Atomic structure of low-index and (1 ln) surfaces in ... - Science Direct

1 downloads 0 Views 324KB Size Report
[7] V. Vitek, G.J. Ackland and J. Cserti, Mater. Res. Soc. Syrup. Proc. 186 (1991) 237. [8] G.J. Ackland and V. Vitek, Phys. Rev. B 41 (t~u) luaz,÷. [9] C. Dumez, M.
surface science ELSEVIER

Surface Science 370 (1997) L163-L167

Surface Science Letters

Atomic structure of low-index and (1 ln) surfaces in ordered

Cu3Au

A. Aslanides, M. Hayoun, V. Pontikis * Laboratoire des Solides Irradids, CEA-CEREM, URA CNRS 1380, Ecole Polytechnique, F-91128 Palaiseau Cedex, France Received 23 May 1996; accepted for publication 20 August 1996

Abstract

By computing the surface energy at T = 0 K, we test the relative stability of various among possible atomic configurations of lowindex and (lln) surfaces in the L12 compound CuaAu. The computations rely on two n-body phenomenological potentials and are performed using a classical energy minimization scheme. The energy of (100) and (110) surfaces is at a minimum for a mixed composition terminal layer, in agreement with available experimental results and previous calculations. For (113) and (115) surfaces the minimum energy is obtained when all (100) terraces are mixed. In this case, the height and width of steps and terraces are twice as large as those of a standard surface configuration. Keywords: Alloys; Computer simulations; Low index single crystal surfaces; Semi-empirical models and model calculations; Surface energy; Vicinal single crystal surfaces

Surfaces are known to undergo a variety of structural transitions, which have been extensively studied mainly in one-component metallic systems [ 1]. In the case of metallic alloys, changes of the surface chemical composition as a function of the temperature, surface orientation and bulk chemistry can influence the surface structure, as they can be the origin of surface structural transitions which do not occur in simple metallic systems [2]. As an illustration, the experimental observation made in the L12 structure alloy CusaPd17 shows that a (110) vicinal surface undergoes a double-step to single-step morphological transition when the bulk order~lisorder critical temperature is crossed [3]. Partly motivated by this observation, we study in present work the relative stability of the simplest * Corresponding author. Fax:+ 33 1 69333022; e-mail: [email protected]

among possible terminations of (113) and (115) facets in the L12 compound Cu3Au by computing the associated surface energies. According to the terrace-ledge-kink model (referred hereafter to as the TLK model), such surfaces are made of (100) terraces separated by steps running along the close-packed [ 110] directions (Fig. la). Due to the stacking sequence of (100) planes in the L12 structure (ABAB...), pure "100% Cu" terraces (A) alternate with gold-rich "50% Au-50% Cu" terraces (B). One may suspect that the TLK-like configurations of (1 ln) surfaces are not the lowest-energy configurations, for it is well established that in the case of (100) and (110) surfaces, a mixed terminal layer is preferred in ordered Cu3Au [2,4,5]. Two possible structures of (lln) surfaces, alternative to the TLK prediction, are shown in Figs. lb and lc for n= 5. They are obtained starting from the TLK configuration

0039-6028/97/$17.00 Copyright © 1997 Elsevier Science B.V. All rights reserved PII S 0 0 3 9 - 6 0 2 8 ( 9 6 ) 0 1 1 2 8 - 4

A. Aslanides et al./Surface Science 370 (1997) L163-L167

# ¢ l ¢

¢

(a)

(b)

I

(c) Fig. 1. Perspective view of the topmost atomic layers of the (115) surface in Cu3Au(Cu: dark spheres, Au: light gray spheres). The diameter of the symbols is chosen proportional to the corresponding atomic radii. (a) The TLK model configuration, (b) mixed terraces are removed, and (c) pure copper terraces are removed. (Fig. la) and by selectively removing either the pure Cu or the gold-rich terrace layers, thereby achieving a uniform surface composition. The remarkable feature here is that these surfaces are made of steps and terraces having a height and width twice as large as the T L K reference surface. Whether these configurations are energetically favored with respect to the T L K model configuration and which among them is preferred are the questions we answer below by computing surface energies at T = 0 K and for values n = 0, 3 and 5. Our computations rely on two implementations of a phenomenological n-body potential to the case of Cu3Au, according which the total energy of an

assembly of N atoms is given by I-6,7]

E=2Z

N

i~=1

3.'#71

"q

/~ j # = . l

(1) where r u = Irj-ril, and the indexes i~(j#) run over all the particles. The functions ~b(rij) and O(ro) are either exponentials (model I) [6] or polynomials (model II) [7], the parameters of which are fitted to experimental quantities, among which are the cohesive energy, the lattice parameter and elastic moduli. These potentials have been shown to

