Li$_{7}$MnN$_{4}$ Structure: A7BC4_cP96_218_bcefi_ad_ei-001
| Prototype | Li$_{7}$MnN$_{4}$ |
| AFLOW prototype label | A7BC4_cP96_218_bcefi_ad_ei-001 |
| ICSD | 154076 |
| Pearson symbol | cP96 |
| Space group number | 218 |
| Space group symbol | $P\overline{4}3n$ |
| AFLOW prototype command |
aflow --proto=A7BC4_cP96_218_bcefi_ad_ei-001
--params=$a, \allowbreak x_{5}, \allowbreak x_{6}, \allowbreak x_{7}, \allowbreak x_{8}, \allowbreak y_{8}, \allowbreak z_{8}, \allowbreak x_{9}, \allowbreak y_{9}, \allowbreak z_{9}$ |
Other compounds with this structure
Li$_{7}$PN$_{4}$, Li$_{7}$VN$_{4}$
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&a \,\mathbf{\hat{x}}\\\mathbf{a_{2}}&=&a \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&a \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $0$ | = | $0$ | (2a) | Mn I |
| $\mathbf{B_{2}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}$ | (2a) | Mn I |
| $\mathbf{B_{3}}$ | = | $\frac{1}{2} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}$ | (6b) | Li I |
| $\mathbf{B_{4}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{z}}$ | (6b) | Li I |
| $\mathbf{B_{5}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}$ | (6b) | Li I |
| $\mathbf{B_{6}}$ | = | $\frac{1}{2} \, \mathbf{a}_{2}$ | = | $\frac{1}{2}a \,\mathbf{\hat{y}}$ | (6b) | Li I |
| $\mathbf{B_{7}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}$ | (6b) | Li I |
| $\mathbf{B_{8}}$ | = | $\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{z}}$ | (6b) | Li I |
| $\mathbf{B_{9}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}$ | (6c) | Li II |
| $\mathbf{B_{10}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}$ | = | $\frac{3}{4}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}$ | (6c) | Li II |
| $\mathbf{B_{11}}$ | = | $\frac{1}{4} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}$ | (6c) | Li II |
| $\mathbf{B_{12}}$ | = | $\frac{3}{4} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{3}{4}a \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}$ | (6c) | Li II |
| $\mathbf{B_{13}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (6c) | Li II |
| $\mathbf{B_{14}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{3}{4}a \,\mathbf{\hat{z}}$ | (6c) | Li II |
| $\mathbf{B_{15}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{z}}$ | (6d) | Mn II |
| $\mathbf{B_{16}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{3}{4}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{z}}$ | (6d) | Mn II |
| $\mathbf{B_{17}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}$ | (6d) | Mn II |
| $\mathbf{B_{18}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{3}{4}a \,\mathbf{\hat{y}}$ | (6d) | Mn II |
| $\mathbf{B_{19}}$ | = | $\frac{1}{2} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (6d) | Mn II |
| $\mathbf{B_{20}}$ | = | $\frac{1}{2} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{3}{4}a \,\mathbf{\hat{z}}$ | (6d) | Mn II |
| $\mathbf{B_{21}}$ | = | $x_{5} \, \mathbf{a}_{1}+x_{5} \, \mathbf{a}_{2}+x_{5} \, \mathbf{a}_{3}$ | = | $a x_{5} \,\mathbf{\hat{x}}+a x_{5} \,\mathbf{\hat{y}}+a x_{5} \,\mathbf{\hat{z}}$ | (8e) | Li III |
| $\mathbf{B_{22}}$ | = | $- x_{5} \, \mathbf{a}_{1}- x_{5} \, \mathbf{a}_{2}+x_{5} \, \mathbf{a}_{3}$ | = | $- a x_{5} \,\mathbf{\hat{x}}- a x_{5} \,\mathbf{\hat{y}}+a x_{5} \,\mathbf{\hat{z}}$ | (8e) | Li III |
| $\mathbf{B_{23}}$ | = | $- x_{5} \, \mathbf{a}_{1}+x_{5} \, \mathbf{a}_{2}- x_{5} \, \mathbf{a}_{3}$ | = | $- a x_{5} \,\mathbf{\hat{x}}+a x_{5} \,\mathbf{\hat{y}}- a x_{5} \,\mathbf{\hat{z}}$ | (8e) | Li III |
| $\mathbf{B_{24}}$ | = | $x_{5} \, \mathbf{a}_{1}- x_{5} \, \mathbf{a}_{2}- x_{5} \, \mathbf{a}_{3}$ | = | $a x_{5} \,\mathbf{\hat{x}}- a x_{5} \,\mathbf{\hat{y}}- a x_{5} \,\mathbf{\hat{z}}$ | (8e) | Li III |
| $\mathbf{B_{25}}$ | = | $\left(x_{5} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{5} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{5} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{5} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(x_{5} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+a \left(x_{5} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8e) | Li III |
