α-LiSn Structure: AB_mP6_10_bn_cm-001
| Prototype | LiSn |
| AFLOW prototype label | AB_mP6_10_bn_cm-001 |
| ICSD | 104782 |
| Pearson symbol | mP6 |
| Space group number | 10 |
| Space group symbol | $P2/m$ |
| AFLOW prototype command |
aflow --proto=AB_mP6_10_bn_cm-001
--params=$a, \allowbreak b/a, \allowbreak c/a, \allowbreak \beta, \allowbreak x_{3}, \allowbreak z_{3}, \allowbreak x_{4}, \allowbreak z_{4}$ |
- This is the low-temperature structure of LiSn. Above 470K LiSn may transform into the tetragonal $\beta$–LiSn structure (Villars, 2018). This structure is apparently metastable at room temperature (Blase, 1990).
- (Müller, 1973) give this structure in the
unique axis-$c$
setting of space group $P2_{1}/m$ #11. We used FINDSYM to transform this to the standardunique axis-$b$
setting. This involves an origin shift.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&a \,\mathbf{\hat{x}}\\\mathbf{a_{2}}&=&b \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \cos{\beta} \,\mathbf{\hat{x}}+c \sin{\beta} \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $\frac{1}{2} \, \mathbf{a}_{2}$ | = | $\frac{1}{2}b \,\mathbf{\hat{y}}$ | (1b) | Li I |
| $\mathbf{B_{2}}$ | = | $\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}c \cos{\beta} \,\mathbf{\hat{x}}+\frac{1}{2}c \sin{\beta} \,\mathbf{\hat{z}}$ | (1c) | Sn I |
| $\mathbf{B_{3}}$ | = | $x_{3} \, \mathbf{a}_{1}+z_{3} \, \mathbf{a}_{3}$ | = | $\left(a x_{3} + c z_{3} \cos{\beta}\right) \,\mathbf{\hat{x}}+c z_{3} \sin{\beta} \,\mathbf{\hat{z}}$ | (2m) | Sn II |
| $\mathbf{B_{4}}$ | = | $- x_{3} \, \mathbf{a}_{1}- z_{3} \, \mathbf{a}_{3}$ | = | $- \left(a x_{3} + c z_{3} \cos{\beta}\right) \,\mathbf{\hat{x}}- c z_{3} \sin{\beta} \,\mathbf{\hat{z}}$ | (2m) | Sn II |
| $\mathbf{B_{5}}$ | = | $x_{4} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+z_{4} \, \mathbf{a}_{3}$ | = | $\left(a x_{4} + c z_{4} \cos{\beta}\right) \,\mathbf{\hat{x}}+\frac{1}{2}b \,\mathbf{\hat{y}}+c z_{4} \sin{\beta} \,\mathbf{\hat{z}}$ | (2n) | Li II |
| $\mathbf{B_{6}}$ | = | $- x_{4} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}- z_{4} \, \mathbf{a}_{3}$ | = | $- \left(a x_{4} + c z_{4} \cos{\beta}\right) \,\mathbf{\hat{x}}+\frac{1}{2}b \,\mathbf{\hat{y}}- c z_{4} \sin{\beta} \,\mathbf{\hat{z}}$ | (2n) | Li II |
References
- W. Müller and H. Schäfer, Die Kristallstruktur der Phase LiSn, Z. Naturforsch. B 28, 246–248 (1973), doi:10.1515/znb-1973-5-604.
- P. Villars, H. Okamoto, and K. Cenzual, eds., ASM Alloy Phase Diagram Database (ASM International, 2018), chap. Lithium-Tin Binary Phase Diagram (1998 Sangster J.). Copyright © 2006-2018 ASM International.
Prototype Generator
aflow --proto=AB_mP6_10_bn_cm --params=$a,b/a,c/a,\beta,x_{3},z_{3},x_{4},z_{4}$