Pyrochlore (Na$_{3}$Co(CO$_{3}$)$_{2}$Cl) Structure: A2BCD3E6_cF208_203_e_c_d_f_g-001
| Prototype | C$_{2}$ClCoNa$_{3}$O$_{6}$ |
| AFLOW prototype label | A2BCD3E6_cF208_203_e_c_d_f_g-001 |
| Mineral name | pyrochlore |
| ICSD | none |
| Pearson symbol | cF208 |
| Space group number | 203 |
| Space group symbol | $Fd\overline{3}$ |
| AFLOW prototype command |
aflow --proto=A2BCD3E6_cF208_203_e_c_d_f_g-001
--params=$a, \allowbreak x_{3}, \allowbreak x_{4}, \allowbreak x_{5}, \allowbreak y_{5}, \allowbreak z_{5}$ |
Other compounds with this structure
Na$_{3}$MgCl(CO$_{3}$)$_{2}$ (northupite), Na$_{3}$MgBr(CO$_{3}$)$_{2}$
- This structure was suggested to us by Prof. Joel Helton, United States Naval Academy. This is a pyrochlore-like antiferromagnet, which we loosely define as a structure with magnetic ions on the corners of corner-sharing tetrahedra.
- We use the structural data taken by (Fu, 2013) at 3.7K
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $0$ | = | $0$ | (16c) | Cl I |
| $\mathbf{B_{2}}$ | = | $\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}$ | (16c) | Cl I |
| $\mathbf{B_{3}}$ | = | $\frac{1}{2} \, \mathbf{a}_{2}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (16c) | Cl I |
| $\mathbf{B_{4}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}$ | = | $\frac{1}{4}a \,\mathbf{\hat{y}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (16c) | Cl I |
| $\mathbf{B_{5}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}$ | (16d) | Co I |
| $\mathbf{B_{6}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}$ | (16d) | Co I |
| $\mathbf{B_{7}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (16d) | Co I |
| $\mathbf{B_{8}}$ | = | $\frac{1}{2} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (16d) | Co I |
| $\mathbf{B_{9}}$ | = | $x_{3} \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{2}+x_{3} \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{x}}+a x_{3} \,\mathbf{\hat{y}}+a x_{3} \,\mathbf{\hat{z}}$ | (32e) | C I |
| $\mathbf{B_{10}}$ | = | $x_{3} \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{2}- \left(3 x_{3} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{3} - \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(x_{3} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a x_{3} \,\mathbf{\hat{z}}$ | (32e) | C I |
| $\mathbf{B_{11}}$ | = | $x_{3} \, \mathbf{a}_{1}- \left(3 x_{3} - \frac{1}{2}\right) \, \mathbf{a}_{2}+x_{3} \, \mathbf{a}_{3}$ | = | $- a \left(x_{3} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a x_{3} \,\mathbf{\hat{y}}- a \left(x_{3} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (32e) | C I |
| $\mathbf{B_{12}}$ | = | $- \left(3 x_{3} - \frac{1}{2}\right) \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{2}+x_{3} \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{x}}- a \left(x_{3} - \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(x_{3} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (32e) | C I |
| $\mathbf{B_{13}}$ | = | $- x_{3} \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}- x_{3} \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}- a x_{3} \,\mathbf{\hat{y}}- a x_{3} \,\mathbf{\hat{z}}$ | (32e) | C I |
