Li$_{17}$Pb$_{4}$ Structure: A17B4_cF420_216_a6efg4h_2efg-001
| Prototype | Li$_{17}$Pb$_{4}$ |
| AFLOW prototype label | A17B4_cF420_216_a6efg4h_2efg-001 |
| ICSD | 107216 |
| Pearson symbol | cF420 |
| Space group number | 216 |
| Space group symbol | $F\overline{4}3m$ |
| AFLOW prototype command |
aflow --proto=A17B4_cF420_216_a6efg4h_2efg-001
--params=$a, \allowbreak x_{2}, \allowbreak x_{3}, \allowbreak x_{4}, \allowbreak x_{5}, \allowbreak x_{6}, \allowbreak x_{7}, \allowbreak x_{8}, \allowbreak x_{9}, \allowbreak x_{10}, \allowbreak x_{11}, \allowbreak x_{12}, \allowbreak x_{13}, \allowbreak x_{14}, \allowbreak z_{14}, \allowbreak x_{15}, \allowbreak z_{15}, \allowbreak x_{16}, \allowbreak z_{16}, \allowbreak x_{17}, \allowbreak z_{17}$ |
Other compounds with this structure
Li$_{17}$Ge$_{4}$, Li$_{17}$Si$_{4}$, Li$_{17}$Sn$_{4}$
- (Goward, 2001) propose this as a replacement for the Li$_{22}$Si$_{5}$ structure. The change in stoichiometry is accounted for by placing extra lithium atoms on the the (4c) site $(1/4 1/4 1/4)$ and an additional (16e) site $(x x x)$, adjusting the stoichiometry to fit Li$_{21}$M$_{5}$ or Li$_{22}$M$_{5}$ as needed. Phase diagrams quoted in (Villars, 2018) support this change.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $0$ | = | $0$ | (4a) | Li 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) | Li II |
| $\mathbf{B_{3}}$ | = | $x_{2} \, \mathbf{a}_{1}+x_{2} \, \mathbf{a}_{2}- 3 x_{2} \, \mathbf{a}_{3}$ | = | $- a x_{2} \,\mathbf{\hat{x}}- a x_{2} \,\mathbf{\hat{y}}+a x_{2} \,\mathbf{\hat{z}}$ | (16e) | Li II |
| $\mathbf{B_{4}}$ | = | $x_{2} \, \mathbf{a}_{1}- 3 x_{2} \, \mathbf{a}_{2}+x_{2} \, \mathbf{a}_{3}$ | = | $- a x_{2} \,\mathbf{\hat{x}}+a x_{2} \,\mathbf{\hat{y}}- a x_{2} \,\mathbf{\hat{z}}$ | (16e) | Li II |
| $\mathbf{B_{5}}$ | = | $- 3 x_{2} \, \mathbf{a}_{1}+x_{2} \, \mathbf{a}_{2}+x_{2} \, \mathbf{a}_{3}$ | = | $a x_{2} \,\mathbf{\hat{x}}- a x_{2} \,\mathbf{\hat{y}}- a x_{2} \,\mathbf{\hat{z}}$ | (16e) | Li II |
| $\mathbf{B_{6}}$ | = | $x_{3} \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{2}+x_{3} \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{x}}+a x_{3} \,\mathbf{\hat{y}}+a x_{3} \,\mathbf{\hat{z}}$ | (16e) | Li III |
| $\mathbf{B_{7}}$ | = | $x_{3} \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{2}- 3 x_{3} \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}- a x_{3} \,\mathbf{\hat{y}}+a x_{3} \,\mathbf{\hat{z}}$ | (16e) | Li III |
| $\mathbf{B_{8}}$ | = | $x_{3} \, \mathbf{a}_{1}- 3 x_{3} \, \mathbf{a}_{2}+x_{3} \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}+a x_{3} \,\mathbf{\hat{y}}- a x_{3} \,\mathbf{\hat{z}}$ | (16e) | Li III |
| $\mathbf{B_{9}}$ | = | $- 3 x_{3} \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{2}+x_{3} \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{x}}- a x_{3} \,\mathbf{\hat{y}}- a x_{3} \,\mathbf{\hat{z}}$ | (16e) | Li III |
| $\mathbf{B_{10}}$ | = | $x_{4} \, \mathbf{a}_{1}+x_{4} \, \mathbf{a}_{2}+x_{4} \, \mathbf{a}_{3}$ | = | $a x_{4} \,\mathbf{\hat{x}}+a x_{4} \,\mathbf{\hat{y}}+a x_{4} \,\mathbf{\hat{z}}$ | (16e) | Li IV |
