbf{a}_{1}+x_{4} \, \mathbf{a}_{2}+x_{4} \, \mathbf{a}_{3}$ | = | $a x_{4} \,\mathbf{\hat{x}}- a \left(x_{4} - \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(x_{4} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (32e) | O I |
| $\mathbf{B_{19}}$ | = | $- x_{4} \, \mathbf{a}_{1}- x_{4} \, \mathbf{a}_{2}+\left(3 x_{4} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{4} + \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(x_{4} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a x_{4} \,\mathbf{\hat{z}}$ | (32e) | O I |
| $\mathbf{B_{20}}$ | = | $- x_{4} \, \mathbf{a}_{1}- x_{4} \, \mathbf{a}_{2}- x_{4} \, \mathbf{a}_{3}$ | = | $- a x_{4} \,\mathbf{\hat{x}}- a x_{4} \,\mathbf{\hat{y}}- a x_{4} \,\mathbf{\hat{z}}$ | (32e) | O I |
| $\mathbf{B_{21}}$ | = | $- x_{4} \, \mathbf{a}_{1}+\left(3 x_{4} + \frac{1}{2}\right) \, \mathbf{a}_{2}- x_{4} \, \mathbf{a}_{3}$ | = | $a \left(x_{4} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a x_{4} \,\mathbf{\hat{y}}+a \left(x_{4} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (32e) | O I |
| $\mathbf{B_{22}}$ | = | $\left(3 x_{4} + \frac{1}{2}\right) \, \mathbf{a}_{1}- x_{4} \, \mathbf{a}_{2}- x_{4} \, \mathbf{a}_{3}$ | = | $- a x_{4} \,\mathbf{\hat{x}}+a \left(x_{4} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(x_{4} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (32e) | O I |
| $\mathbf{B_{23}}$ | = | $- \left(x_{5} - \frac{1}{4}\right) \, \mathbf{a}_{1}+x_{5} \, \mathbf{a}_{2}+x_{5} \, \mathbf{a}_{3}$ | = | $a x_{5} \,\mathbf{\hat{x}}+\frac{1}{8}a \,\mathbf{\hat{y}}+\frac{1}{8}a \,\mathbf{\hat{z}}$ | (48f) | Na I |
| $\mathbf{B_{24}}$ | = | $x_{5} \, \mathbf{a}_{1}- \left(x_{5} - \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(x_{5} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{5} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+\frac{1}{8}a \,\mathbf{\hat{y}}+\frac{1}{8}a \,\mathbf{\hat{z}}$ | (48f) | Na I |
| $\mathbf{B_{25}}$ | = | $x_{5} \, \mathbf{a}_{1}- \left(x_{5} - \frac{1}{4}\right) \, \mathbf{a}_{2}+x_{5} \, \mathbf{a}_{3}$ | = | $\frac{1}{8}a \,\mathbf{\hat{x}}+a x_{5} \,\mathbf{\hat{y}}+\frac{1}{8}a \,\mathbf{\hat{z}}$ | (48f) | Na I |
| $\mathbf{B_{26}}$ | = | $- \left(x_{5} - \frac{1}{4}\right) \, \mathbf{a}_{1}+x_{5} \, \mathbf{a}_{2}- \left(x_{5} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{8}a \,\mathbf{\hat{x}}- a \left(x_{5} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+\frac{1}{8}a \,\mathbf{\hat{z}}$ | (48f) | Na I |
| $\mathbf{B_{27}}$ | = | $x_{5} \, \mathbf{a}_{1}+x_{5} \, \mathbf{a}_{2}- \left(x_{5} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{8}a \,\mathbf{\hat{x}}+\frac{1}{8}a \,\mathbf{\hat{y}}+a x_{5} \,\mathbf{\hat{z}}$ | (48f) | Na I |
| $\mathbf{B_{28}}$ | = | $- \left(x_{5} - \frac{1}{4}\right) \, \mathbf{a}_{1}- \left(x_{5} - \frac{1}{4}\right) \, \mathbf{a}_{2}+x_{5} \, \mathbf{a}_{3}$ | = | $\frac{1}{8}a \,\mathbf{\hat{x}}+\frac{1}{8}a \,\mathbf{\hat{y}}- a \left(x_{5} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (48f) | Na I |
