Li$_{2}$Pd$_{3}$B Structure: AB2C3_cP24_212_a_c_d-001
| Prototype | BLi$_{2}$Pt$_{3}$ |
| AFLOW prototype label | AB2C3_cP24_212_a_c_d-001 |
| ICSD | 84931 |
| Pearson symbol | cP24 |
| Space group number | 212 |
| Space group symbol | $P4_332$ |
| AFLOW prototype command |
aflow --proto=AB2C3_cP24_212_a_c_d-001
--params=$a, \allowbreak x_{2}, \allowbreak y_{3}$ |
Other compounds with this structure
Li$_{2}$Pt$_{3}$B
- This structure can also be expressed in the enantiomorphic space group $P4_{1}32$ #213.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&a \,\mathbf{\hat{x}}\\\mathbf{a_{2}}&=&a \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&a \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $\frac{1}{8} \, \mathbf{a}_{1}+\frac{1}{8} \, \mathbf{a}_{2}+\frac{1}{8} \, \mathbf{a}_{3}$ | = | $\frac{1}{8}a \,\mathbf{\hat{x}}+\frac{1}{8}a \,\mathbf{\hat{y}}+\frac{1}{8}a \,\mathbf{\hat{z}}$ | (4a) | B I |
| $\mathbf{B_{2}}$ | = | $\frac{3}{8} \, \mathbf{a}_{1}+\frac{7}{8} \, \mathbf{a}_{2}+\frac{5}{8} \, \mathbf{a}_{3}$ | = | $\frac{3}{8}a \,\mathbf{\hat{x}}+\frac{7}{8}a \,\mathbf{\hat{y}}+\frac{5}{8}a \,\mathbf{\hat{z}}$ | (4a) | B I |
| $\mathbf{B_{3}}$ | = | $\frac{7}{8} \, \mathbf{a}_{1}+\frac{5}{8} \, \mathbf{a}_{2}+\frac{3}{8} \, \mathbf{a}_{3}$ | = | $\frac{7}{8}a \,\mathbf{\hat{x}}+\frac{5}{8}a \,\mathbf{\hat{y}}+\frac{3}{8}a \,\mathbf{\hat{z}}$ | (4a) | B I |
| $\mathbf{B_{4}}$ | = | $\frac{5}{8} \, \mathbf{a}_{1}+\frac{3}{8} \, \mathbf{a}_{2}+\frac{7}{8} \, \mathbf{a}_{3}$ | = | $\frac{5}{8}a \,\mathbf{\hat{x}}+\frac{3}{8}a \,\mathbf{\hat{y}}+\frac{7}{8}a \,\mathbf{\hat{z}}$ | (4a) | B I |
| $\mathbf{B_{5}}$ | = | $x_{2} \, \mathbf{a}_{1}+x_{2} \, \mathbf{a}_{2}+x_{2} \, \mathbf{a}_{3}$ | = | $a x_{2} \,\mathbf{\hat{x}}+a x_{2} \,\mathbf{\hat{y}}+a x_{2} \,\mathbf{\hat{z}}$ | (8c) | Li I |
| $\mathbf{B_{6}}$ | = | $- \left(x_{2} - \frac{1}{2}\right) \, \mathbf{a}_{1}- x_{2} \, \mathbf{a}_{2}+\left(x_{2} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{2} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a x_{2} \,\mathbf{\hat{y}}+a \left(x_{2} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8c) | Li I |
| $\mathbf{B_{7}}$ | = | $- x_{2} \, \mathbf{a}_{1}+\left(x_{2} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{2} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{2} \,\mathbf{\hat{x}}+a \left(x_{2} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(x_{2} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8c) | Li I |
| $\mathbf{B_{8}}$ | = | $\left(x_{2} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{2} - \frac{1}{2}\right) \, \mathbf{a}_{2}- x_{2} \, \mathbf{a}_{3}$ | = | $a \left(x_{2} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(x_{2} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- a x_{2} \,\mathbf{\hat{z}}$ | (8c) | Li I |
| $\mathbf{B_{9}}$ | = | $\left(x_{2} + \frac{1}{4}\right) \, \mathbf{a}_{1}+\left(x_{2} + \frac{3}{4}\right) \, \mathbf{a}_{2}- \left(x_{2} - \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{2} + \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(x_{2} + \frac{3}{4}\right) \,\mathbf{\hat{y}}- a \left(x_{2} - \frac{3}{4}\right) \,\mathbf{\hat{z}}$ | (8c) | Li I |
| $\mathbf{B_{10}}$ | = | $- \left(x_{2} - \frac{1}{4}\right) \, \mathbf{a}_{1}- \left(x_{2} - \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(x_{2} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{2} - \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(x_{2} - \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(x_{2} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (8c) | Li I |
| $\mathbf{B_{11}}$ | = | $\left(x_{2} + \frac{3}{4}\right) \, \mathbf{a}_{1}- \left(x_{2} - \frac{3}{4}\right) \, \mathbf{a}_{2}+\left(x_{2} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{2} + \frac{3}{4}\right) \,\mathbf{\hat{x}}- a \left(x_{2} - \frac{3}{4}\right) \,\mathbf{\hat{y}}+a \left(x_{2} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (8c) | Li I |
| $\mathbf{B_{12}}$ | = | $- \left(x_{2} - \frac{3}{4}\right) \, \mathbf{a}_{1}+\left(x_{2} + \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(x_{2} + \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{2} - \frac{3}{4}\right) \,\mathbf{\hat{x}}+a \left(x_{2} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(x_{2} + \frac{3}{4}\right) \,\mathbf{\hat{z}}$ | (8c) | Li I |
