U$_{2}$Mn$_{3}$Si$_{5}$ Structure: A3B5C2_tP40_128_dh_egh_h-001
| Prototype | Mn$_{3}$Si$_{5}$U$_{2}$ |
| AFLOW prototype label | A3B5C2_tP40_128_dh_egh_h-001 |
| ICSD | 20929 |
| Pearson symbol | tP40 |
| Space group number | 128 |
| Space group symbol | $P4/mnc$ |
| AFLOW prototype command |
aflow --proto=A3B5C2_tP40_128_dh_egh_h-001
--params=$a, \allowbreak c/a, \allowbreak z_{2}, \allowbreak x_{3}, \allowbreak x_{4}, \allowbreak y_{4}, \allowbreak x_{5}, \allowbreak y_{5}, \allowbreak x_{6}, \allowbreak y_{6}$ |
Other compounds with this structure
Ce$_{2}$Co$_{3}$Si$_{5}$, Ce$_{2}$Ni$_{3}$Si$_{5}$, Ce$_{2}$Ru$_{3}$Ga$_{5}$, Dy$_{2}$Ni$_{3}$Si$_{5}$, Dy$_{2}$Ru$_{3}$Ge$_{5}$, Dy$_{2}$Ru$_{3}$Si$_{5}$, Er$_{2}$Mn$_{3}$Si$_{5}$, Gd$_{2}$Re$_{3}$Si$_{5}$, La$_{2}$Ru$_{3}$Ga$_{5}$, Lu$_{2}$Fe$_{3}$Si$_{5}$, Lu$_{2}$Ru$_{3}$Si$_{5}$, Nd$_{2}$Os$_{3}$Ga$_{5}$, Nd$_{2}$Ru$_{3}$Ga$_{5}$, Np$_{2}$Re$_{3}$Ga$_{5}$, Pr$_{2}$Ru$_{3}$Ga$_{5}$, Pr$_{2}$Ru$_{3}$Ge$_{5}$, Pu$_{2}$Fe$_{3}$Ga$_{5}$, Pu$_{2}$Re$_{3}$Ga$_{5}$, Pu$_{2}$Tc$_{3}$Ga$_{5}$, Rb$_{2}$Os$_{3}$Si$_{5}$, Sc$_{2}$Fe$_{3}$Si$_{5}$, Sm$_{2}$Ru$_{3}$Ga$_{5}$, Sm$_{2}$Ru$_{3}$Ge$_{5}$, Tb$_{2}$Mn$_{3}$Si$_{5}$, U$_{2}$Tc$_{3}$Ga$_{5}$, Y$_{2}$Ni$_{3}$Si$_{5}$
- Some authors refer to this as the Sc$_{2}$Fe$_{3}$Si$_{5}$ type.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&a \,\mathbf{\hat{x}}\\\mathbf{a_{2}}&=&a \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $\frac{1}{2} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (4d) | Mn I |
| $\mathbf{B_{2}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (4d) | Mn I |
| $\mathbf{B_{3}}$ | = | $\frac{1}{2} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ | (4d) | Mn I |
| $\mathbf{B_{4}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ | (4d) | Mn I |
| $\mathbf{B_{5}}$ | = | $z_{2} \, \mathbf{a}_{3}$ | = | $c z_{2} \,\mathbf{\hat{z}}$ | (4e) | Si I |
| $\mathbf{B_{6}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}- \left(z_{2} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}- c \left(z_{2} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4e) | Si I |
| $\mathbf{B_{7}}$ | = | $- z_{2} \, \mathbf{a}_{3}$ | = | $- c z_{2} \,\mathbf{\hat{z}}$ | (4e) | Si I |
| $\mathbf{B_{8}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+\left(z_{2} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+c \left(z_{2} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4e) | Si I |
| $\mathbf{B_{9}}$ | = | $x_{3} \, \mathbf{a}_{1}+\left(x_{3} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{x}}+a \left(x_{3} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (8g) | Si II |
| $\mathbf{B_{10}}$ | = | $- x_{3} \, \mathbf{a}_{1}- \left(x_{3} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}- a \left(x_{3} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (8g) | Si II |
| $\mathbf{B_{11}}$ | = | $- \left(x_{3} - \frac{1}{2}\right) \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $- a \left(x_{3} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a x_{3} \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (8g) | Si II |
| $\mathbf{B_{12}}$ | = | $\left(x_{3} + \frac{1}{2}\right) \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $a \left(x_{3} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a x_{3} \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (8g) | Si II |
