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Embedded atom method study of surface-confined Al on Ni(001)
Surface Science 442 (1999) 256–264 www.elsevier.nl/locate/susc
Embedded atom method study of surface-confined Al on Ni(001) A. Bilic´ *, B.V. King, D.J. O’Connor Department of Physics, University of Newcastle, Callaghan NSW 2308, Australia Received 25 January 1999; accepted for publication 22 July 1999
Abstract We have simulated the structure and energetics of thin films created by the deposition of Al onto Ni(001). The study has been carried out within the semi-empirical embedded atom ( EAM ) method, utilizing three sets of Ni–Al potentials. It is found that the dissolution of Al into the Ni bulk and the creation of a Ni Al multilayer alloy is 3 energetically favorable. However, a simulation of the kinetics shows that the surface penetration of Al takes place extremely slowly. Such kinetics turns out to be the decisive factor in the formation of the experimentally observed top layer c(2×2) phase in the submonolayer coverage regime. © 1999 Elsevier Science B.V. All rights reserved. Keywords: Alloys; Aluminum; Computer simulations; Nickel; Semi-empirical models and model calculations; Surface diffusion
1. Introduction The nickel–aluminum system is among the most investigated intermetallics due in part to the unusual mechanical properties of the Ni Al alloy. Ni Al 3 3 has a face-centered cubic L1 structure. The 2 Ni Al(001) surface has a termination correspond3 ing to bulk truncation, with the 50%–50% mixed composition. The second layer is pure Ni. Deeper layers continue this structure, with alternate layers being 50% Al 50% Ni and pure Ni, respectively. ˚ , although close The Ni Al lattice constant of 3.56 A 3 ˚ to that of pure Ni (3.516 A), agrees with the mismatch in the atomic size between Ni and Al, as found from the difference in the interatomic dis˚ tances within the pure elements (2.86 and 2.49 A for Al and Ni, respectively). The strain due to the mismatch is greater in the bulk than on the surface, * Corresponding author. Fax: +61-2-49-216907. E-mail address: [email protected] (A. Bilic´)
and therefore, surface-confined intermixing could be favored. The existence of a stable Ni Al alloy 3 with the lattice constant matching closely that of pure Ni on one hand and the atomic size mismatch of the two elements on the other hand indicate that intermixing for Al/Ni(001) should be possible. In an early experimental study of Al deposition onto Ni(001) [1], the formation of a Ni Al multilayer 3 surface alloy with c(2×2) top layer was reported. This is consistent with a bulk Ni Al(001) termina3 tion. More recently, a similar study [2] of Al deposition on Ni(001) was performed. In this work, carried out by low and medium energy ion scattering with a range of projectiles and energies, a somewhat different structure was determined. It confirmed that the top layer was an ordered c(2×2) phase and that the second layer was almost pure Ni. However, the results also showed that a steady 10%–15% fraction of Al was also present in the third layer. Such a three-layer alloy was stable against annealing up to 600°C.
0039-6028/99/$ - see front matter © 1999 Elsevier Science B.V. All rights reserved. PII: S0 0 39 - 6 0 28 ( 99 ) 0 09 2 5 -5
A. Bilic´ et al. / Surface Science 442 (1999) 256–264
This paper presents a simulation study of the structure and energetics of Al adsorption and mixing on the Ni(001) surface. As a part of this work, the above model, which proposes a very low Al concentration in the third layer, was tested. However, in order to have a 10% Al layer concentration, a supercell with at least 10 Ni atoms per layer is required. Such a geometry then becomes a formidable task for first-principles calculation, even for a supercomputer. Therefore, we have simulated the system utilizing the EAM [3]. It is computationally a very efficient method, designed for the description of metals and alloys, and has become a well-established tool in the atomistic simulations of these systems. Extensive work has been carried out on Ni–Al intermetallics with the EAM [4]. It has also proven successful in the simulation of surface alloys [5,6 ].
