Na$_{5}$Co$_{15.5}$Te$_{6}$O$_{36}$ (NCTO) Structure: A7B5C18D3_hP66_176_ci_bef_2h2i_h-001
| Prototype | Co$_{15.5}$Na$_{5}$O$_{36}$Te$_{6}$ |
| AFLOW prototype label | A7B5C18D3_hP66_176_ci_bef_2h2i_h-001 |
| Mineral name | NCTO |
| ICSD | none |
| Pearson symbol | hP66 |
| Space group number | 176 |
| Space group symbol | $P6_3/m$ |
| AFLOW prototype command |
aflow --proto=A7B5C18D3_hP66_176_ci_bef_2h2i_h-001
--params=$a, \allowbreak c/a, \allowbreak z_{3}, \allowbreak z_{4}, \allowbreak x_{5}, \allowbreak y_{5}, \allowbreak x_{6}, \allowbreak y_{6}, \allowbreak x_{7}, \allowbreak y_{7}, \allowbreak x_{8}, \allowbreak y_{8}, \allowbreak z_{8}, \allowbreak x_{9}, \allowbreak y_{9}, \allowbreak z_{9}, \allowbreak x_{10}, \allowbreak y_{10}, \allowbreak z_{10}$ |
- (Saha, 2021) set the $z$-coordinate of the tellurium atom to zero, but this is not consistent with the stoichiometry of the system. We set $z = 1/4$, putting the tellurium atom on a (6h) site.
- Several sites have only partial or mixed occupations: The Na-I (2b) site is 30% occupied. The Na-II (4e) site is 50% occupied. The Na-III (4f) site is 63% sodium and 37% cobalt, which we show as pure sodium.
- FINDSYM rotated the system so that the Co-I atom is on the (2c) Wyckoff position rather than the (2d) position given by (Saha, 2021).
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \,\mathbf{\hat{y}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $0$ | = | $0$ | (2b) | Na I |
| $\mathbf{B_{2}}$ | = | $\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}c \,\mathbf{\hat{z}}$ | (2b) | Na I |
| $\mathbf{B_{3}}$ | = | $\frac{1}{3} \, \mathbf{a}_{1}+\frac{2}{3} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (2c) | Co I |
| $\mathbf{B_{4}}$ | = | $\frac{2}{3} \, \mathbf{a}_{1}+\frac{1}{3} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ | (2c) | Co I |
| $\mathbf{B_{5}}$ | = | $z_{3} \, \mathbf{a}_{3}$ | = | $c z_{3} \,\mathbf{\hat{z}}$ | (4e) | Na II |
| $\mathbf{B_{6}}$ | = | $\left(z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $c \left(z_{3} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4e) | Na II |
| $\mathbf{B_{7}}$ | = | $- z_{3} \, \mathbf{a}_{3}$ | = | $- c z_{3} \,\mathbf{\hat{z}}$ | (4e) | Na II |
| $\mathbf{B_{8}}$ | = | $- \left(z_{3} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- c \left(z_{3} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4e) | Na II |
| $\mathbf{B_{9}}$ | = | $\frac{1}{3} \, \mathbf{a}_{1}+\frac{2}{3} \, \mathbf{a}_{2}+z_{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+c z_{4} \,\mathbf{\hat{z}}$ | (4f) | Na III |
| $\mathbf{B_{10}}$ | = | $\frac{2}{3} \, \mathbf{a}_{1}+\frac{1}{3} \, \mathbf{a}_{2}+\left(z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+c \left(z_{4} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4f) | Na III |
| $\mathbf{B_{11}}$ | = | $\frac{2}{3} \, \mathbf{a}_{1}+\frac{1}{3} \, \mathbf{a}_{2}- z_{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}- c z_{4} \,\mathbf{\hat{z}}$ | (4f) | Na III |
| $\mathbf{B_{12}}$ | = | $\frac{1}{3} \, \mathbf{a}_{1}+\frac{2}{3} \, \mathbf{a}_{2}- \left(z_{4} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}- c \left(z_{4} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4f) | Na III |
| $\mathbf{B_{13}}$ | = | $x_{5} \, \mathbf{a}_{1}+y_{5} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{5} + y_{5}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \left(x_{5} - y_{5}\right) \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (6h) | O I |
| $\mathbf{B_{14}}$ | = | $- y_{5} \, \mathbf{a}_{1}+\left(x_{5} - y_{5}\right) \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{5} - 2 y_{5}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{5} \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (6h) | O I |
| $\mathbf{B_{15}}$ | = | $- \left(x_{5} - y_{5}\right) \, \mathbf{a}_{1}- x_{5} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(2 x_{5} - y_{5}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a y_{5} \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (6h) | O I |