| $\mathbf{B_{14}}$ | = | $- x_{3} \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}+\left(3 x_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{3} + \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(x_{3} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a x_{3} \,\mathbf{\hat{z}}$ | (32e) | C I |
| $\mathbf{B_{15}}$ | = | $- x_{3} \, \mathbf{a}_{1}+\left(3 x_{3} + \frac{1}{2}\right) \, \mathbf{a}_{2}- x_{3} \, \mathbf{a}_{3}$ | = | $a \left(x_{3} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a x_{3} \,\mathbf{\hat{y}}+a \left(x_{3} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (32e) | C I |
| $\mathbf{B_{16}}$ | = | $\left(3 x_{3} + \frac{1}{2}\right) \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}- x_{3} \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}+a \left(x_{3} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(x_{3} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (32e) | C I |
| $\mathbf{B_{17}}$ | = | $- \left(x_{4} - \frac{1}{4}\right) \, \mathbf{a}_{1}+x_{4} \, \mathbf{a}_{2}+x_{4} \, \mathbf{a}_{3}$ | = | $a x_{4} \,\mathbf{\hat{x}}+\frac{1}{8}a \,\mathbf{\hat{y}}+\frac{1}{8}a \,\mathbf{\hat{z}}$ | (48f) | Na I |
| $\mathbf{B_{18}}$ | = | $x_{4} \, \mathbf{a}_{1}- \left(x_{4} - \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(x_{4} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{4} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+\frac{1}{8}a \,\mathbf{\hat{y}}+\frac{1}{8}a \,\mathbf{\hat{z}}$ | (48f) | Na I |
| $\mathbf{B_{19}}$ | = | $x_{4} \, \mathbf{a}_{1}- \left(x_{4} - \frac{1}{4}\right) \, \mathbf{a}_{2}+x_{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{8}a \,\mathbf{\hat{x}}+a x_{4} \,\mathbf{\hat{y}}+\frac{1}{8}a \,\mathbf{\hat{z}}$ | (48f) | Na I |
| $\mathbf{B_{20}}$ | = | $- \left(x_{4} - \frac{1}{4}\right) \, \mathbf{a}_{1}+x_{4} \, \mathbf{a}_{2}- \left(x_{4} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{8}a \,\mathbf{\hat{x}}- a \left(x_{4} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+\frac{1}{8}a \,\mathbf{\hat{z}}$ | (48f) | Na I |
| $\mathbf{B_{21}}$ | = | $x_{4} \, \mathbf{a}_{1}+x_{4} \, \mathbf{a}_{2}- \left(x_{4} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{8}a \,\mathbf{\hat{x}}+\frac{1}{8}a \,\mathbf{\hat{y}}+a x_{4} \,\mathbf{\hat{z}}$ | (48f) | Na I |
| $\mathbf{B_{22}}$ | = | $- \left(x_{4} - \frac{1}{4}\right) \, \mathbf{a}_{1}- \left(x_{4} - \frac{1}{4}\right) \, \mathbf{a}_{2}+x_{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{8}a \,\mathbf{\hat{x}}+\frac{1}{8}a \,\mathbf{\hat{y}}- a \left(x_{4} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (48f) | Na I |
| $\mathbf{B_{23}}$ | = | $\left(x_{4} + \frac{3}{4}\right) \, \mathbf{a}_{1}- x_{4} \, \mathbf{a}_{2}- x_{4} \, \mathbf{a}_{3}$ | = | $- a x_{4} \,\mathbf{\hat{x}}+\frac{3}{8}a \,\mathbf{\hat{y}}+\frac{3}{8}a \,\mathbf{\hat{z}}$ | (48f) | Na I |
| $\mathbf{B_{24}}$ | = | $- x_{4} \, \mathbf{a}_{1}+\left(x_{4} + \frac{3}{4}\right) \, \mathbf{a}_{2}+\left(x_{4} + \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{4} + \frac{3}{4}\right) \,\mathbf{\hat{x}}+\frac{3}{8}a \,\mathbf{\hat{y}}+\frac{3}{8}a \,\mathbf{\hat{z}}$ | (48f) | Na I |
| $\mathbf{B_{25}}$ | = | $- x_{4} \, \mathbf{a}_{1}+\left(x_{4} + \frac{3}{4}\right) \, \mathbf{a}_{2}- x_{4} \, \mathbf{a}_{3}$ | = | $\frac{3}{8}a \,\mathbf{\hat{x}}- a x_{4} \,\mathbf{\hat{y}}+\frac{3}{8}a \,\mathbf{\hat{z}}$ | (48f) | Na I |
