Ce$_{8}$Pd$_{24}$Sb Structure: A8B24C_cP33_221_g_efh_a-001
| Prototype | Ce$_{8}$Pd$_{24}$Sb |
| AFLOW prototype label | A8B24C_cP33_221_g_efh_a-001 |
| ICSD | 83378 |
| Pearson symbol | cP33 |
| Space group number | 221 |
| Space group symbol | $Pm\overline{3}m$ |
| AFLOW prototype command |
aflow --proto=A8B24C_cP33_221_g_efh_a-001
--params=$a, \allowbreak x_{2}, \allowbreak x_{3}, \allowbreak x_{4}, \allowbreak x_{5}$ |
- CePd$_{3}$ forms in the $L1_{2}$ Cu$_{3}$Au Structure. Adding antimony at some octahedral sites gives this structure. Alternatively, this can be viewed as a cubic perovskite ($E2_{1}$) structure with 7/8 of the B atoms removed in an ordered manner.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&a \,\mathbf{\hat{x}}\\\mathbf{a_{2}}&=&a \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&a \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $0$ | = | $0$ | (1a) | Sb I |
| $\mathbf{B_{2}}$ | = | $x_{2} \, \mathbf{a}_{1}$ | = | $a x_{2} \,\mathbf{\hat{x}}$ | (6e) | Pd I |
| $\mathbf{B_{3}}$ | = | $- x_{2} \, \mathbf{a}_{1}$ | = | $- a x_{2} \,\mathbf{\hat{x}}$ | (6e) | Pd I |
| $\mathbf{B_{4}}$ | = | $x_{2} \, \mathbf{a}_{2}$ | = | $a x_{2} \,\mathbf{\hat{y}}$ | (6e) | Pd I |
| $\mathbf{B_{5}}$ | = | $- x_{2} \, \mathbf{a}_{2}$ | = | $- a x_{2} \,\mathbf{\hat{y}}$ | (6e) | Pd I |
| $\mathbf{B_{6}}$ | = | $x_{2} \, \mathbf{a}_{3}$ | = | $a x_{2} \,\mathbf{\hat{z}}$ | (6e) | Pd I |
| $\mathbf{B_{7}}$ | = | $- x_{2} \, \mathbf{a}_{3}$ | = | $- a x_{2} \,\mathbf{\hat{z}}$ | (6e) | Pd I |
| $\mathbf{B_{8}}$ | = | $x_{3} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}$ | (6f) | Pd II |
| $\mathbf{B_{9}}$ | = | $- x_{3} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}$ | (6f) | Pd II |
| $\mathbf{B_{10}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+a x_{3} \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}$ | (6f) | Pd II |
| $\mathbf{B_{11}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- a x_{3} \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}$ | (6f) | Pd II |
| $\mathbf{B_{12}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+x_{3} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+a x_{3} \,\mathbf{\hat{z}}$ | (6f) | Pd II |
| $\mathbf{B_{13}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}- x_{3} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}- a x_{3} \,\mathbf{\hat{z}}$ | (6f) | Pd II |
| $\mathbf{B_{14}}$ | = | $x_{4} \, \mathbf{a}_{1}+x_{4} \, \mathbf{a}_{2}+x_{4} \, \mathbf{a}_{3}$ | = | $a x_{4} \,\mathbf{\hat{x}}+a x_{4} \,\mathbf{\hat{y}}+a x_{4} \,\mathbf{\hat{z}}$ | (8g) | Ce I |
| $\mathbf{B_{15}}$ | = | $- x_{4} \, \mathbf{a}_{1}- x_{4} \, \mathbf{a}_{2}+x_{4} \, \mathbf{a}_{3}$ | = | $- a x_{4} \,\mathbf{\hat{x}}- a x_{4} \,\mathbf{\hat{y}}+a x_{4} \,\mathbf{\hat{z}}$ | (8g) | Ce I |
| $\mathbf{B_{16}}$ | = | $- x_{4} \, \mathbf{a}_{1}+x_{4} \, \mathbf{a}_{2}- x_{4} \, \mathbf{a}_{3}$ | = | $- a x_{4} \,\mathbf{\hat{x}}+a x_{4} \,\mathbf{\hat{y}}- a x_{4} \,\mathbf{\hat{z}}$ | (8g) | Ce I |
| $\mathbf{B_{17}}$ | = | $x_{4} \, \mathbf{a}_{1}- x_{4} \, \mathbf{a}_{2}- x_{4} \, \mathbf{a}_{3}$ | = | $a x_{4} \,\mathbf{\hat{x}}- a x_{4} \,\mathbf{\hat{y}}- a x_{4} \,\mathbf{\hat{z}}$ | (8g) | Ce I |