A. Aslanides et al./ Surface Science 370 (1997) L163-L167

where, Us and Ni are, respectively, th_ energy and the number of atoms of species i (i = Au, Cu), in the system with free surfaces, and U~, is the internal energy of species i in the perfect bulk system. Surface energy values for the different configurations of (110), (113) and (115) faces explored in this work (Table 1) are given in Table 2. The lattice parameter used in the calculations is fixed at values leading to zero pressure in the perfect bulk system (model I: 0.3733 nm [6], model II: 0.3748 nm). For the sake of comparison with previous work [ 10], the energies of the (100) and (111) faces have also been calculated. Both potential models lead to comparable surface energies for the low-index faces, the agreement being better for pure copper than for mixed-surface truncations (100) and (110). Moreover, both models weakly stabilize the nonreconstructed surface (110). Strikingly, in model I the energy of the mixed surface (100) is lower than that of surface (111), while for model II the corresponding values are almost identical. Similar to low-index surfaces, (113) and (115) surface energy values from both models are only slightly different. Among the configurations explored, bulk terminations (Fig. la) and surfaces made of pure copper terraces (Fig. l b) are of higher energy than the mixed-composition surface termination (Fig. lc). This is an astonishing result in

reproduce satisfactorily various surface and bulk properties of the alloy [7-10] and of the pure metals copper [ 11-12] and gold [ 13]. When dealing with such n-body potentials, the forces acting on particles have an effective range twice as large as the cut-off radius used in computing the energy. In the present study, care has been taken in defining the dimensions of the geometrical models we used so that they are large enough to cope with this constraint. Periodic boundary conditions are applied to the computational box in two space directions chosen parallel to the appropriate crystallographic axes, so that a pseudo-infinite slab is created, the free surfaces of which have the desired orientation (Table 1). Where relevant, care has been paid that the geometrical model has identical terminal layers (of A or B type). The energy minimizations have been performed using a quasidynamic procedure [-14], with a time step fit= 10 -15 s. Convergence of the potential energy toward the minimum has been obtained within n = 1000 time steps. The surface energy at absolute zero temperature is identical to the potential energy difference between the system with free surfaces and a reference bulk system, normalized to the free surface area A: 1

Es = -~ (Us-Nc~UbCu --NA~UbAu ),

(2)

Table 1 Details of the various geometrical models used in the present study (hkl)

Type

Dimensions

Number of atoms

(111) (100)

M P M P M TLK P M TLK P M

311i0] 61100] 61100] 41110] 41110] 41332] 41332] 41332] 41552] 41552] 41552]

2160 (Au: 540, Cu: 1620) 1368 (Au: 324, Cu: 1044) 1368 (Au: 360, Cu: 1008) 1080 (Au: 252, Cu: 828) 1080 (Au: 288, Cu: 792) 1760 (Au: 440, Cu: 1320) 1680 (Au: 400, Cu: 1280) 1680 (Au: 440, Cu: 1240) 6048 (Au: 1512, Cu: 4536) 5824 (Au: 1400, Cu: 4424) 5824 (Au: 1512, Cu: 4312)

(110) (113)

(115)

x 31-112] x 101,111] x 61,010] x 10[001] x 61010] x 10[-001] x 61,1i0 ] x 61001] x 6[110] x 61001] x 10[110] × 21113] x 101,110] × 21113] x 101-110] × 21113] x 14[110] × 21115] × 14[110] x 21115] × 14[110] × 21115]

Symbols P and M indicate, respectively, pure copper or mixed composition (Cu: 1, Au: 1) terminal layers. For stepped surfaces ((113) to (115)) of type P or M to be constructed, one has to remove selectively pure copper or mixed terraces. Thereby, terrace width and step height are doubled with respect to the corresponding TLK-type configuration (see also Figs. lb and lc).

A. Aslanides et al./ Surface Science 370 (1997) L163-L167

Surface energies (in mJ m 2) for the different orientations studied (hkl)

Type

Es, model I [6]

Es, model II [7]

(111) (100)

M P M P/NR M/NR P/R M/R TLK P M TLK P M

882 (895) 1183 (1221) 783(790) 1186 (1239) 938 (963) 1078 (1122) 1053 (1088) 1055 (1097) 1171 (1214) 929 (959) 1049 (1088) 1179 (1245) 892 (916)

863 (882)a 1171 (1192)" 865 (896)a 1173 (1240~ 1024 (1051)a 1070 (1122) 1093 (1129) 1091 (1142) 1169 (1209) 987 (1034) 1088 (1135) 1199 (1235) 964 (1008)

(110)

(113)

(115)

Values before energy minimization are given between parentheses. Symbols P, M and TLK are as in Table 1, whereas R and NR stand respectively for the "missing-row" reconstructed and the non-reconstructed (110) surface. Bold characters highlight the lowest-energy configuration in presence of structural multiplicity. a From Ref. [10].

