Sn$_{4}$As$_{3}$ Structure: A3B4_hR7_160_3a_4a-001
| Prototype | As$_{3}$Sn$_{4}$ |
| AFLOW prototype label | A3B4_hR7_160_3a_4a-001 |
| ICSD | 419884 |
| Pearson symbol | hR7 |
| Space group number | 160 |
| Space group symbol | $R3m$ |
| AFLOW prototype command |
aflow --proto=A3B4_hR7_160_3a_4a-001
--params=$a, \allowbreak c/a, \allowbreak x_{1}, \allowbreak x_{2}, \allowbreak x_{3}, \allowbreak x_{4}, \allowbreak x_{5}, \allowbreak x_{6}, \allowbreak x_{7}$ |
- Most earlier e.g. (Pearson, 1967) work places this in space group $R\overline{3}m$ #166, in which case this would be in the Al$_{4}$C$_{3}$ ($D7_{1}$) structure. (Kovnir, 2009) argue that there is actually no inversion site, so the structure is as presented here, in space group $R3m$ #160. The two structures are very close - if we allow a 0.1Å uncertainty in the atomic positions the structure becomes $D7_{1}$. As we already have that structure, we present the Kovnir et al. structure here.
- 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 | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $x_{1} \, \mathbf{a}_{1}+x_{1} \, \mathbf{a}_{2}+x_{1} \, \mathbf{a}_{3}$ | = | $c x_{1} \,\mathbf{\hat{z}}$ | (1a) | As I |
| $\mathbf{B_{2}}$ | = | $x_{2} \, \mathbf{a}_{1}+x_{2} \, \mathbf{a}_{2}+x_{2} \, \mathbf{a}_{3}$ | = | $c x_{2} \,\mathbf{\hat{z}}$ | (1a) | As II |
| $\mathbf{B_{3}}$ | = | $x_{3} \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{2}+x_{3} \, \mathbf{a}_{3}$ | = | $c x_{3} \,\mathbf{\hat{z}}$ | (1a) | As III |
| $\mathbf{B_{4}}$ | = | $x_{4} \, \mathbf{a}_{1}+x_{4} \, \mathbf{a}_{2}+x_{4} \, \mathbf{a}_{3}$ | = | $c x_{4} \,\mathbf{\hat{z}}$ | (1a) | Sn I |
| $\mathbf{B_{5}}$ | = | $x_{5} \, \mathbf{a}_{1}+x_{5} \, \mathbf{a}_{2}+x_{5} \, \mathbf{a}_{3}$ | = | $c x_{5} \,\mathbf{\hat{z}}$ | (1a) | Sn II |
| $\mathbf{B_{6}}$ | = | $x_{6} \, \mathbf{a}_{1}+x_{6} \, \mathbf{a}_{2}+x_{6} \, \mathbf{a}_{3}$ | = | $c x_{6} \,\mathbf{\hat{z}}$ | (1a) | Sn III |
| $\mathbf{B_{7}}$ | = | $x_{7} \, \mathbf{a}_{1}+x_{7} \, \mathbf{a}_{2}+x_{7} \, \mathbf{a}_{3}$ | = | $c x_{7} \,\mathbf{\hat{z}}$ | (1a) | Sn IV |
References
- K. Kovnir, Y. V. Kolen'ko, A. I. Baranov, I. S. Neira, A. V. Sobolev, M. Yoshimura, I. A. .Presniakov, and A. V. Shevelkov, Sn$_{4}$As$_{3}$ revisited: Solvothermal synthesis and crystal and electronic structure, J. Solid State Chem. 182, 630–639 (2009), doi:10.1016/j.jssc.2008.12.007.
- W. B. Pearson, A Handbook of Lattice Spacings and Structures of Metals and Alloys, Volume 2, International Series of Monographs on Metal Physics and Physical Metallurgy, vol. 8 (Pergamon Press, Oxford, London, Edinburgh, New York, Toronto, Sydney, Paris, Braunschweig, 1967).
Prototype Generator
aflow --proto=A3B4_hR7_160_3a_4a --params=$a,c/a,x_{1},x_{2},x_{3},x_{4},x_{5},x_{6},x_{7}$