Ordering and segregation of a ${\mathrm{Cu}}_{75}{\mathrm{Pt}}_{25}\left(111\right)$ surface: A first-principles cluster expansion study

Configurational thermodynamics for ${\mathrm{Cu}}_{75}{\mathrm{Pt}}_{25}\left(111\right)$ surfaces is examined by a first-principles calculation in conjunction with the cluster-expansion technique. The calculated surface segregation profile just below the bulk order-disorder transition temperature exhibits Pt segregation to the top and the third layers and Cu segregation to the second layer. No long-range ordered structure is found at the top layer. However, the simulated short-range-order parameter shows a small negative value, indicating a weak ordering tendency at the ${\mathrm{Cu}}_{75}{\mathrm{Pt}}_{25}$ alloy surface. This fact can be interpreted by the competition between the layer-confined spontaneous $p(2\times 2)$ ordering tendency and the Pt segregation and interlayer surface ordering, which certainly disrupts the $p(2\times 2)$ ordering. Five possible surface ground-state structures are found for the bulk $L{1}_2$ structure. The surface ground-state structures exhibit strongly localized electronic states composed of Pt and Cu $d$ states at the topmost layer around $3\mathrm{eV}$ below the Fermi energy, which is consistent with the previous ultraviolet photoelectron spectroscopy measurement. One of the surface ground-state structures possesses additional surface states just below and above the Fermi energy, which are composed of Pt $d$ states at the topmost layer. A significant ordering effect on the surface electronic states is confirmed for the ${\mathrm{Cu}}_{75}{\mathrm{Pt}}_{25}$ alloy.

Figure 1

(Color online) Optimal set of selected clusters for the bulk $\mathrm{Cu}\text{−}\mathrm{Pt}$ alloy obtained by minimizing the CV score using GA.

Figure 2

Fitted ECIs for the bulk $\mathrm{Cu}\text{−}\mathrm{Pt}$ alloy. The abscissa represents the cluster numbers shown in Fig. 1.

Figure 3

(Color online) Clusters for the ${\mathrm{Cu}}_{75}{\mathrm{Pt}}_{25}\left(111\right)$ surface.

Figure 4

Fitted ECIs per cluster for the ${\mathrm{Cu}}_{75}{\mathrm{Pt}}_{25}\left(111\right)$ surface. The horizontal bars represent the corresponding bulk ECIs.

Figure 5

Surface composition profile of Pt for the ${\mathrm{Cu}}_{75}{\mathrm{Pt}}_{25}\left(111\right)$ surface. Open circles denote the results from the present MC simulation $(T=800\mathrm{K})$. Open triangles, LEED study $(T=800–820\mathrm{K})$ (Ref. 20); open squares, LEED study $(T=850\mathrm{K})$ (Ref. 18).

Figure 6

Ground-state convex hull for the top three layer atomic arrangements of the top three layers on $L{1}_2$ as a function of surface Pt composition $x_{\mathrm{Pt}}$. A total of five ground-state atomic arrangements are recognized, as represented by the large filled circles.

Figure 7

(Color online) Projected electronic density of states (PDOS) of $d$-state contribution at the top layer for the (a) type I structure, (b) type II structure, (c) bulk $L{1}_2$ structure, and (d) UPS for the $p(2\times 2)$ ordered surface. (Reference 17) (a)–(c): Dotted curves represent the Cu contribution, and the solid curves represent Pt. Energies are measured from the Fermi level.

Figure 8

(Color online) Surface-band structure for the type I (upper figure) and type II (lower figure) ordered structures. The Fermi energy is set at $0\mathrm{eV}$. The plots are along the same direction, with indicated symmetry points referring to the underlying fcc (111) surface 2D Brillouin zone. The filled and open circles represent strongly and weakly localized surface states containing more than 80 and $60\%$ contributions of the top layer, respectively.