Fe$_{3}$Sn$_{2}$ Structure: A3B2_hR10_166_h_2c-001
| Prototype | Fe$_{3}$Sn$_{2}$ |
| AFLOW prototype label | A3B2_hR10_166_h_2c-001 |
| ICSD | 71 |
| Pearson symbol | hR10 |
| Space group number | 166 |
| Space group symbol | $R\overline{3}m$ |
| AFLOW prototype command |
aflow --proto=A3B2_hR10_166_h_2c-001
--params=$a, \allowbreak c/a, \allowbreak x_{1}, \allowbreak x_{2}, \allowbreak x_{3}, \allowbreak z_{3}$ |
Other compounds with this structure
V$_{3}$Sb$_{2}$
- There is no ICSD entry for (Dally, 2021), so we use the one from the earlier work of (Malaman, 1976).
- 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 | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $x_{1} \, \mathbf{a}_{1}+x_{1} \, \mathbf{a}_{2}+x_{1} \, \mathbf{a}_{3}$ | = | $c x_{1} \,\mathbf{\hat{z}}$ | (2c) | Sn I |
| $\mathbf{B_{2}}$ | = | $- x_{1} \, \mathbf{a}_{1}- x_{1} \, \mathbf{a}_{2}- x_{1} \, \mathbf{a}_{3}$ | = | $- c x_{1} \,\mathbf{\hat{z}}$ | (2c) | Sn I |
| $\mathbf{B_{3}}$ | = | $x_{2} \, \mathbf{a}_{1}+x_{2} \, \mathbf{a}_{2}+x_{2} \, \mathbf{a}_{3}$ | = | $c x_{2} \,\mathbf{\hat{z}}$ | (2c) | Sn II |
| $\mathbf{B_{4}}$ | = | $- x_{2} \, \mathbf{a}_{1}- x_{2} \, \mathbf{a}_{2}- x_{2} \, \mathbf{a}_{3}$ | = | $- c x_{2} \,\mathbf{\hat{z}}$ | (2c) | Sn II |
| $\mathbf{B_{5}}$ | = | $x_{3} \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{2}+z_{3} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{3} - z_{3}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(x_{3} - z_{3}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(2 x_{3} + z_{3}\right) \,\mathbf{\hat{z}}$ | (6h) | Fe I |
| $\mathbf{B_{6}}$ | = | $z_{3} \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{2}+x_{3} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{3} - z_{3}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(x_{3} - z_{3}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(2 x_{3} + z_{3}\right) \,\mathbf{\hat{z}}$ | (6h) | Fe I |
| $\mathbf{B_{7}}$ | = | $x_{3} \, \mathbf{a}_{1}+z_{3} \, \mathbf{a}_{2}+x_{3} \, \mathbf{a}_{3}$ | = | $- \frac{1}{\sqrt{3}}a \left(x_{3} - z_{3}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(2 x_{3} + z_{3}\right) \,\mathbf{\hat{z}}$ | (6h) | Fe I |
| $\mathbf{B_{8}}$ | = | $- z_{3} \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}- x_{3} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{3} - z_{3}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(x_{3} - z_{3}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(2 x_{3} + z_{3}\right) \,\mathbf{\hat{z}}$ | (6h) | Fe I |
| $\mathbf{B_{9}}$ | = | $- x_{3} \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}- z_{3} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{3} - z_{3}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(x_{3} - z_{3}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(2 x_{3} + z_{3}\right) \,\mathbf{\hat{z}}$ | (6h) | Fe I |
| $\mathbf{B_{10}}$ | = | $- x_{3} \, \mathbf{a}_{1}- z_{3} \, \mathbf{a}_{2}- x_{3} \, \mathbf{a}_{3}$ | = | $\frac{1}{\sqrt{3}}a \left(x_{3} - z_{3}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(2 x_{3} + z_{3}\right) \,\mathbf{\hat{z}}$ | (6h) | Fe I |
References
- R. L. Dally, D. Phelan, N. Bishop, N. J. Ghimire, and J. W. Lynn, Isotropic Nature of the Metallic Kagome Ferromagnet Fe$_{3}$Sn$_{2}$ at High Temperatures, Crystals 11, 307 (2021), doi:10.3390/cryst11030307.
- B. Malaman, B. Roques, A. Courtois, and J. Protas, Structure cristalline du stannure de fer Fe$_{3}$Sn$_{2}$, Acta Crystallographica B 32, 1348–1351 (1976), doi:10.1107/S0567740876005323.
Prototype Generator
aflow --proto=A3B2_hR10_166_h_2c --params=$a,c/a,x_{1},x_{2},x_{3},z_{3}$