CoGe$_{2}$ Structure: AB2_oC24_64_d_ef-002
| Prototype | CoGe$_{2}$ |
| AFLOW prototype label | AB2_oC24_64_d_ef-002 |
| ICSD | 52964 |
| Pearson symbol | oC24 |
| Space group number | 64 |
| Space group symbol | $Cmce$ |
| AFLOW prototype command |
aflow --proto=AB2_oC24_64_d_ef-002
--params=$a, \allowbreak b/a, \allowbreak c/a, \allowbreak x_{1}, \allowbreak y_{2}, \allowbreak y_{3}, \allowbreak z_{3}$ |
- The actual stoichiometry is Co$_{7}$Ge$_{16}$, as the Co (8d) sites are 87.5% occupied.
- (Schubert, 1950) described this compound as being isotypic to PdSn$_{2}$ ($C_{e}$) in space group $Aba2$ #41.
- (Cenzual, 1991) showed that the given $z$ coordinates for the cobalt atoms were consistent with space group $Cmca$ #64.
- Although (Schubert, 1950) give the lattice parameters in Ångstroms, (Cenzual, 1991) asserts that they were actually in kX units and converts them to Ångstroms. We use the later values for the lattice parameters.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{1}{2}b \,\mathbf{\hat{y}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}b \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $x_{1} \, \mathbf{a}_{1}+x_{1} \, \mathbf{a}_{2}$ | = | $a x_{1} \,\mathbf{\hat{x}}$ | (8d) | Co I |
| $\mathbf{B_{2}}$ | = | $- \left(x_{1} - \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{1} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- a \left(x_{1} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (8d) | Co I |
| $\mathbf{B_{3}}$ | = | $- x_{1} \, \mathbf{a}_{1}- x_{1} \, \mathbf{a}_{2}$ | = | $- a x_{1} \,\mathbf{\hat{x}}$ | (8d) | Co I |
| $\mathbf{B_{4}}$ | = | $\left(x_{1} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{1} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $a \left(x_{1} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (8d) | Co I |
| $\mathbf{B_{5}}$ | = | $- \left(y_{2} - \frac{1}{4}\right) \, \mathbf{a}_{1}+\left(y_{2} + \frac{1}{4}\right) \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+b y_{2} \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (8e) | Ge I |
| $\mathbf{B_{6}}$ | = | $\left(y_{2} + \frac{1}{4}\right) \, \mathbf{a}_{1}- \left(y_{2} - \frac{1}{4}\right) \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}- b y_{2} \,\mathbf{\hat{y}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ | (8e) | Ge I |
| $\mathbf{B_{7}}$ | = | $\left(y_{2} + \frac{3}{4}\right) \, \mathbf{a}_{1}- \left(y_{2} - \frac{3}{4}\right) \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{3}{4}a \,\mathbf{\hat{x}}- b y_{2} \,\mathbf{\hat{y}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ | (8e) | Ge I |
| $\mathbf{B_{8}}$ | = | $- \left(y_{2} - \frac{3}{4}\right) \, \mathbf{a}_{1}+\left(y_{2} + \frac{3}{4}\right) \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{3}{4}a \,\mathbf{\hat{x}}+b y_{2} \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (8e) | Ge I |
| $\mathbf{B_{9}}$ | = | $- y_{3} \, \mathbf{a}_{1}+y_{3} \, \mathbf{a}_{2}+z_{3} \, \mathbf{a}_{3}$ | = | $b y_{3} \,\mathbf{\hat{y}}+c z_{3} \,\mathbf{\hat{z}}$ | (8f) | Ge II |
| $\mathbf{B_{10}}$ | = | $\left(y_{3} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{3} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- b y_{3} \,\mathbf{\hat{y}}+c \left(z_{3} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8f) | Ge II |
| $\mathbf{B_{11}}$ | = | $- \left(y_{3} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{3} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{3} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+b y_{3} \,\mathbf{\hat{y}}- c \left(z_{3} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8f) | Ge II |
| $\mathbf{B_{12}}$ | = | $y_{3} \, \mathbf{a}_{1}- y_{3} \, \mathbf{a}_{2}- z_{3} \, \mathbf{a}_{3}$ | = | $- b y_{3} \,\mathbf{\hat{y}}- c z_{3} \,\mathbf{\hat{z}}$ | (8f) | Ge II |
References
- K. Schubert and H. Pfisterer, Zur Kristallchemie der B-Metall-reichsten Phasen in Legierungen von Ü"bergangsmetallen der Eisen- und Platintriaden mit Elementen der vierten Nebengruppe, Zeitschrift für Metallkunde 41, 433–441 (1950).
Found in
- K. Cenzual, L. M. Gelato, M. Penzo, and E. Parthé, Inorganic structure types with revised space groups. I, Acta Crystallogr. Sect. B 47, 433–439 (1991), doi:10.1107/S0108768191000903.
Prototype Generator
aflow --proto=AB2_oC24_64_d_ef --params=$a,b/a,c/a,x_{1},y_{2},y_{3},z_{3}$