that the latter is made of double steps which are energetically unfavored in face-centered cubic (fcc) one-component systems. It implies that by crossing the critical temperature, the Llz-to-fcc structural change in the bulk should trigger a double-step to single-step surface transition. If confirmed by the experiment, this prediction anticipates a behavior of (lln) surfaces in Cu3Au qualitatively similar to that observed in the case of a Cu83Pd17(110) vicinal surface, except that the lowest energy is obtained in the latter system for a pure Cu terminal layer [3]. Similar to the experimental approach, our present calculations do not permit us to determine the details of the mechanism underlying the transition, which might be revealed by molecular dynamics and Monte Carlo simulations of (1 ln) surfaces. The present results, as well as those of previous work [10], may be questioned by arguing that in the calculations, energy minimization is performed by relaxing only atomic positions and not the composition. Segregation can indeed change surface energies and thereby alter the present conclusions. However, experiments as well as theoretical work have established that in Cu3Au, (100) and

(110) surfaces are always mixed, both below and above T~. More specifically, below T~ the surface composition is very close to that of a mixed bulk plane and does not change above it in the first two planes ofa (100) surface [4,15]. The above strongly supports the opinion that results reported in present and previous works on (100), (110) and (lln) surfaces are not affected by the fact that the surface composition is not explicitly considered in the energy-minimization procedure. This conclusion is certainly not valid for the (111) face, for which the bulk composition value used in present computations, 25% Au-75% Cu, does not minimize the surface energy. One indeed expects that all the equilibrium faces of a crystal would have the same composition. Therefore, we conclude that the unphysical trend displayed by the (111) surface in model I simply indicates that the surface energy has not reached a minimum value, and that composition has to be included among minimization variables. In conclusion, we have computed the surface energies for low-index and (1 ln) surfaces in Cu3Au using two phenomenological models of cohesion. The results show that mixed-composition terminal layers are always preferred, and that in the case of (lln) surfaces, this compositional constraint leads to surfaces made of double-height steps and double-width terraces with respect to the standard bulk surface termination. The prediction is also made that the order-disorder transition in the bulk should trigger a double-step to single-step surface transition on crossing the critical temperature, similar to that observed experimentally on a Cu83Pd17(110) vicinal surface. Work in progress aims at a better understanding of the details of the mechanisms underlying the double-step to single-step transition, of the interaction with the bulk order-disorder transition, and of the role of surface segregation [16].

Acknowledgements We are indebted to O. Hardouin Duparc for bringing in to our attention Ref. [14], in which the quasi-dynamic procedure used in this work is firstly described.

A. Aslanides et al./ Surface Science 370 (1997) L163-L167

References [1] B. Salanon, L. Barbier and P. Hecquet, in: Computer Simulation in Materials Science, Nano/Meso/ Macroscopic Space and Time Scales, Series E: Applied Sciences, Vol. 308, Eds. H.O. Kirchner, L. Kubin and V. Pontikis (Kluwer, Dordrecht, 1996) p. 149. [2] U. Bardi, Rep. Prog. Phys. 57 (1994) 939. [3] L. Barbier, B. Salanon and A. Loiseau, Phys. Rev. B 50 (1994) 4929. [4] T.M. Buck, G.H. Wheatley and L. Marchut, Phys. Rev. Lett. B 43 (1983) 43. [5] H. Niehus and C. Achete, Surf. Sci. 289 (1993) 19. [6] C. Rey Losada, M. Hayoun and V. Pontikis, Mater. Res. Soc. Syrup. Proc. 291 (1993) 549. [7] V. Vitek, G.J. Ackland and J. Cserti, Mater. Res. Soc. Syrup. Proc. 186 (1991) 237.

[8] G.J. Ackland and V. Vitek, Phys. Rev. B 41 ( t ~ u ) luaz,÷. [9] C. Dumez, M. Hayoun, C. Rey Losada and V. Pontikis, Interface Sci. 2 (1994) 45. [10] W.E. Wallace and G.J. Ackland, Surf. Sci. 275 (1992) L685. [11] B. Loisel, D. Gorse, V. Pontikis and J. Lapujoulade, Surf. Sci. 221 (1989) 365. [12] B. Loisel, J. Lapujoulade and V. Pontikis, Surf. Sci. 256 (1991) 242. [13] G.J. Ackland, G. Tichy, V, Vitek and M.W. Finnis, Philos. Mag. A 56 (1987) 735. [14] J.R. Beeler and G.L. Kulcinski, in: Interatomic Potentials and Simulation of Lattice Defects, Eds. P.C. Gehlen, J.R, Beeler and R.I. Jaffee (Plenum, New York, 1972) p. 735. [15] M. Hayoun, V. Pontikis and C. Winter, in preparation. [16] M. Hayoun and V. Pontikis, in preparation.