| $\mathbf{B_{29}}$ | = | $\left(x_{5} + \frac{3}{4}\right) \, \mathbf{a}_{1}- x_{5} \, \mathbf{a}_{2}+\left(x_{5} + \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $\frac{3}{8}a \,\mathbf{\hat{x}}+a \left(x_{5} + \frac{3}{4}\right) \,\mathbf{\hat{y}}+\frac{3}{8}a \,\mathbf{\hat{z}}$ | (48f) | Na I |
| $\mathbf{B_{30}}$ | = | $- x_{5} \, \mathbf{a}_{1}+\left(x_{5} + \frac{3}{4}\right) \, \mathbf{a}_{2}- x_{5} \, \mathbf{a}_{3}$ | = | $\frac{3}{8}a \,\mathbf{\hat{x}}- a x_{5} \,\mathbf{\hat{y}}+\frac{3}{8}a \,\mathbf{\hat{z}}$ | (48f) | Na I |
| $\mathbf{B_{31}}$ | = | $- x_{5} \, \mathbf{a}_{1}+\left(x_{5} + \frac{3}{4}\right) \, \mathbf{a}_{2}+\left(x_{5} + \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{5} + \frac{3}{4}\right) \,\mathbf{\hat{x}}+\frac{3}{8}a \,\mathbf{\hat{y}}+\frac{3}{8}a \,\mathbf{\hat{z}}$ | (48f) | Na I |
| $\mathbf{B_{32}}$ | = | $\left(x_{5} + \frac{3}{4}\right) \, \mathbf{a}_{1}- x_{5} \, \mathbf{a}_{2}- x_{5} \, \mathbf{a}_{3}$ | = | $- a x_{5} \,\mathbf{\hat{x}}+\frac{3}{8}a \,\mathbf{\hat{y}}+\frac{3}{8}a \,\mathbf{\hat{z}}$ | (48f) | Na I |
| $\mathbf{B_{33}}$ | = | $- x_{5} \, \mathbf{a}_{1}- x_{5} \, \mathbf{a}_{2}+\left(x_{5} + \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $\frac{3}{8}a \,\mathbf{\hat{x}}+\frac{3}{8}a \,\mathbf{\hat{y}}- a x_{5} \,\mathbf{\hat{z}}$ | (48f) | Na I |
| $\mathbf{B_{34}}$ | = | $\left(x_{5} + \frac{3}{4}\right) \, \mathbf{a}_{1}+\left(x_{5} + \frac{3}{4}\right) \, \mathbf{a}_{2}- x_{5} \, \mathbf{a}_{3}$ | = | $\frac{3}{8}a \,\mathbf{\hat{x}}+\frac{3}{8}a \,\mathbf{\hat{y}}+a \left(x_{5} + \frac{3}{4}\right) \,\mathbf{\hat{z}}$ | (48f) | Na I |
| $\mathbf{B_{35}}$ | = | $z_{6} \, \mathbf{a}_{1}+z_{6} \, \mathbf{a}_{2}+\left(2 x_{6} - z_{6}\right) \, \mathbf{a}_{3}$ | = | $a x_{6} \,\mathbf{\hat{x}}+a x_{6} \,\mathbf{\hat{y}}+a z_{6} \,\mathbf{\hat{z}}$ | (96g) | O II |
| $\mathbf{B_{36}}$ | = | $z_{6} \, \mathbf{a}_{1}+z_{6} \, \mathbf{a}_{2}- \left(2 x_{6} + z_{6} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{6} - \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(x_{6} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a z_{6} \,\mathbf{\hat{z}}$ | (96g) | O II |
| $\mathbf{B_{37}}$ | = | $\left(2 x_{6} - z_{6}\right) \, \mathbf{a}_{1}- \left(2 x_{6} + z_{6} - \frac{1}{2}\right) \, \mathbf{a}_{2}+z_{6} \, \mathbf{a}_{3}$ | = | $- a \left(x_{6} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a x_{6} \,\mathbf{\hat{y}}- a \left(z_{6} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96g) | O II |
| $\mathbf{B_{38}}$ | = | $- \left(2 x_{6} + z_{6} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(2 x_{6} - z_{6}\right) \, \mathbf{a}_{2}+z_{6} \, \mathbf{a}_{3}$ | = | $a x_{6} \,\mathbf{\hat{x}}- a \left(x_{6} - \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(z_{6} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96g) | O II |
| $\mathbf{B_{39}}$ | = | $\left(2 x_{6} - z_{6}\right) \, \mathbf{a}_{1}+z_{6} \, \mathbf{a}_{2}+z_{6} \, \mathbf{a}_{3}$ | = | $a z_{6} \,\mathbf{\hat{x}}+a x_{6} \,\mathbf{\hat{y}}+a x_{6} \,\mathbf{\hat{z}}$ | (96g) | O II |
| $\mathbf{B_{40}}$ | = | $- \left(2 x_{6} + z_{6} - \frac{1}{2}\right) \, \mathbf{a}_{1}+z_{6} \, \mathbf{a}_{2}+z_{6} \, \mathbf{a}_{3}$ | = | $a z_{6} \,\mathbf{\hat{x}}- a \left(x_{6} - \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(x_{6} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96g) | O II |