| $\mathbf{B_{13}}$ | = | $- x_{3} \, \mathbf{a}_{1}- \left(x_{3} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}- a \left(x_{3} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ | (8g) | Si II |
| $\mathbf{B_{14}}$ | = | $x_{3} \, \mathbf{a}_{1}+\left(x_{3} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{x}}+a \left(x_{3} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ | (8g) | Si II |
| $\mathbf{B_{15}}$ | = | $\left(x_{3} + \frac{1}{2}\right) \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $a \left(x_{3} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a x_{3} \,\mathbf{\hat{y}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ | (8g) | Si II |
| $\mathbf{B_{16}}$ | = | $- \left(x_{3} - \frac{1}{2}\right) \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $- a \left(x_{3} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a x_{3} \,\mathbf{\hat{y}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ | (8g) | Si II |
| $\mathbf{B_{17}}$ | = | $x_{4} \, \mathbf{a}_{1}+y_{4} \, \mathbf{a}_{2}$ | = | $a x_{4} \,\mathbf{\hat{x}}+a y_{4} \,\mathbf{\hat{y}}$ | (8h) | Mn II |
| $\mathbf{B_{18}}$ | = | $- x_{4} \, \mathbf{a}_{1}- y_{4} \, \mathbf{a}_{2}$ | = | $- a x_{4} \,\mathbf{\hat{x}}- a y_{4} \,\mathbf{\hat{y}}$ | (8h) | Mn II |
| $\mathbf{B_{19}}$ | = | $- y_{4} \, \mathbf{a}_{1}+x_{4} \, \mathbf{a}_{2}$ | = | $- a y_{4} \,\mathbf{\hat{x}}+a x_{4} \,\mathbf{\hat{y}}$ | (8h) | Mn II |
| $\mathbf{B_{20}}$ | = | $y_{4} \, \mathbf{a}_{1}- x_{4} \, \mathbf{a}_{2}$ | = | $a y_{4} \,\mathbf{\hat{x}}- a x_{4} \,\mathbf{\hat{y}}$ | (8h) | Mn II |
| $\mathbf{B_{21}}$ | = | $- \left(x_{4} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{4} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- a \left(x_{4} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(y_{4} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (8h) | Mn II |
| $\mathbf{B_{22}}$ | = | $\left(x_{4} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{4} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $a \left(x_{4} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(y_{4} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (8h) | Mn II |
| $\mathbf{B_{23}}$ | = | $\left(y_{4} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{4} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $a \left(y_{4} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(x_{4} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (8h) | Mn II |
| $\mathbf{B_{24}}$ | = | $- \left(y_{4} - \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{4} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- a \left(y_{4} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(x_{4} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (8h) | Mn II |
| $\mathbf{B_{25}}$ | = | $x_{5} \, \mathbf{a}_{1}+y_{5} \, \mathbf{a}_{2}$ | = | $a x_{5} \,\mathbf{\hat{x}}+a y_{5} \,\mathbf{\hat{y}}$ | (8h) | Si III |
| $\mathbf{B_{26}}$ | = | $- x_{5} \, \mathbf{a}_{1}- y_{5} \, \mathbf{a}_{2}$ | = | $- a x_{5} \,\mathbf{\hat{x}}- a y_{5} \,\mathbf{\hat{y}}$ | (8h) | Si III |
| $\mathbf{B_{27}}$ | = | $- y_{5} \, \mathbf{a}_{1}+x_{5} \, \mathbf{a}_{2}$ | = | $- a y_{5} \,\mathbf{\hat{x}}+a x_{5} \,\mathbf{\hat{y}}$ | (8h) | Si III |
| $\mathbf{B_{28}}$ | = | $y_{5} \, \mathbf{a}_{1}- x_{5} \, \mathbf{a}_{2}$ | = | $a y_{5} \,\mathbf{\hat{x}}- a x_{5} \,\mathbf{\hat{y}}$ | (8h) | Si III |