2. Method Utilizing the total energy given by the EAM, Monte Carlo (MC ) simulations [7] and molecular statics (MS) calculations of Al mixing into the surface and subsurface layers of Ni(001) are carried out in order to find the optimum structure. Molecular dynamics (MD) simulations can also be very instructive when an insight into the kinetics of the problem is required. In MD calculations, the classical motion of the atoms is computed by solving Newton’s equations of motion, while MC simulations proceed by generating a sampling of the appropriate statistical ensemble, and MS involve energy optimization via relaxations of atom positions. The EAM, as well as other similar semiempirical models, utilizes potentials that are fitted to limited sets of material properties and consequently are not completely transferable to problems where the geometry and atomic coordination are different from those used in the fitting procedure. Therefore, to minimize the risk of drawing wrong conclusions arising from the use of an inadequate set of Ni and Al potentials, the problem is treated with three sets of potentials that describe Ni, Al, and their intermetallics rather adequately. The first set by Foiles and Daw [8] (hereafter, FD)
257
is generated in the manner of the original EAM [3], which produced highly reliable potentials for a range of d-band metals and their alloys. The set of Voter and Chen ( VC ) ([9]; see also Ref. [4]) potentials are known to fit more accurately some of the material properties with lower coordination or dimensionality (e.g. bonding of diatomic molecules, vacancy formation energy, surface relaxations [10]) and are the most widely cited. Therefore, the results obtained with this set are believed to be the most relevant to the current work. The Rubini and Ballone (RB) set [11], while following the original generating prescription, attempted to improve the structural and dynamic features of the FD set by adding the frequency of the zone boundary vibrations to the properties that the FD set fits well. In order to simulate the Ni(001) surface, a slab geometry is employed. The calculations utilize a p(10×10) supercell with periodic boundary conditions in the two directions parallel to the surface. The cell consists of 10 atomic layers. Usually, the three bottom layers are kept fixed (unless stated otherwise) in order to mimic a semi-infinite substrate. As a first step, MC simulations are performed. This method has successfully reproduced the structure of Au thin films on Cu low-index surfaces [5], as well as the unreconstructed Pd/Cu(001) structure [6 ]. It involves attempting various configurations of the system and computing their total energies and statistical probabilities from a Boltzman distribution. The decision to retain or reject a new configuration is made depending on the relative probability of the new and old arrangement of the atoms. Two types of modifications are taken into account. First, the atoms are spatially displaced in random directions. Second, every atom is allowed to change its chemical identity during the course of simulations. In this way, a rapid convergence to the equilibrium structure is achieved since there is no need for a real interdiffusion of the atoms, i.e. kinetic considerations are circumvented. The simulations are carried out with a fixed difference between chemical potentials for the two elements and a fixed total number of atoms. The chemical potentials are varied so as to generate the alloy with the
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desired composition. Each simulation considered forty million modifications. The simulations are performed at temperatures of 300 and 600 K, with the the spatial displacements of the atoms up to ˚ . Initially, the periodic cell contains only Ni 0.2 A atoms, while the Al atoms are created by the simulation. In order to investigate the effects of the kinetics on the formation of the alloy, MD simulations are carried out employing the same Ni supercell with four separated non-interacting Al adatoms on the surface. The runs are performed in the canonical ensemble at a temperature of 1000 K. The time step for the integration of the equations of motion is 2×10−15 s. The reason for four adatoms, rather than a single one, as well as for the elevated temperature, is to enhance the rate of diffusion events that presumably has an Arrhenius form. A similar study has been carried out for the Pd/Cu(001) system [12].
3. Results Regardless of the potential set employed in the MC, if the chemical potentials are chosen to yield a 50%–50% top layer composition, the result is always a multilayer Ni Al alloy. This seems to 3 confirm the experimental findings of Lu et al. [1] of the formation of the epitaxial alloy. However, different results are obtained if an even number, e.g. eight, of the cell layers is allowed to relax. The FD potentials, although correctly giving a lower surface energy for the mixed top phase than for the pure Ni, apparently give a fault in this case, resulting in the epitaxial alloy with the pure Ni termination. For the RB set and an even number of mobile layers, the surface consists of c(2×2) and pure Ni patches in both the first and second layer. In this sense, VC potentials behave the most satisfactorily, yielding always the c(2×2) termination, regardless of whether an odd or even number of layers are unconstrained, in the later case with the creation of antisite defects in inner layers. While the MC procedure described above correctly reproduces the c(2×2) surface alloy for Au/Cu(001) and Pd/Cu(001), it clearly fails to
Table 1 Heat of solution of a single Al substitutional atom in a layer of Ni(001) slab, given in electron-volts Atomic layer
FD
RB
VC
1 2 3–8
−1.57 −1.83 −1.90
−1.67 −1.86 −1.79
−1.46 −1.42 −1.55
Table 2 Heat of solution of a single Al substitutional atom in a layer of the structure with a single-layer c(2×2) NiAl alloy on top of pure Ni(001) slab, given in electron-volts Atomic layer
FD
RB
VC
1 2 3–7
−1.52 −1.54 −1.56
−1.55 −1.56 −1.58
−1.00 −1.01 −1.02
produce such a structure for Al/Ni(001). If the chemical potentials are chosen to create a small Al fraction in the cell, the result is a random solid solution. The c(2×2) single-layer surface alloy, with a rippled profile, is created only when all the subsurface layers are kept frozen. The magnitude ˚ with Al relaxing of rippling is 0.02 and 0.1 A outward for the FD and VC sets, respectively. ˚ has been Such an Al outward rippling of 0.06 A seen for the Ni Al(001) surface. For the RB set, 3 ˚ is obtained from an inward Al relaxation of 0.08 A MS. The structure with the additional small fraction of Al in the third layer, as suggested in Ref. [2], could not be reproduced in this way. Hence, the MC simulations do not reproduce the structure found experimentally. This is a consequence of a simple zero-temperature energetics of a substitutional Al atom in Ni substrate, as shown in Table 1. The FD and VC sets favor the Al mixing in the bulk-like layers, while the RB set favors mixing into the second layer. The energy differences are the lowest for the VC set, which also yields a higher energy for the impurity in the second than in the first layer. Table 2 shows the energetics of the c(2×2) single-layer structure with a single substitutional Al impurity. The trend is similar to that of an Al impurity in the pure Ni, except that now, all the sets favor the impurity in
A. Bilic´ et al. / Surface Science 442 (1999) 256–264
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Fig. 1. Exchange event observed with the use of the FD set. The white sphere is an Al adatom, gray spheres are Ni atoms, and the dark sphere is used to highlight the Ni atom that pops onto the surface in the exchange.