| $\mathbf{B_{26}}$ | = | $- \left(x_{5} - \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{5} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{5} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{5} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(x_{5} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+a \left(x_{5} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8e) | Li III |
| $\mathbf{B_{27}}$ | = | $\left(x_{5} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{5} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{5} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{5} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(x_{5} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(x_{5} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8e) | Li III |
| $\mathbf{B_{28}}$ | = | $- \left(x_{5} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{5} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{5} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{5} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(x_{5} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(x_{5} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8e) | Li III |
| $\mathbf{B_{29}}$ | = | $x_{6} \, \mathbf{a}_{1}+x_{6} \, \mathbf{a}_{2}+x_{6} \, \mathbf{a}_{3}$ | = | $a x_{6} \,\mathbf{\hat{x}}+a x_{6} \,\mathbf{\hat{y}}+a x_{6} \,\mathbf{\hat{z}}$ | (8e) | N I |
| $\mathbf{B_{30}}$ | = | $- x_{6} \, \mathbf{a}_{1}- x_{6} \, \mathbf{a}_{2}+x_{6} \, \mathbf{a}_{3}$ | = | $- a x_{6} \,\mathbf{\hat{x}}- a x_{6} \,\mathbf{\hat{y}}+a x_{6} \,\mathbf{\hat{z}}$ | (8e) | N I |
| $\mathbf{B_{31}}$ | = | $- x_{6} \, \mathbf{a}_{1}+x_{6} \, \mathbf{a}_{2}- x_{6} \, \mathbf{a}_{3}$ | = | $- a x_{6} \,\mathbf{\hat{x}}+a x_{6} \,\mathbf{\hat{y}}- a x_{6} \,\mathbf{\hat{z}}$ | (8e) | N I |
| $\mathbf{B_{32}}$ | = | $x_{6} \, \mathbf{a}_{1}- x_{6} \, \mathbf{a}_{2}- x_{6} \, \mathbf{a}_{3}$ | = | $a x_{6} \,\mathbf{\hat{x}}- a x_{6} \,\mathbf{\hat{y}}- a x_{6} \,\mathbf{\hat{z}}$ | (8e) | N I |
| $\mathbf{B_{33}}$ | = | $\left(x_{6} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{6} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{6} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{6} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(x_{6} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+a \left(x_{6} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8e) | N I |
| $\mathbf{B_{34}}$ | = | $- \left(x_{6} - \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{6} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{6} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{6} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(x_{6} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+a \left(x_{6} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8e) | N I |
| $\mathbf{B_{35}}$ | = | $\left(x_{6} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{6} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{6} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{6} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(x_{6} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(x_{6} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8e) | N I |
| $\mathbf{B_{36}}$ | = | $- \left(x_{6} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{6} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{6} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{6} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(x_{6} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(x_{6} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8e) | N I |
| $\mathbf{B_{37}}$ | = | $x_{7} \, \mathbf{a}_{1}$ | = | $a x_{7} \,\mathbf{\hat{x}}$ | (12f) | Li IV |
| $\mathbf{B_{38}}$ | = | $- x_{7} \, \mathbf{a}_{1}$ | = | $- a x_{7} \,\mathbf{\hat{x}}$ | (12f) | Li IV |
| $\mathbf{B_{39}}$ | = | $x_{7} \, \mathbf{a}_{2}$ | = | $a x_{7} \,\mathbf{\hat{y}}$ | (12f) | Li IV |
| $\mathbf{B_{40}}$ | = | $- x_{7} \, \mathbf{a}_{2}$ | = | $- a x_{7} \,\mathbf{\hat{y}}$ | (12f) | Li IV |
| $\mathbf{B_{41}}$ | = | $x_{7} \, \mathbf{a}_{3}$ | = | $a x_{7} \,\mathbf{\hat{z}}$ | (12f) | Li IV |
