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2007, 111, 2823-2826 Published on Web 01/26/2007
Transient Atomic Configurations of Supported Gold Nanocrystallites at Finite Temperature Keith P. McKenna,* Peter V. Sushko, and Alexander L. Shluger Department of Physics and Astronomy, UniVersity College London, Gower Street, London, WC1 6BT, U.K., and London Centre for Nanotechnology, 17-19 Gordon Street, London, WC1E 0AH, U.K. ReceiVed: NoVember 23, 2006; In Final Form: January 15, 2007
A Monte Carlo method has been developed to investigate the dynamic configurations of nanometer-sized Au nanocrystallites (NCs) supported on the MgO(100) surface. We have found significant concentrations of Au atoms that transiently occupy adatom positions on Au(111) facets. Their concentration increases from 10-4 per NC at 250 K to 10-2 per NC at 550 K. A complex roughening transition involving the creation of steps on Au(111) facets is observed close to 500 K. The appreciable numbers of various local atom configurations that may transiently appear on NC at finite temperature may be important for many applications using NCs.
1. Introduction Nanocrystallites (NC) are a particularly interesting class of ordered solid in that they have a significant proportion of their atoms on their surface. The local electronic structure of atoms on surfaces is often quite different from that in the bulk and can dominate the properties of NCs. This is a rather general fact reflected in the optical, electronic, and magnetic properties of a wide range of materials. Often surface atoms of particularly low coordination, which may be few in number, have special importance. For example they may interact with light at certain wavelengths,1 trap electrons or holes more easily, or bind molecules more strongly.2 The properties and concentrations of such special sites are key to understanding a variety of nanoscale phenomena. At finite temperature, atoms at the surface of NCs can diffuse. In many cases, configurational changes can take place over timescales that are relevant for applications3 on the order of seconds or longer. For many materials, even at room temperature, atoms may transiently occupy different positions on the surface and consequently affect the overall properties of NCs. The dynamic behavior of the surface of NCs has been well studied in relation to growth4 and melting,5 but little attention has been paid to NCs close to equilibrium and in the solid state. As we demonstrate below, such transient behavior may be important for numerous systems studied in nanotechnology and surface science. To investigate these issues, it is necessary for one to compare the relative energies and likelihoods of the various possible NC configurations. In this Letter, we highlight these general issues by considering a specific system that has broad interest: nanometer-sized Au NCs supported on the MgO(100) surface. This system has been studied as a model catalyst and has application for roomtemperature oxidation of CO to CO2.6 The catalytic activity of Au NCs has been interpreted in terms of Au atoms of particularly low coordination7 such as corners, edges, and atoms * Author to whom correspondance should be addressed. E-mail:
[email protected]; tel: +44 (0)20 7679 9932; fax: +44 (0)20 7679 1360.