| $\mathbf{B_{11}}$ | = | $x_{4} \, \mathbf{a}_{1}+x_{4} \, \mathbf{a}_{2}- 3 x_{4} \, \mathbf{a}_{3}$ | = | $- a x_{4} \,\mathbf{\hat{x}}- a x_{4} \,\mathbf{\hat{y}}+a x_{4} \,\mathbf{\hat{z}}$ | (16e) | Li IV |
| $\mathbf{B_{12}}$ | = | $x_{4} \, \mathbf{a}_{1}- 3 x_{4} \, \mathbf{a}_{2}+x_{4} \, \mathbf{a}_{3}$ | = | $- a x_{4} \,\mathbf{\hat{x}}+a x_{4} \,\mathbf{\hat{y}}- a x_{4} \,\mathbf{\hat{z}}$ | (16e) | Li IV |
| $\mathbf{B_{13}}$ | = | $- 3 x_{4} \, \mathbf{a}_{1}+x_{4} \, \mathbf{a}_{2}+x_{4} \, \mathbf{a}_{3}$ | = | $a x_{4} \,\mathbf{\hat{x}}- a x_{4} \,\mathbf{\hat{y}}- a x_{4} \,\mathbf{\hat{z}}$ | (16e) | Li IV |
| $\mathbf{B_{14}}$ | = | $x_{5} \, \mathbf{a}_{1}+x_{5} \, \mathbf{a}_{2}+x_{5} \, \mathbf{a}_{3}$ | = | $a x_{5} \,\mathbf{\hat{x}}+a x_{5} \,\mathbf{\hat{y}}+a x_{5} \,\mathbf{\hat{z}}$ | (16e) | Li V |
| $\mathbf{B_{15}}$ | = | $x_{5} \, \mathbf{a}_{1}+x_{5} \, \mathbf{a}_{2}- 3 x_{5} \, \mathbf{a}_{3}$ | = | $- a x_{5} \,\mathbf{\hat{x}}- a x_{5} \,\mathbf{\hat{y}}+a x_{5} \,\mathbf{\hat{z}}$ | (16e) | Li V |
| $\mathbf{B_{16}}$ | = | $x_{5} \, \mathbf{a}_{1}- 3 x_{5} \, \mathbf{a}_{2}+x_{5} \, \mathbf{a}_{3}$ | = | $- a x_{5} \,\mathbf{\hat{x}}+a x_{5} \,\mathbf{\hat{y}}- a x_{5} \,\mathbf{\hat{z}}$ | (16e) | Li V |
| $\mathbf{B_{17}}$ | = | $- 3 x_{5} \, \mathbf{a}_{1}+x_{5} \, \mathbf{a}_{2}+x_{5} \, \mathbf{a}_{3}$ | = | $a x_{5} \,\mathbf{\hat{x}}- a x_{5} \,\mathbf{\hat{y}}- a x_{5} \,\mathbf{\hat{z}}$ | (16e) | Li V |
| $\mathbf{B_{18}}$ | = | $x_{6} \, \mathbf{a}_{1}+x_{6} \, \mathbf{a}_{2}+x_{6} \, \mathbf{a}_{3}$ | = | $a x_{6} \,\mathbf{\hat{x}}+a x_{6} \,\mathbf{\hat{y}}+a x_{6} \,\mathbf{\hat{z}}$ | (16e) | Li VI |
| $\mathbf{B_{19}}$ | = | $x_{6} \, \mathbf{a}_{1}+x_{6} \, \mathbf{a}_{2}- 3 x_{6} \, \mathbf{a}_{3}$ | = | $- a x_{6} \,\mathbf{\hat{x}}- a x_{6} \,\mathbf{\hat{y}}+a x_{6} \,\mathbf{\hat{z}}$ | (16e) | Li VI |
| $\mathbf{B_{20}}$ | = | $x_{6} \, \mathbf{a}_{1}- 3 x_{6} \, \mathbf{a}_{2}+x_{6} \, \mathbf{a}_{3}$ | = | $- a x_{6} \,\mathbf{\hat{x}}+a x_{6} \,\mathbf{\hat{y}}- a x_{6} \,\mathbf{\hat{z}}$ | (16e) | Li VI |
| $\mathbf{B_{21}}$ | = | $- 3 x_{6} \, \mathbf{a}_{1}+x_{6} \, \mathbf{a}_{2}+x_{6} \, \mathbf{a}_{3}$ | = | $a x_{6} \,\mathbf{\hat{x}}- a x_{6} \,\mathbf{\hat{y}}- a x_{6} \,\mathbf{\hat{z}}$ | (16e) | Li VI |
| $\mathbf{B_{22}}$ | = | $x_{7} \, \mathbf{a}_{1}+x_{7} \, \mathbf{a}_{2}+x_{7} \, \mathbf{a}_{3}$ | = | $a x_{7} \,\mathbf{\hat{x}}+a x_{7} \,\mathbf{\hat{y}}+a x_{7} \,\mathbf{\hat{z}}$ | (16e) | Li VII |
| $\mathbf{B_{23}}$ | = | $x_{7} \, \mathbf{a}_{1}+x_{7} \, \mathbf{a}_{2}- 3 x_{7} \, \mathbf{a}_{3}$ | = | $- a x_{7} \,\mathbf{\hat{x}}- a x_{7} \,\mathbf{\hat{y}}+a x_{7} \,\mathbf{\hat{z}}$ | (16e) | Li VII |
| $\mathbf{B_{24}}$ | = | $x_{7} \, \mathbf{a}_{1}- 3 x_{7} \, \mathbf{a}_{2}+x_{7} \, \mathbf{a}_{3}$ | = | $- a x_{7} \,\mathbf{\hat{x}}+a x_{7} \,\mathbf{\hat{y}}- a x_{7} \,\mathbf{\hat{z}}$ | (16e) | Li VII |
| $\mathbf{B_{25}}$ | = | $- 3 x_{7} \, \mathbf{a}_{1}+x_{7} \, \mathbf{a}_{2}+x_{7} \, \mathbf{a}_{3}$ | = | $a x_{7} \,\mathbf{\hat{x}}- a x_{7} \,\mathbf{\hat{y}}- a x_{7} \,\mathbf{\hat{z}}$ | (16e) | Li VII |
| $\mathbf{B_{26}}$ | = | $x_{8} \, \mathbf{a}_{1}+x_{8} \, \mathbf{a}_{2}+x_{8} \, \mathbf{a}_{3}$ | = | $a x_{8} \,\mathbf{\hat{x}}+a x_{8} \,\mathbf{\hat{y}}+a x_{8} \,\mathbf{\hat{z}}$ | (16e) | Pb I |
