U$_{2}$Cr$_{3}$Si Structure: A3BC2_hP12_194_h_a_f-002
| Prototype | Cr$_{3}$SiU$_{2}$ |
| AFLOW prototype label | A3BC2_hP12_194_h_a_f-002 |
| ICSD | 626830 |
| CCDC | 1752198 |
| Pearson symbol | hP12 |
| Space group number | 194 |
| Space group symbol | $P6_3/mmc$ |
| AFLOW prototype command |
aflow --proto=A3BC2_hP12_194_h_a_f-002
--params=$a, \allowbreak c/a, \allowbreak z_{2}, \allowbreak x_{3}$ |
Other compounds with this structure
Dy$_{2}$Al$_{3}$Co, Co$_{2}$Nb$_{3}$Si, Er$_{2}$Al$_{3}$Co, Eu$_{2}$Ga$_{3}$Ir, Lu$_{2}$Al$_{3}$Co, Mg$_{2}$Cu$_{3}$Si, Mg$_{2}$Ir$_{3}$Si, Mn$_{2}$Co$_{3}$Ge, Mo$_{2}$Co$_{3}$Si, Nb$_{2}$Ni$_{3}$Si, Pd$_{2}$Ga$_{3}$U, Ru$_{2}$Al$_{3}$Sc, Sc$_{2}$Fe$_{3}$Si, Ta$_{2}$Cr$_{3}$Cu, Ta$_{2}$Ni$_{3}$Si, Ti$_{2}$Ni$_{3}$Si, U$_{2}$Al$_{3}$Cu, U$_{2}$Mn$_{3}$Ge, W$_{2}$Co$_{3}$Si, Zr$_{2}$Fe$_{3}$Ga, Zr$_{2}$Fe$_{3}$Ge, Zr$_{2}$V$_{3}$Ru
- This is a ternary form of the $C14$ hexagonal Laves structure. The ICSD lists the prototype ac $C14$/MgZn$_{2}$, so we chose U$_{2}$Cr$_{3}$Si as the prototype, as it has a readily available reference.
- U$_{2}$Cr$_{3}$Si, AFLOW label A3BC2_hP12_194_h_a_f-002, and Ba$_{x}$Pt$_{3}$B$_{2}$, A2BC3_hP12_194_f_a_h, occupy the same Wyckoff positions in space group $P6_{3}/mmc$ # 194. They differ in the c/a ratio, with U$_{2}$Cr$_{3}$Si having $c/a ≈ 1.6$ and Ba$_{x}$Pt$_{3}$B$_{2}$ $c/a ≈ 0.85$.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \,\mathbf{\hat{y}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $0$ | = | $0$ | (2a) | Si I |
| $\mathbf{B_{2}}$ | = | $\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}c \,\mathbf{\hat{z}}$ | (2a) | Si I |
| $\mathbf{B_{3}}$ | = | $\frac{1}{3} \, \mathbf{a}_{1}+\frac{2}{3} \, \mathbf{a}_{2}+z_{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+c z_{2} \,\mathbf{\hat{z}}$ | (4f) | U I |
| $\mathbf{B_{4}}$ | = | $\frac{2}{3} \, \mathbf{a}_{1}+\frac{1}{3} \, \mathbf{a}_{2}+\left(z_{2} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+c \left(z_{2} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4f) | U I |
| $\mathbf{B_{5}}$ | = | $\frac{2}{3} \, \mathbf{a}_{1}+\frac{1}{3} \, \mathbf{a}_{2}- z_{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}- c z_{2} \,\mathbf{\hat{z}}$ | (4f) | U I |
| $\mathbf{B_{6}}$ | = | $\frac{1}{3} \, \mathbf{a}_{1}+\frac{2}{3} \, \mathbf{a}_{2}- \left(z_{2} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}- c \left(z_{2} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4f) | U I |
| $\mathbf{B_{7}}$ | = | $x_{3} \, \mathbf{a}_{1}+2 x_{3} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{3}{2}a x_{3} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{3} \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (6h) | Cr I |
| $\mathbf{B_{8}}$ | = | $- 2 x_{3} \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $- \frac{3}{2}a x_{3} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{3} \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (6h) | Cr I |
| $\mathbf{B_{9}}$ | = | $x_{3} \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $- \sqrt{3}a x_{3} \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (6h) | Cr I |
| $\mathbf{B_{10}}$ | = | $- x_{3} \, \mathbf{a}_{1}- 2 x_{3} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $- \frac{3}{2}a x_{3} \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{3} \,\mathbf{\hat{y}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ | (6h) | Cr I |
| $\mathbf{B_{11}}$ | = | $2 x_{3} \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{3}{2}a x_{3} \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{3} \,\mathbf{\hat{y}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ | (6h) | Cr I |
| $\mathbf{B_{12}}$ | = | $- x_{3} \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\sqrt{3}a x_{3} \,\mathbf{\hat{y}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ | (6h) | Cr I |
References
- J. B. Kusma and H. Nowotny, Die Kristallstruktur von U$_{2}$Cr$_{3}$Si, U$_{4}$Mn$_{5}$Si$_{3}$ und U$_{2}$Co$_{3}$Si, Monat. Chemie 95, 1219–1224 (1964), doi:10.1007/BF00904717.
Found in
- Inorganic Crystal Structure Database. Entry 626830 [U2Cr3Si].
First cited in
- N. Anderson, M. J. Mehl, H. Eckert, S. Divilov, X. Campilongo, S. Curtarolo, The AFLOW Library of Crystallographic Prototypes: Part 5. Submitted to Computational Materials Science (2026).
Geometry files
Prototype Generator
aflow --proto=A3BC2_hP12_194_h_a_f --params=$a,c/a,z_{2},x_{3}$