$L1_{a}$ (disputed CuPt$_{3}$ Structure): AB7_cF32_225_a_bd-001
| Prototype | CuPt$_{3}$ |
| AFLOW prototype label | AB7_cF32_225_a_bd-001 |
| Strukturbericht designation | $L1_{a}$ |
| ICSD | none |
| Pearson symbol | cF32 |
| Space group number | 225 |
| Space group symbol | $Fm\overline{3}m$ |
| AFLOW prototype command |
aflow --proto=AB7_cF32_225_a_bd-001
--params=$a$ |
- According to (Tang, 1951), the (24d) sites have the composition Pt$_{0.8}$Cu$_{0.2}$ in stoichiometric CuPt$_{3}$. Here we use
Pt
to specify the atoms on this site. - (Tang, 1951) states that the crystal structure of CuPt$_{3}$ must be cubic, but (Mshumi, 2014) argue that it is orthorhombic, and is in fact the $L1_{3}$ structure.
- (Smithells, 1955) gave this structure the $L1_{a}$ designation as part of his extension of the original Strukturbericht labels. He does note that an alternative orthorhombic structure had been proposed.
- (Smithells, 1955) assigns this structure to space group $F432$ #209, but the positions given by (Tang, 1951) are also consistent with $Fm\overline{3}m$ #225, so we assign this structure to the higher symmetry space group.
- (Tang, 1951) does not give the lattice constant, so we use the value estimated by (Smithells, 1955).
- The Wyckoff positions are identical to those of the Ca$_{7}$Ge structure.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $0$ | = | $0$ | (4a) | Cu I |
| $\mathbf{B_{2}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}$ | (4b) | Pt I |
| $\mathbf{B_{3}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}$ | = | $\frac{1}{4}a \,\mathbf{\hat{y}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (24d) | Pt II |
| $\mathbf{B_{4}}$ | = | $\frac{1}{2} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (24d) | Pt II |
| $\mathbf{B_{5}}$ | = | $\frac{1}{2} \, \mathbf{a}_{2}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (24d) | Pt II |
| $\mathbf{B_{6}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (24d) | Pt II |
| $\mathbf{B_{7}}$ | = | $\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}$ | (24d) | Pt II |
| $\mathbf{B_{8}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}$ | (24d) | Pt II |
References
- Y.-C. Tang, A cubic structure for the phase Pt$_{3}$Cu, Acta Cryst. 4, 377–378 (1951), doi:10.1107/S0365110X51001185.
- C. J. Smithells, Metals Reference Book (Butterworths Scientific, London, 1955), second edn.
Found in
- C. Mshumi, C. I. Lang, L. R. Richey, K. C. Erb, C. W. Rosenbrock, L. J.Nelson, R. R. Vanfleet, H. T. Stokes, B. J. Campbell, and G. L. W. Hart, Revisiting the CuPt$_{3}$ prototype and the $L1_{3}$ structure, Acta Mat. 73, 326–336 (2014), doi:10.1016/j.actamat.2014.03.029.
Prototype Generator
aflow --proto=AB7_cF32_225_a_bd --params=$a$