| $\mathbf{B_{42}}$ | = | $- x_{7} \, \mathbf{a}_{3}$ | = | $- a x_{7} \,\mathbf{\hat{z}}$ | (12f) | Li IV |
| $\mathbf{B_{43}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\left(x_{7} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+a \left(x_{7} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}$ | (12f) | Li IV |
| $\mathbf{B_{44}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}- \left(x_{7} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- a \left(x_{7} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}$ | (12f) | Li IV |
| $\mathbf{B_{45}}$ | = | $\left(x_{7} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $a \left(x_{7} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}$ | (12f) | Li IV |
| $\mathbf{B_{46}}$ | = | $- \left(x_{7} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- a \left(x_{7} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}$ | (12f) | Li IV |
| $\mathbf{B_{47}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+\left(x_{7} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+a \left(x_{7} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (12f) | Li IV |
| $\mathbf{B_{48}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}- \left(x_{7} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}- a \left(x_{7} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (12f) | Li IV |
| $\mathbf{B_{49}}$ | = | $x_{8} \, \mathbf{a}_{1}+y_{8} \, \mathbf{a}_{2}+z_{8} \, \mathbf{a}_{3}$ | = | $a x_{8} \,\mathbf{\hat{x}}+a y_{8} \,\mathbf{\hat{y}}+a z_{8} \,\mathbf{\hat{z}}$ | (24i) | Li V |
| $\mathbf{B_{50}}$ | = | $- x_{8} \, \mathbf{a}_{1}- y_{8} \, \mathbf{a}_{2}+z_{8} \, \mathbf{a}_{3}$ | = | $- a x_{8} \,\mathbf{\hat{x}}- a y_{8} \,\mathbf{\hat{y}}+a z_{8} \,\mathbf{\hat{z}}$ | (24i) | Li V |
| $\mathbf{B_{51}}$ | = | $- x_{8} \, \mathbf{a}_{1}+y_{8} \, \mathbf{a}_{2}- z_{8} \, \mathbf{a}_{3}$ | = | $- a x_{8} \,\mathbf{\hat{x}}+a y_{8} \,\mathbf{\hat{y}}- a z_{8} \,\mathbf{\hat{z}}$ | (24i) | Li V |
| $\mathbf{B_{52}}$ | = | $x_{8} \, \mathbf{a}_{1}- y_{8} \, \mathbf{a}_{2}- z_{8} \, \mathbf{a}_{3}$ | = | $a x_{8} \,\mathbf{\hat{x}}- a y_{8} \,\mathbf{\hat{y}}- a z_{8} \,\mathbf{\hat{z}}$ | (24i) | Li V |
| $\mathbf{B_{53}}$ | = | $z_{8} \, \mathbf{a}_{1}+x_{8} \, \mathbf{a}_{2}+y_{8} \, \mathbf{a}_{3}$ | = | $a z_{8} \,\mathbf{\hat{x}}+a x_{8} \,\mathbf{\hat{y}}+a y_{8} \,\mathbf{\hat{z}}$ | (24i) | Li V |
| $\mathbf{B_{54}}$ | = | $z_{8} \, \mathbf{a}_{1}- x_{8} \, \mathbf{a}_{2}- y_{8} \, \mathbf{a}_{3}$ | = | $a z_{8} \,\mathbf{\hat{x}}- a x_{8} \,\mathbf{\hat{y}}- a y_{8} \,\mathbf{\hat{z}}$ | (24i) | Li V |
| $\mathbf{B_{55}}$ | = | $- z_{8} \, \mathbf{a}_{1}- x_{8} \, \mathbf{a}_{2}+y_{8} \, \mathbf{a}_{3}$ | = | $- a z_{8} \,\mathbf{\hat{x}}- a x_{8} \,\mathbf{\hat{y}}+a y_{8} \,\mathbf{\hat{z}}$ | (24i) | Li V |
| $\mathbf{B_{56}}$ | = | $- z_{8} \, \mathbf{a}_{1}+x_{8} \, \mathbf{a}_{2}- y_{8} \, \mathbf{a}_{3}$ | = | $- a z_{8} \,\mathbf{\hat{x}}+a x_{8} \,\mathbf{\hat{y}}- a y_{8} \,\mathbf{\hat{z}}$ | (24i) | Li V |
| $\mathbf{B_{57}}$ | = | $y_{8} \, \mathbf{a}_{1}+z_{8} \, \mathbf{a}_{2}+x_{8} \, \mathbf{a}_{3}$ | = | $a y_{8} \,\mathbf{\hat{x}}+a z_{8} \,\mathbf{\hat{y}}+a x_{8} \,\mathbf{\hat{z}}$ | (24i) | Li V |
| $\mathbf{B_{58}}$ | = | $- y_{8} \, \mathbf{a}_{1}+z_{8} \, \mathbf{a}_{2}- x_{8} \, \mathbf{a}_{3}$ | = | $- a y_{8} \,\mathbf{\hat{x}}+a z_{8} \,\mathbf{\hat{y}}- a x_{8} \,\mathbf{\hat{z}}$ | (24i) | Li V |
| $\mathbf{B_{59}}$ | = | $y_{8} \, \mathbf{a}_{1}- z_{8} \, \mathbf{a}_{2}- x_{8} \, \mathbf{a}_{3}$ | = | $a y_{8} \,\mathbf{\hat{x}}- a z_{8} \,\mathbf{\hat{y}}- a x_{8} \,\mathbf{\hat{z}}$ | (24i) | Li V |
| $\mathbf{B_{60}}$ | = | $- y_{8} \, \mathbf{a}_{1}- z_{8} \, \mathbf{a}_{2}+x_{8} \, \mathbf{a}_{3}$ | = | $- a y_{8} \,\mathbf{\hat{x}}- a z_{8} \,\mathbf{\hat{y}}+a x_{8} \,\mathbf{\hat{z}}$ | (24i) | Li V |
| $\mathbf{B_{61}}$ | = | $\left(y_{8} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{8} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(z_{8} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{8} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(x_{8} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+a \left(z_{8} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24i) | Li V |