| $\mathbf{B_{18}}$ | = | $x_{4} \, \mathbf{a}_{1}+x_{4} \, \mathbf{a}_{2}- x_{4} \, \mathbf{a}_{3}$ | = | $a x_{4} \,\mathbf{\hat{x}}+a x_{4} \,\mathbf{\hat{y}}- a x_{4} \,\mathbf{\hat{z}}$ | (8g) | Ce I |
| $\mathbf{B_{19}}$ | = | $- x_{4} \, \mathbf{a}_{1}- x_{4} \, \mathbf{a}_{2}- x_{4} \, \mathbf{a}_{3}$ | = | $- a x_{4} \,\mathbf{\hat{x}}- a x_{4} \,\mathbf{\hat{y}}- a x_{4} \,\mathbf{\hat{z}}$ | (8g) | Ce I |
| $\mathbf{B_{20}}$ | = | $x_{4} \, \mathbf{a}_{1}- x_{4} \, \mathbf{a}_{2}+x_{4} \, \mathbf{a}_{3}$ | = | $a x_{4} \,\mathbf{\hat{x}}- a x_{4} \,\mathbf{\hat{y}}+a x_{4} \,\mathbf{\hat{z}}$ | (8g) | Ce I |
| $\mathbf{B_{21}}$ | = | $- x_{4} \, \mathbf{a}_{1}+x_{4} \, \mathbf{a}_{2}+x_{4} \, \mathbf{a}_{3}$ | = | $- a x_{4} \,\mathbf{\hat{x}}+a x_{4} \,\mathbf{\hat{y}}+a x_{4} \,\mathbf{\hat{z}}$ | (8g) | Ce I |
| $\mathbf{B_{22}}$ | = | $x_{5} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}$ | = | $a x_{5} \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}$ | (12h) | Pd III |
| $\mathbf{B_{23}}$ | = | $- x_{5} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}$ | = | $- a x_{5} \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}$ | (12h) | Pd III |
| $\mathbf{B_{24}}$ | = | $x_{5} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $a x_{5} \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}$ | (12h) | Pd III |
| $\mathbf{B_{25}}$ | = | $- x_{5} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- a x_{5} \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}$ | (12h) | Pd III |
| $\mathbf{B_{26}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+x_{5} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+a x_{5} \,\mathbf{\hat{z}}$ | (12h) | Pd III |
| $\mathbf{B_{27}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}- x_{5} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- a x_{5} \,\mathbf{\hat{z}}$ | (12h) | Pd III |
| $\mathbf{B_{28}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+x_{5} \, \mathbf{a}_{2}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+a x_{5} \,\mathbf{\hat{y}}$ | (12h) | Pd III |
| $\mathbf{B_{29}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}- x_{5} \, \mathbf{a}_{2}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- a x_{5} \,\mathbf{\hat{y}}$ | (12h) | Pd III |
| $\mathbf{B_{30}}$ | = | $x_{5} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $a x_{5} \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{z}}$ | (12h) | Pd III |
| $\mathbf{B_{31}}$ | = | $- x_{5} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- a x_{5} \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{z}}$ | (12h) | Pd III |
| $\mathbf{B_{32}}$ | = | $\frac{1}{2} \, \mathbf{a}_{2}- x_{5} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{y}}- a x_{5} \,\mathbf{\hat{z}}$ | (12h) | Pd III |
| $\mathbf{B_{33}}$ | = | $\frac{1}{2} \, \mathbf{a}_{2}+x_{5} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{y}}+a x_{5} \,\mathbf{\hat{z}}$ | (12h) | Pd III |
References
- R. A. Gordon and F. J. DiSalvo, Crystal Structure and Magnetic Susceptibility of Ce$_{8}$Pd$_{24}$Sb, Z. Naturforsch. B 51, 52–56 (1996), doi:10.1515/znb-1996-0112.
Prototype Generator
aflow --proto=A8B24C_cP33_221_g_efh_a --params=$a,x_{2},x_{3},x_{4},x_{5}$