GdSn$_{3}$ Structure: AB3_oC16_38_ab_3a3b-001
| Prototype | GdSn$_{3}$ |
| AFLOW prototype label | AB3_oC16_38_ab_3a3b-001 |
| ICSD | 104154 |
| Pearson symbol | oC16 |
| Space group number | 38 |
| Space group symbol | $Amm2$ |
| AFLOW prototype command |
aflow --proto=AB3_oC16_38_ab_3a3b-001
--params=$a, \allowbreak b/a, \allowbreak c/a, \allowbreak z_{1}, \allowbreak z_{2}, \allowbreak z_{3}, \allowbreak z_{4}, \allowbreak z_{5}, \allowbreak z_{6}, \allowbreak z_{7}, \allowbreak z_{8}$ |
Other compounds with this structure
DySn$_{3}$, HoSn$_{3}$, ReSn$_{3}$, TbSn$_{3}$, TmSn$_{3}$, YSn$_{3}$
- (Palenzona, 1993) identify this as the low-temperature structure of GdSn$_{3}$, transforming into the CuAu$_{3}$ ($L1_{2}$) structure at high temperatures.
- (Palenzona, 1993) do not provide the coordinates for this structure within the paper, however ICSD entry 104154 gives the structure and lists this paper as the source.
- Space group $Amm2$ #38 does not specify the origin of the $z$-axis. Here it is fixed by setting $z_{2} = 0$ for the Sn-I atom.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&a \,\mathbf{\hat{x}}\\\mathbf{a_{2}}&=&\frac{1}{2}b \,\mathbf{\hat{y}}- \frac{1}{2}c \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&\frac{1}{2}b \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $- z_{1} \, \mathbf{a}_{2}+z_{1} \, \mathbf{a}_{3}$ | = | $c z_{1} \,\mathbf{\hat{z}}$ | (2a) | Gd I |
| $\mathbf{B_{2}}$ | = | $- z_{2} \, \mathbf{a}_{2}+z_{2} \, \mathbf{a}_{3}$ | = | $c z_{2} \,\mathbf{\hat{z}}$ | (2a) | Sn I |
| $\mathbf{B_{3}}$ | = | $- z_{3} \, \mathbf{a}_{2}+z_{3} \, \mathbf{a}_{3}$ | = | $c z_{3} \,\mathbf{\hat{z}}$ | (2a) | Sn II |
| $\mathbf{B_{4}}$ | = | $- z_{4} \, \mathbf{a}_{2}+z_{4} \, \mathbf{a}_{3}$ | = | $c z_{4} \,\mathbf{\hat{z}}$ | (2a) | Sn III |
| $\mathbf{B_{5}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}- z_{5} \, \mathbf{a}_{2}+z_{5} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+c z_{5} \,\mathbf{\hat{z}}$ | (2b) | Gd II |
| $\mathbf{B_{6}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}- z_{6} \, \mathbf{a}_{2}+z_{6} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+c z_{6} \,\mathbf{\hat{z}}$ | (2b) | Sn IV |
| $\mathbf{B_{7}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}- z_{7} \, \mathbf{a}_{2}+z_{7} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+c z_{7} \,\mathbf{\hat{z}}$ | (2b) | Sn V |
| $\mathbf{B_{8}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}- z_{8} \, \mathbf{a}_{2}+z_{8} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+c z_{8} \,\mathbf{\hat{z}}$ | (2b) | Sn VI |
References
- A. Palenzona and P. Manfrinetti, The tin-rich side of the rare earth-tin systems (R = Gd, Tb, Dy, Ho, Er, Tm, Lu and Y), J. Alloys Compd. 201, 43–47 (1993), doi:10.1016/0925-8388(93)90859-L.
- F. Karlsruhe and NIST, Inorganic Crystal Structure Database, http://icsd.fiz-karlsruhe.de/.
Prototype Generator
aflow --proto=AB3_oC16_38_ab_3a3b --params=$a,b/a,c/a,z_{1},z_{2},z_{3},z_{4},z_{5},z_{6},z_{7},z_{8}$