| $\mathbf{B_{62}}$ | = | $- \left(y_{8} - \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{8} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(z_{8} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{8} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(x_{8} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+a \left(z_{8} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24i) | Li V |
| $\mathbf{B_{63}}$ | = | $\left(y_{8} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{8} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{8} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{8} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(x_{8} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(z_{8} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24i) | Li V |
| $\mathbf{B_{64}}$ | = | $- \left(y_{8} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{8} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{8} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{8} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(x_{8} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(z_{8} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24i) | Li V |
| $\mathbf{B_{65}}$ | = | $\left(x_{8} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(z_{8} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(y_{8} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{8} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(z_{8} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+a \left(y_{8} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24i) | Li V |
| $\mathbf{B_{66}}$ | = | $- \left(x_{8} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(z_{8} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(y_{8} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{8} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(z_{8} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(y_{8} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24i) | Li V |
| $\mathbf{B_{67}}$ | = | $- \left(x_{8} - \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(z_{8} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(y_{8} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{8} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(z_{8} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+a \left(y_{8} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24i) | Li V |
| $\mathbf{B_{68}}$ | = | $\left(x_{8} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(z_{8} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(y_{8} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{8} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(z_{8} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(y_{8} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24i) | Li V |
| $\mathbf{B_{69}}$ | = | $\left(z_{8} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{8} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{8} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(z_{8} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(y_{8} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+a \left(x_{8} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24i) | Li V |
| $\mathbf{B_{70}}$ | = | $\left(z_{8} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{8} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{8} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(z_{8} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(y_{8} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(x_{8} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24i) | Li V |
| $\mathbf{B_{71}}$ | = | $- \left(z_{8} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{8} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{8} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(z_{8} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(y_{8} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(x_{8} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24i) | Li V |