| $\mathbf{B_{27}}$ | = | $x_{8} \, \mathbf{a}_{1}+x_{8} \, \mathbf{a}_{2}- 3 x_{8} \, \mathbf{a}_{3}$ | = | $- a x_{8} \,\mathbf{\hat{x}}- a x_{8} \,\mathbf{\hat{y}}+a x_{8} \,\mathbf{\hat{z}}$ | (16e) | Pb I |
| $\mathbf{B_{28}}$ | = | $x_{8} \, \mathbf{a}_{1}- 3 x_{8} \, \mathbf{a}_{2}+x_{8} \, \mathbf{a}_{3}$ | = | $- a x_{8} \,\mathbf{\hat{x}}+a x_{8} \,\mathbf{\hat{y}}- a x_{8} \,\mathbf{\hat{z}}$ | (16e) | Pb I |
| $\mathbf{B_{29}}$ | = | $- 3 x_{8} \, \mathbf{a}_{1}+x_{8} \, \mathbf{a}_{2}+x_{8} \, \mathbf{a}_{3}$ | = | $a x_{8} \,\mathbf{\hat{x}}- a x_{8} \,\mathbf{\hat{y}}- a x_{8} \,\mathbf{\hat{z}}$ | (16e) | Pb I |
| $\mathbf{B_{30}}$ | = | $x_{9} \, \mathbf{a}_{1}+x_{9} \, \mathbf{a}_{2}+x_{9} \, \mathbf{a}_{3}$ | = | $a x_{9} \,\mathbf{\hat{x}}+a x_{9} \,\mathbf{\hat{y}}+a x_{9} \,\mathbf{\hat{z}}$ | (16e) | Pb II |
| $\mathbf{B_{31}}$ | = | $x_{9} \, \mathbf{a}_{1}+x_{9} \, \mathbf{a}_{2}- 3 x_{9} \, \mathbf{a}_{3}$ | = | $- a x_{9} \,\mathbf{\hat{x}}- a x_{9} \,\mathbf{\hat{y}}+a x_{9} \,\mathbf{\hat{z}}$ | (16e) | Pb II |
| $\mathbf{B_{32}}$ | = | $x_{9} \, \mathbf{a}_{1}- 3 x_{9} \, \mathbf{a}_{2}+x_{9} \, \mathbf{a}_{3}$ | = | $- a x_{9} \,\mathbf{\hat{x}}+a x_{9} \,\mathbf{\hat{y}}- a x_{9} \,\mathbf{\hat{z}}$ | (16e) | Pb II |
| $\mathbf{B_{33}}$ | = | $- 3 x_{9} \, \mathbf{a}_{1}+x_{9} \, \mathbf{a}_{2}+x_{9} \, \mathbf{a}_{3}$ | = | $a x_{9} \,\mathbf{\hat{x}}- a x_{9} \,\mathbf{\hat{y}}- a x_{9} \,\mathbf{\hat{z}}$ | (16e) | Pb II |
| $\mathbf{B_{34}}$ | = | $- x_{10} \, \mathbf{a}_{1}+x_{10} \, \mathbf{a}_{2}+x_{10} \, \mathbf{a}_{3}$ | = | $a x_{10} \,\mathbf{\hat{x}}$ | (24f) | Li VIII |
| $\mathbf{B_{35}}$ | = | $x_{10} \, \mathbf{a}_{1}- x_{10} \, \mathbf{a}_{2}- x_{10} \, \mathbf{a}_{3}$ | = | $- a x_{10} \,\mathbf{\hat{x}}$ | (24f) | Li VIII |
| $\mathbf{B_{36}}$ | = | $x_{10} \, \mathbf{a}_{1}- x_{10} \, \mathbf{a}_{2}+x_{10} \, \mathbf{a}_{3}$ | = | $a x_{10} \,\mathbf{\hat{y}}$ | (24f) | Li VIII |
| $\mathbf{B_{37}}$ | = | $- x_{10} \, \mathbf{a}_{1}+x_{10} \, \mathbf{a}_{2}- x_{10} \, \mathbf{a}_{3}$ | = | $- a x_{10} \,\mathbf{\hat{y}}$ | (24f) | Li VIII |
| $\mathbf{B_{38}}$ | = | $x_{10} \, \mathbf{a}_{1}+x_{10} \, \mathbf{a}_{2}- x_{10} \, \mathbf{a}_{3}$ | = | $a x_{10} \,\mathbf{\hat{z}}$ | (24f) | Li VIII |
| $\mathbf{B_{39}}$ | = | $- x_{10} \, \mathbf{a}_{1}- x_{10} \, \mathbf{a}_{2}+x_{10} \, \mathbf{a}_{3}$ | = | $- a x_{10} \,\mathbf{\hat{z}}$ | (24f) | Li VIII |
| $\mathbf{B_{40}}$ | = | $- x_{11} \, \mathbf{a}_{1}+x_{11} \, \mathbf{a}_{2}+x_{11} \, \mathbf{a}_{3}$ | = | $a x_{11} \,\mathbf{\hat{x}}$ | (24f) | Pb III |
| $\mathbf{B_{41}}$ | = | $x_{11} \, \mathbf{a}_{1}- x_{11} \, \mathbf{a}_{2}- x_{11} \, \mathbf{a}_{3}$ | = | $- a x_{11} \,\mathbf{\hat{x}}$ | (24f) | Pb III |
| $\mathbf{B_{42}}$ | = | $x_{11} \, \mathbf{a}_{1}- x_{11} \, \mathbf{a}_{2}+x_{11} \, \mathbf{a}_{3}$ | = | $a x_{11} \,\mathbf{\hat{y}}$ | (24f) | Pb III |
| $\mathbf{B_{43}}$ | = | $- x_{11} \, \mathbf{a}_{1}+x_{11} \, \mathbf{a}_{2}- x_{11} \, \mathbf{a}_{3}$ | = | $- a x_{11} \,\mathbf{\hat{y}}$ | (24f) | Pb III |