10.1021/jp067801u CCC: $37.00
at the MgO interface8 (the bulk Au surfaces are inert). However, adatoms on Au(111) facets are usually neglected, but our calculations show that appreciable concentrations of these sites can exist even at room temperature. On Au NCs, even the largest barriers to surface diffusion imply diffusion rates on the order of 105 Hz at room temperature.9 There is also direct evidence from transmission electron microscopy (TEM)10,11 and scanning tunneling microscopy12 studies that metallic NCs deposited on various surfaces readily adopt equilibrium morphologies. In fact, barriers to surface diffusion on a wide range of materials, including most metals and metal-oxides, typically vary between 0.1 and 0.6 eV. These barriers lead to diffusion times on the order of 0.1 ns to 1.0 ms at room temperature. In most cases, these timescales are much longer than typical vibrational times and cannot be simulated effectively using molecular dynamics methods. Therefore, to obtain statistical information on the transient NC configurations that occur at finite temperatures we have developed a Monte Carlo (MC) methodology. An important part of this method is a “trial move” that enables NC configurations to be explored efficiently by rearrangements of surface atoms. It can be used to calculate the equilibrium concentrations of particular structural features on NCs at finite temperature. The concentrations that are obtained are converged to less than 0.1%. 2. Model and Method The most probable NC configuration corresponds to the global minimum of the free energy, which at finite temperature includes a contribution due to configurational entropy. Therefore, NC configurations with relatively high energy have a finite probability of occurring, which depends upon the temperature. To statistically characterize the equilibrium structural properties, we use a MC method to generate NC configurations representative of a thermodynamic NPT ensemble. However, in the calculations presented here the effect of an atmosphere is neglected (P ) 0). The sequence of configurations is generated using several types of trial move. The proposed configurations are accepted © 2007 American Chemical Society
2824 J. Phys. Chem. C, Vol. 111, No. 7, 2007
Letters are assumed to reside in a fcc lattice with the (100) plane aligned with the O sub-lattice of the MgO(100) surface (see the inset of Figure 1). Bulk Au has a small lattice mismatch with the MgO(100) surface (3%), which promotes the bulk fcc lattice structure for supported Au NCs. Static energy minimization calculations and TEM studies indicate that this model is reasonable for this system and is valid below the melting temperature (expected to be around 700 K for small clusters compared with 1090 K for bulk Au20). Using this model, the statistics for low-probability NC configurations are improved at the expense of neglecting the vibrational degrees of freedom. Although the inclusion of vibrations may have an effect, it should not alter the general conclusions. The on-lattice model also has the advantage of enabling surface atoms and unoccupied near-surface sites to be identified more easily. The energies of different configurations of Au NC on the MgO surface are represented by a phenomenological coordination dependent potential that takes the following form
Figure 1. Equilibrium morphology of a 1.6 nm Au nanocrystallite supported on the MgO(100) surface. The inset shows a view from directly above the surface. An example trial move is also indicated: a surface atom (a) selected at random is moved to an unoccupied nearsurface site (b). Atom shading corresponds to the local Au-Au coordination number (labeled in the figure).
or rejected with a probability designed to achieve detailed balance.13 For crystalline systems, the often-used trial move consisting of the local displacement of an atom chosen at random is only effective for exploring vibrations. Therefore we introduce a “surface atom” trial move, which consists of choosing a surface atom at random and attempting to move it to a randomly selected unoccupied site near the surface. In this scheme, a surface atom is defined as any atom that is not fully coordinated. Unoccupied sites near the surface can in general be identified based upon knowledge of the underlying lattice structure. Figure 1 depicts an example of this type of move for a supported Au NC (see the figure caption). This trial move is not intended to mimic any real diffusion process but provides a means to explore the configuration space of the NC by rearranging surface atoms. It bears some relation to atom exchange moves that have been used to simulate the equilibrium configurations of alloys.14-16 The transition matrix for the surface atom trial move is, in general, asymmetric because the number of surface atoms and near-surface sites may change after moving an atom. Therefore, to ensure detailed balance the following acceptance probability is used
(( )
pacc ) min 1, a Ni(f)
Nai Nbi
Naf
Nbf
2
exp
( )) -∆E kBT
(1)
where is the number of available surface atoms before (i) b and after (f) the trial move and Ni(f) is the number of available unoccupied near-surface sites. ∆E is the difference in energy between the old and new configurations, and T is the temperature. At low temperature, MC methods may explore only a restricted subset of the configuration space and ergodicity can be lost. To overcome this problem, we employ a multiple-stage jump-walking (J-walking) technique, which couples MC simulations at different temperatures.17-19 Typical acceptance rates for J-walking trial moves are ∼50%, ensuring that ergodicity is maintained. A particular implementation of the general Monte Carlo scheme described above is used to investigate supported Au NCs. We use an on-lattice approximation in which Au atoms