| $\mathbf{B_{16}}$ | = | $- x_{5} \, \mathbf{a}_{1}- y_{5} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{5} + y_{5}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \left(x_{5} - y_{5}\right) \,\mathbf{\hat{y}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ | (6h) | O I |
| $\mathbf{B_{17}}$ | = | $y_{5} \, \mathbf{a}_{1}- \left(x_{5} - y_{5}\right) \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(- x_{5} + 2 y_{5}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{5} \,\mathbf{\hat{y}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ | (6h) | O I |
| $\mathbf{B_{18}}$ | = | $\left(x_{5} - y_{5}\right) \, \mathbf{a}_{1}+x_{5} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(2 x_{5} - y_{5}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a y_{5} \,\mathbf{\hat{y}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ | (6h) | O I |
| $\mathbf{B_{19}}$ | = | $x_{6} \, \mathbf{a}_{1}+y_{6} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{6} + y_{6}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \left(x_{6} - y_{6}\right) \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (6h) | O II |
| $\mathbf{B_{20}}$ | = | $- y_{6} \, \mathbf{a}_{1}+\left(x_{6} - y_{6}\right) \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{6} - 2 y_{6}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{6} \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (6h) | O II |
| $\mathbf{B_{21}}$ | = | $- \left(x_{6} - y_{6}\right) \, \mathbf{a}_{1}- x_{6} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(2 x_{6} - y_{6}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a y_{6} \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (6h) | O II |
| $\mathbf{B_{22}}$ | = | $- x_{6} \, \mathbf{a}_{1}- y_{6} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{6} + y_{6}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \left(x_{6} - y_{6}\right) \,\mathbf{\hat{y}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ | (6h) | O II |
| $\mathbf{B_{23}}$ | = | $y_{6} \, \mathbf{a}_{1}- \left(x_{6} - y_{6}\right) \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(- x_{6} + 2 y_{6}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{6} \,\mathbf{\hat{y}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ | (6h) | O II |
| $\mathbf{B_{24}}$ | = | $\left(x_{6} - y_{6}\right) \, \mathbf{a}_{1}+x_{6} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(2 x_{6} - y_{6}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a y_{6} \,\mathbf{\hat{y}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ | (6h) | O II |
| $\mathbf{B_{25}}$ | = | $x_{7} \, \mathbf{a}_{1}+y_{7} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{7} + y_{7}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \left(x_{7} - y_{7}\right) \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (6h) | Te I |
| $\mathbf{B_{26}}$ | = | $- y_{7} \, \mathbf{a}_{1}+\left(x_{7} - y_{7}\right) \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{7} - 2 y_{7}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{7} \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (6h) | Te I |
| $\mathbf{B_{27}}$ | = | $- \left(x_{7} - y_{7}\right) \, \mathbf{a}_{1}- x_{7} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(2 x_{7} - y_{7}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a y_{7} \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (6h) | Te I |
| $\mathbf{B_{28}}$ | = | $- x_{7} \, \mathbf{a}_{1}- y_{7} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{7} + y_{7}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \left(x_{7} - y_{7}\right) \,\mathbf{\hat{y}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ | (6h) | Te I |
| $\mathbf{B_{29}}$ | = | $y_{7} \, \mathbf{a}_{1}- \left(x_{7} - y_{7}\right) \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(- x_{7} + 2 y_{7}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{7} \,\mathbf{\hat{y}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ | (6h) | Te I |