| $\mathbf{B_{13}}$ | = | $\frac{1}{8} \, \mathbf{a}_{1}+y_{3} \, \mathbf{a}_{2}- \left(y_{3} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{8}a \,\mathbf{\hat{x}}+a y_{3} \,\mathbf{\hat{y}}- a \left(y_{3} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (12d) | Pd I |
| $\mathbf{B_{14}}$ | = | $\frac{3}{8} \, \mathbf{a}_{1}- y_{3} \, \mathbf{a}_{2}- \left(y_{3} - \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $\frac{3}{8}a \,\mathbf{\hat{x}}- a y_{3} \,\mathbf{\hat{y}}- a \left(y_{3} - \frac{3}{4}\right) \,\mathbf{\hat{z}}$ | (12d) | Pd I |
| $\mathbf{B_{15}}$ | = | $\frac{7}{8} \, \mathbf{a}_{1}+\left(y_{3} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(y_{3} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $\frac{7}{8}a \,\mathbf{\hat{x}}+a \left(y_{3} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+a \left(y_{3} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (12d) | Pd I |
| $\mathbf{B_{16}}$ | = | $\frac{5}{8} \, \mathbf{a}_{1}- \left(y_{3} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(y_{3} + \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $\frac{5}{8}a \,\mathbf{\hat{x}}- a \left(y_{3} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+a \left(y_{3} + \frac{3}{4}\right) \,\mathbf{\hat{z}}$ | (12d) | Pd I |
| $\mathbf{B_{17}}$ | = | $- \left(y_{3} - \frac{1}{4}\right) \, \mathbf{a}_{1}+\frac{1}{8} \, \mathbf{a}_{2}+y_{3} \, \mathbf{a}_{3}$ | = | $- a \left(y_{3} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+\frac{1}{8}a \,\mathbf{\hat{y}}+a y_{3} \,\mathbf{\hat{z}}$ | (12d) | Pd I |
| $\mathbf{B_{18}}$ | = | $- \left(y_{3} - \frac{3}{4}\right) \, \mathbf{a}_{1}+\frac{3}{8} \, \mathbf{a}_{2}- y_{3} \, \mathbf{a}_{3}$ | = | $- a \left(y_{3} - \frac{3}{4}\right) \,\mathbf{\hat{x}}+\frac{3}{8}a \,\mathbf{\hat{y}}- a y_{3} \,\mathbf{\hat{z}}$ | (12d) | Pd I |
| $\mathbf{B_{19}}$ | = | $\left(y_{3} + \frac{1}{4}\right) \, \mathbf{a}_{1}+\frac{7}{8} \, \mathbf{a}_{2}+\left(y_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{3} + \frac{1}{4}\right) \,\mathbf{\hat{x}}+\frac{7}{8}a \,\mathbf{\hat{y}}+a \left(y_{3} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (12d) | Pd I |
| $\mathbf{B_{20}}$ | = | $\left(y_{3} + \frac{3}{4}\right) \, \mathbf{a}_{1}+\frac{5}{8} \, \mathbf{a}_{2}- \left(y_{3} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{3} + \frac{3}{4}\right) \,\mathbf{\hat{x}}+\frac{5}{8}a \,\mathbf{\hat{y}}- a \left(y_{3} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (12d) | Pd I |
| $\mathbf{B_{21}}$ | = | $y_{3} \, \mathbf{a}_{1}- \left(y_{3} - \frac{1}{4}\right) \, \mathbf{a}_{2}+\frac{1}{8} \, \mathbf{a}_{3}$ | = | $a y_{3} \,\mathbf{\hat{x}}- a \left(y_{3} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+\frac{1}{8}a \,\mathbf{\hat{z}}$ | (12d) | Pd I |
| $\mathbf{B_{22}}$ | = | $- y_{3} \, \mathbf{a}_{1}- \left(y_{3} - \frac{3}{4}\right) \, \mathbf{a}_{2}+\frac{3}{8} \, \mathbf{a}_{3}$ | = | $- a y_{3} \,\mathbf{\hat{x}}- a \left(y_{3} - \frac{3}{4}\right) \,\mathbf{\hat{y}}+\frac{3}{8}a \,\mathbf{\hat{z}}$ | (12d) | Pd I |
| $\mathbf{B_{23}}$ | = | $\left(y_{3} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{3} + \frac{1}{4}\right) \, \mathbf{a}_{2}+\frac{7}{8} \, \mathbf{a}_{3}$ | = | $a \left(y_{3} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(y_{3} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+\frac{7}{8}a \,\mathbf{\hat{z}}$ | (12d) | Pd I |
| $\mathbf{B_{24}}$ | = | $- \left(y_{3} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{3} + \frac{3}{4}\right) \, \mathbf{a}_{2}+\frac{5}{8} \, \mathbf{a}_{3}$ | = | $- a \left(y_{3} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(y_{3} + \frac{3}{4}\right) \,\mathbf{\hat{y}}+\frac{5}{8}a \,\mathbf{\hat{z}}$ | (12d) | Pd I |
References
- U. Eibenstein and W. Jung, Li$_{2}$Pd$_{3}$B and Li$_{2}$Pt$_{3}$B: Ternary Lithium Borides of Palladium and Platinum with Boron in Octahedral Coordination, J. Solid State Chem. 133, 21–24 (1997), doi:10.1006/jssc.1997.7310.
Found in
- K. Togano, P. Badica, Y. Nakamori, S. Orimo, H. Takeya, and K. Hirata, Superconductivity in the Metal Rich Li-Pd-B Ternary Boride, Phys. Rev. Lett. 93, 247004 (2004), doi:10.1103/PhysRevLett.93.247004.
Prototype Generator
aflow --proto=AB2C3_cP24_212_a_c_d --params=$a,x_{2},y_{3}$