The Atomistic Structure of an MgO Cluster, Supported on BaO

One particular crystallite is characterized as conforming to vicinal (ca. ... for Heterogeneous Catalysis: What We Can Learn from Molecular Dynamics ...
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J. Phys. Chem. B 2002, 106, 3916-3925

The Atomistic Structure of an MgO Cluster, Supported on BaO, Synthesized Using Simulated Amorphization and Recrystallization Dean C. Sayle* Department of EnVironmental and Ordnance Systems, Cranfield UniVersity, Royal Military College of Science, ShriVenham, Swindon, UK, SN6 8LA

Graeme W. Watson Department of Chemistry, Trinity College, Dublin 2, Ireland ReceiVed: July 5, 2001; In Final Form: NoVember 6, 2001

A 25088-atom MgO cluster, supported on a BaO(100) substrate, has been simulated using an amorphization and recrystallization technique. The structure of the MgO cluster comprises a central MgO “plateau” region (vicinal MgO(100)/BaO(100)) intersected at each of the four corners by misaligned MgO crystallites, which can be characterized loosely as exhibiting triangular pyramidal morphologies. One particular crystallite is characterized as conforming to vicinal (ca. 10°) MgO(111)/BaO(100), indicating a dipolar MgO surface, which comprises a complex combination of mono-, di-, and tri-atomic steps and ledges at one particular face: the other two surfaces remaining perfect MgO{100} faces. The central MgO region is rotated by ca. 6° about an angle normal to the interfacial plane with respect to the underlying BaO and comprises various mixed screw-edge dislocations, the atomistic core structures of which are presented graphically. The interfacial region has a reduced ionic density, owing to the many voids and includes significant intermixing of Mg and Ba ions. In addition, significant migration of Ba ions around the sides of the MgO cluster is observed.

Introduction The presence of structural features, such as defects, within an oxide can influence profoundly the properties of the material. Moreover, when a thin oxide film is supported on a substrate, structural modifications are induced within the material as the thin film responds to the interfacial interactions and the lattice misfit associated with the system. The resulting changes in the properties of the supported material, compared with the parent or unsupported material, can be profound. Indeed, such a phenomenon has been exploited in many applications spanning catalysis,1 sensors, and electronic devices.2,3 However, while some structural changes can be beneficial for example in catalytic systems,4 others such as dislocation evolution within supported superconductors, may prove deleterious.5 Clearly, it is desirable to control such modifications to optimize and exploit fully the particular properties of the material. One important approach in realizing this objective is to characterize fully the structural features induced within a material when supported. Experimentally, the development of molecular beam epitaxy (MBE) has enabled one to exercise control over the supported thin-film structure at the atomic level leading to the fabrication of high quality films of materials not readily grown as bulk crystals.6 However, much of the work has been directed at metals and semiconducting materials with comparatively less on oxides. One reason for this is the problems associated with the insulating nature of oxides. Clearly, oxides are an important class of material with diverse properties and applications and therefore it is important that these materials enjoy similar attention as that given to metals and semiconductors. Accordingly, one must endeavor to overcome the problems associated * Corresponding author. E-mail: [email protected].

with this class of materials and enable their exploitation in various applications. One potential avenue of exploration is the application of computer simulation, which can provide a valuable complementary tool in evaluating the structural features of oxides and supported oxide thin films. However, there are considerable obstacles to simulating supported thin films, which must be overcome if one is to generate realistic models to aid experiment. The major difficulties one must address in generating realistic models are presented below, together with references indicating how the simulations have been devised to accommodate such issues. (a) Strain Relief. The lattice misfit associated with the system can have a profound influence on the structure of both the supported thin film and the underlying substrate material as the system evolves to accommodate the strain associated with the lattice misfit. These structural modifications, which also influence the material properties, may include lattice slip,7 critical thicknesses8 leading to the formation of dislocations9-15 and dislocation networks,16,17 defects (vacancies, interstitials and substitutionals),11 and grain boundaries.18,19 (b) Epitaxy. Although clearly, the substrate material has a profound influence on the structure and hence properties of the overlying thin film, the particular surface exposed (i.e. MgO(100) or MgO(111)) by the substrate can also affect the thin-film.6,20 In addition, for many materials, the particular surface may be associated with several terminations, for example, TiO2, or SrOterminated SrTiO3(001), which has been shown to influence structurally the overlying thin film.11 Finally, one must also consider the quality (i.e. surface roughness) of the substrate.6 While these arguments imply an exhaustive study of many permutations, one might also suggest, more optimistically, that it provides an avenue of control. Specifically, by modifying