the bulk, thus maximizing the number of heterogeneous bonds. Thermodynamics clearly support the formation of a solid solution or the multilayer Ni Al alloy, 3 depending on the chemical potentials, as predicted from the MC simulations. Since this is in dis-
agreement with experimental results, it is worthwhile to look closely at kinetics. The kinetics of intermixing is inspected by MD simulations employing the cell with four isolated Al adatoms and following the motion of atoms in the system for 1 ns. A striking difference is observed in the
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Fig. 2. Exchange event observed with the use of RB potential. See Fig. 1 for an explanation of the sphere shades.
exchange rate between this system and Pd/Cu(001) or Au/Cu(001). A time of only 1 ps is enough for the first Pd [12] or Au [13] adatom to enter the Cu(001) surface. However, it takes 30, 108, and 190 ps for the first exchange of an Al adatom with a Ni surface atom using the FD, RB, and VC potentials, respectively. Another exchange event is
observed only with the FD set, after a total run of 64 ps. Both the events observed with the FD set take place via an Al-assisted creation of a Frenkel pair consisting of a surface vacancy and Ni adatom, and subsequent filling the vacancy with Al, presented in Fig. 1 for the first exchange. The process is termed adatom-assisted exchange
A. Bilic´ et al. / Surface Science 442 (1999) 256–264
261
Fig. 3. Exchange event observed with the use of VC potential. See Fig. 1 for an explanation of the sphere shades.
via Frenkel pair formation (‘ad-Fp’ briefly). For the RB set, the event proceeds via a simple exchange (Fig. 2) and the process is termed ‘simple’. For the VC set, the exchange involves the creation of Al interstitial, with a significant buckling along the corresponding atomic row, which results in the ejection of a Ni atom ( Fig. 3). We
term the process as interstitial-mediated exchange (‘intst’). The energy difference between a Ni(001) surface with a single Al adatom and the energy of a Ni(001) surface with a Ni adatom and a Al substitutional atom in the surface layer E −E , ad sub calculated by MS, confirms that the incorporation of Al into the surface is energetically favored
A. Bilic´ et al. / Surface Science 442 (1999) 256–264
262
Table 3 Total energy difference E −E between on-surface and subad sub stitutional in-surface adsorption of a single Al adatom, surface vacancy formation energy Ef , and distant surface Frenkel pair v formation energy Ef on Ni(001), given in electron-voltsa Fp
E −E ad sub Ef v Ef Fp Eb ad−Fp Eb simple Eb intst
FD
RB
VC
Pd/Cu
0.24 0.51 1.21 1.57 1.04 1.27
0.38 0.63 1.36 1.67 0.90 1.12
0.06 0.78 1.82 2.02 1.15 1.45
0.23 0.60 1.29 1.44 0.69 0.82
a Eb , Eb , and Eb represent the activation barrier ad−Fp simple intst heights as obtained by the NEB. For comparison, the calculated values for Pd/Cu(001) system are given in the last column
( Table 3) for each of the three sets. However, for the incorporation to proceed so slowly, there must exist an energy barrier. In what follows, the values for the kinetic barriers for the observed exchange processes are calculated. The diffusion of adatoms into the surface is realized through the creation of surface defects. The height of activation barrier for an exchange process is sometimes roughly estimated as the energy of the formation of a distant surface Frenkel pair, Ef [14–16 ], since this is a simple Fp way of the formation of a vacancy, which can be subsequently filled with an adatom. The values as given in Table 3 show the trend which is qualitatively consistent with the exchange event rates observed in the MD procedure. However, these values cannot account for such a low rate of exchange since they are very close to Ef obtained Fp for Cu(001) surface. Therefore, the minimum energy paths and transition states for the observed exchange processes, ‘ad-Fp’, simple, and ‘intst’, are calculated using the nudged elastic band (NEB) method [17]. This method has already been used in a study of surface diffusion [18]. The quantities Eb , Eb , and Eb are given by the differad−Fp simple intst ence between the transition states energies and a perfect surface with Al adatom E . The lowest ad value of Eb is obtained with the FD set ad−Fp ( Table 3), for which the observed exchange events proceed via this process. Eb takes the lowest simple value with the RB set ( Table 3), for which the simple exchange is indeed observed in MD. The
lowest value of Eb is also obtained with the RB intst set ( Table 3), but, being higher than Eb , makes simple such an exchange less probable in a MD run. It is interesting to note that Eb is the lowest for all simple the sets employed, but is observed only for the RB set. In order to confirm this, an additional MD run is carried out with the VC set on a p(20×20) cell and 16 isolated Al adatoms for 1 ns. Altogether, four Al–Ni and one Ni–Ni exchange events are observed (not shown), for a run time of 247, 342, 428, 675, and 904 ps, respectively, all taking place via an interstitial. The fact that a simple exchange is not observed with the FD and VC sets could also be a consequence of other effects, such as different attempt frequencies, or entropy. These effects could also account for the fact that it takes a much longer time for an exchange with the RB set than with the FD, although Eb for the RB set is absolutely the simple lowest of all the barrier heights. It is again worth comparing the barrier values with those that we calculate for Pd/Cu(001) since analogous events are observed for this system [12]. Being lower for Pd/Cu(001), they could justify the higher observed exchange rate. In conclusion, the barrier heights for an adatom–substrate exchange are consistently higher for Al/Ni(001) than for Pd/Cu(001), thus providing a plausible explanation for the difference in the exchange rate observed in MD runs.