| $\mathbf{B_{44}}$ | = | $x_{11} \, \mathbf{a}_{1}+x_{11} \, \mathbf{a}_{2}- x_{11} \, \mathbf{a}_{3}$ | = | $a x_{11} \,\mathbf{\hat{z}}$ | (24f) | Pb III |
| $\mathbf{B_{45}}$ | = | $- x_{11} \, \mathbf{a}_{1}- x_{11} \, \mathbf{a}_{2}+x_{11} \, \mathbf{a}_{3}$ | = | $- a x_{11} \,\mathbf{\hat{z}}$ | (24f) | Pb III |
| $\mathbf{B_{46}}$ | = | $- \left(x_{12} - \frac{1}{2}\right) \, \mathbf{a}_{1}+x_{12} \, \mathbf{a}_{2}+x_{12} \, \mathbf{a}_{3}$ | = | $a x_{12} \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (24g) | Li IX |
| $\mathbf{B_{47}}$ | = | $x_{12} \, \mathbf{a}_{1}- \left(x_{12} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{12} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{12} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (24g) | Li IX |
| $\mathbf{B_{48}}$ | = | $x_{12} \, \mathbf{a}_{1}- \left(x_{12} - \frac{1}{2}\right) \, \mathbf{a}_{2}+x_{12} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+a x_{12} \,\mathbf{\hat{y}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (24g) | Li IX |
| $\mathbf{B_{49}}$ | = | $- \left(x_{12} - \frac{1}{2}\right) \, \mathbf{a}_{1}+x_{12} \, \mathbf{a}_{2}- \left(x_{12} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}- a \left(x_{12} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (24g) | Li IX |
| $\mathbf{B_{50}}$ | = | $x_{12} \, \mathbf{a}_{1}+x_{12} \, \mathbf{a}_{2}- \left(x_{12} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+a x_{12} \,\mathbf{\hat{z}}$ | (24g) | Li IX |
| $\mathbf{B_{51}}$ | = | $- \left(x_{12} - \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{12} - \frac{1}{2}\right) \, \mathbf{a}_{2}+x_{12} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}- a \left(x_{12} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24g) | Li IX |
| $\mathbf{B_{52}}$ | = | $- \left(x_{13} - \frac{1}{2}\right) \, \mathbf{a}_{1}+x_{13} \, \mathbf{a}_{2}+x_{13} \, \mathbf{a}_{3}$ | = | $a x_{13} \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (24g) | Pb IV |
| $\mathbf{B_{53}}$ | = | $x_{13} \, \mathbf{a}_{1}- \left(x_{13} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{13} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{13} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (24g) | Pb IV |
| $\mathbf{B_{54}}$ | = | $x_{13} \, \mathbf{a}_{1}- \left(x_{13} - \frac{1}{2}\right) \, \mathbf{a}_{2}+x_{13} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+a x_{13} \,\mathbf{\hat{y}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (24g) | Pb IV |
| $\mathbf{B_{55}}$ | = | $- \left(x_{13} - \frac{1}{2}\right) \, \mathbf{a}_{1}+x_{13} \, \mathbf{a}_{2}- \left(x_{13} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}- a \left(x_{13} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (24g) | Pb IV |
| $\mathbf{B_{56}}$ | = | $x_{13} \, \mathbf{a}_{1}+x_{13} \, \mathbf{a}_{2}- \left(x_{13} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+a x_{13} \,\mathbf{\hat{z}}$ | (24g) | Pb IV |
| $\mathbf{B_{57}}$ | = | $- \left(x_{13} - \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{13} - \frac{1}{2}\right) \, \mathbf{a}_{2}+x_{13} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}- a \left(x_{13} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24g) | Pb IV |