10.1021/jp012538c CCC: $22.00 © 2002 American Chemical Society Published on Web 03/19/2002

Atomistic Structure of an MgO Cluster suitably the structure of the substrate surface one might optimize the properties of the particular system. (c) Interfacial Interdiffusion. Many experimental studies have reported interdiffusion across the interfacial plane6,20 due to mutual solubility of the substrate and overlying thin-film. Moreover, Tasker and Stoneham have suggested on theoretical grounds that a reduced density of ions across the interfacial region enhances the stability;21 the resulting enhanced relaxational freedom of ions within the interfacial region enabling dissipation of the strain. It has been suggested20 that the misfit discontinuity at the interface is alleviated, in part, via a “strain gradient” (generated via the interfacial diffusion) an issue alluded to in this present study. Indeed, this argument also relates to the success of introducing thin buffer layers between the substrate and overlying thin film,22 although clearly such a simplistic reasoning is clouded by many other competing factors. (d) Nucleation and Growth. It is well-documented experimentally that the structure of the thin film can be controlled by the particular preparative (growth) procedure.6,20 Accordingly, theoretical approaches, which attempt to model the structure of supported thin films, must therefore include also a mechanism for simulating the growth process. Attempts have been made to implement such features within the simulation,23-26 although this area remains in its infancy, as clearly simulating the nucleation and growth processes is the most challenging of the four (sections a-d). Conversely, if such processes are modeled adequately, the epitaxy, interfacial interdiffusion, and accommodation of the misfit strain leading to the evolution of, for example, dislocations, grain-boundaries, and defects, will be implicit within the simulation; a powerful impetus for introducing such functionality within the simulation. In previous studies, we have constructed models of thin-film oxides supported on an oxide substrate using an “atom deposition” simulation methodology.24 Specifically, ions comprising the thin film were deposited onto the surface of the substrate material with dynamical simulation in conjunction with energy minimization employed to direct the deposited ions into low energy configurations. Here, information pertaining to nucleation and growth in conjunction with structural data was derived. However, this technique is computationally highly expensive since dynamical simulation and/or energy minimization is applied after each deposition step and the simulation is limited (computationally) to small simulation cell sizes. This prohibits the evolution of certain structural features within the thin film, such as dislocations and dislocation networks, which are larger compared with the simulation cell. Clearly, for a realistic model of a supported thin film, dislocations must be incorporated into the model since they can influence profoundly the properties of a material. An alternative approach was therefore developed to address this issue. In particular, we employed a simulated “amorphization and recrystallization” methodology to generate models of supported thin films.16 This procedure involves placing the complete thin film on top of the substrate material and forcing it to undergo a controlled amorphization prior to recrystallizing under dynamical simulation into a low-energy configuration. Since only one dynamical simulation step is employed (albeit of long duration), the methodology is computationally less demanding compared with atom deposition, enabling larger simulation cells to be considered. Surprisingly, this methodology facilitated the eVolution of many structural features within the supported thin-film as the material responded to the lattice misfit and interfacial interactions associated with the system.16,19 These included, within a