4. Discussion It has been shown that the Al/Ni(001) system exhibits a rather different behavior, regarding both thermodynamics and kinetics, than Pd/Cu(001), for example, although similar structures have been observed experimentally. In an attempt to understand the experimental observation of a surface confined NiAl alloy, a macroscopic approach to the growth morphology could be invoked. This addresses the intermixing in terms of surface and interface energies. When Al is deposited on Ni, the system can lower its energy by intermixing, on the condition that the interface energy c ≤0, which i is supposedly satisfied for these two elements as they make ordered bulk alloys, maximizing the interface area. The surface-confined mixing, rather
A. Bilic´ et al. / Surface Science 442 (1999) 256–264
than dissolving of Al into the Ni substrate, in this picture could take place due to the very low Al surface energy c , yielding c +c %c However, Al Al i Ni one can argue that this viewpoint is wrong. Namely, all three sets of the potentials give a good estimation for the Ni(001) surface energy. While VC also correctly reproduces the Al surface energy, the other two sets underestimate it by nearly a factor of 2. Therefore, one would expect that they would act so as to confine Al in the surface layer, but the MC simulations show that this is not the case. One can argue that it is not solely a strain energy that confines Al to a Ni surface. Although there is an atomic size mismatch between the two elements, thermodynamics still favor the formation of the multi-layer Ni Al alloy if the layers are 3 allowed to relax, as predicted by the MC simulations. However, thermodynamics does not favor the formation of the top layer c(2×2) phase in the 0.5≤h <1 ML regime for Al/Ni(001), Al unlike the case of Pd/Cu(001) or Au/Cu(001), clearly implying that it is not the equilibrium phase. Therefore, we believe that the formation of such a surface alloy, as observed experimentally, is a consequence of the sluggish kinetics. The MD simulations show that the penetration of Al adatoms to the surface layer proceeds extremely slowly. One can argue that a further penetration of Al into the subsurface layers would take a much longer time since the formation energies of bulk defects are higher. Such kinetics could provide the explanation for the formation of an alloy confined to the surface. Clearly, further information is required on the Al/Ni(001) system. It would be a fairly easy task to address the energetics of dilute solutions with ab-initio calculations in order to confirm that surface confinement of Al is not favored. However, a further series of experiments is necessary to verify our findings on the kinetics of the system.
5. Conclusions In summary, we have simulated mixing of Al into Ni(001) surface utilizing the total energy as given by the EAM. Three sets of the Ni–Al poten-
263
tials from the literature have been employed. From the MC and MS optimization, it is found that dissolution of Al into the bulk is energetically favored. However, the MD simulations show that that the kinetics of the Al surface penetration proceeds much slower than that of similar systems. Due to such kinetics, the intermixing could be limited to the surface, accounting for a non-equilibrium c(2×2) phase in top layer, as observed in experiments. However, the potential sets employed yield rather different results for the dilute heat of solution of Al in Ni(001), surface rippling of the ordered c(2×2) single-layer phase, and the kinetics of Al adatom exchange with substrate atoms. Moreover, the FD set in particular, but also RB, suffers from the deficiency of yielding an inconsistent surface termination of the multilayer Ni Al 3 alloy depending on the number of relaxed layers, and underestimating the formation energy of defects on a clean Ni(001) surface. We could therefore favor the use of the VC set for further calculations on the Ni–Al system.
Acknowledgements The work was supported by the Australian Research Grant Scheme. A.B. gratefully acknowledges the Australian Government and the University of Newcastle for the funding through the OPRS and UNRS scholarships. We are indebted to M.S. Daw and S.J. Plimpton for providing us with their EAM codes, and we wish to thank H. Jo´nsson for the help on using the NEB method.
References [1] S.H. Lu, D. Tian, Z.Q. Wang, Y.S. Li, F. Jona, Solid State Commun. 67 (1988) 325. [2] D.J. O’Connor, M. Draeger, A.M. Molenbroek, Y.G. Shen, Surf. Sci. 357–358 (1996) 202. [3] S.M. Foiles, M.I. Baskes, M.S. Daw, Phys. Rev. B 33 (1986) 7983. [4] A.F. Voter, J.H. Westbrook, R.L. Fleischer ( Eds.), Intermetallic Compounds: Principles and Practice Vol. 1, Wiley, Chichester, UK, 1995, p. 77, and references therein. [5] S.M. Foiles, Surf. Sci 191 (1987) 329.