E)
1
ΦZi + xF Zi + ZOi ad ∑ 2 i)1,N
(2)
where Zi is the Au-Au nearest neighbor coordination number and ZiO is the Au-O coordination number.21 The first two terms account for the binding between Au atoms and are based upon an embedded atom model potential.22 The parameters Φ and F represent short-range repulsion and embedding energy contributions, respectively, and have been fitted to the SuttonChen (SC) parametrization for Au.23 The third term represents the adhesion of Au atoms to O on the MgO surface. The parameter ad that is used is based upon recent ab initio calculations performed for supported Au NCs.24 However, to obtain the correct wetting behavior the ab initio adhesion energy is rescaled by 40% because SC surface energies are underestimated when compared to ab initio calculations. It is important to note that the use of a simple model potential is essential because on the order of 108 energy evaluations must be made in order to accumulate reliable statistics. As a validation of this model, we have calculated and compared a number of important energies. The ratio of the Au(111) and Au(100) surface energy (γ100/γ111 ) 1.3) is in good agreement with experiments. The adsorption of an adatom on the Au(100) facet is favored by 0.4 eV compared to the Au(111) facet, which is also in reasonable agreement with the results obtained using a more accurate model potential.9 We conclude that despite the simplicity of this potential it can describe the relative energies of supported NCs of nanometer dimensions. 3. Results MC simulations of supported Au NCs containing between 181 and 191 atoms (ranging in size between 1.4 and 1.8 nm) have been made. We considered this size range because of its relevance for catalysis and molecular electronics and because such distributions are observed experimentally.25 Although properties at room temperature are of particular interest for applications, we have simulated temperatures between 250 and 800 K. Equilibration consists of 5 × 104 MC steps followed by 5 × 105 MC steps of production (each MC step consists of Nat attempted trial moves, where Nat is the number of atoms). In the following, angled brackets, 〈 〉, are used to indicate that the enclosed quantity is the thermodynamic equilibrium average at a given temperature that is also averaged over the size range considered (181-191 atoms). These averages are well-converged meaningful quantities representative of 1.6 nm
Letters
Figure 2. Temperature dependence of the average number of Au(111) adatoms (3C) and Au(100) adatoms (4C) per NC. N3C ) 0 for the zerotemperature equilibrium NC configuration.
Au NCs. We begin the discussion of the results with 6- and 7-coordinated atoms (6C and 7C), which correspond to corner and edge atoms, respectively. The average number of 6C atoms is almost independent of temperature for the size range considered. There are approximately 15-16 per NC as one would expect from consideration of the ground-state morphology (Figure 1). The average number of 7C atoms decreases from 27 to 21 between 250 and 800 K; however, this is a relatively small percentage change. Three-coordinated (3C) atoms, which correspond to adatoms on Au(111) facets, are not present on NCs at zero temperature. However, they do appear at finite temperature. The average number of 3C atoms per NC, 〈N3C〉, is shown in Figure 2. At room temperature 〈N3C〉 ) 2.7 × 10-4, which implies a significant concentration of such atoms (∼107 cm-2 for a typical NC concentration of ∼1011 cm-2). The average number of fourcoordinated (4C) atoms per NC, 〈N4C〉, which corresponds to adatoms on Au(100) facets, is also shown in the figure and is fairly independent of temperature below ∼500 K.
J. Phys. Chem. C, Vol. 111, No. 7, 2007 2825 The equilibrium potential energy as a function of temperature is shown in Figure 3a for three representative NC sizes. The abrupt change in slope close to 500 K is indicative of a second-order phase transition in which the configurational contribution to the specific heat (which is of course small compared to electron and phonon contributions) changes. This transition occurs at approximately the same temperature for all NC sizes we have simulated. Also shown in Figure 3 are the average numbers of 9-coordinated (9C) atoms corresponding to ideal Au(111) facets, 〈N9C〉, and 7C Au atoms that are also coordinated by an O atom, 〈NO7C〉. Au atoms coordinated by 7 Au atoms and an O atom correspond to atoms along the edge of the Au(100) plane that contacts the MgO surface. These also have abrupt changes in their temperature dependence just below 500 K, indicating a connection with the phase transition. Figure 4 helps to further clarify the nature of the phase transition. It shows the probability of finding a given number of 8C Au atoms in the interface layer adjacent to the MgO surface, p(NO8C), for three different temperatures. Such atoms are fully coordinated, surrounded by 8 Au atoms and 1 O atom. At temperatures below 500 K, the probability distribution only has peaks at numbers of the form nm, corresponding to ideal rectangular Au(100) interfaces, with n ) m ) 3 being favored at low temperature. At temperatures above 500 K, there is an increasing probability for nonideal interface layers corresponding to kinks on the perimeter. This trend is also indicated by the decreasing numbers of interface layer edge atoms with increasing temperature (Figure 3c). On the basis of these calculations, we conclude that the phase transition can be identified as an effective roughening transition, corresponding to the creation of steps on Au(111) facets and disordering of the Au interface layer. This is an interesting example of a complex solid-tosolid transition that can occur for NCs adsorbed on surfaces. Similar effects can be expected to be important for other systems.
