BaNiSn$_{3}$ Structure: ABC3_tI10_107_a_a_ab-001
| Prototype | BaNiSn$_{3}$ |
| AFLOW prototype label | ABC3_tI10_107_a_a_ab-001 |
| ICSD | 58662 |
| Pearson symbol | tI10 |
| Space group number | 107 |
| Space group symbol | $I4mm$ |
| AFLOW prototype command |
aflow --proto=ABC3_tI10_107_a_a_ab-001
--params=$a, \allowbreak c/a, \allowbreak z_{1}, \allowbreak z_{2}, \allowbreak z_{3}, \allowbreak z_{4}$ |
Other compounds with this structure
BaPdSn$_{3}$, BaPtSn$_{3}$, CeCuAl$_{3}$, EuPdGe$_{3}$, LaOsSb$_{3}$, SrIrAl$_{3}$, SrNiSn$_{3}$, SrPdAl$_{3}$, SrPtAl$_{3}$
- This is a ternary form of the $D1_{3}$ (BaAl$_{4}$) structure. The atomic positions in both conventional cells are approximately the same, but the distribution of the atoms on those sites and the resulting relaxation leads to a different structure.
- Although (Dörrscheidt, 1978) give the structural information for BaPtSn$_{3}$ before that of BaNiSn$_{3}$, (Shatruk, 2019) and others list BaNiSn$_{3}$ as the prototype for this structure.
- Space group $I4mm$ #107 does not specify the origin of the $z$-axis. (Dörrscheidt, 1978) places the barium atom at the origin.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&- \frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}- \frac{1}{2}c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $z_{1} \, \mathbf{a}_{1}+z_{1} \, \mathbf{a}_{2}$ | = | $c z_{1} \,\mathbf{\hat{z}}$ | (2a) | Ba I |
| $\mathbf{B_{2}}$ | = | $z_{2} \, \mathbf{a}_{1}+z_{2} \, \mathbf{a}_{2}$ | = | $c z_{2} \,\mathbf{\hat{z}}$ | (2a) | Ni I |
| $\mathbf{B_{3}}$ | = | $z_{3} \, \mathbf{a}_{1}+z_{3} \, \mathbf{a}_{2}$ | = | $c z_{3} \,\mathbf{\hat{z}}$ | (2a) | Sn I |
| $\mathbf{B_{4}}$ | = | $\left(z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{1}+z_{4} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{y}}+c z_{4} \,\mathbf{\hat{z}}$ | (4b) | Sn II |
| $\mathbf{B_{5}}$ | = | $z_{4} \, \mathbf{a}_{1}+\left(z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+c z_{4} \,\mathbf{\hat{z}}$ | (4b) | Sn II |
References
- W. Dörrscheidt and H. Schäfer, Die struktur des BaPtSn$_{3}$, BaNiSn$_{3}$ und SrNiSn$_{3}$ und ihre verwandtschaft zum ThCr$_{2}$Si$_{2}$-strukturtyp, J. Less-Common Met. 58, 209–216 (1978), doi:10.1016/0022-5088(78)90202-3.
Prototype Generator
aflow --proto=ABC3_tI10_107_a_a_ab --params=$a,c/a,z_{1},z_{2},z_{3},z_{4}$