α-PdSn$_{2}$ Structure: AB2_tI48_142_d_ef-001
| Prototype | PdSn$_{2}$ |
| AFLOW prototype label | AB2_tI48_142_d_ef-001 |
| ICSD | 30235 |
| Pearson symbol | tI48 |
| Space group number | 142 |
| Space group symbol | $I4_1/acd$ |
| AFLOW prototype command |
aflow --proto=AB2_tI48_142_d_ef-001
--params=$a, \allowbreak c/a, \allowbreak z_{1}, \allowbreak x_{2}, \allowbreak x_{3}$ |
- This structure is stable up to 600$^\circ$C. (Villars, 2016)
- PdSn$_{2}$ has also been found in the orthorhombic $C_{e}$ structure.
- The ICSD entry is from (Hellner, 1956), but we use the refined data from (Künnen, 2000) for this presentation.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&- \frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}- \frac{1}{2}c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $\left(z_{1} + \frac{1}{4}\right) \, \mathbf{a}_{1}+z_{1} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{y}}+c z_{1} \,\mathbf{\hat{z}}$ | (16d) | Pd I |
| $\mathbf{B_{2}}$ | = | $z_{1} \, \mathbf{a}_{1}+\left(z_{1} + \frac{1}{4}\right) \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+c \left(z_{1} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16d) | Pd I |
| $\mathbf{B_{3}}$ | = | $- \left(z_{1} - \frac{1}{4}\right) \, \mathbf{a}_{1}- \left(z_{1} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}- c z_{1} \,\mathbf{\hat{z}}$ | (16d) | Pd I |
| $\mathbf{B_{4}}$ | = | $- \left(z_{1} - \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(z_{1} - \frac{1}{4}\right) \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{y}}- c \left(z_{1} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16d) | Pd I |
| $\mathbf{B_{5}}$ | = | $- \left(z_{1} - \frac{3}{4}\right) \, \mathbf{a}_{1}- z_{1} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{3}{4}a \,\mathbf{\hat{y}}- c z_{1} \,\mathbf{\hat{z}}$ | (16d) | Pd I |
| $\mathbf{B_{6}}$ | = | $- z_{1} \, \mathbf{a}_{1}- \left(z_{1} - \frac{3}{4}\right) \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{1}{4}a \,\mathbf{\hat{y}}- c \left(z_{1} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16d) | Pd I |
| $\mathbf{B_{7}}$ | = | $\left(z_{1} + \frac{3}{4}\right) \, \mathbf{a}_{1}+\left(z_{1} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{y}}+c \left(z_{1} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (16d) | Pd I |
| $\mathbf{B_{8}}$ | = | $\left(z_{1} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(z_{1} + \frac{3}{4}\right) \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+c \left(z_{1} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16d) | Pd I |
| $\mathbf{B_{9}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+\left(x_{2} + \frac{1}{4}\right) \, \mathbf{a}_{2}+x_{2} \, \mathbf{a}_{3}$ | = | $a x_{2} \,\mathbf{\hat{x}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (16e) | Sn I |
| $\mathbf{B_{10}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}- \left(x_{2} - \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(x_{2} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{2} \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (16e) | Sn I |
| $\mathbf{B_{11}}$ | = | $\left(x_{2} + \frac{1}{4}\right) \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}+x_{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+a \left(x_{2} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (16e) | Sn I |
| $\mathbf{B_{12}}$ | = | $- \left(x_{2} - \frac{1}{4}\right) \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}- \left(x_{2} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}- a \left(x_{2} - \frac{1}{4}\right) \,\mathbf{\hat{y}}$ | (16e) | Sn I |
| $\mathbf{B_{13}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}- \left(x_{2} - \frac{3}{4}\right) \, \mathbf{a}_{2}- x_{2} \, \mathbf{a}_{3}$ | = | $- a x_{2} \,\mathbf{\hat{x}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ | (16e) | Sn I |