| $\mathbf{B_{30}}$ | = | $\left(x_{7} - y_{7}\right) \, \mathbf{a}_{1}+x_{7} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(2 x_{7} - y_{7}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a y_{7} \,\mathbf{\hat{y}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ | (6h) | Te I |
| $\mathbf{B_{31}}$ | = | $x_{8} \, \mathbf{a}_{1}+y_{8} \, \mathbf{a}_{2}+z_{8} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{8} + y_{8}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \left(x_{8} - y_{8}\right) \,\mathbf{\hat{y}}+c z_{8} \,\mathbf{\hat{z}}$ | (12i) | Co II |
| $\mathbf{B_{32}}$ | = | $- y_{8} \, \mathbf{a}_{1}+\left(x_{8} - y_{8}\right) \, \mathbf{a}_{2}+z_{8} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{8} - 2 y_{8}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{8} \,\mathbf{\hat{y}}+c z_{8} \,\mathbf{\hat{z}}$ | (12i) | Co II |
| $\mathbf{B_{33}}$ | = | $- \left(x_{8} - y_{8}\right) \, \mathbf{a}_{1}- x_{8} \, \mathbf{a}_{2}+z_{8} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(2 x_{8} - y_{8}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a y_{8} \,\mathbf{\hat{y}}+c z_{8} \,\mathbf{\hat{z}}$ | (12i) | Co II |
| $\mathbf{B_{34}}$ | = | $- x_{8} \, \mathbf{a}_{1}- y_{8} \, \mathbf{a}_{2}+\left(z_{8} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{8} + y_{8}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \left(x_{8} - y_{8}\right) \,\mathbf{\hat{y}}+c \left(z_{8} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (12i) | Co II |
| $\mathbf{B_{35}}$ | = | $y_{8} \, \mathbf{a}_{1}- \left(x_{8} - y_{8}\right) \, \mathbf{a}_{2}+\left(z_{8} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(- x_{8} + 2 y_{8}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{8} \,\mathbf{\hat{y}}+c \left(z_{8} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (12i) | Co II |
| $\mathbf{B_{36}}$ | = | $\left(x_{8} - y_{8}\right) \, \mathbf{a}_{1}+x_{8} \, \mathbf{a}_{2}+\left(z_{8} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(2 x_{8} - y_{8}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a y_{8} \,\mathbf{\hat{y}}+c \left(z_{8} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (12i) | Co II |
| $\mathbf{B_{37}}$ | = | $- x_{8} \, \mathbf{a}_{1}- y_{8} \, \mathbf{a}_{2}- z_{8} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{8} + y_{8}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \left(x_{8} - y_{8}\right) \,\mathbf{\hat{y}}- c z_{8} \,\mathbf{\hat{z}}$ | (12i) | Co II |
| $\mathbf{B_{38}}$ | = | $y_{8} \, \mathbf{a}_{1}- \left(x_{8} - y_{8}\right) \, \mathbf{a}_{2}- z_{8} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(- x_{8} + 2 y_{8}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{8} \,\mathbf{\hat{y}}- c z_{8} \,\mathbf{\hat{z}}$ | (12i) | Co II |
| $\mathbf{B_{39}}$ | = | $\left(x_{8} - y_{8}\right) \, \mathbf{a}_{1}+x_{8} \, \mathbf{a}_{2}- z_{8} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(2 x_{8} - y_{8}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a y_{8} \,\mathbf{\hat{y}}- c z_{8} \,\mathbf{\hat{z}}$ | (12i) | Co II |
| $\mathbf{B_{40}}$ | = | $x_{8} \, \mathbf{a}_{1}+y_{8} \, \mathbf{a}_{2}- \left(z_{8} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{8} + y_{8}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \left(x_{8} - y_{8}\right) \,\mathbf{\hat{y}}- c \left(z_{8} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (12i) | Co II |
| $\mathbf{B_{41}}$ | = | $- y_{8} \, \mathbf{a}_{1}+\left(x_{8} - y_{8}\right) \, \mathbf{a}_{2}- \left(z_{8} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{8} - 2 y_{8}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{8} \,\mathbf{\hat{y}}- c \left(z_{8} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (12i) | Co II |
| $\mathbf{B_{42}}$ | = | $- \left(x_{8} - y_{8}\right) \, \mathbf{a}_{1}- x_{8} \, \mathbf{a}_{2}- \left(z_{8} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(2 x_{8} - y_{8}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a y_{8} \,\mathbf{\hat{y}}- c \left(z_{8} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (12i) | Co II |