Figure 3. (a) Equilibrium potential energy as a function of temperature for NCs containing between 184 and 186 Au atoms. (b) The average number of 9C Au atoms (ideal Au(111) facets). (c) The average number of 7C Au atoms that are adjacent to the MgO surface.
2826 J. Phys. Chem. C, Vol. 111, No. 7, 2007
Figure 4. Probability distributions for the number of 8C Au atoms adjacent to the MgO surface. The insets show possible configurations of the Au plane that is in contact with the MgO surface.
4. Discussion and Conclusions We have considered the atomic structure of Au NCs supported on the MgO(100) surface. A MC method has been developed and applied to obtain the configurations that minimize the free energy at finite temperature. Equilibrium concentrations of particular local atom arrangements on the surface of NCs, such as adatoms, have been calculated as a function of temperature. These structural features that appear transiently on NCs at finite temperature may influence numerous properties yet are often neglected. We apply the MC method to calculate thermodynamic equilibrium properties for NCs that contain a fixed number of atoms. For Au NCs, equilibrium properties are appropriate because typical diffusion rates are fast compared to the relevant experimental timescales. It is also reasonable to consider Au NCs as isolated on the MgO surface because of the large difference in Au-Au and Au-MgO adhesion energies. To sample the configurations of NCs adequately, we employed a simplified phenomenological model. This is necessary because a large number of energy calculations is needed to obtain converged statistics for low-probability configurations. To direct the computational efforts toward the most relevant degrees of freedom, we used an on-lattice model in conjunction with a simplified coordination-dependent potential. The use of more realistic models or different parametrizations of the potential will affect the quantitative results; however, we expect that our qualitative conclusions will remain unchanged. Therefore, the concentrations and transition temperatures we report should be considered as indicative only. Our principle results are now summarized. We have found significant concentrations of adatoms on Au(111) facets at finite temperature. The average number of these atoms at room temperature is about 10-4 per nanoparticle for 1.6-nm-sized NCs. Possible mechanisms for the appearance of transient 3C atoms are the diffusion of corner or edge atoms onto facets. However, in general the diffusion pathways can be complex and cooperative in nature. Kinetic barriers for these processes may be large but surmountable over relevant timescales. The advantage of a MC method is that the equilibrium probabilities are obtained without requiring identification of the diffusion processes. Interestingly, Au(111) adatoms can be thermally