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[6 ] A. Bilic´, Y.G. Shen, B.V. King, D.J. O’Connor, Surf. Rev. Lett. 5 (1998) 959. [7] S.M. Foiles, Phys. Rev. B 32 (1985) 7685. [8] S.M. Foiles, M.S. Daw, J. Mater. Res. 2 (1987) 5. [9] A.F. Voter, S.P. Chen, Mater. Res. Symp. Proc. 82 (1987) 175. [10] S.P. Chen, A.F. Voter, D.J. Srolovitz, Phys. Rev. Lett. 57 (1986) 1308. [11] S. Rubini, P. Ballone, Phys. Rev. B 48 (1992) 99. [12] J.E. Black, Z.-J. Tian, Comments Cond. Mater. Phys. 16 (1993) 281.
[13] A. Bilic´, unpublished. [14] J. Neugebauer, M. Scheffler, Phys. Rev. B 46 (1992) 16067. [15] S. Oppo, V. Fiorentini, M. Scheffler, Phys. Rev. Lett. 71 (1993) 2437. [16 ] V. Fiorentini, D. Fois, S. Oppo, Phys. Rev. Lett. 77 (1996) 695. [17] H. Jo´nsson, G. Mills, K.W. Jacobsen, in: B.J. Berne, G. Ciccotti, D.F. Coker ( Eds.), Classical and Quantum Dynamics in Condensed Phase Simulations, World Scientific, Singapore, 1998, p. 385. [18] M. Villarbe, H. Jo´nsson, Surf. Sci. 317 (1994) 15.
Embedded atom method study of surface-confined Al on Ni(001) A. Bilic´ *, B.V. King, D.J. O’Connor Department of Physics, University of Newcastle, Callaghan NSW 2308, Australia Received 25 January 1999; accepted for publication 22 July 1999
Abstract We have simulated the structure and energetics of thin films created by the deposition of Al onto Ni(001). The study has been carried out within the semi-empirical embedded atom ( EAM ) method, utilizing three sets of Ni–Al potentials. It is found that the dissolution of Al into the Ni bulk and the creation of a Ni Al multilayer alloy is 3 energetically favorable. However, a simulation of the kinetics shows that the surface penetration of Al takes place extremely slowly. Such kinetics turns out to be the decisive factor in the formation of the experimentally observed top layer c(2×2) phase in the submonolayer coverage regime. © 1999 Elsevier Science B.V. All rights reserved. Keywords: Alloys; Aluminum; Computer simulations; Nickel; Semi-empirical models and model calculations; Surface diffusion
1. Introduction The nickel–aluminum system is among the most investigated intermetallics due in part to the unusual mechanical properties of the Ni Al alloy. Ni Al 3 3 has a face-centered cubic L1 structure. The 2 Ni Al(001) surface has a termination correspond3 ing to bulk truncation, with the 50%–50% mixed composition. The second layer is pure Ni. Deeper layers continue this structure, with alternate layers being 50% Al 50% Ni and pure Ni, respectively. ˚ , although close The Ni Al lattice constant of 3.56 A 3 ˚ to that of pure Ni (3.516 A), agrees with the mismatch in the atomic size between Ni and Al, as found from the difference in the interatomic dis˚ tances within the pure elements (2.86 and 2.49 A for Al and Ni, respectively). The strain due to the mismatch is greater in the bulk than on the surface, * Corresponding author. Fax: +61-2-49-216907. E-mail address: [email protected] (A. Bilic´)
and therefore, surface-confined intermixing could be favored. The existence of a stable Ni Al alloy 3 with the lattice constant matching closely that of pure Ni on one hand and the atomic size mismatch of the two elements on the other hand indicate that intermixing for Al/Ni(001) should be possible. In an early experimental study of Al deposition onto Ni(001) [1], the formation of a Ni Al multilayer 3 surface alloy with c(2×2) top layer was reported. This is consistent with a bulk Ni Al(001) termina3 tion. More recently, a similar study [2] of Al deposition on Ni(001) was performed. In this work, carried out by low and medium energy ion scattering with a range of projectiles and energies, a somewhat different structure was determined. It confirmed that the top layer was an ordered c(2×2) phase and that the second layer was almost pure Ni. However, the results also showed that a steady 10%–15% fraction of Al was also present in the third layer. Such a three-layer alloy was stable against annealing up to 600°C.
0039-6028/99/$ - see front matter © 1999 Elsevier Science B.V. All rights reserved. PII: S0 0 39 - 6 0 28 ( 99 ) 0 09 2 5 -5
A. Bilic´ et al. / Surface Science 442 (1999) 256–264
This paper presents a simulation study of the structure and energetics of Al adsorption and mixing on the Ni(001) surface. As a part of this work, the above model, which proposes a very low Al concentration in the third layer, was tested. However, in order to have a 10% Al layer concentration, a supercell with at least 10 Ni atoms per layer is required. Such a geometry then becomes a formidable task for first-principles calculation, even for a supercomputer. Therefore, we have simulated the system utilizing the EAM [3]. It is computationally a very efficient method, designed for the description of metals and alloys, and has become a well-established tool in the atomistic simulations of these systems. Extensive work has been carried out on Ni–Al intermetallics with the EAM [4]. It has also proven successful in the simulation of surface alloys [5,6 ].