| $\mathbf{B_{43}}$ | = | $x_{9} \, \mathbf{a}_{1}+y_{9} \, \mathbf{a}_{2}+z_{9} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{9} + y_{9}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \left(x_{9} - y_{9}\right) \,\mathbf{\hat{y}}+c z_{9} \,\mathbf{\hat{z}}$ | (12i) | O III |
| $\mathbf{B_{44}}$ | = | $- y_{9} \, \mathbf{a}_{1}+\left(x_{9} - y_{9}\right) \, \mathbf{a}_{2}+z_{9} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{9} - 2 y_{9}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{9} \,\mathbf{\hat{y}}+c z_{9} \,\mathbf{\hat{z}}$ | (12i) | O III |
| $\mathbf{B_{45}}$ | = | $- \left(x_{9} - y_{9}\right) \, \mathbf{a}_{1}- x_{9} \, \mathbf{a}_{2}+z_{9} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(2 x_{9} - y_{9}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a y_{9} \,\mathbf{\hat{y}}+c z_{9} \,\mathbf{\hat{z}}$ | (12i) | O III |
| $\mathbf{B_{46}}$ | = | $- x_{9} \, \mathbf{a}_{1}- y_{9} \, \mathbf{a}_{2}+\left(z_{9} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{9} + y_{9}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \left(x_{9} - y_{9}\right) \,\mathbf{\hat{y}}+c \left(z_{9} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (12i) | O III |
| $\mathbf{B_{47}}$ | = | $y_{9} \, \mathbf{a}_{1}- \left(x_{9} - y_{9}\right) \, \mathbf{a}_{2}+\left(z_{9} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(- x_{9} + 2 y_{9}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{9} \,\mathbf{\hat{y}}+c \left(z_{9} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (12i) | O III |
| $\mathbf{B_{48}}$ | = | $\left(x_{9} - y_{9}\right) \, \mathbf{a}_{1}+x_{9} \, \mathbf{a}_{2}+\left(z_{9} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(2 x_{9} - y_{9}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a y_{9} \,\mathbf{\hat{y}}+c \left(z_{9} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (12i) | O III |
| $\mathbf{B_{49}}$ | = | $- x_{9} \, \mathbf{a}_{1}- y_{9} \, \mathbf{a}_{2}- z_{9} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{9} + y_{9}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \left(x_{9} - y_{9}\right) \,\mathbf{\hat{y}}- c z_{9} \,\mathbf{\hat{z}}$ | (12i) | O III |
| $\mathbf{B_{50}}$ | = | $y_{9} \, \mathbf{a}_{1}- \left(x_{9} - y_{9}\right) \, \mathbf{a}_{2}- z_{9} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(- x_{9} + 2 y_{9}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{9} \,\mathbf{\hat{y}}- c z_{9} \,\mathbf{\hat{z}}$ | (12i) | O III |
| $\mathbf{B_{51}}$ | = | $\left(x_{9} - y_{9}\right) \, \mathbf{a}_{1}+x_{9} \, \mathbf{a}_{2}- z_{9} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(2 x_{9} - y_{9}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a y_{9} \,\mathbf{\hat{y}}- c z_{9} \,\mathbf{\hat{z}}$ | (12i) | O III |
| $\mathbf{B_{52}}$ | = | $x_{9} \, \mathbf{a}_{1}+y_{9} \, \mathbf{a}_{2}- \left(z_{9} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{9} + y_{9}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \left(x_{9} - y_{9}\right) \,\mathbf{\hat{y}}- c \left(z_{9} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (12i) | O III |
| $\mathbf{B_{53}}$ | = | $- y_{9} \, \mathbf{a}_{1}+\left(x_{9} - y_{9}\right) \, \mathbf{a}_{2}- \left(z_{9} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{9} - 2 y_{9}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{9} \,\mathbf{\hat{y}}- c \left(z_{9} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (12i) | O III |
| $\mathbf{B_{54}}$ | = | $- \left(x_{9} - y_{9}\right) \, \mathbf{a}_{1}- x_{9} \, \mathbf{a}_{2}- \left(z_{9} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(2 x_{9} - y_{9}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a y_{9} \,\mathbf{\hat{y}}- c \left(z_{9} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (12i) | O III |
| $\mathbf{B_{55}}$ | = | $x_{10} \, \mathbf{a}_{1}+y_{10} \, \mathbf{a}_{2}+z_{10} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{10} + y_{10}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \left(x_{10} - y_{10}\right) \,\mathbf{\hat{y}}+c z_{10} \,\mathbf{\hat{z}}$ | (12i) | O IV |