| $\mathbf{B_{29}}$ | = | $- \left(x_{5} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{5} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- a \left(x_{5} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(y_{5} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (8h) | Si III |
| $\mathbf{B_{30}}$ | = | $\left(x_{5} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{5} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $a \left(x_{5} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(y_{5} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (8h) | Si III |
| $\mathbf{B_{31}}$ | = | $\left(y_{5} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{5} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $a \left(y_{5} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(x_{5} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (8h) | Si III |
| $\mathbf{B_{32}}$ | = | $- \left(y_{5} - \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{5} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- a \left(y_{5} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(x_{5} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (8h) | Si III |
| $\mathbf{B_{33}}$ | = | $x_{6} \, \mathbf{a}_{1}+y_{6} \, \mathbf{a}_{2}$ | = | $a x_{6} \,\mathbf{\hat{x}}+a y_{6} \,\mathbf{\hat{y}}$ | (8h) | U I |
| $\mathbf{B_{34}}$ | = | $- x_{6} \, \mathbf{a}_{1}- y_{6} \, \mathbf{a}_{2}$ | = | $- a x_{6} \,\mathbf{\hat{x}}- a y_{6} \,\mathbf{\hat{y}}$ | (8h) | U I |
| $\mathbf{B_{35}}$ | = | $- y_{6} \, \mathbf{a}_{1}+x_{6} \, \mathbf{a}_{2}$ | = | $- a y_{6} \,\mathbf{\hat{x}}+a x_{6} \,\mathbf{\hat{y}}$ | (8h) | U I |
| $\mathbf{B_{36}}$ | = | $y_{6} \, \mathbf{a}_{1}- x_{6} \, \mathbf{a}_{2}$ | = | $a y_{6} \,\mathbf{\hat{x}}- a x_{6} \,\mathbf{\hat{y}}$ | (8h) | U I |
| $\mathbf{B_{37}}$ | = | $- \left(x_{6} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{6} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- a \left(x_{6} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(y_{6} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (8h) | U I |
| $\mathbf{B_{38}}$ | = | $\left(x_{6} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{6} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $a \left(x_{6} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(y_{6} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (8h) | U I |
| $\mathbf{B_{39}}$ | = | $\left(y_{6} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{6} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $a \left(y_{6} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(x_{6} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (8h) | U I |
| $\mathbf{B_{40}}$ | = | $- \left(y_{6} - \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{6} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- a \left(y_{6} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(x_{6} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (8h) | U I |
References
- Y. P. Yarmolyuk, L. G. Aksel'rud, and E. I. Gladyshevskii, Crystal structure of the compound U$_{2}$Mn$_{3}$Si$_{5}$, Sov. Phys. Crystallogr. 22, 358–359 (1977).
Found in
- W. Jeitschko and M. Schlüter, Rare Earth Ruthenium Gallides with the Ideal Composition Ln$_{2}$Ru3Ga$_{5}$ (Ln = La–Nd, Sm) crystallizing with U$_{2}$Mn3Si$_{5}$ (Sc$_{2}$Fe3Si$_{5}$) Type Structure, Z. Anorganische und Allgemeine Chemie 636, 1100–1105 (2010), doi:10.1002/zaac.200900530.
Prototype Generator
aflow --proto=A3B5C2_tP40_128_dh_egh_h --params=$a,c/a,z_{2},x_{3},x_{4},y_{4},x_{5},y_{5},x_{6},y_{6}$