Cubic CuPt ($L1_{3}$ (I), $D4$) Structure : AB_cF32_227_c_d

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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 (Villars, 2007) prefers the later structure, listing the current one as superceded.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:

\[ \begin{array}{ccccccc} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{Atom Type} \\ \mathbf{B}_{1} & = & 0 \, \mathbf{a}_{1} + 0 \, \mathbf{a}_{2} + 0 \, \mathbf{a}_{3} & = & 0 \, \mathbf{\hat{x}} + 0 \, \mathbf{\hat{y}} + 0 \, \mathbf{\hat{z}} & \left(16c\right) & \mbox{Cu} \\ \mathbf{B}_{2} & = & \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + \frac{1}{4}a \, \mathbf{\hat{y}} & \left(16c\right) & \mbox{Cu} \\ \mathbf{B}_{3} & = & \frac{1}{2} \, \mathbf{a}_{2} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + \frac{1}{4}a \, \mathbf{\hat{z}} & \left(16c\right) & \mbox{Cu} \\ \mathbf{B}_{4} & = & \frac{1}{2} \, \mathbf{a}_{1} & = & \frac{1}{4}a \, \mathbf{\hat{y}} + \frac{1}{4}a \, \mathbf{\hat{z}} & \left(16c\right) & \mbox{Cu} \\ \mathbf{B}_{5} & = & \frac{1}{2} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + \frac{1}{2}a \, \mathbf{\hat{y}} + \frac{1}{2}a \, \mathbf{\hat{z}} & \left(16d\right) & \mbox{Pt} \\ \mathbf{B}_{6} & = & \frac{1}{2} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{2} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + \frac{1}{4}a \, \mathbf{\hat{y}} + \frac{1}{2}a \, \mathbf{\hat{z}} & \left(16d\right) & \mbox{Pt} \\ \mathbf{B}_{7} & = & \frac{1}{2} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + \frac{1}{2}a \, \mathbf{\hat{y}} + \frac{1}{4}a \, \mathbf{\hat{z}} & \left(16d\right) & \mbox{Pt} \\ \mathbf{B}_{8} & = & \frac{1}{2} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + \frac{1}{4}a \, \mathbf{\hat{y}} + \frac{1}{4}a \, \mathbf{\hat{z}} & \left(16d\right) & \mbox{Pt} \\ \end{array} \]

References

  • C. H. Johansson and J. O. Linde, Gitterstruktur und elektrisches Leitvermögen der Mischkristallreihen Au–Cu, Pd–Cu und Pt–Cu, 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) $R$–$3m$ \textperiodcentered CuPt: Datasheet from Landolt–Börnstein – Group III Condensed Matter \textperiodcentered 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).

Geometry files


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