2. Method Utilizing the total energy given by the EAM, Monte Carlo (MC ) simulations [7] and molecular statics (MS) calculations of Al mixing into the surface and subsurface layers of Ni(001) are carried out in order to find the optimum structure. Molecular dynamics (MD) simulations can also be very instructive when an insight into the kinetics of the problem is required. In MD calculations, the classical motion of the atoms is computed by solving Newton’s equations of motion, while MC simulations proceed by generating a sampling of the appropriate statistical ensemble, and MS involve energy optimization via relaxations of atom positions. The EAM, as well as other similar semiempirical models, utilizes potentials that are fitted to limited sets of material properties and consequently are not completely transferable to problems where the geometry and atomic coordination are different from those used in the fitting procedure. Therefore, to minimize the risk of drawing wrong conclusions arising from the use of an inadequate set of Ni and Al potentials, the problem is treated with three sets of potentials that describe Ni, Al, and their intermetallics rather adequately. The first set by Foiles and Daw [8] (hereafter, FD)
257
is generated in the manner of the original EAM [3], which produced highly reliable potentials for a range of d-band metals and their alloys. The set of Voter and Chen ( VC ) ([9]; see also Ref. [4]) potentials are known to fit more accurately some of the material properties with lower coordination or dimensionality (e.g. bonding of diatomic molecules, vacancy formation energy, surface relaxations [10]) and are the most widely cited. Therefore, the results obtained with this set are believed to be the most relevant to the current work. The Rubini and Ballone (RB) set [11], while following the original generating prescription, attempted to improve the structural and dynamic features of the FD set by adding the frequency of the zone boundary vibrations to the properties that the FD set fits well. In order to simulate the Ni(001) surface, a slab geometry is employed. The calculations utilize a p(10×10) supercell with periodic boundary conditions in the two directions parallel to the surface. The cell consists of 10 atomic layers. Usually, the three bottom layers are kept fixed (unless stated otherwise) in order to mimic a semi-infinite substrate. As a first step, MC simulations are performed. This method has successfully reproduced the structure of Au thin films on Cu low-index surfaces [5], as well as the unreconstructed Pd/Cu(001) structure [6 ]. It involves attempting various configurations of the system and computing their total energies and statistical probabilities from a Boltzman distribution. The decision to retain or reject a new configuration is made depending on the relative probability of the new and old arrangement of the atoms. Two types of modifications are taken into account. First, the atoms are spatially displaced in random directions. Second, every atom is allowed to change its chemical identity during the course of simulations. In this way, a rapid convergence to the equilibrium structure is achieved since there is no need for a real interdiffusion of the atoms, i.e. kinetic considerations are circumvented. The simulations are carried out with a fixed difference between chemical potentials for the two elements and a fixed total number of atoms. The chemical potentials are varied so as to generate the alloy with the
258
A. Bilic´ et al. / Surface Science 442 (1999) 256–264
desired composition. Each simulation considered forty million modifications. The simulations are performed at temperatures of 300 and 600 K, with the the spatial displacements of the atoms up to ˚ . Initially, the periodic cell contains only Ni 0.2 A atoms, while the Al atoms are created by the simulation. In order to investigate the effects of the kinetics on the formation of the alloy, MD simulations are carried out employing the same Ni supercell with four separated non-interacting Al adatoms on the surface. The runs are performed in the canonical ensemble at a temperature of 1000 K. The time step for the integration of the equations of motion is 2×10−15 s. The reason for four adatoms, rather than a single one, as well as for the elevated temperature, is to enhance the rate of diffusion events that presumably has an Arrhenius form. A similar study has been carried out for the Pd/Cu(001) system [12].
3. Results Regardless of the potential set employed in the MC, if the chemical potentials are chosen to yield a 50%–50% top layer composition, the result is always a multilayer Ni Al alloy. This seems to 3 confirm the experimental findings of Lu et al. [1] of the formation of the epitaxial alloy. However, different results are obtained if an even number, e.g. eight, of the cell layers is allowed to relax. The FD potentials, although correctly giving a lower surface energy for the mixed top phase than for the pure Ni, apparently give a fault in this case, resulting in the epitaxial alloy with the pure Ni termination. For the RB set and an even number of mobile layers, the surface consists of c(2×2) and pure Ni patches in both the first and second layer. In this sense, VC potentials behave the most satisfactorily, yielding always the c(2×2) termination, regardless of whether an odd or even number of layers are unconstrained, in the later case with the creation of antisite defects in inner layers. While the MC procedure described above correctly reproduces the c(2×2) surface alloy for Au/Cu(001) and Pd/Cu(001), it clearly fails to
Table 1 Heat of solution of a single Al substitutional atom in a layer of Ni(001) slab, given in electron-volts Atomic layer
FD
RB
VC
1 2 3–8
−1.57 −1.83 −1.90
−1.67 −1.86 −1.79
−1.46 −1.42 −1.55
Table 2 Heat of solution of a single Al substitutional atom in a layer of the structure with a single-layer c(2×2) NiAl alloy on top of pure Ni(001) slab, given in electron-volts Atomic layer
FD
RB
VC
1 2 3–7
−1.52 −1.54 −1.56
−1.55 −1.56 −1.58
−1.00 −1.01 −1.02
produce such a structure for Al/Ni(001). If the chemical potentials are chosen to create a small Al fraction in the cell, the result is a random solid solution. The c(2×2) single-layer surface alloy, with a rippled profile, is created only when all the subsurface layers are kept frozen. The magnitude ˚ with Al relaxing of rippling is 0.02 and 0.1 A outward for the FD and VC sets, respectively. ˚ has been Such an Al outward rippling of 0.06 A seen for the Ni Al(001) surface. For the RB set, 3 ˚ is obtained from an inward Al relaxation of 0.08 A MS. The structure with the additional small fraction of Al in the third layer, as suggested in Ref. [2], could not be reproduced in this way. Hence, the MC simulations do not reproduce the structure found experimentally. This is a consequence of a simple zero-temperature energetics of a substitutional Al atom in Ni substrate, as shown in Table 1. The FD and VC sets favor the Al mixing in the bulk-like layers, while the RB set favors mixing into the second layer. The energy differences are the lowest for the VC set, which also yields a higher energy for the impurity in the second than in the first layer. Table 2 shows the energetics of the c(2×2) single-layer structure with a single substitutional Al impurity. The trend is similar to that of an Al impurity in the pure Ni, except that now, all the sets favor the impurity in
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Fig. 1. Exchange event observed with the use of the FD set. The white sphere is an Al adatom, gray spheres are Ni atoms, and the dark sphere is used to highlight the Ni atom that pops onto the surface in the exchange.
