PtSn$_{4}$ ($D1_{c}$) Structure: AB4_oC20_41_a_2b-001
| Prototype | PtSn$_{4}$ |
| AFLOW prototype label | AB4_oC20_41_a_2b-001 |
| Strukturbericht designation | $D1_{c}$ |
| ICSD | 105793 |
| Pearson symbol | oC20 |
| Space group number | 41 |
| Space group symbol | $Aea2$ |
| AFLOW prototype command |
aflow --proto=AB4_oC20_41_a_2b-001
--params=$a, \allowbreak b/a, \allowbreak c/a, \allowbreak z_{1}, \allowbreak x_{2}, \allowbreak y_{2}, \allowbreak z_{2}, \allowbreak x_{3}, \allowbreak y_{3}, \allowbreak z_{3}$ |
Other compounds with this structure
AuSn$_{4}$, IrSn$_{4}$, PdSn$_{4}$
- The published atomic positions have $x_{2}=y_{3}$, $x_{3}=y_{2}$ and $z_{2}=-z_{3}$. This puts the system into space group $Ccce$ #68, very similar to PdSn$_{4}$.
- To get space group $Aba2$ #41 we shifted the $y_{2}$ and $z_{3}$ positions slightly. Even then we could not place this in space group $Aba2$ until we adjusted the tolerance. The original structure can be recovered using the command:
- aflow --proto=AB4_oC20_41_a_2b:Pt:Sn --tolerance=0.001 --params=a,b/a,c/a,x$_{2}$,y$_{2}$,z$_{2}$,x$_{3}$,y$_{3}$,z$_{3}$
- (Schubert, 1950) give the lattice constants in kX units. We used the factor of 1.00202Å/kX from (Wood, 1947) to convert to Ångströms.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&a \,\mathbf{\hat{x}}\\\mathbf{a_{2}}&=&\frac{1}{2}b \,\mathbf{\hat{y}}- \frac{1}{2}c \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&\frac{1}{2}b \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $- z_{1} \, \mathbf{a}_{2}+z_{1} \, \mathbf{a}_{3}$ | = | $c z_{1} \,\mathbf{\hat{z}}$ | (4a) | Pt I |
| $\mathbf{B_{2}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}- \left(z_{1} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(z_{1} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}b \,\mathbf{\hat{y}}+c z_{1} \,\mathbf{\hat{z}}$ | (4a) | Pt I |
| $\mathbf{B_{3}}$ | = | $x_{2} \, \mathbf{a}_{1}+\left(y_{2} - z_{2}\right) \, \mathbf{a}_{2}+\left(y_{2} + z_{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{2} \,\mathbf{\hat{x}}+b y_{2} \,\mathbf{\hat{y}}+c z_{2} \,\mathbf{\hat{z}}$ | (8b) | Sn I |
| $\mathbf{B_{4}}$ | = | $- x_{2} \, \mathbf{a}_{1}- \left(y_{2} + z_{2}\right) \, \mathbf{a}_{2}- \left(y_{2} - z_{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{2} \,\mathbf{\hat{x}}- b y_{2} \,\mathbf{\hat{y}}+c z_{2} \,\mathbf{\hat{z}}$ | (8b) | Sn I |
| $\mathbf{B_{5}}$ | = | $\left(x_{2} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{2} + z_{2} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(- y_{2} + z_{2} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{2} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- b \left(y_{2} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c z_{2} \,\mathbf{\hat{z}}$ | (8b) | Sn I |
| $\mathbf{B_{6}}$ | = | $- \left(x_{2} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{2} - z_{2} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(y_{2} + z_{2} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{2} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+b \left(y_{2} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+c z_{2} \,\mathbf{\hat{z}}$ | (8b) | Sn I |
| $\mathbf{B_{7}}$ | = | $x_{3} \, \mathbf{a}_{1}+\left(y_{3} - z_{3}\right) \, \mathbf{a}_{2}+\left(y_{3} + z_{3}\right) \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{x}}+b y_{3} \,\mathbf{\hat{y}}+c z_{3} \,\mathbf{\hat{z}}$ | (8b) | Sn II |
| $\mathbf{B_{8}}$ | = | $- x_{3} \, \mathbf{a}_{1}- \left(y_{3} + z_{3}\right) \, \mathbf{a}_{2}- \left(y_{3} - z_{3}\right) \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}- b y_{3} \,\mathbf{\hat{y}}+c z_{3} \,\mathbf{\hat{z}}$ | (8b) | Sn II |
| $\mathbf{B_{9}}$ | = | $\left(x_{3} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{3} + z_{3} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(- y_{3} + z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{3} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- b \left(y_{3} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c z_{3} \,\mathbf{\hat{z}}$ | (8b) | Sn II |
| $\mathbf{B_{10}}$ | = | $- \left(x_{3} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{3} - z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(y_{3} + z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{3} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+b \left(y_{3} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+c z_{3} \,\mathbf{\hat{z}}$ | (8b) | Sn II |
References
- K. Schubert and U. Rösler, Die Kristallstruktur von PtSn$_4$, Z. Metallkd. 41, 298–300 (1950).
- E. A. Wood, The Conversion Factor for kX Units to Angström Units, J. Appl. Phys. 18, 929–930 (1947), doi:10.1063/1.1697570.
Found in
- P. Villars and L. Calvert, Pearson's Handbook of Crystallographic Data for Intermetallic Phases (ASM International, Materials Park, OH, 1991), 2nd edn.
Prototype Generator
aflow --proto=AB4_oC20_41_a_2b --params=$a,b/a,c/a,z_{1},x_{2},y_{2},z_{2},x_{3},y_{3},z_{3}$