U$_{2}$Co$_{3}$Si$_{5}$ Structure: A3B5C2_oI40_72_aj_bfj_j-001
| Prototype | Co$_{3}$Si$_{5}$U$_{2}$ |
| AFLOW prototype label | A3B5C2_oI40_72_aj_bfj_j-001 |
| ICSD | 20930 |
| Pearson symbol | oI40 |
| Space group number | 72 |
| Space group symbol | $Ibam$ |
| AFLOW prototype command |
aflow --proto=A3B5C2_oI40_72_aj_bfj_j-001
--params=$a, \allowbreak b/a, \allowbreak c/a, \allowbreak x_{3}, \allowbreak x_{4}, \allowbreak y_{4}, \allowbreak x_{5}, \allowbreak y_{5}, \allowbreak x_{6}, \allowbreak y_{6}$ |
Other compounds with this structure
Ce$_{2}$Co$_{3}$Si$_{5}$, Ce$_{2}$Pt$_{3}$Si$_{5}$, Ce$_{2}$Rh$_{3}$Ge$_{5}$, Ce$_{2}$Ru$_{3}$Ge$_{5}$, Dy$_{2}$Ni$_{3}$Si$_{5}$, Gd$_{2}$Ru$_{3}$Ge$_{5}$, Ho$_{2}$Ni$_{3}$Si$_{5}$, La$_{2}$Ru$_{3}$Ge$_{5}$, Li$_{2}$Ir$_{3}$Si$_{5}$, Lu$_{2}$Ir$_{3}$Si$_{5}$, Lu$_{2}$Ru$_{3}$Si$_{5}$, Nd$_{2}$Ru$_{3}$Ge$_{5}$, Pu$_{2}$Pt$_{3}$Si$_{5}$, Tb$_{2}$Ni$_{3}$Si$_{5}$, Tb$_{2}$Ru$_{3}$Ge$_{5}$, Y$_{2}$Ni$_{3}$Si$_{5}$
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&- \frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}b \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{1}{2}b \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}b \,\mathbf{\hat{y}}- \frac{1}{2}c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}$ | = | $\frac{1}{4}c \,\mathbf{\hat{z}}$ | (4a) | Co I |
| $\mathbf{B_{2}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}$ | = | $\frac{3}{4}c \,\mathbf{\hat{z}}$ | (4a) | Co I |
| $\mathbf{B_{3}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (4b) | Si I |
| $\mathbf{B_{4}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}b \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (4b) | Si I |
| $\mathbf{B_{5}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+\left(x_{3} + \frac{1}{4}\right) \, \mathbf{a}_{2}+x_{3} \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{x}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (8f) | Si II |
| $\mathbf{B_{6}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}- \left(x_{3} - \frac{1}{4}\right) \, \mathbf{a}_{2}- x_{3} \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (8f) | Si II |
| $\mathbf{B_{7}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}- \left(x_{3} - \frac{3}{4}\right) \, \mathbf{a}_{2}- x_{3} \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ | (8f) | Si II |
| $\mathbf{B_{8}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}+\left(x_{3} + \frac{3}{4}\right) \, \mathbf{a}_{2}+x_{3} \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{x}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ | (8f) | Si II |
| $\mathbf{B_{9}}$ | = | $y_{4} \, \mathbf{a}_{1}+x_{4} \, \mathbf{a}_{2}+\left(x_{4} + y_{4}\right) \, \mathbf{a}_{3}$ | = | $a x_{4} \,\mathbf{\hat{x}}+b y_{4} \,\mathbf{\hat{y}}$ | (8j) | Co II |
| $\mathbf{B_{10}}$ | = | $- y_{4} \, \mathbf{a}_{1}- x_{4} \, \mathbf{a}_{2}- \left(x_{4} + y_{4}\right) \, \mathbf{a}_{3}$ | = | $- a x_{4} \,\mathbf{\hat{x}}- b y_{4} \,\mathbf{\hat{y}}$ | (8j) | Co II |
| $\mathbf{B_{11}}$ | = | $\left(y_{4} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{4} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{4} - y_{4}\right) \, \mathbf{a}_{3}$ | = | $- a x_{4} \,\mathbf{\hat{x}}+b y_{4} \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (8j) | Co II |
| $\mathbf{B_{12}}$ | = | $- \left(y_{4} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{4} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{4} - y_{4}\right) \, \mathbf{a}_{3}$ | = | $a x_{4} \,\mathbf{\hat{x}}- b y_{4} \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (8j) | Co II |
| $\mathbf{B_{13}}$ | = | $y_{5} \, \mathbf{a}_{1}+x_{5} \, \mathbf{a}_{2}+\left(x_{5} + y_{5}\right) \, \mathbf{a}_{3}$ | = | $a x_{5} \,\mathbf{\hat{x}}+b y_{5} \,\mathbf{\hat{y}}$ | (8j) | Si III |
| $\mathbf{B_{14}}$ | = | $- y_{5} \, \mathbf{a}_{1}- x_{5} \, \mathbf{a}_{2}- \left(x_{5} + y_{5}\right) \, \mathbf{a}_{3}$ | = | $- a x_{5} \,\mathbf{\hat{x}}- b y_{5} \,\mathbf{\hat{y}}$ | (8j) | Si III |
| $\mathbf{B_{15}}$ | = | $\left(y_{5} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{5} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{5} - y_{5}\right) \, \mathbf{a}_{3}$ | = | $- a x_{5} \,\mathbf{\hat{x}}+b y_{5} \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (8j) | Si III |
| $\mathbf{B_{16}}$ | = | $- \left(y_{5} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{5} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{5} - y_{5}\right) \, \mathbf{a}_{3}$ | = | $a x_{5} \,\mathbf{\hat{x}}- b y_{5} \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (8j) | Si III |
| $\mathbf{B_{17}}$ | = | $y_{6} \, \mathbf{a}_{1}+x_{6} \, \mathbf{a}_{2}+\left(x_{6} + y_{6}\right) \, \mathbf{a}_{3}$ | = | $a x_{6} \,\mathbf{\hat{x}}+b y_{6} \,\mathbf{\hat{y}}$ | (8j) | U I |
| $\mathbf{B_{18}}$ | = | $- y_{6} \, \mathbf{a}_{1}- x_{6} \, \mathbf{a}_{2}- \left(x_{6} + y_{6}\right) \, \mathbf{a}_{3}$ | = | $- a x_{6} \,\mathbf{\hat{x}}- b y_{6} \,\mathbf{\hat{y}}$ | (8j) | U I |
| $\mathbf{B_{19}}$ | = | $\left(y_{6} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{6} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{6} - y_{6}\right) \, \mathbf{a}_{3}$ | = | $- a x_{6} \,\mathbf{\hat{x}}+b y_{6} \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (8j) | U I |
| $\mathbf{B_{20}}$ | = | $- \left(y_{6} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{6} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{6} - y_{6}\right) \, \mathbf{a}_{3}$ | = | $a x_{6} \,\mathbf{\hat{x}}- b y_{6} \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (8j) | U I |
References
- L. G. Aksel'rud, Y. P. Yarmolyuk, and E. I. Gladyshevskii, Crystal structure of the compound U$_{2}$Co$_{3}$Si$_{5}$, Sov. Phys. Crystallogr. 22, 492–493 (1997).
Prototype Generator
aflow --proto=A3B5C2_oI40_72_aj_bfj_j --params=$a,b/a,c/a,x_{3},x_{4},y_{4},x_{5},y_{5},x_{6},y_{6}$