J. Phys. Chem. B, Vol. 106, No. 15, 2002 3917 single simulation cell, the epitaxial relationships, dislocation networks, grain-boundaries, interfacial mixing, and defects (vacancies, voids, interstitials, and substitutionals) including defect associations. Conversely, information regarding the nucleation and growth of the thin film was obscured since the (simulated) recrystallization procedure bears little resemblance to a physical growth process. Clearly, it is desirable to develop a computationally tractable methodology, which enables the simulation of nucleation and growth in conjunction with suitably large simulation cells to ensure all structural modifications are represented. One possible avenue is to develop further the simulated amorphization and recrystallization methodology to ensure that the recrystallization stage reflects recrystallization in real (experimental systems). However, this has proved to be difficult. An alternative approach, which we consider here, is to employ the technique to generate supported clusters as a preliminary stage in understanding potential nucleation sites for growth. The models thus generated can then be considered further, using, perhaps, atom-deposition, to explore the growth of the thinfilms. Specifically, by using the computationally less demanding amorphization and recrystallization approach as a preliminary step, prior to growing the thin film using atom deposition, affords a much faster route in generating nucleation sites compared with following a wholly “atom deposition” methodology. Growth, via atom deposition, will be considered in a future study, based upon the cluster models developed here. Accordingly, to explore the viability of simulating supported clusters using this approach we consider initially MgO supported on BaO(100) as a model system representative of oxide clusters supported on an oxide substrate with large associated lattice misfits. An additional driving force to the study of clusters is the wealth of applications that have been conceived owing to the unique changes in the chemical, physical, and mechanical properties of clusters and supported clusters compared with the (bulk) parent material. Applications include, for example, catalysis, nanotechnology, biomedicine, electronics, optics, sensors, luminescent materials, quantum dots, and magnetism.25-35 Methodology In this section, we describe the force-field, which we have used to describe the interactions within the materials considered, the simulation codes and how they can be manipulated to perform surface calculations and finally, the basic mechanism underlying the operation of the simulated amorphization and recrystallization procedure. (a) Potential Models. The reliability of any simulation rests ultimately with the potential parameters.36 Our calculations are based on the Born model of the ionic solid in which the ions interact via long-range Coulombic interactions, calculated via the Ewald summation37 and short-range parametrized interactions. In this study, we have employed the potential parameters of Lewis and Catlow38 with the additional approximation of the rigid ion model, imposed to reduce the computational expense. The potential parameters have been extensively employed previously to model structures, which have nonoptimal geometries, with good correlation to experiment.20 These include, for static simulations, interfacial defects,23 dislocations,39 and grain-boundaries,20 and for dynamical simulations, interfacial structures,10 and surface defects.40 We suggest therefore that the potential parameters are well suited to explore supported metal-oxide thin films, which may include many structural defects.

3918 J. Phys. Chem. B, Vol. 106, No. 15, 2002 (b) Simulation Codes. In this study, we employ the DL_POLY code41 to perform the dynamical simulations. Since this code utilizes three-dimensional periodic boundary conditions, the surface is simulated using a periodic array of slabs with a void introduced, perpendicular to the interfacial plane to represent the vacuum above the surface of the thin film. The size of the void is, of course, suitably large to ensure that the interactions between slabs is negligible. In addition, the distance between neighboring clusters is also sufficiently large to inhibit any artificial interactions between the cluster and its periodic images parallel to the interfacial plane. We employ a two-region approach:39 region I contains the MgO cluster and one repeat unit of the underlying BaO support and ions within this region are allowed to move within the dynamical simulation, while ions in region II (three BaO repeat units thick) are held fixed to reproduce the potential of the bulk lattice on region I. The reason for using DL_POLY (codes using two-dimensional periodicity are available42), is that it offers a considerable speed advantage for our particular application. (We have found previously (see refs 30 and 34) that simulating interfaces using an amorphization and recrystallization methodology with either two-dimensional (2D) or three-dimensional (3D) periodic boundary conditions give equivalent results.) In particular, for simulating interfaces, the interfacial area must be large to accommodate the incommensurate relationships between the lattice parameters of the supported thin film and underlying substrate material. Moreover, the structural modifications, such as dislocation networks and grain-boundaries that evolve as the overlying material responds to the misfit strain, are large, and hence, the simulation cell must be suitably large to accommodate such features. Accordingly, the vector introduced perpendicular to the surface to generate the vacuum above the thin film, while being sufficiently large to prohibit any artificial interactions between the system and its periodic images, is also our smallest vector, which facilitates a very efficient 3D simulation. Many simulations of surfaces performed using 3D codes are inefficient owing to the large sampling of reciprocal lattice vectors perpendicular to the surface in the Ewald sum compared with the other two directions. In addition, by performing the dynamical simulations on a parallel computer (typically such calculations require 10 days using 16 processors of an Origin 2000), we benefit also from the efficiency of the DL_POLY code when run in parallel. The thin-film interface energy for this system is defined as:

