Cubic CuPt ($L1_{3}$ (I), $D4$) Structure : AB_cF32_227_c_d
| Prototype | : | CuPt |
| AFLOW prototype label | : | AB_cF32_227_c_d |
| Strukturbericht designation | : | $L1_{3}$ (I) |
| Pearson symbol | : | cF32 |
| Space group number | : | 227 |
| Space group symbol | : | $Fd\bar{3}m$ |
| AFLOW prototype command | : | aflow --proto=AB_cF32_227_c_d --params=$a$ |
- (Johansson, 1929) described two possible structures for CuPt. (Ewald, 1929) and later (Villars, 2007) used the description to determine the space group and atomic positions. This page describes the cubic structure, which (Ewald, 1929) labeled Strukturbericht $L1_{1}$. The other structure is rhombohedral, and was listed as $L1_{1}$. (Villars, 2007) prefers the later structure, listing the current one as
superceded.
- (Barrett, 1980) noted that even slight additions of platinum above stoichiometry will cause a change in the crystal structure.
- This structure is equivalent to the $D4$ structure of (Lu, 1991).
- This structure should not be confused with the CuPt3 structure, which has also been given the $L1_{3}$ label, and which we will often refer to as $L1_{3}$ (II).
Face-centered Cubic primitive vectors:
\[ \begin{array}{ccc} \mathbf{a}_1 & = & \frac12 \, a \, \mathbf{\hat{y}} + \frac12 \, a \, \mathbf{\hat{z}} \\ \mathbf{a}_2 & = & \frac12 \, a \, \mathbf{\hat{x}} + \frac12 \, a \, \mathbf{\hat{z}} \\ \mathbf{a}_3 & = & \frac12 \, a \, \mathbf{\hat{x}} + \frac12 \, a \, \mathbf{\hat{y}} \\ \end{array} \]
Basis vectors:
\[ \begin{array}{ccccccc} & & \text{Lattice Coordinates} & & \text{Cartesian Coordinates} &\text{Wyckoff Position} & \text{Atom Type} \\ \mathbf{B}_{1} & = & 0 \, \mathbf{a}_{1} + 0 \, \mathbf{a}_{2} + 0 \, \mathbf{a}_{3} & = & 0 \, \mathbf{\hat{x}} + 0 \, \mathbf{\hat{y}} + 0 \, \mathbf{\hat{z}} & \left(16c\right) & \text{Cu} \\ \mathbf{B}_{2} & = & \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + \frac{1}{4}a \, \mathbf{\hat{y}} & \left(16c\right) & \text{Cu} \\ \mathbf{B}_{3} & = & \frac{1}{2} \, \mathbf{a}_{2} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + \frac{1}{4}a \, \mathbf{\hat{z}} & \left(16c\right) & \text{Cu} \\ \mathbf{B}_{4} & = & \frac{1}{2} \, \mathbf{a}_{1} & = & \frac{1}{4}a \, \mathbf{\hat{y}} + \frac{1}{4}a \, \mathbf{\hat{z}} & \left(16c\right) & \text{Cu} \\ \mathbf{B}_{5} & = & \frac{1}{2} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + \frac{1}{2}a \, \mathbf{\hat{y}} + \frac{1}{2}a \, \mathbf{\hat{z}} & \left(16d\right) & \text{Pt} \\ \mathbf{B}_{6} & = & \frac{1}{2} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{2} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + \frac{1}{4}a \, \mathbf{\hat{y}} + \frac{1}{2}a \, \mathbf{\hat{z}} & \left(16d\right) & \text{Pt} \\ \mathbf{B}_{7} & = & \frac{1}{2} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + \frac{1}{2}a \, \mathbf{\hat{y}} + \frac{1}{4}a \, \mathbf{\hat{z}} & \left(16d\right) & \text{Pt} \\ \mathbf{B}_{8} & = & \frac{1}{2} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + \frac{1}{4}a \, \mathbf{\hat{y}} + \frac{1}{4}a \, \mathbf{\hat{z}} & \left(16d\right) & \text{Pt} \\ \end{array} \]References
- C. H. Johansson and J. O. Linde, Gitterstruktur und elektrisches Leitvermögen der Mischkristallreihen Au–Cu, Pd–Cu und Pt–Cu, Ann. Phys. 387, 449–478 (1927), doi:10.1002/andp.19273870402.
- P. Villars, K. Cenzual, J. Daams, R. Gladyshevskii, O. Shcherban, V. Dubenskyy, N. Melnichenko–Koblyuk, O. Pavlyuk, I. Savysyuk, S. Stoyko, and L. Sysa, Structure Types. Part 5: Space Groups (173) $P6_{3}$ – (166) $R$–$3m$ · CuPt: Datasheet from Landolt–Börnstein – Group III Condensed Matter · Volume 43A5:
Structure Types. Part 5: Space Groups (173) $P6_{3}$ – (166) $R$–$3m$
in SpringerMaterials, doi:10.1007/978-3-540-46933-9_359. Copyright 2007 Springer–Verlag", Part of SpringerMaterials.
- C. Barrett and T. B. Massalski, Structure of Metals – Crystallographic Methods, Principles, and Data (Pergammon Press, Oxford, New York, 1980).
- Z. W. Lu, S.–H. Wei, A. Zunger, S. Frota–Pessoa, and L. G. Ferreira, First–principles statistical mechanics of structural stability of intermetallic compounds, Phys. Rev. B 44, 512–544 (1991), doi:10.1103/PhysRevB.44.512.
Found in
- P. P. Ewald and C. Hermann, eds., Strukturbericht 1913–1928 (Akademische Verlagsgesellschaft M. B. H., Leipzig, 1931).