| $\mathbf{B_{41}}$ | = | $z_{6} \, \mathbf{a}_{1}+\left(2 x_{6} - z_{6}\right) \, \mathbf{a}_{2}- \left(2 x_{6} + z_{6} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(z_{6} - \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(x_{6} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a x_{6} \,\mathbf{\hat{z}}$ | (96g) | O II |
| $\mathbf{B_{42}}$ | = | $z_{6} \, \mathbf{a}_{1}- \left(2 x_{6} + z_{6} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(2 x_{6} - z_{6}\right) \, \mathbf{a}_{3}$ | = | $- a \left(z_{6} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a x_{6} \,\mathbf{\hat{y}}- a \left(x_{6} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96g) | O II |
| $\mathbf{B_{43}}$ | = | $z_{6} \, \mathbf{a}_{1}+\left(2 x_{6} - z_{6}\right) \, \mathbf{a}_{2}+z_{6} \, \mathbf{a}_{3}$ | = | $a x_{6} \,\mathbf{\hat{x}}+a z_{6} \,\mathbf{\hat{y}}+a x_{6} \,\mathbf{\hat{z}}$ | (96g) | O II |
| $\mathbf{B_{44}}$ | = | $z_{6} \, \mathbf{a}_{1}- \left(2 x_{6} + z_{6} - \frac{1}{2}\right) \, \mathbf{a}_{2}+z_{6} \, \mathbf{a}_{3}$ | = | $- a \left(x_{6} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a z_{6} \,\mathbf{\hat{y}}- a \left(x_{6} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96g) | O II |
| $\mathbf{B_{45}}$ | = | $- \left(2 x_{6} + z_{6} - \frac{1}{2}\right) \, \mathbf{a}_{1}+z_{6} \, \mathbf{a}_{2}+\left(2 x_{6} - z_{6}\right) \, \mathbf{a}_{3}$ | = | $a x_{6} \,\mathbf{\hat{x}}- a \left(z_{6} - \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(x_{6} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96g) | O II |
| $\mathbf{B_{46}}$ | = | $\left(2 x_{6} - z_{6}\right) \, \mathbf{a}_{1}+z_{6} \, \mathbf{a}_{2}- \left(2 x_{6} + z_{6} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{6} - \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(z_{6} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a x_{6} \,\mathbf{\hat{z}}$ | (96g) | O II |
| $\mathbf{B_{47}}$ | = | $- z_{6} \, \mathbf{a}_{1}- z_{6} \, \mathbf{a}_{2}+\left(2 x_{6} + z_{6} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{6} + \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(x_{6} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a z_{6} \,\mathbf{\hat{z}}$ | (96g) | O II |
| $\mathbf{B_{48}}$ | = | $- z_{6} \, \mathbf{a}_{1}- z_{6} \, \mathbf{a}_{2}- \left(2 x_{6} - z_{6}\right) \, \mathbf{a}_{3}$ | = | $- a x_{6} \,\mathbf{\hat{x}}- a x_{6} \,\mathbf{\hat{y}}- a z_{6} \,\mathbf{\hat{z}}$ | (96g) | O II |
| $\mathbf{B_{49}}$ | = | $- \left(2 x_{6} - z_{6}\right) \, \mathbf{a}_{1}+\left(2 x_{6} + z_{6} + \frac{1}{2}\right) \, \mathbf{a}_{2}- z_{6} \, \mathbf{a}_{3}$ | = | $a \left(x_{6} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a x_{6} \,\mathbf{\hat{y}}+a \left(z_{6} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96g) | O II |
| $\mathbf{B_{50}}$ | = | $\left(2 x_{6} + z_{6} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(2 x_{6} - z_{6}\right) \, \mathbf{a}_{2}- z_{6} \, \mathbf{a}_{3}$ | = | $- a x_{6} \,\mathbf{\hat{x}}+a \left(x_{6} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(z_{6} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96g) | O II |
