CeAuAl$_{4}$Ge$_{2}$ Structure: A4BCD2_hR8_166_2c_a_b_c-001
| Prototype | Al$_{4}$AuCeGe$_{2}$ |
| AFLOW prototype label | A4BCD2_hR8_166_2c_a_b_c-001 |
| ICSD | 415287 |
| CCDC | 1729371 |
| Pearson symbol | hR8 |
| Space group number | 166 |
| Space group symbol | $R\overline{3}m$ |
| AFLOW prototype command |
aflow --proto=A4BCD2_hR8_166_2c_a_b_c-001
--params=$a, \allowbreak c/a, \allowbreak x_{3}, \allowbreak x_{4}, \allowbreak x_{5}$ |
Other compounds with this structure
CeAuAl$_{4}$Ge$_{2}$, CePtAl$_{4}$Ge$_{2}$, DyAuAl$_{4}$Ge$_{2}$, ErAuAl$_{4}$Ge$_{2}$, EuAuAl$_{4}$Ge$_{2}$, GdAuAl$_{4}$Ge$_{2}$, GdNiAl$_{4}$Ge$_{2}$, LuNiAl$_{4}$Ge$_{2}$, NdAuAl$_{4}$Ge$_{2}$, PrAuAl$_{4}$Ge$_{2}$, SmAuAl$_{4}$Ge$_{2}$, TbAuAl$_{4}$Ge$_{2}$, TmAuAl$_{4}$Ge$_{2}$, YNiAl$_{4}$Ge$_{2}$
- Like EuAuAl$_{4}$(Au$_{1-x}$Ge$_{x}$)$_{2}$, the rare earth atoms in this structure have a complex antiferromagnetic ordering at low temperatures (Feng, 2024).
- Hexagonal settings of this structure can be obtained with the option
--hex.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+\frac{1}{3}c \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{\sqrt{3}}a \,\mathbf{\hat{y}}+\frac{1}{3}c \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&- \frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+\frac{1}{3}c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $0$ | = | $0$ | (1a) | Au I |
| $\mathbf{B_{2}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}c \,\mathbf{\hat{z}}$ | (1b) | Ce I |
| $\mathbf{B_{3}}$ | = | $x_{3} \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{2}+x_{3} \, \mathbf{a}_{3}$ | = | $c x_{3} \,\mathbf{\hat{z}}$ | (2c) | Al I |
| $\mathbf{B_{4}}$ | = | $- x_{3} \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}- x_{3} \, \mathbf{a}_{3}$ | = | $- c x_{3} \,\mathbf{\hat{z}}$ | (2c) | Al I |
| $\mathbf{B_{5}}$ | = | $x_{4} \, \mathbf{a}_{1}+x_{4} \, \mathbf{a}_{2}+x_{4} \, \mathbf{a}_{3}$ | = | $c x_{4} \,\mathbf{\hat{z}}$ | (2c) | Al II |
| $\mathbf{B_{6}}$ | = | $- x_{4} \, \mathbf{a}_{1}- x_{4} \, \mathbf{a}_{2}- x_{4} \, \mathbf{a}_{3}$ | = | $- c x_{4} \,\mathbf{\hat{z}}$ | (2c) | Al II |
| $\mathbf{B_{7}}$ | = | $x_{5} \, \mathbf{a}_{1}+x_{5} \, \mathbf{a}_{2}+x_{5} \, \mathbf{a}_{3}$ | = | $c x_{5} \,\mathbf{\hat{z}}$ | (2c) | Ge I |
| $\mathbf{B_{8}}$ | = | $- x_{5} \, \mathbf{a}_{1}- x_{5} \, \mathbf{a}_{2}- x_{5} \, \mathbf{a}_{3}$ | = | $- c x_{5} \,\mathbf{\hat{z}}$ | (2c) | Ge I |
References
- X. Wu and M. G. Kanatzidis, REAuAl$_{4}$Ge$_{2}$ and REAuAl$_{4}$(Au$_{x}$Ge$_{1-x}$)$_{2}$ (RE=rare earth element): Quaternary intermetallics grown in liquid aluminum, J. Solid State Chem. 178, 3233–3242 (2005), doi:10.1103/PhysRevB.109.014436.
Found in
- K. Feng, C. Bush, O. Oladehin, M. Lee, and R. Baumbach, Complex antiferromagnetic order in the metallic triangular lattice compound SmAuAl$_{4}$Ge$_{2}$, Phys. Rev. B 109, 014436 (2024), doi:10.1103/PhysRevB.109.014436.
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=A4BCD2_hR8_166_2c_a_b_c --params=$a,c/a,x_{3},x_{4},x_{5}$