| $\mathbf{B_{72}}$ | = | $- \left(z_{8} - \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{8} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{8} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(z_{8} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(y_{8} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+a \left(x_{8} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24i) | Li V |
| $\mathbf{B_{73}}$ | = | $x_{9} \, \mathbf{a}_{1}+y_{9} \, \mathbf{a}_{2}+z_{9} \, \mathbf{a}_{3}$ | = | $a x_{9} \,\mathbf{\hat{x}}+a y_{9} \,\mathbf{\hat{y}}+a z_{9} \,\mathbf{\hat{z}}$ | (24i) | N II |
| $\mathbf{B_{74}}$ | = | $- x_{9} \, \mathbf{a}_{1}- y_{9} \, \mathbf{a}_{2}+z_{9} \, \mathbf{a}_{3}$ | = | $- a x_{9} \,\mathbf{\hat{x}}- a y_{9} \,\mathbf{\hat{y}}+a z_{9} \,\mathbf{\hat{z}}$ | (24i) | N II |
| $\mathbf{B_{75}}$ | = | $- x_{9} \, \mathbf{a}_{1}+y_{9} \, \mathbf{a}_{2}- z_{9} \, \mathbf{a}_{3}$ | = | $- a x_{9} \,\mathbf{\hat{x}}+a y_{9} \,\mathbf{\hat{y}}- a z_{9} \,\mathbf{\hat{z}}$ | (24i) | N II |
| $\mathbf{B_{76}}$ | = | $x_{9} \, \mathbf{a}_{1}- y_{9} \, \mathbf{a}_{2}- z_{9} \, \mathbf{a}_{3}$ | = | $a x_{9} \,\mathbf{\hat{x}}- a y_{9} \,\mathbf{\hat{y}}- a z_{9} \,\mathbf{\hat{z}}$ | (24i) | N II |
| $\mathbf{B_{77}}$ | = | $z_{9} \, \mathbf{a}_{1}+x_{9} \, \mathbf{a}_{2}+y_{9} \, \mathbf{a}_{3}$ | = | $a z_{9} \,\mathbf{\hat{x}}+a x_{9} \,\mathbf{\hat{y}}+a y_{9} \,\mathbf{\hat{z}}$ | (24i) | N II |
| $\mathbf{B_{78}}$ | = | $z_{9} \, \mathbf{a}_{1}- x_{9} \, \mathbf{a}_{2}- y_{9} \, \mathbf{a}_{3}$ | = | $a z_{9} \,\mathbf{\hat{x}}- a x_{9} \,\mathbf{\hat{y}}- a y_{9} \,\mathbf{\hat{z}}$ | (24i) | N II |
| $\mathbf{B_{79}}$ | = | $- z_{9} \, \mathbf{a}_{1}- x_{9} \, \mathbf{a}_{2}+y_{9} \, \mathbf{a}_{3}$ | = | $- a z_{9} \,\mathbf{\hat{x}}- a x_{9} \,\mathbf{\hat{y}}+a y_{9} \,\mathbf{\hat{z}}$ | (24i) | N II |
| $\mathbf{B_{80}}$ | = | $- z_{9} \, \mathbf{a}_{1}+x_{9} \, \mathbf{a}_{2}- y_{9} \, \mathbf{a}_{3}$ | = | $- a z_{9} \,\mathbf{\hat{x}}+a x_{9} \,\mathbf{\hat{y}}- a y_{9} \,\mathbf{\hat{z}}$ | (24i) | N II |
| $\mathbf{B_{81}}$ | = | $y_{9} \, \mathbf{a}_{1}+z_{9} \, \mathbf{a}_{2}+x_{9} \, \mathbf{a}_{3}$ | = | $a y_{9} \,\mathbf{\hat{x}}+a z_{9} \,\mathbf{\hat{y}}+a x_{9} \,\mathbf{\hat{z}}$ | (24i) | N II |
| $\mathbf{B_{82}}$ | = | $- y_{9} \, \mathbf{a}_{1}+z_{9} \, \mathbf{a}_{2}- x_{9} \, \mathbf{a}_{3}$ | = | $- a y_{9} \,\mathbf{\hat{x}}+a z_{9} \,\mathbf{\hat{y}}- a x_{9} \,\mathbf{\hat{z}}$ | (24i) | N II |
| $\mathbf{B_{83}}$ | = | $y_{9} \, \mathbf{a}_{1}- z_{9} \, \mathbf{a}_{2}- x_{9} \, \mathbf{a}_{3}$ | = | $a y_{9} \,\mathbf{\hat{x}}- a z_{9} \,\mathbf{\hat{y}}- a x_{9} \,\mathbf{\hat{z}}$ | (24i) | N II |
| $\mathbf{B_{84}}$ | = | $- y_{9} \, \mathbf{a}_{1}- z_{9} \, \mathbf{a}_{2}+x_{9} \, \mathbf{a}_{3}$ | = | $- a y_{9} \,\mathbf{\hat{x}}- a z_{9} \,\mathbf{\hat{y}}+a x_{9} \,\mathbf{\hat{z}}$ | (24i) | N II |
| $\mathbf{B_{85}}$ | = | $\left(y_{9} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{9} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(z_{9} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{9} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(x_{9} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+a \left(z_{9} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24i) | N II |
| $\mathbf{B_{86}}$ | = | $- \left(y_{9} - \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{9} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(z_{9} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{9} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(x_{9} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+a \left(z_{9} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24i) | N II |
| $\mathbf{B_{87}}$ | = | $\left(y_{9} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{9} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{9} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{9} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(x_{9} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(z_{9} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24i) | N II |