| $\mathbf{B_{58}}$ | = | $z_{14} \, \mathbf{a}_{1}+z_{14} \, \mathbf{a}_{2}+\left(2 x_{14} - z_{14}\right) \, \mathbf{a}_{3}$ | = | $a x_{14} \,\mathbf{\hat{x}}+a x_{14} \,\mathbf{\hat{y}}+a z_{14} \,\mathbf{\hat{z}}$ | (48h) | Li X |
| $\mathbf{B_{59}}$ | = | $z_{14} \, \mathbf{a}_{1}+z_{14} \, \mathbf{a}_{2}- \left(2 x_{14} + z_{14}\right) \, \mathbf{a}_{3}$ | = | $- a x_{14} \,\mathbf{\hat{x}}- a x_{14} \,\mathbf{\hat{y}}+a z_{14} \,\mathbf{\hat{z}}$ | (48h) | Li X |
| $\mathbf{B_{60}}$ | = | $\left(2 x_{14} - z_{14}\right) \, \mathbf{a}_{1}- \left(2 x_{14} + z_{14}\right) \, \mathbf{a}_{2}+z_{14} \, \mathbf{a}_{3}$ | = | $- a x_{14} \,\mathbf{\hat{x}}+a x_{14} \,\mathbf{\hat{y}}- a z_{14} \,\mathbf{\hat{z}}$ | (48h) | Li X |
| $\mathbf{B_{61}}$ | = | $- \left(2 x_{14} + z_{14}\right) \, \mathbf{a}_{1}+\left(2 x_{14} - z_{14}\right) \, \mathbf{a}_{2}+z_{14} \, \mathbf{a}_{3}$ | = | $a x_{14} \,\mathbf{\hat{x}}- a x_{14} \,\mathbf{\hat{y}}- a z_{14} \,\mathbf{\hat{z}}$ | (48h) | Li X |
| $\mathbf{B_{62}}$ | = | $\left(2 x_{14} - z_{14}\right) \, \mathbf{a}_{1}+z_{14} \, \mathbf{a}_{2}+z_{14} \, \mathbf{a}_{3}$ | = | $a z_{14} \,\mathbf{\hat{x}}+a x_{14} \,\mathbf{\hat{y}}+a x_{14} \,\mathbf{\hat{z}}$ | (48h) | Li X |
| $\mathbf{B_{63}}$ | = | $- \left(2 x_{14} + z_{14}\right) \, \mathbf{a}_{1}+z_{14} \, \mathbf{a}_{2}+z_{14} \, \mathbf{a}_{3}$ | = | $a z_{14} \,\mathbf{\hat{x}}- a x_{14} \,\mathbf{\hat{y}}- a x_{14} \,\mathbf{\hat{z}}$ | (48h) | Li X |
| $\mathbf{B_{64}}$ | = | $z_{14} \, \mathbf{a}_{1}+\left(2 x_{14} - z_{14}\right) \, \mathbf{a}_{2}- \left(2 x_{14} + z_{14}\right) \, \mathbf{a}_{3}$ | = | $- a z_{14} \,\mathbf{\hat{x}}- a x_{14} \,\mathbf{\hat{y}}+a x_{14} \,\mathbf{\hat{z}}$ | (48h) | Li X |
| $\mathbf{B_{65}}$ | = | $z_{14} \, \mathbf{a}_{1}- \left(2 x_{14} + z_{14}\right) \, \mathbf{a}_{2}+\left(2 x_{14} - z_{14}\right) \, \mathbf{a}_{3}$ | = | $- a z_{14} \,\mathbf{\hat{x}}+a x_{14} \,\mathbf{\hat{y}}- a x_{14} \,\mathbf{\hat{z}}$ | (48h) | Li X |
| $\mathbf{B_{66}}$ | = | $z_{14} \, \mathbf{a}_{1}+\left(2 x_{14} - z_{14}\right) \, \mathbf{a}_{2}+z_{14} \, \mathbf{a}_{3}$ | = | $a x_{14} \,\mathbf{\hat{x}}+a z_{14} \,\mathbf{\hat{y}}+a x_{14} \,\mathbf{\hat{z}}$ | (48h) | Li X |
| $\mathbf{B_{67}}$ | = | $z_{14} \, \mathbf{a}_{1}- \left(2 x_{14} + z_{14}\right) \, \mathbf{a}_{2}+z_{14} \, \mathbf{a}_{3}$ | = | $- a x_{14} \,\mathbf{\hat{x}}+a z_{14} \,\mathbf{\hat{y}}- a x_{14} \,\mathbf{\hat{z}}$ | (48h) | Li X |
| $\mathbf{B_{68}}$ | = | $- \left(2 x_{14} + z_{14}\right) \, \mathbf{a}_{1}+z_{14} \, \mathbf{a}_{2}+\left(2 x_{14} - z_{14}\right) \, \mathbf{a}_{3}$ | = | $a x_{14} \,\mathbf{\hat{x}}- a z_{14} \,\mathbf{\hat{y}}- a x_{14} \,\mathbf{\hat{z}}$ | (48h) | Li X |
| $\mathbf{B_{69}}$ | = | $\left(2 x_{14} - z_{14}\right) \, \mathbf{a}_{1}+z_{14} \, \mathbf{a}_{2}- \left(2 x_{14} + z_{14}\right) \, \mathbf{a}_{3}$ | = | $- a x_{14} \,\mathbf{\hat{x}}- a z_{14} \,\mathbf{\hat{y}}+a x_{14} \,\mathbf{\hat{z}}$ | (48h) | Li X |
| $\mathbf{B_{70}}$ | = | $z_{15} \, \mathbf{a}_{1}+z_{15} \, \mathbf{a}_{2}+\left(2 x_{15} - z_{15}\right) \, \mathbf{a}_{3}$ | = | $a x_{15} \,\mathbf{\hat{x}}+a x_{15} \,\mathbf{\hat{y}}+a z_{15} \,\mathbf{\hat{z}}$ | (48h) | Li XI |