| $\mathbf{B_{26}}$ | = | $\left(x_{4} + \frac{3}{4}\right) \, \mathbf{a}_{1}- x_{4} \, \mathbf{a}_{2}+\left(x_{4} + \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $\frac{3}{8}a \,\mathbf{\hat{x}}+a \left(x_{4} + \frac{3}{4}\right) \,\mathbf{\hat{y}}+\frac{3}{8}a \,\mathbf{\hat{z}}$ | (48f) | Na I |
| $\mathbf{B_{27}}$ | = | $- x_{4} \, \mathbf{a}_{1}- x_{4} \, \mathbf{a}_{2}+\left(x_{4} + \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $\frac{3}{8}a \,\mathbf{\hat{x}}+\frac{3}{8}a \,\mathbf{\hat{y}}- a x_{4} \,\mathbf{\hat{z}}$ | (48f) | Na I |
| $\mathbf{B_{28}}$ | = | $\left(x_{4} + \frac{3}{4}\right) \, \mathbf{a}_{1}+\left(x_{4} + \frac{3}{4}\right) \, \mathbf{a}_{2}- x_{4} \, \mathbf{a}_{3}$ | = | $\frac{3}{8}a \,\mathbf{\hat{x}}+\frac{3}{8}a \,\mathbf{\hat{y}}+a \left(x_{4} + \frac{3}{4}\right) \,\mathbf{\hat{z}}$ | (48f) | Na I |
| $\mathbf{B_{29}}$ | = | $\left(- x_{5} + y_{5} + z_{5}\right) \, \mathbf{a}_{1}+\left(x_{5} - y_{5} + z_{5}\right) \, \mathbf{a}_{2}+\left(x_{5} + y_{5} - z_{5}\right) \, \mathbf{a}_{3}$ | = | $a x_{5} \,\mathbf{\hat{x}}+a y_{5} \,\mathbf{\hat{y}}+a z_{5} \,\mathbf{\hat{z}}$ | (96g) | O I |
| $\mathbf{B_{30}}$ | = | $\left(x_{5} - y_{5} + z_{5}\right) \, \mathbf{a}_{1}+\left(- x_{5} + y_{5} + z_{5}\right) \, \mathbf{a}_{2}- \left(x_{5} + y_{5} + z_{5} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{5} - \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(y_{5} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a z_{5} \,\mathbf{\hat{z}}$ | (96g) | O I |
| $\mathbf{B_{31}}$ | = | $\left(x_{5} + y_{5} - z_{5}\right) \, \mathbf{a}_{1}- \left(x_{5} + y_{5} + z_{5} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(- x_{5} + y_{5} + z_{5}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{5} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a y_{5} \,\mathbf{\hat{y}}- a \left(z_{5} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96g) | O I |
| $\mathbf{B_{32}}$ | = | $- \left(x_{5} + y_{5} + z_{5} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{5} + y_{5} - z_{5}\right) \, \mathbf{a}_{2}+\left(x_{5} - y_{5} + z_{5}\right) \, \mathbf{a}_{3}$ | = | $a x_{5} \,\mathbf{\hat{x}}- a \left(y_{5} - \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(z_{5} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96g) | O I |
| $\mathbf{B_{33}}$ | = | $\left(x_{5} + y_{5} - z_{5}\right) \, \mathbf{a}_{1}+\left(- x_{5} + y_{5} + z_{5}\right) \, \mathbf{a}_{2}+\left(x_{5} - y_{5} + z_{5}\right) \, \mathbf{a}_{3}$ | = | $a z_{5} \,\mathbf{\hat{x}}+a x_{5} \,\mathbf{\hat{y}}+a y_{5} \,\mathbf{\hat{z}}$ | (96g) | O I |
| $\mathbf{B_{34}}$ | = | $- \left(x_{5} + y_{5} + z_{5} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{5} - y_{5} + z_{5}\right) \, \mathbf{a}_{2}+\left(- x_{5} + y_{5} + z_{5}\right) \, \mathbf{a}_{3}$ | = | $a z_{5} \,\mathbf{\hat{x}}- a \left(x_{5} - \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(y_{5} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96g) | O I |
| $\mathbf{B_{35}}$ | = | $\left(- x_{5} + y_{5} + z_{5}\right) \, \mathbf{a}_{1}+\left(x_{5} + y_{5} - z_{5}\right) \, \mathbf{a}_{2}- \left(x_{5} + y_{5} + z_{5} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(z_{5} - \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(x_{5} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a y_{5} \,\mathbf{\hat{z}}$ | (96g) | O I |