| $\mathbf{B_{51}}$ | = | $- \left(2 x_{6} - z_{6}\right) \, \mathbf{a}_{1}- z_{6} \, \mathbf{a}_{2}+\left(2 x_{6} + z_{6} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{6} + \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(z_{6} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a x_{6} \,\mathbf{\hat{z}}$ | (96g) | O II |
| $\mathbf{B_{52}}$ | = | $\left(2 x_{6} + z_{6} + \frac{1}{2}\right) \, \mathbf{a}_{1}- z_{6} \, \mathbf{a}_{2}- \left(2 x_{6} - z_{6}\right) \, \mathbf{a}_{3}$ | = | $- a x_{6} \,\mathbf{\hat{x}}+a \left(z_{6} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(x_{6} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96g) | O II |
| $\mathbf{B_{53}}$ | = | $- z_{6} \, \mathbf{a}_{1}- \left(2 x_{6} - z_{6}\right) \, \mathbf{a}_{2}- z_{6} \, \mathbf{a}_{3}$ | = | $- a x_{6} \,\mathbf{\hat{x}}- a z_{6} \,\mathbf{\hat{y}}- a x_{6} \,\mathbf{\hat{z}}$ | (96g) | O II |
| $\mathbf{B_{54}}$ | = | $- z_{6} \, \mathbf{a}_{1}+\left(2 x_{6} + z_{6} + \frac{1}{2}\right) \, \mathbf{a}_{2}- z_{6} \, \mathbf{a}_{3}$ | = | $a \left(x_{6} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a z_{6} \,\mathbf{\hat{y}}+a \left(x_{6} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96g) | O II |
| $\mathbf{B_{55}}$ | = | $- z_{6} \, \mathbf{a}_{1}- \left(2 x_{6} - z_{6}\right) \, \mathbf{a}_{2}+\left(2 x_{6} + z_{6} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(z_{6} + \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(x_{6} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a x_{6} \,\mathbf{\hat{z}}$ | (96g) | O II |
| $\mathbf{B_{56}}$ | = | $- z_{6} \, \mathbf{a}_{1}+\left(2 x_{6} + z_{6} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(2 x_{6} - z_{6}\right) \, \mathbf{a}_{3}$ | = | $a \left(z_{6} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a x_{6} \,\mathbf{\hat{y}}+a \left(x_{6} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96g) | O II |
| $\mathbf{B_{57}}$ | = | $\left(2 x_{6} + z_{6} + \frac{1}{2}\right) \, \mathbf{a}_{1}- z_{6} \, \mathbf{a}_{2}- z_{6} \, \mathbf{a}_{3}$ | = | $- a z_{6} \,\mathbf{\hat{x}}+a \left(x_{6} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(x_{6} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96g) | O II |
| $\mathbf{B_{58}}$ | = | $- \left(2 x_{6} - z_{6}\right) \, \mathbf{a}_{1}- z_{6} \, \mathbf{a}_{2}- z_{6} \, \mathbf{a}_{3}$ | = | $- a z_{6} \,\mathbf{\hat{x}}- a x_{6} \,\mathbf{\hat{y}}- a x_{6} \,\mathbf{\hat{z}}$ | (96g) | O II |
References
- H. Shiba and T. Watanabé, Les structures des cristaux de northupite, de northupite bromée et de tychite, Compt. Rend. 193, 1421–1423 (1931).
- C. Hermann, O. Lohrmann, and H. Philipp, eds., Strukturbericht Band II 1928-1932 (Akademische Verlagsgesellschaft M. B. H., Leipzig, 1937).
Found in
- G. R. Schmidt, R. Jacqueline, H. Yang, and R. T. Downs, Tychite, Na$_{6}$Mg$_{2}$(SO$_{4}$)(CO$_{3}$)$_{4}$: Structure analysis and Raman spectroscopic data, Acta Crystallogr. Sect. E 62, i207–i209 (2006), doi:10.1107/S160053680603491X.
Prototype Generator
aflow --proto=A4B2C6D16E_cF232_227_e_c_f_eg_b --params=$a,x_{3},x_{4},x_{5},x_{6},z_{6}$