Rhombohedral CuPt ($L1_{1}$) Structure: AB_hR2_166_a_b

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Prototype : CuPt
AFLOW prototype label : AB_hR2_166_a_b
Strukturbericht designation : $L1_{1}$
Pearson symbol : hR2
Space group number : 166
Space group symbol : $\mbox{R}\bar{3}\mbox{m}$
AFLOW prototype command : aflow --proto=AB_hR2_166_a_b [--hex]
--params=
$a$,$c/a$


  • (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 rhombohedral structure, which (Ewald, 1929) labeled Strukturbericht $L1_{1}$. The other structure is cubic, and was listed as $L1_{3}$. (Barrett, 1980) noted that even slight additions of platinum above stoichiometry will cause a change in the crystal structure. This structure is given in the rhombohedral setting of space group $R\overline{3}m$ #66. Hexagonal settings of this structure can be obtained with the option ––hex.

Rhombohedral primitive vectors:

\[ \begin{array}{ccc} \mathbf{a}_1 & = & ~ \frac12 \, a \, \mathbf{\hat{x}} - \frac{1}{2\sqrt{3}} \, a \, \mathbf{\hat{y}} + \frac13 \, c \, \mathbf{\hat{z}} \\ \mathbf{a}_2 & = & \frac{1}{\sqrt{3}} \, a \, \mathbf{\hat{y}} + \frac13 \, c \, \mathbf{\hat{z}} \\ \mathbf{a}_3 & = & - \frac12 \, a \, \mathbf{\hat{x}} - \frac{1}{2\sqrt{3}} \, a \, \mathbf{\hat{y}} + \frac13 \, c \, \mathbf{\hat{z}} \\ \end{array} \]

Basis vectors:

\[ \begin{array}{ccccccc} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{Atom Type} \\ \mathbf{B}_{1} & =&0 \, \mathbf{a}_{1} + 0 \, \mathbf{a}_{2} + 0 \, \mathbf{a}_{3} & =&0 \mathbf{\hat{x}} + 0 \mathbf{\hat{y}} + 0 \mathbf{\hat{z}} & \left(1a\right) & \mbox{Cu} \\ \mathbf{B}_{2} & =&\frac12 \, \mathbf{a}_{1}+ \frac12 \, \mathbf{a}_{2}+ \frac12 \, \mathbf{a}_{3}& =&\frac12 \, c \, \mathbf{\hat{z}}& \left(1b\right) & \mbox{Pt} \\ \end{array} \]

References

  • C. H. Johansson and J. O. Linde, Gitterstruktur und elektrisches Leitvermögen der Mischkristallreihen Au–Cu, Pd–Cu und Pt–Cu, Annalen der Physik 387, 449–478 (1927), doi:10.1002/andp.19273870402.

Found in

  • P. P. Ewald and C. Hermann, Strukturbericht Band I, 1913–1928 (Akademsiche Verlagsgesellschaft M. B. H., Leipzig, 1931)., pp. 485.
  • W. B. Pearson, The Crystal Chemistry and Physics of Metals and Alloys (Wiley– Interscience, New York, London, Sydney, Toronto, 1972)., pp. 311-312.
  • C. S. Barrett and T. B. Massalski, Structure of Metals: Crystallographic Methods, Principles, and Data (Pergamon Press, Oxford, 1980), 3rd revised edn., pp. 275.
  • P. Villars, K. Cenzual, J. Daams, R. Gladyshevskii, O. Shcherban, V. Dubenskyy, N. Melnichenko–Koblyuk, O. Pavlyuk, I. Savesyuk, S. Stoiko, and L. Sysa, Landolt–Börnstein – Group III Condensed Matter 43A5 (Structure Types. Part 5: Space Groups (173) P63 – (166) R–3m) (Springer–Verlag, 2007). Accessed through the Springer Materials site.

Geometry files


Prototype Generator

aflow --proto=AB_hR2_166_a_b --params=

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