| $\mathbf{B_{71}}$ | = | $z_{15} \, \mathbf{a}_{1}+z_{15} \, \mathbf{a}_{2}- \left(2 x_{15} + z_{15}\right) \, \mathbf{a}_{3}$ | = | $- a x_{15} \,\mathbf{\hat{x}}- a x_{15} \,\mathbf{\hat{y}}+a z_{15} \,\mathbf{\hat{z}}$ | (48h) | Li XI |
| $\mathbf{B_{72}}$ | = | $\left(2 x_{15} - z_{15}\right) \, \mathbf{a}_{1}- \left(2 x_{15} + z_{15}\right) \, \mathbf{a}_{2}+z_{15} \, \mathbf{a}_{3}$ | = | $- a x_{15} \,\mathbf{\hat{x}}+a x_{15} \,\mathbf{\hat{y}}- a z_{15} \,\mathbf{\hat{z}}$ | (48h) | Li XI |
| $\mathbf{B_{73}}$ | = | $- \left(2 x_{15} + z_{15}\right) \, \mathbf{a}_{1}+\left(2 x_{15} - z_{15}\right) \, \mathbf{a}_{2}+z_{15} \, \mathbf{a}_{3}$ | = | $a x_{15} \,\mathbf{\hat{x}}- a x_{15} \,\mathbf{\hat{y}}- a z_{15} \,\mathbf{\hat{z}}$ | (48h) | Li XI |
| $\mathbf{B_{74}}$ | = | $\left(2 x_{15} - z_{15}\right) \, \mathbf{a}_{1}+z_{15} \, \mathbf{a}_{2}+z_{15} \, \mathbf{a}_{3}$ | = | $a z_{15} \,\mathbf{\hat{x}}+a x_{15} \,\mathbf{\hat{y}}+a x_{15} \,\mathbf{\hat{z}}$ | (48h) | Li XI |
| $\mathbf{B_{75}}$ | = | $- \left(2 x_{15} + z_{15}\right) \, \mathbf{a}_{1}+z_{15} \, \mathbf{a}_{2}+z_{15} \, \mathbf{a}_{3}$ | = | $a z_{15} \,\mathbf{\hat{x}}- a x_{15} \,\mathbf{\hat{y}}- a x_{15} \,\mathbf{\hat{z}}$ | (48h) | Li XI |
| $\mathbf{B_{76}}$ | = | $z_{15} \, \mathbf{a}_{1}+\left(2 x_{15} - z_{15}\right) \, \mathbf{a}_{2}- \left(2 x_{15} + z_{15}\right) \, \mathbf{a}_{3}$ | = | $- a z_{15} \,\mathbf{\hat{x}}- a x_{15} \,\mathbf{\hat{y}}+a x_{15} \,\mathbf{\hat{z}}$ | (48h) | Li XI |
| $\mathbf{B_{77}}$ | = | $z_{15} \, \mathbf{a}_{1}- \left(2 x_{15} + z_{15}\right) \, \mathbf{a}_{2}+\left(2 x_{15} - z_{15}\right) \, \mathbf{a}_{3}$ | = | $- a z_{15} \,\mathbf{\hat{x}}+a x_{15} \,\mathbf{\hat{y}}- a x_{15} \,\mathbf{\hat{z}}$ | (48h) | Li XI |
| $\mathbf{B_{78}}$ | = | $z_{15} \, \mathbf{a}_{1}+\left(2 x_{15} - z_{15}\right) \, \mathbf{a}_{2}+z_{15} \, \mathbf{a}_{3}$ | = | $a x_{15} \,\mathbf{\hat{x}}+a z_{15} \,\mathbf{\hat{y}}+a x_{15} \,\mathbf{\hat{z}}$ | (48h) | Li XI |
| $\mathbf{B_{79}}$ | = | $z_{15} \, \mathbf{a}_{1}- \left(2 x_{15} + z_{15}\right) \, \mathbf{a}_{2}+z_{15} \, \mathbf{a}_{3}$ | = | $- a x_{15} \,\mathbf{\hat{x}}+a z_{15} \,\mathbf{\hat{y}}- a x_{15} \,\mathbf{\hat{z}}$ | (48h) | Li XI |
| $\mathbf{B_{80}}$ | = | $- \left(2 x_{15} + z_{15}\right) \, \mathbf{a}_{1}+z_{15} \, \mathbf{a}_{2}+\left(2 x_{15} - z_{15}\right) \, \mathbf{a}_{3}$ | = | $a x_{15} \,\mathbf{\hat{x}}- a z_{15} \,\mathbf{\hat{y}}- a x_{15} \,\mathbf{\hat{z}}$ | (48h) | Li XI |
| $\mathbf{B_{81}}$ | = | $\left(2 x_{15} - z_{15}\right) \, \mathbf{a}_{1}+z_{15} \, \mathbf{a}_{2}- \left(2 x_{15} + z_{15}\right) \, \mathbf{a}_{3}$ | = | $- a x_{15} \,\mathbf{\hat{x}}- a z_{15} \,\mathbf{\hat{y}}+a x_{15} \,\mathbf{\hat{z}}$ | (48h) | Li XI |
| $\mathbf{B_{82}}$ | = | $z_{16} \, \mathbf{a}_{1}+z_{16} \, \mathbf{a}_{2}+\left(2 x_{16} - z_{16}\right) \, \mathbf{a}_{3}$ | = | $a x_{16} \,\mathbf{\hat{x}}+a x_{16} \,\mathbf{\hat{y}}+a z_{16} \,\mathbf{\hat{z}}$ | (48h) | Li XII |