γthin-film ) [Ethin-film-interface - Ebulk - nEthin-film]/area (1) where Ethin-film-interface is the total energy of the interface (simulation cell); Ebulk, the bulk energy of the BaO(100) support; Ethin-film, the standard 3D periodic bulk energy for the supported thin film per formulation unit; n, the number of formulation units of the supported thin film; and area, the surface area of the BaO covered by the MgO cluster. (c) Amorphization and Recrystallization. This simulation technique involves forcing the overlying material to undergo, under dynamical simulation, a controlled amorphization. The prolonged application of dynamical simulation to this amorphized thin film results in its recrystallization together with the evolution of structural features relating to the accommodation of the associated lattice misfit, such as grain-boundaries, dislocations, defects, and reduced interfacial ion densities. The final thin-film structure is therefore governed solely by the interfacial interaction and lattice misfit associated with the system rather than the (perhaps artificial) starting configuration.

Sayle and Watson The very short time scales accessible to atomistic dynamical simulations (typically a nano-second) is a major limitation with the technique. Consequently, for highly crystalline materials, such as MgO, where ionic migration is slow, dynamical simulation is not appropriate to explore the energy barriers for migration since no migration would be observed within the time scales accessible. Conversely, central to the methodology employed in this present study, for an amorphous material the ions will have a much higher mobility and can therefore migrate more quickly (within the time scales available) compared with the analogous crystalline solid. This allows the ions to evolve and assemble into an appropriate (low-energy) configuration, which would not be possible by applying dynamical simulation to crystalline materials. The amorphization and recrystallization strategy provides therefore a mechanism for overcoming, in part, the considerable (time) limitation associated with dynamical simulation. To induce the initial amorphization, the supported material can be constrained under high, either compressive or tensile, stresses. The subsequent application of high-temperature dynamical simulation to the system then results in its amorphization. Further details of the technique can be found elsewhere.10,16 Here we induce amorphization by constraining the MgO cluster under tension. For clusters this is perhaps more appropriate than amorphization induction via compression since the amorphization will result in a contraction of the supported MgO cluster as it amorphizes. Consequently, the minimum distance between the cluster and its periodic images is more easily controlled. In addition, the simulation must be controlled to ensure that the cluster does not melt as this is likely to result in the complete spreading of the cluster over the surface of the underlying support. Accordingly, the dynamical simulation is performed at a sufficiently high temperature to maximize ionic mobility (within the amorphous solid) without resulting in melting. The starting configuration was constructed by placing an MgO cluster 56 × 56 atoms in area (or 28 repeat units in each direction) and eight atoms in height (25088 atoms in total) on a 84 × 84-atom BaO(100) substrate (ca. 231.6 × 231.6 Å, giving a surface area of approximately 54000 Å2). The MgO was then expanded by 27% to generate the considerable tensile stresses within the supported MgO cluster required to facilitate amorphization under dynamical simulation. The size of the BaO substrate was carefully chosen to enable a large (154 Å) distance between periodic clusters, which is sufficient to ensure negligible interactions between the cluster and its periodic images, while minimizing the computational cost of the simulation. All simulations were performed within the NVE ensemble: constant number of particles, constant volume, and constant energy with instantaneous velocity scaling to the simulation temperature used throughout. This prevents the large build up of kinetic energy as the thin film evolves from the highly strained initial configuration, via an amorphous transition, to a crystalline phase with reduced strain and a range of defects. Dynamical simulation, with a time step of 5 × 10-3 ps, was performed on the system for 855 ps at 2500 K; 5 ps at 1500, 1000, and 500 K and 110 ps at 0 K. The duration of the initial and final dynamical simulation steps (2500 and 0 K, respectively) were determined by ensuring that the system was no longer evolving either structurally or energetically. Results To monitor structurally, the amorphization and recrystallization, radial distribution functions (RDF) and mean square displacements (MSD) were calculated in addition to using