Letters excited onto facets that are very close to the MgO surface as well as onto facets on the top of the NC. A complex roughening transition for the creation of steps on Au(111) facets occurs just below 500 K. This transition is closely tied up with the structure of the Au-MgO interface layer. This is because in the presence of a kink in the interface layer, a step in the adjacent Au(111) facet is energetically favored. The appearance of steps on Au(111) facets and kinks in the Au-MgO interface layer are significant morphological changes. The introduction of such local atom configurations above a particular temperature may be important for a variety of applications: selective heterogeneous catalysis, for example. The appreciable numbers of transient 3C atoms may be very important in relation to catalysis. Calculations have shown that the adsorption energy for CO on various Au sites increases with decreasing coordination of the neighboring Au atom, and activation barriers for oxidation follow a similar trend.2 The barrier for a given reaction need only be about 0.3 eV smaller on 3C atoms than on 6C atoms for both sites to contribute equally to the overall activity at room temperature. This simple estimate is made assuming catalytic activity is determined primarily by an activation barrier that depends on the coordination of the site. It is clearly important to calculate barriers for specific reactions on 3C atoms in order to check this possibility. Acknowledgment. We gratefully acknowledge useful discussions with John A. Venables. K.P.M. is supported by the EPSRC grant GR/S80080/01 and PVS by a Grant-in-Aid for Creative Scientific Research Grant No. 16GS0205 from the Japanese Ministry of Education, Culture, Sports, Science and Technology. References and Notes (1) Sushko, P.; Shluger, A. Surf. Sci. 1999, 421, L157. (2) Lopez, N.; Norskov, J. K. J. Am. Chem. Soc. 2002, 124, 11262. (3) Combe, N.; Jensen, P.; Pimpinelli, A. Phys. ReV. Lett. 2000, 85, 110. (4) Venables, J. Introduction to Surface and Thin Film Processes; Cambridge University Press: New York, 2000. (5) Cleaveland, C. L.; Luedtke, W. D.; Landman, U. Phys. ReV. Lett. 1998, 81, 2036. (6) Meyer, R.; Lemire, C.; Shaikhutdinov, S. K.; Freund, H.-J. Gold Bull. 2004, 37, 72. (7) Lopez, N.; Janssens, T. V. W.; Clausen, B. S.; Xu, Y.; Mavrikakis, M.; Bligaard, T.; Norskov, J. K. J. Catal. 2004, 223, 232. (8) Molina, L. M.; Hammer, B. Phys. ReV. B 2004, 69, 155424. (9) Baletto, F.; Mottet, C.; Ferrando, R. Surf. Sci. 2000, 446, 31. (10) Kizuka, T.; Tanaka, N. Phys. ReV. B 1997, 56, R10079. (11) Pauwels, B.; Tendeloo, G. V.; Bouwen, W.; Kuhn, L. T.; Lievens, P.; Lei, H.; Hou, M. Phys. ReV. B 2000, 62, 10383. (12) Trafas, B. M.; Yang, Y.-N.; Siefert, R. L.; Weaver, J. H. Phys. ReV. B 1991, 43, 14107-14114. (13) Landau, D. P.; Binder, K. A Guide to Monte Carlo Simulations in Statistical Physics; Cambridge University Press: New York, 2000. (14) Purton, J. A.; Barrera, G. D.; Allan, N. L.; Blundy, J. D. J. Phys. Chem. B 1998, 102, 5202. (15) Purton, J. A.; Lavrentiev, M. Y.; Allan, N. L.; Todorov, I. T. Phys. Chem. Chem. Phys. 2005, 7, 3601. (16) Muller, M.; Albe, K. Phys. ReV. B 2005, 72, 094203. (17) Frantz, D. D.; Freeman, D. L.; Doll, J. D. J. Chem. Phys. 1990, 93, 2769. (18) Leach, A. Molecular Modelling: Principles and Applications; Prentice Hall: New York, 2001. (19) Brown, S.; Head-Gordon, T. J. Comput. Chem. 2002, 24, 68. (20) Baletto, F.; Ferrando, R. ReV. Mod. Phys. 2005, 77, 371. (21) The parameters used are Φ ) 14878.01 eV, F ) 16352.12 eV2, and ad ) 0.18 eV. (22) Pettifor, D. Bonding and Structure of Molecules and Solids; Oxford Science Publications: New York, 1995. (23) Sutton, A. P.; Chen, J. Philos. Mag. Lett. 1990, 61, 139. (24) Molina, L. M.; Hammer, B. Phys. ReV. Lett. 2003, 90, 206102. (25) Baumer, M.; Freund, H.-J. Prog. Surf. Sci. 1999, 61, 127.