| $\mathbf{B_{83}}$ | = | $z_{16} \, \mathbf{a}_{1}+z_{16} \, \mathbf{a}_{2}- \left(2 x_{16} + z_{16}\right) \, \mathbf{a}_{3}$ | = | $- a x_{16} \,\mathbf{\hat{x}}- a x_{16} \,\mathbf{\hat{y}}+a z_{16} \,\mathbf{\hat{z}}$ | (48h) | Li XII |
| $\mathbf{B_{84}}$ | = | $\left(2 x_{16} - z_{16}\right) \, \mathbf{a}_{1}- \left(2 x_{16} + z_{16}\right) \, \mathbf{a}_{2}+z_{16} \, \mathbf{a}_{3}$ | = | $- a x_{16} \,\mathbf{\hat{x}}+a x_{16} \,\mathbf{\hat{y}}- a z_{16} \,\mathbf{\hat{z}}$ | (48h) | Li XII |
| $\mathbf{B_{85}}$ | = | $- \left(2 x_{16} + z_{16}\right) \, \mathbf{a}_{1}+\left(2 x_{16} - z_{16}\right) \, \mathbf{a}_{2}+z_{16} \, \mathbf{a}_{3}$ | = | $a x_{16} \,\mathbf{\hat{x}}- a x_{16} \,\mathbf{\hat{y}}- a z_{16} \,\mathbf{\hat{z}}$ | (48h) | Li XII |
| $\mathbf{B_{86}}$ | = | $\left(2 x_{16} - z_{16}\right) \, \mathbf{a}_{1}+z_{16} \, \mathbf{a}_{2}+z_{16} \, \mathbf{a}_{3}$ | = | $a z_{16} \,\mathbf{\hat{x}}+a x_{16} \,\mathbf{\hat{y}}+a x_{16} \,\mathbf{\hat{z}}$ | (48h) | Li XII |
| $\mathbf{B_{87}}$ | = | $- \left(2 x_{16} + z_{16}\right) \, \mathbf{a}_{1}+z_{16} \, \mathbf{a}_{2}+z_{16} \, \mathbf{a}_{3}$ | = | $a z_{16} \,\mathbf{\hat{x}}- a x_{16} \,\mathbf{\hat{y}}- a x_{16} \,\mathbf{\hat{z}}$ | (48h) | Li XII |
| $\mathbf{B_{88}}$ | = | $z_{16} \, \mathbf{a}_{1}+\left(2 x_{16} - z_{16}\right) \, \mathbf{a}_{2}- \left(2 x_{16} + z_{16}\right) \, \mathbf{a}_{3}$ | = | $- a z_{16} \,\mathbf{\hat{x}}- a x_{16} \,\mathbf{\hat{y}}+a x_{16} \,\mathbf{\hat{z}}$ | (48h) | Li XII |
| $\mathbf{B_{89}}$ | = | $z_{16} \, \mathbf{a}_{1}- \left(2 x_{16} + z_{16}\right) \, \mathbf{a}_{2}+\left(2 x_{16} - z_{16}\right) \, \mathbf{a}_{3}$ | = | $- a z_{16} \,\mathbf{\hat{x}}+a x_{16} \,\mathbf{\hat{y}}- a x_{16} \,\mathbf{\hat{z}}$ | (48h) | Li XII |
| $\mathbf{B_{90}}$ | = | $z_{16} \, \mathbf{a}_{1}+\left(2 x_{16} - z_{16}\right) \, \mathbf{a}_{2}+z_{16} \, \mathbf{a}_{3}$ | = | $a x_{16} \,\mathbf{\hat{x}}+a z_{16} \,\mathbf{\hat{y}}+a x_{16} \,\mathbf{\hat{z}}$ | (48h) | Li XII |
| $\mathbf{B_{91}}$ | = | $z_{16} \, \mathbf{a}_{1}- \left(2 x_{16} + z_{16}\right) \, \mathbf{a}_{2}+z_{16} \, \mathbf{a}_{3}$ | = | $- a x_{16} \,\mathbf{\hat{x}}+a z_{16} \,\mathbf{\hat{y}}- a x_{16} \,\mathbf{\hat{z}}$ | (48h) | Li XII |
| $\mathbf{B_{92}}$ | = | $- \left(2 x_{16} + z_{16}\right) \, \mathbf{a}_{1}+z_{16} \, \mathbf{a}_{2}+\left(2 x_{16} - z_{16}\right) \, \mathbf{a}_{3}$ | = | $a x_{16} \,\mathbf{\hat{x}}- a z_{16} \,\mathbf{\hat{y}}- a x_{16} \,\mathbf{\hat{z}}$ | (48h) | Li XII |
| $\mathbf{B_{93}}$ | = | $\left(2 x_{16} - z_{16}\right) \, \mathbf{a}_{1}+z_{16} \, \mathbf{a}_{2}- \left(2 x_{16} + z_{16}\right) \, \mathbf{a}_{3}$ | = | $- a x_{16} \,\mathbf{\hat{x}}- a z_{16} \,\mathbf{\hat{y}}+a x_{16} \,\mathbf{\hat{z}}$ | (48h) | Li XII |
| $\mathbf{B_{94}}$ | = | $z_{17} \, \mathbf{a}_{1}+z_{17} \, \mathbf{a}_{2}+\left(2 x_{17} - z_{17}\right) \, \mathbf{a}_{3}$ | = | $a x_{17} \,\mathbf{\hat{x}}+a x_{17} \,\mathbf{\hat{y}}+a z_{17} \,\mathbf{\hat{z}}$ | (48h) | Li XIII |
| $\mathbf{B_{95}}$ | = | $z_{17} \, \mathbf{a}_{1}+z_{17} \, \mathbf{a}_{2}- \left(2 x_{17} + z_{17}\right) \, \mathbf{a}_{3}$ | = | $- a x_{17} \,\mathbf{\hat{x}}- a x_{17} \,\mathbf{\hat{y}}+a z_{17} \,\mathbf{\hat{z}}$ | (48h) | Li XIII |