| $\mathbf{B_{14}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+\left(x_{2} + \frac{3}{4}\right) \, \mathbf{a}_{2}+\left(x_{2} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{2} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (16e) | Sn I |
| $\mathbf{B_{15}}$ | = | $- \left(x_{2} - \frac{3}{4}\right) \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}- x_{2} \, \mathbf{a}_{3}$ | = | $- \frac{1}{4}a \,\mathbf{\hat{x}}- a \left(x_{2} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (16e) | Sn I |
| $\mathbf{B_{16}}$ | = | $\left(x_{2} + \frac{3}{4}\right) \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}+\left(x_{2} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+a \left(x_{2} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (16e) | Sn I |
| $\mathbf{B_{17}}$ | = | $\left(x_{3} + \frac{3}{8}\right) \, \mathbf{a}_{1}+\left(x_{3} + \frac{1}{8}\right) \, \mathbf{a}_{2}+\left(2 x_{3} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{x}}+a \left(x_{3} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+\frac{1}{8}c \,\mathbf{\hat{z}}$ | (16f) | Sn II |
| $\mathbf{B_{18}}$ | = | $- \left(x_{3} - \frac{3}{8}\right) \, \mathbf{a}_{1}- \left(x_{3} - \frac{1}{8}\right) \, \mathbf{a}_{2}- \left(2 x_{3} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}- a \left(x_{3} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+\frac{1}{8}c \,\mathbf{\hat{z}}$ | (16f) | Sn II |
| $\mathbf{B_{19}}$ | = | $\left(x_{3} + \frac{1}{8}\right) \, \mathbf{a}_{1}- \left(x_{3} - \frac{3}{8}\right) \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $- a \left(x_{3} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(x_{3} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- \frac{1}{8}c \,\mathbf{\hat{z}}$ | (16f) | Sn II |
| $\mathbf{B_{20}}$ | = | $- \left(x_{3} - \frac{1}{8}\right) \, \mathbf{a}_{1}+\left(x_{3} + \frac{3}{8}\right) \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $a \left(x_{3} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(x_{3} - \frac{1}{4}\right) \,\mathbf{\hat{y}}- \frac{1}{8}c \,\mathbf{\hat{z}}$ | (16f) | Sn II |
| $\mathbf{B_{21}}$ | = | $- \left(x_{3} - \frac{5}{8}\right) \, \mathbf{a}_{1}- \left(x_{3} - \frac{7}{8}\right) \, \mathbf{a}_{2}- \left(2 x_{3} - \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{3} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(x_{3} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+\frac{3}{8}c \,\mathbf{\hat{z}}$ | (16f) | Sn II |
| $\mathbf{B_{22}}$ | = | $\left(x_{3} + \frac{5}{8}\right) \, \mathbf{a}_{1}+\left(x_{3} + \frac{7}{8}\right) \, \mathbf{a}_{2}+\left(2 x_{3} + \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{3} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(x_{3} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+\frac{3}{8}c \,\mathbf{\hat{z}}$ | (16f) | Sn II |
| $\mathbf{B_{23}}$ | = | $- \left(x_{3} - \frac{7}{8}\right) \, \mathbf{a}_{1}+\left(x_{3} + \frac{5}{8}\right) \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{x}}- a \left(x_{3} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+\frac{5}{8}c \,\mathbf{\hat{z}}$ | (16f) | Sn II |
| $\mathbf{B_{24}}$ | = | $\left(x_{3} + \frac{7}{8}\right) \, \mathbf{a}_{1}- \left(x_{3} - \frac{5}{8}\right) \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}+a \left(x_{3} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+\frac{5}{8}c \,\mathbf{\hat{z}}$ | (16f) | Sn II |
References
- E. Hellner, Flußspat-Misch-Typen, Zeitschrift für Kristallographie 107, 99–123 (1956), doi:10.1524/zkri.1956.107.16.99.
- P. Villars, ed., PAULING FILE (Springer, 2016), chap. Pd-Sn Binary Phase Diagram 0-100 at.% Sn.
Found in
- B. Künnen, D. Niepmann, and W. Jeitschko, Structure refinements and some properties of the transition metal stannides Os$_{3}$Sn$_{7}$, Ir$_{5}$Sn$_{7}$, Ni$_{0.402(4)}$Pd$_{0.598}$Sn$_{4}$, $\alpha$-PdSn$_{2}$ and PtSn$_{4}$, J. Alloys Compd. 309, 1–9 (2000), doi:10.1016/S0925-8388(00)01042-2.
Prototype Generator
aflow --proto=AB2_tI48_142_d_ef --params=$a,c/a,z_{1},x_{2},x_{3}$