Atomistic Structure of an MgO Cluster

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Figure 1. 1. Calculated magnesium MSD within the MgO/BaO(100) system during dynamical simulation performed at 2500K. The units for the MSD are Å2.

graphical techniques to provide a visual display of the evolving structures during the dynamical simulation. (a) Amorphization and Recrystallization Analysis. The MSD (20-800 ps) of magnesium ions during the dynamical simulation is shown in Figure 1. The MSD increases rapidly at the start of the simulation, indicating the high initial mobility of the magnesium ions as the MgO thin film amorphizes. It then plateaus after about 100 ps, which reflects the muchreduced mobility as the MgO thin film recrystallizes. If the MgO had melted during the dynamical simulation, the MSD would have shown a linear increase (high gradient) with time toward the end of the simulation as expected for a molten material. The calculated atom positions, after 1 cycle (0.005ps) of dynamical simulation, is presented in Figure 2a, together with the corresponding RDF (Figure 2b), and show the MgO cluster supported on the BaO(100) surface. The peaks of the RDF have already started to broaden, with respect to the starting structure, as the MgO starts to respond to the considerable tension within the lattice although the RDF clearly demonstrates a crystalline (rocksalt) structure. The RDF also shows a nearest neighbor peak of ca. 2.7 Å, illustrating the initial 27% increase in the MgO lattice parameter (the lattice parameter of the parent MgO is 2.1 Å) required to facilitate tensile induced amorphization. The calculated atom positions after 200 time steps (1 ps), are presented graphically together with the corresponding Mg-O RDF in Figure 3a and Figure 3b, respectively. Visual inspection of the system suggests that the MgO is amorphous with the structure having contracted thereby covering less surface area of the underlying BaO. Moreover, the RDF indicates that the system has lost some long-range order indicated by the broad peaks above 2.5 Å supporting the supposition that the MgO has amorphized. The peak corresponding to Mg-O nearest neighbor distances is now at approximately 1.9 Å or 0.2 Å lower than the parent MgO and is quite broad with Mg-O bond distances within the amorphous cluster ranging from 1.5 to 2.5 Å. Even so, the first peak is well defined as would be expected from an ionic material since opposite charges would likely form a close nearest neighbor coordination shell. Close inspection of the MgO cluster reveals also that even after 1ps, the corners of the MgO cluster have started to recrystallize back into the rocksalt structure. At the end of the simulation, the MgO has clearly recrystallized back into the rocksalt structure as demonstrated by Figure 4a, which depicts the lattice positions for this final structure together with the corresponding RDF in Figure 4b. In addition, the RDF for the underlying BaO was calculated and presented in Figure 4c. An interesting feature of this graph is the split nearest neighbor peak. Two peaks are clearly visible, one at 2.63 Å, and the other at 2.73 Å. While the latter larger peak corresponds to the parent BaO (ca 2.75 Å), the former reflects the perturbation of the underlying BaO in response to the MgO cluster above.

Figure 2. (a) Sphere model representation of the atom positions for the MgO/BaO(100) system calculated after one iteration of dynamical simulation, performed at 2500K. Magnesium ions are colored yellow; oxygen, red; and barium, blue; and (b) the corresponding Mg-O RDF within the supported MgO cluster. Values for the abscissa are measured in angstroms.