the bulk, thus maximizing the number of heterogeneous bonds. Thermodynamics clearly support the formation of a solid solution or the multilayer Ni Al alloy, 3 depending on the chemical potentials, as predicted from the MC simulations. Since this is in dis-
agreement with experimental results, it is worthwhile to look closely at kinetics. The kinetics of intermixing is inspected by MD simulations employing the cell with four isolated Al adatoms and following the motion of atoms in the system for 1 ns. A striking difference is observed in the
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Fig. 2. Exchange event observed with the use of RB potential. See Fig. 1 for an explanation of the sphere shades.
exchange rate between this system and Pd/Cu(001) or Au/Cu(001). A time of only 1 ps is enough for the first Pd [12] or Au [13] adatom to enter the Cu(001) surface. However, it takes 30, 108, and 190 ps for the first exchange of an Al adatom with a Ni surface atom using the FD, RB, and VC potentials, respectively. Another exchange event is
observed only with the FD set, after a total run of 64 ps. Both the events observed with the FD set take place via an Al-assisted creation of a Frenkel pair consisting of a surface vacancy and Ni adatom, and subsequent filling the vacancy with Al, presented in Fig. 1 for the first exchange. The process is termed adatom-assisted exchange
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Fig. 3. Exchange event observed with the use of VC potential. See Fig. 1 for an explanation of the sphere shades.
via Frenkel pair formation (‘ad-Fp’ briefly). For the RB set, the event proceeds via a simple exchange (Fig. 2) and the process is termed ‘simple’. For the VC set, the exchange involves the creation of Al interstitial, with a significant buckling along the corresponding atomic row, which results in the ejection of a Ni atom ( Fig. 3). We
term the process as interstitial-mediated exchange (‘intst’). The energy difference between a Ni(001) surface with a single Al adatom and the energy of a Ni(001) surface with a Ni adatom and a Al substitutional atom in the surface layer E −E , ad sub calculated by MS, confirms that the incorporation of Al into the surface is energetically favored
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Table 3 Total energy difference E −E between on-surface and subad sub stitutional in-surface adsorption of a single Al adatom, surface vacancy formation energy Ef , and distant surface Frenkel pair v formation energy Ef on Ni(001), given in electron-voltsa Fp
E −E ad sub Ef v Ef Fp Eb ad−Fp Eb simple Eb intst
FD
RB
VC
Pd/Cu
0.24 0.51 1.21 1.57 1.04 1.27
0.38 0.63 1.36 1.67 0.90 1.12
0.06 0.78 1.82 2.02 1.15 1.45
0.23 0.60 1.29 1.44 0.69 0.82
a Eb , Eb , and Eb represent the activation barrier ad−Fp simple intst heights as obtained by the NEB. For comparison, the calculated values for Pd/Cu(001) system are given in the last column
( Table 3) for each of the three sets. However, for the incorporation to proceed so slowly, there must exist an energy barrier. In what follows, the values for the kinetic barriers for the observed exchange processes are calculated. The diffusion of adatoms into the surface is realized through the creation of surface defects. The height of activation barrier for an exchange process is sometimes roughly estimated as the energy of the formation of a distant surface Frenkel pair, Ef [14–16 ], since this is a simple Fp way of the formation of a vacancy, which can be subsequently filled with an adatom. The values as given in Table 3 show the trend which is qualitatively consistent with the exchange event rates observed in the MD procedure. However, these values cannot account for such a low rate of exchange since they are very close to Ef obtained Fp for Cu(001) surface. Therefore, the minimum energy paths and transition states for the observed exchange processes, ‘ad-Fp’, simple, and ‘intst’, are calculated using the nudged elastic band (NEB) method [17]. This method has already been used in a study of surface diffusion [18]. The quantities Eb , Eb , and Eb are given by the differad−Fp simple intst ence between the transition states energies and a perfect surface with Al adatom E . The lowest ad value of Eb is obtained with the FD set ad−Fp ( Table 3), for which the observed exchange events proceed via this process. Eb takes the lowest simple value with the RB set ( Table 3), for which the simple exchange is indeed observed in MD. The