| $\mathbf{B_{36}}$ | = | $\left(x_{5} - y_{5} + z_{5}\right) \, \mathbf{a}_{1}- \left(x_{5} + y_{5} + z_{5} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{5} + y_{5} - z_{5}\right) \, \mathbf{a}_{3}$ | = | $- a \left(z_{5} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a x_{5} \,\mathbf{\hat{y}}- a \left(y_{5} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96g) | O I |
| $\mathbf{B_{37}}$ | = | $\left(x_{5} - y_{5} + z_{5}\right) \, \mathbf{a}_{1}+\left(x_{5} + y_{5} - z_{5}\right) \, \mathbf{a}_{2}+\left(- x_{5} + y_{5} + z_{5}\right) \, \mathbf{a}_{3}$ | = | $a y_{5} \,\mathbf{\hat{x}}+a z_{5} \,\mathbf{\hat{y}}+a x_{5} \,\mathbf{\hat{z}}$ | (96g) | O I |
| $\mathbf{B_{38}}$ | = | $\left(- x_{5} + y_{5} + z_{5}\right) \, \mathbf{a}_{1}- \left(x_{5} + y_{5} + z_{5} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{5} - y_{5} + z_{5}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{5} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a z_{5} \,\mathbf{\hat{y}}- a \left(x_{5} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96g) | O I |
| $\mathbf{B_{39}}$ | = | $- \left(x_{5} + y_{5} + z_{5} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(- x_{5} + y_{5} + z_{5}\right) \, \mathbf{a}_{2}+\left(x_{5} + y_{5} - z_{5}\right) \, \mathbf{a}_{3}$ | = | $a y_{5} \,\mathbf{\hat{x}}- a \left(z_{5} - \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(x_{5} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96g) | O I |
| $\mathbf{B_{40}}$ | = | $\left(x_{5} + y_{5} - z_{5}\right) \, \mathbf{a}_{1}+\left(x_{5} - y_{5} + z_{5}\right) \, \mathbf{a}_{2}- \left(x_{5} + y_{5} + z_{5} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{5} - \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(z_{5} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a x_{5} \,\mathbf{\hat{z}}$ | (96g) | O I |
| $\mathbf{B_{41}}$ | = | $\left(x_{5} - y_{5} - z_{5}\right) \, \mathbf{a}_{1}- \left(x_{5} - y_{5} + z_{5}\right) \, \mathbf{a}_{2}- \left(x_{5} + y_{5} - z_{5}\right) \, \mathbf{a}_{3}$ | = | $- a x_{5} \,\mathbf{\hat{x}}- a y_{5} \,\mathbf{\hat{y}}- a z_{5} \,\mathbf{\hat{z}}$ | (96g) | O I |
| $\mathbf{B_{42}}$ | = | $- \left(x_{5} - y_{5} + z_{5}\right) \, \mathbf{a}_{1}+\left(x_{5} - y_{5} - z_{5}\right) \, \mathbf{a}_{2}+\left(x_{5} + y_{5} + z_{5} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{5} + \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(y_{5} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a z_{5} \,\mathbf{\hat{z}}$ | (96g) | O I |
| $\mathbf{B_{43}}$ | = | $- \left(x_{5} + y_{5} - z_{5}\right) \, \mathbf{a}_{1}+\left(x_{5} + y_{5} + z_{5} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{5} - y_{5} - z_{5}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{5} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a y_{5} \,\mathbf{\hat{y}}+a \left(z_{5} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96g) | O I |
| $\mathbf{B_{44}}$ | = | $\left(x_{5} + y_{5} + z_{5} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{5} + y_{5} - z_{5}\right) \, \mathbf{a}_{2}- \left(x_{5} - y_{5} + z_{5}\right) \, \mathbf{a}_{3}$ | = | $- a x_{5} \,\mathbf{\hat{x}}+a \left(y_{5} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(z_{5} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96g) | O I |
