K$_{2}$CdPb Structure: AB2C_oC16_40_a_2b_b-001
| Prototype | CdK$_{2}$Pb |
| AFLOW prototype label | AB2C_oC16_40_a_2b_b-001 |
| ICSD | 10041 |
| Pearson symbol | oC16 |
| Space group number | 40 |
| Space group symbol | $Ama2$ |
| AFLOW prototype command |
aflow --proto=AB2C_oC16_40_a_2b_b-001
--params=$a, \allowbreak b/a, \allowbreak c/a, \allowbreak z_{1}, \allowbreak y_{2}, \allowbreak z_{2}, \allowbreak y_{3}, \allowbreak z_{3}, \allowbreak y_{4}, \allowbreak z_{4}$ |
Other compounds with this structure
K$_{2}$CdSn
- Space group $Ama2$ #40 allows an arbitrary choice of the origin of the $z$-axis. We use this to place the cadmium (4a) atom at the origin.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&a \,\mathbf{\hat{x}}\\\mathbf{a_{2}}&=&\frac{1}{2}b \,\mathbf{\hat{y}}- \frac{1}{2}c \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&\frac{1}{2}b \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $- z_{1} \, \mathbf{a}_{2}+z_{1} \, \mathbf{a}_{3}$ | = | $c z_{1} \,\mathbf{\hat{z}}$ | (4a) | Cd I |
| $\mathbf{B_{2}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}- z_{1} \, \mathbf{a}_{2}+z_{1} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+c z_{1} \,\mathbf{\hat{z}}$ | (4a) | Cd I |
| $\mathbf{B_{3}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+\left(y_{2} - z_{2}\right) \, \mathbf{a}_{2}+\left(y_{2} + z_{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+b y_{2} \,\mathbf{\hat{y}}+c z_{2} \,\mathbf{\hat{z}}$ | (4b) | K I |
| $\mathbf{B_{4}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}- \left(y_{2} + z_{2}\right) \, \mathbf{a}_{2}- \left(y_{2} - z_{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{3}{4}a \,\mathbf{\hat{x}}- b y_{2} \,\mathbf{\hat{y}}+c z_{2} \,\mathbf{\hat{z}}$ | (4b) | K I |
| $\mathbf{B_{5}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+\left(y_{3} - z_{3}\right) \, \mathbf{a}_{2}+\left(y_{3} + z_{3}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+b y_{3} \,\mathbf{\hat{y}}+c z_{3} \,\mathbf{\hat{z}}$ | (4b) | K II |
| $\mathbf{B_{6}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}- \left(y_{3} + z_{3}\right) \, \mathbf{a}_{2}- \left(y_{3} - z_{3}\right) \, \mathbf{a}_{3}$ | = | $\frac{3}{4}a \,\mathbf{\hat{x}}- b y_{3} \,\mathbf{\hat{y}}+c z_{3} \,\mathbf{\hat{z}}$ | (4b) | K II |
| $\mathbf{B_{7}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+\left(y_{4} - z_{4}\right) \, \mathbf{a}_{2}+\left(y_{4} + z_{4}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+b y_{4} \,\mathbf{\hat{y}}+c z_{4} \,\mathbf{\hat{z}}$ | (4b) | Pb I |
| $\mathbf{B_{8}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}- \left(y_{4} + z_{4}\right) \, \mathbf{a}_{2}- \left(y_{4} - z_{4}\right) \, \mathbf{a}_{3}$ | = | $\frac{3}{4}a \,\mathbf{\hat{x}}- b y_{4} \,\mathbf{\hat{y}}+c z_{4} \,\mathbf{\hat{z}}$ | (4b) | Pb I |
References
- R. Matthes and H.-U. Schuster, Synthese und Struktur der Phasen K$_{2}$CdSn und K$_{2}$CdPb, Z. Naturforsch. B 34, 541–543 (1979), doi:10.1515/znb-1979-0403.
Found in
- P. Villars and K. Cenzual, Pearson's Crystal Data – Crystal Structure Database for Inorganic Compounds (2013). ASM International.
Prototype Generator
aflow --proto=AB2C_oC16_40_a_2b_b --params=$a,b/a,c/a,z_{1},y_{2},z_{2},y_{3},z_{3},y_{4},z_{4}$