lowest value of Eb is also obtained with the RB intst set ( Table 3), but, being higher than Eb , makes simple such an exchange less probable in a MD run. It is interesting to note that Eb is the lowest for all simple the sets employed, but is observed only for the RB set. In order to confirm this, an additional MD run is carried out with the VC set on a p(20×20) cell and 16 isolated Al adatoms for 1 ns. Altogether, four Al–Ni and one Ni–Ni exchange events are observed (not shown), for a run time of 247, 342, 428, 675, and 904 ps, respectively, all taking place via an interstitial. The fact that a simple exchange is not observed with the FD and VC sets could also be a consequence of other effects, such as different attempt frequencies, or entropy. These effects could also account for the fact that it takes a much longer time for an exchange with the RB set than with the FD, although Eb for the RB set is absolutely the simple lowest of all the barrier heights. It is again worth comparing the barrier values with those that we calculate for Pd/Cu(001) since analogous events are observed for this system [12]. Being lower for Pd/Cu(001), they could justify the higher observed exchange rate. In conclusion, the barrier heights for an adatom–substrate exchange are consistently higher for Al/Ni(001) than for Pd/Cu(001), thus providing a plausible explanation for the difference in the exchange rate observed in MD runs.
4. Discussion It has been shown that the Al/Ni(001) system exhibits a rather different behavior, regarding both thermodynamics and kinetics, than Pd/Cu(001), for example, although similar structures have been observed experimentally. In an attempt to understand the experimental observation of a surface confined NiAl alloy, a macroscopic approach to the growth morphology could be invoked. This addresses the intermixing in terms of surface and interface energies. When Al is deposited on Ni, the system can lower its energy by intermixing, on the condition that the interface energy c ≤0, which i is supposedly satisfied for these two elements as they make ordered bulk alloys, maximizing the interface area. The surface-confined mixing, rather
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than dissolving of Al into the Ni substrate, in this picture could take place due to the very low Al surface energy c , yielding c +c %c However, Al Al i Ni one can argue that this viewpoint is wrong. Namely, all three sets of the potentials give a good estimation for the Ni(001) surface energy. While VC also correctly reproduces the Al surface energy, the other two sets underestimate it by nearly a factor of 2. Therefore, one would expect that they would act so as to confine Al in the surface layer, but the MC simulations show that this is not the case. One can argue that it is not solely a strain energy that confines Al to a Ni surface. Although there is an atomic size mismatch between the two elements, thermodynamics still favor the formation of the multi-layer Ni Al alloy if the layers are 3 allowed to relax, as predicted by the MC simulations. However, thermodynamics does not favor the formation of the top layer c(2×2) phase in the 0.5≤h <1 ML regime for Al/Ni(001), Al unlike the case of Pd/Cu(001) or Au/Cu(001), clearly implying that it is not the equilibrium phase. Therefore, we believe that the formation of such a surface alloy, as observed experimentally, is a consequence of the sluggish kinetics. The MD simulations show that the penetration of Al adatoms to the surface layer proceeds extremely slowly. One can argue that a further penetration of Al into the subsurface layers would take a much longer time since the formation energies of bulk defects are higher. Such kinetics could provide the explanation for the formation of an alloy confined to the surface. Clearly, further information is required on the Al/Ni(001) system. It would be a fairly easy task to address the energetics of dilute solutions with ab-initio calculations in order to confirm that surface confinement of Al is not favored. However, a further series of experiments is necessary to verify our findings on the kinetics of the system.
5. Conclusions In summary, we have simulated mixing of Al into Ni(001) surface utilizing the total energy as given by the EAM. Three sets of the Ni–Al poten-
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tials from the literature have been employed. From the MC and MS optimization, it is found that dissolution of Al into the bulk is energetically favored. However, the MD simulations show that that the kinetics of the Al surface penetration proceeds much slower than that of similar systems. Due to such kinetics, the intermixing could be limited to the surface, accounting for a non-equilibrium c(2×2) phase in top layer, as observed in experiments. However, the potential sets employed yield rather different results for the dilute heat of solution of Al in Ni(001), surface rippling of the ordered c(2×2) single-layer phase, and the kinetics of Al adatom exchange with substrate atoms. Moreover, the FD set in particular, but also RB, suffers from the deficiency of yielding an inconsistent surface termination of the multilayer Ni Al 3 alloy depending on the number of relaxed layers, and underestimating the formation energy of defects on a clean Ni(001) surface. We could therefore favor the use of the VC set for further calculations on the Ni–Al system.
Acknowledgements The work was supported by the Australian Research Grant Scheme. A.B. gratefully acknowledges the Australian Government and the University of Newcastle for the funding through the OPRS and UNRS scholarships. We are indebted to M.S. Daw and S.J. Plimpton for providing us with their EAM codes, and we wish to thank H. Jo´nsson for the help on using the NEB method.
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