| $\mathbf{B_{45}}$ | = | $- \left(x_{5} + y_{5} - z_{5}\right) \, \mathbf{a}_{1}+\left(x_{5} - y_{5} - z_{5}\right) \, \mathbf{a}_{2}- \left(x_{5} - y_{5} + z_{5}\right) \, \mathbf{a}_{3}$ | = | $- a z_{5} \,\mathbf{\hat{x}}- a x_{5} \,\mathbf{\hat{y}}- a y_{5} \,\mathbf{\hat{z}}$ | (96g) | O I |
| $\mathbf{B_{46}}$ | = | $\left(x_{5} + y_{5} + z_{5} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{5} - y_{5} + z_{5}\right) \, \mathbf{a}_{2}+\left(x_{5} - y_{5} - z_{5}\right) \, \mathbf{a}_{3}$ | = | $- a z_{5} \,\mathbf{\hat{x}}+a \left(x_{5} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(y_{5} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96g) | O I |
| $\mathbf{B_{47}}$ | = | $\left(x_{5} - y_{5} - z_{5}\right) \, \mathbf{a}_{1}- \left(x_{5} + y_{5} - z_{5}\right) \, \mathbf{a}_{2}+\left(x_{5} + y_{5} + z_{5} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(z_{5} + \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(x_{5} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a y_{5} \,\mathbf{\hat{z}}$ | (96g) | O I |
| $\mathbf{B_{48}}$ | = | $- \left(x_{5} - y_{5} + z_{5}\right) \, \mathbf{a}_{1}+\left(x_{5} + y_{5} + z_{5} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{5} + y_{5} - z_{5}\right) \, \mathbf{a}_{3}$ | = | $a \left(z_{5} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a x_{5} \,\mathbf{\hat{y}}+a \left(y_{5} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96g) | O I |
| $\mathbf{B_{49}}$ | = | $- \left(x_{5} - y_{5} + z_{5}\right) \, \mathbf{a}_{1}- \left(x_{5} + y_{5} - z_{5}\right) \, \mathbf{a}_{2}+\left(x_{5} - y_{5} - z_{5}\right) \, \mathbf{a}_{3}$ | = | $- a y_{5} \,\mathbf{\hat{x}}- a z_{5} \,\mathbf{\hat{y}}- a x_{5} \,\mathbf{\hat{z}}$ | (96g) | O I |
| $\mathbf{B_{50}}$ | = | $\left(x_{5} - y_{5} - z_{5}\right) \, \mathbf{a}_{1}+\left(x_{5} + y_{5} + z_{5} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{5} - y_{5} + z_{5}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{5} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a z_{5} \,\mathbf{\hat{y}}+a \left(x_{5} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96g) | O I |
| $\mathbf{B_{51}}$ | = | $\left(x_{5} + y_{5} + z_{5} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{5} - y_{5} - z_{5}\right) \, \mathbf{a}_{2}- \left(x_{5} + y_{5} - z_{5}\right) \, \mathbf{a}_{3}$ | = | $- a y_{5} \,\mathbf{\hat{x}}+a \left(z_{5} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(x_{5} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (96g) | O I |
| $\mathbf{B_{52}}$ | = | $- \left(x_{5} + y_{5} - z_{5}\right) \, \mathbf{a}_{1}- \left(x_{5} - y_{5} + z_{5}\right) \, \mathbf{a}_{2}+\left(x_{5} + y_{5} + z_{5} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{5} + \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(z_{5} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a x_{5} \,\mathbf{\hat{z}}$ | (96g) | O I |
References
- Z. Fu, Y. Zheng, Y. Xiao, S. Bedanta, A. Senyshyn, G. G. Simeoni, Y. Su, U. Rücker, P. Kögerler, and T. Brückel, Coexistence of magnetic order and spin-glass-like phase in the pyrochlore antiferromagnet Na$_3$Co(CO$_3$)$_2$Cl, Phys. Rev. B 87, 214406 (2013), doi:10.1103/PhysRevB.87.214406.
Prototype Generator
aflow --proto=A2BCD3E6_cF208_203_e_c_d_f_g --params=$a,x_{3},x_{4},x_{5},y_{5},z_{5}$