Ni$_{3}$Sn ($D0_{19}$) Structure: A3B_hP8_194_h_c-001
| Prototype | Ni$_{3}$Sn |
| AFLOW prototype label | A3B_hP8_194_h_c-001 |
| Strukturbericht designation | $D0_{19}$ |
| ICSD | 411928 |
| Pearson symbol | hP8 |
| Space group number | 194 |
| Space group symbol | $P6_3/mmc$ |
| AFLOW prototype command |
aflow --proto=A3B_hP8_194_h_c-001
--params=$a, \allowbreak c/a, \allowbreak x_{2}$ |
Other compounds with this structure
Al$_{3}$Gd, Al$_{3}$Sm (LT), Al$_{3}$Th, Cd$_{3}$Mg, Cd$_{3}$Sc, Ce$_{3}$Al (LT), Co$_{3}$Mo, Co$_{3}$W, Fe$_{3}$Ge (HT), Fe$_{3}$Sn, Ga$_{3}$Pu (LT), Hg$_{3}$Ce, Hg$_{3}$Sc, Hg$_{3}$Sm, Hg$_{3}$Y, Ir$_{3}$Mo, Mg$_{3}$Cd, Mg$_{3}$In, Mn$_{3}$Sn, Ni$_{3}$In, Ni$_{3}$Sn (LT), Pt$_{3}$U, Rh$_{3}$W, Sc$_{3}$In, Ti$_{3}$Al, Ti$_{3}$Ga, Ti$_{3}$Sn (HT), Tl$_{3}$Sn, Zn$_{3}$Mn
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \,\mathbf{\hat{y}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $\frac{1}{3} \, \mathbf{a}_{1}+\frac{2}{3} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (2c) | Sn I |
| $\mathbf{B_{2}}$ | = | $\frac{2}{3} \, \mathbf{a}_{1}+\frac{1}{3} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ | (2c) | Sn I |
| $\mathbf{B_{3}}$ | = | $x_{2} \, \mathbf{a}_{1}+2 x_{2} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{3}{2}a x_{2} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{2} \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (6h) | Ni I |
| $\mathbf{B_{4}}$ | = | $- 2 x_{2} \, \mathbf{a}_{1}- x_{2} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $- \frac{3}{2}a x_{2} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{2} \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (6h) | Ni I |
| $\mathbf{B_{5}}$ | = | $x_{2} \, \mathbf{a}_{1}- x_{2} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $- \sqrt{3}a x_{2} \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (6h) | Ni I |
| $\mathbf{B_{6}}$ | = | $- x_{2} \, \mathbf{a}_{1}- 2 x_{2} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $- \frac{3}{2}a x_{2} \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{2} \,\mathbf{\hat{y}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ | (6h) | Ni I |
| $\mathbf{B_{7}}$ | = | $2 x_{2} \, \mathbf{a}_{1}+x_{2} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{3}{2}a x_{2} \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{2} \,\mathbf{\hat{y}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ | (6h) | Ni I |
| $\mathbf{B_{8}}$ | = | $- x_{2} \, \mathbf{a}_{1}+x_{2} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\sqrt{3}a x_{2} \,\mathbf{\hat{y}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ | (6h) | Ni I |
References
- A. L. Lyubimtsev, A. I. Baranov, A. Fischer, L. Kloo, and B. A. Popovkin, The structure and bonding of Ni$_3$Sn, J. Alloys Compd. 340, 167–172 (2002), doi:10.1063/1.1662996.
Prototype Generator
aflow --proto=A3B_hP8_194_h_c --params=$a,c/a,x_{2}$