| $\mathbf{B_{88}}$ | = | $- \left(y_{9} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{9} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{9} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{9} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(x_{9} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(z_{9} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24i) | N II |
| $\mathbf{B_{89}}$ | = | $\left(x_{9} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(z_{9} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(y_{9} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{9} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(z_{9} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+a \left(y_{9} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24i) | N II |
| $\mathbf{B_{90}}$ | = | $- \left(x_{9} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(z_{9} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(y_{9} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{9} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(z_{9} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(y_{9} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24i) | N II |
| $\mathbf{B_{91}}$ | = | $- \left(x_{9} - \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(z_{9} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(y_{9} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{9} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(z_{9} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+a \left(y_{9} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24i) | N II |
| $\mathbf{B_{92}}$ | = | $\left(x_{9} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(z_{9} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(y_{9} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{9} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(z_{9} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(y_{9} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24i) | N II |
| $\mathbf{B_{93}}$ | = | $\left(z_{9} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{9} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{9} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(z_{9} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(y_{9} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+a \left(x_{9} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24i) | N II |
| $\mathbf{B_{94}}$ | = | $\left(z_{9} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{9} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{9} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(z_{9} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(y_{9} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(x_{9} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24i) | N II |
| $\mathbf{B_{95}}$ | = | $- \left(z_{9} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{9} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{9} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(z_{9} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(y_{9} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(x_{9} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24i) | N II |
| $\mathbf{B_{96}}$ | = | $- \left(z_{9} - \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{9} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{9} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(z_{9} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(y_{9} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+a \left(x_{9} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24i) | N II |
References
- J. Cabana, N. Duprë, G. Rousse, C. P. Grey, and M. R. Palacín, Ex situ NMR and neutron diffraction study of structure and lithium motion in Li$_{7}$MnN$_{4}$, Solid State Ion. 176, 2205–2218 (2005), doi:10.1016/j.ssi.2005.07.001.
Found in
- K. Kushida, Y. Ichihashi, Y. Suzuki, and K. Kuriyama, Electronic structural difference between Li$_{7}$VN$_{4}$ and Li$_{7}$MnN$_{4}$ due to the replacement of V with Mn: A simulation by a discrete variational X$\alpha$ method, Physica B 405, 2305–2310 (2010), doi:10.1016/j.physb.2010.02.033.
Prototype Generator
aflow --proto=A7BC4_cP96_218_bcefi_ad_ei --params=$a,x_{5},x_{6},x_{7},x_{8},y_{8},z_{8},x_{9},y_{9},z_{9}$