| $\mathbf{B_{96}}$ | = | $\left(2 x_{17} - z_{17}\right) \, \mathbf{a}_{1}- \left(2 x_{17} + z_{17}\right) \, \mathbf{a}_{2}+z_{17} \, \mathbf{a}_{3}$ | = | $- a x_{17} \,\mathbf{\hat{x}}+a x_{17} \,\mathbf{\hat{y}}- a z_{17} \,\mathbf{\hat{z}}$ | (48h) | Li XIII |
| $\mathbf{B_{97}}$ | = | $- \left(2 x_{17} + z_{17}\right) \, \mathbf{a}_{1}+\left(2 x_{17} - z_{17}\right) \, \mathbf{a}_{2}+z_{17} \, \mathbf{a}_{3}$ | = | $a x_{17} \,\mathbf{\hat{x}}- a x_{17} \,\mathbf{\hat{y}}- a z_{17} \,\mathbf{\hat{z}}$ | (48h) | Li XIII |
| $\mathbf{B_{98}}$ | = | $\left(2 x_{17} - z_{17}\right) \, \mathbf{a}_{1}+z_{17} \, \mathbf{a}_{2}+z_{17} \, \mathbf{a}_{3}$ | = | $a z_{17} \,\mathbf{\hat{x}}+a x_{17} \,\mathbf{\hat{y}}+a x_{17} \,\mathbf{\hat{z}}$ | (48h) | Li XIII |
| $\mathbf{B_{99}}$ | = | $- \left(2 x_{17} + z_{17}\right) \, \mathbf{a}_{1}+z_{17} \, \mathbf{a}_{2}+z_{17} \, \mathbf{a}_{3}$ | = | $a z_{17} \,\mathbf{\hat{x}}- a x_{17} \,\mathbf{\hat{y}}- a x_{17} \,\mathbf{\hat{z}}$ | (48h) | Li XIII |
| $\mathbf{B_{100}}$ | = | $z_{17} \, \mathbf{a}_{1}+\left(2 x_{17} - z_{17}\right) \, \mathbf{a}_{2}- \left(2 x_{17} + z_{17}\right) \, \mathbf{a}_{3}$ | = | $- a z_{17} \,\mathbf{\hat{x}}- a x_{17} \,\mathbf{\hat{y}}+a x_{17} \,\mathbf{\hat{z}}$ | (48h) | Li XIII |
| $\mathbf{B_{101}}$ | = | $z_{17} \, \mathbf{a}_{1}- \left(2 x_{17} + z_{17}\right) \, \mathbf{a}_{2}+\left(2 x_{17} - z_{17}\right) \, \mathbf{a}_{3}$ | = | $- a z_{17} \,\mathbf{\hat{x}}+a x_{17} \,\mathbf{\hat{y}}- a x_{17} \,\mathbf{\hat{z}}$ | (48h) | Li XIII |
| $\mathbf{B_{102}}$ | = | $z_{17} \, \mathbf{a}_{1}+\left(2 x_{17} - z_{17}\right) \, \mathbf{a}_{2}+z_{17} \, \mathbf{a}_{3}$ | = | $a x_{17} \,\mathbf{\hat{x}}+a z_{17} \,\mathbf{\hat{y}}+a x_{17} \,\mathbf{\hat{z}}$ | (48h) | Li XIII |
| $\mathbf{B_{103}}$ | = | $z_{17} \, \mathbf{a}_{1}- \left(2 x_{17} + z_{17}\right) \, \mathbf{a}_{2}+z_{17} \, \mathbf{a}_{3}$ | = | $- a x_{17} \,\mathbf{\hat{x}}+a z_{17} \,\mathbf{\hat{y}}- a x_{17} \,\mathbf{\hat{z}}$ | (48h) | Li XIII |
| $\mathbf{B_{104}}$ | = | $- \left(2 x_{17} + z_{17}\right) \, \mathbf{a}_{1}+z_{17} \, \mathbf{a}_{2}+\left(2 x_{17} - z_{17}\right) \, \mathbf{a}_{3}$ | = | $a x_{17} \,\mathbf{\hat{x}}- a z_{17} \,\mathbf{\hat{y}}- a x_{17} \,\mathbf{\hat{z}}$ | (48h) | Li XIII |
| $\mathbf{B_{105}}$ | = | $\left(2 x_{17} - z_{17}\right) \, \mathbf{a}_{1}+z_{17} \, \mathbf{a}_{2}- \left(2 x_{17} + z_{17}\right) \, \mathbf{a}_{3}$ | = | $- a x_{17} \,\mathbf{\hat{x}}- a z_{17} \,\mathbf{\hat{y}}+a x_{17} \,\mathbf{\hat{z}}$ | (48h) | Li XIII |
References
- G. R. Goward, N. J. Taylor, D. C. S. Souza, and L. F. Nazar, The true crystal structure of Li$_{17}$M$_{4}$ (M=Ge, Sn, Pb)-revised from Li$_{22}$M$_{5}$, J. Alloys Compd. 329, 82–91 (2001), doi:10.1016/S0925-8388(01)01567-5.
- P. Villars, H. Okamoto, and K. Cenzual, eds., ASM Alloy Phase Diagram Database (ASM International, 2018), chap. Bismuth-Palladium Binary Phase Diagram (1994 Okamoto H.). Copyright © 2006-2018 ASM International.
Prototype Generator
aflow --proto=A17B4_cF420_216_a6efg4h_2efg --params=$a,x_{2},x_{3},x_{4},x_{5},x_{6},x_{7},x_{8},x_{9},x_{10},x_{11},x_{12},x_{13},x_{14},z_{14},x_{15},z_{15},x_{16},z_{16},x_{17},z_{17}$