| $\mathbf{B_{56}}$ | = | $- y_{10} \, \mathbf{a}_{1}+\left(x_{10} - y_{10}\right) \, \mathbf{a}_{2}+z_{10} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{10} - 2 y_{10}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{10} \,\mathbf{\hat{y}}+c z_{10} \,\mathbf{\hat{z}}$ | (12i) | O IV |
| $\mathbf{B_{57}}$ | = | $- \left(x_{10} - y_{10}\right) \, \mathbf{a}_{1}- x_{10} \, \mathbf{a}_{2}+z_{10} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(2 x_{10} - y_{10}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a y_{10} \,\mathbf{\hat{y}}+c z_{10} \,\mathbf{\hat{z}}$ | (12i) | O IV |
| $\mathbf{B_{58}}$ | = | $- x_{10} \, \mathbf{a}_{1}- y_{10} \, \mathbf{a}_{2}+\left(z_{10} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{10} + y_{10}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \left(x_{10} - y_{10}\right) \,\mathbf{\hat{y}}+c \left(z_{10} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (12i) | O IV |
| $\mathbf{B_{59}}$ | = | $y_{10} \, \mathbf{a}_{1}- \left(x_{10} - y_{10}\right) \, \mathbf{a}_{2}+\left(z_{10} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(- x_{10} + 2 y_{10}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{10} \,\mathbf{\hat{y}}+c \left(z_{10} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (12i) | O IV |
| $\mathbf{B_{60}}$ | = | $\left(x_{10} - y_{10}\right) \, \mathbf{a}_{1}+x_{10} \, \mathbf{a}_{2}+\left(z_{10} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(2 x_{10} - y_{10}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a y_{10} \,\mathbf{\hat{y}}+c \left(z_{10} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (12i) | O IV |
| $\mathbf{B_{61}}$ | = | $- x_{10} \, \mathbf{a}_{1}- y_{10} \, \mathbf{a}_{2}- z_{10} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{10} + y_{10}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \left(x_{10} - y_{10}\right) \,\mathbf{\hat{y}}- c z_{10} \,\mathbf{\hat{z}}$ | (12i) | O IV |
| $\mathbf{B_{62}}$ | = | $y_{10} \, \mathbf{a}_{1}- \left(x_{10} - y_{10}\right) \, \mathbf{a}_{2}- z_{10} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(- x_{10} + 2 y_{10}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{10} \,\mathbf{\hat{y}}- c z_{10} \,\mathbf{\hat{z}}$ | (12i) | O IV |
| $\mathbf{B_{63}}$ | = | $\left(x_{10} - y_{10}\right) \, \mathbf{a}_{1}+x_{10} \, \mathbf{a}_{2}- z_{10} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(2 x_{10} - y_{10}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a y_{10} \,\mathbf{\hat{y}}- c z_{10} \,\mathbf{\hat{z}}$ | (12i) | O IV |
| $\mathbf{B_{64}}$ | = | $x_{10} \, \mathbf{a}_{1}+y_{10} \, \mathbf{a}_{2}- \left(z_{10} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{10} + y_{10}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \left(x_{10} - y_{10}\right) \,\mathbf{\hat{y}}- c \left(z_{10} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (12i) | O IV |
| $\mathbf{B_{65}}$ | = | $- y_{10} \, \mathbf{a}_{1}+\left(x_{10} - y_{10}\right) \, \mathbf{a}_{2}- \left(z_{10} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{10} - 2 y_{10}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{10} \,\mathbf{\hat{y}}- c \left(z_{10} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (12i) | O IV |
| $\mathbf{B_{66}}$ | = | $- \left(x_{10} - y_{10}\right) \, \mathbf{a}_{1}- x_{10} \, \mathbf{a}_{2}- \left(z_{10} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(2 x_{10} - y_{10}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a y_{10} \,\mathbf{\hat{y}}- c \left(z_{10} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (12i) | O IV |
References
- R. A. Saha, J. Sannigrahi, I. Carlomagno, S. Kaushik, C. Meneghini, M. Itoh, V. Siruguri, and S. Ray, Short range magnetic correlation, metamagnetism and coincident dielectric anomaly in Na$_{5}$Co$_{15.5}$Te$_{6}$O$_{36}$, Physical Review B 107, 155105 (2023), doi:10.1103/PhysRevB.107.155105.
Prototype Generator
aflow --proto=A7B5C18D3_hP66_176_ci_bef_2h2i_h --params=$a,c/a,z_{3},z_{4},x_{5},y_{5},x_{6},y_{6},x_{7},y_{7},x_{8},y_{8},z_{8},x_{9},y_{9},z_{9},x_{10},y_{10},z_{10}$