We also note that the duration of the dynamical simulation required to recrystallize fully the MgO from the starting amorphous structure is commensurate (ca. 855 ps) with that of previous studies of fully covered thin films (655 ps19), and thus, the methodology is no more computationally expensive. The thin-film interface energy for this cluster was calculated to be 5.6 J m-2 based upon an interfacial area covered by the MgO cluster of 21000 Å2. (b) Structural Features of the MgO Cluster. The final structure (Figure 4a) for the MgO cluster supported on BaO(100) is somewhat surprising. For example, rather than the rectangular cuboid that one might expect with the MgO exposing the (100) plane at each of the five exposed surfaces, a rather more complex structure has evolved. Owing to the complexity of the resulting cluster, structural characterization is perhaps best described using visual representations of the atom positions. In addition, the cluster demonstrates significant curvature of the various planes, which increases further the complexity of structural characterization. Inspection of Figure 4a reveals a central MgO “plateau” in which the MgO exposes the (100) plane at the surface, although upon closer inspection one can observe steps emanating from the center and going down in both the [01h0] and [001h] directions as one traverses from the center of the cluster to the far left corner of the cluster (Figure 4a). Surprisingly, as one progresses down the steps from the center to the far left of the cluster, the thickness of the cluster increases. This indicates that the

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Figure 3. (a) Sphere model representation of the atom positions for the MgO/BaO(100) system calculated after 200 iterations (1 ps) of dynamical simulation, performed at 2500 K. Magnesium ions are colored yellow; oxygen, red; and barium, blue; and (b) the corresponding Mg-O RDF within the supported MgO cluster. Values for the abscissa are measured in angstroms.

MgO(100) is vicinal to the underlying BaO(100) support. The vicinal angle of each MgO(100) surface separated by the steps relative to the underlying BaO(100) support was calculated to increase from ca. 3° at the center of the cluster to ca. 20° (far left). The vicinal angle was calculated as the angle subtended by the surface MgO(100) planes relative to the underlying BaO(100). Moreover, the MgO(100) planes demonstrate significant curvature owing to this gradual change in vicinal angle. At the far left of the figure (an enlarged segment is shown in Figure 5) the angles of each of the three MgO{100} surfaces (for the region of the MgO cluster colored purple) relative to the BaO(100) was calculated as ca. 20, 73, and 78° for the MgO(100), (01h0), and (001h) planes, respectively. This segment of the MgO clusters appears to exhibit trigonal pyramidal morphology with respect to the underlying BaO. Geometrically, for a perfect trigonal pyramidal cluster, the MgO(111) face would be exposed at the interface with all three MgO{100} faces subtending angles of 54.7° to the underlying BaO(100). We now consider the top of the cluster, an enlarged segment of this part of the cluster is shown in Figure 6 Again this region of the MgO cluster lies at some vicinal angle with respect to the underlying BaO. Moreover, a grain-boundary exists where this part of the cluster (blue) intersects with the “plateau” region of the cluster (red and purple). At the far right corner of the MgO cluster (Figure 4a), colored yellow in Figure 6, the MgO again appears to evolve into a trigonal pyramidal morphology.

Figure 4. (a) Sphere model representation of the atom positions for the MgO/BaO(100) system calculated at the end of the simulation. Magnesium ions are colored yellow; oxygen, red; and barium, blue; (b) the corresponding Mg-O RDF within the supported MgO cluster; and (c) corresponding Ba-O RDF within the underlying BaO substrate. Values for the abscissa are measured in angstroms.

However, this structure lacks an apex; rather mono, di and triatomic steps are observed. Such a structure has been suggested as a mechanism for stabilizing a dipolar (111) face of a rocksalt structured material.39,43-46 To determine whether the MgO(111) is indeed exposed at the interface, the cluster was cleaved to reveal an MgO(111) face (Mg-terminated) together with the three adjoining MgO{100} surfaces (Figure 7). The angles subtended by each of the three MgO{100} faces were calculated as 43 (top), 60 (bottom) and 58° (right); geometrically, for the parent rocksalt, the angle between a (111) and adjoining {100} faces would be 54.7°. In addition the angle of the MgO(111) relative to the underlying BaO(100) is ca. 10° suggesting perhaps vicinal MgO(111)/BaO(100). Again, a complex grain-boundary structure arises at the intersection between this region (yellow) of the MgO cluster and the plateau region (red).

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Figure 5. Sphere model representation of an enlarged segment, to the left of Figure 4a, depicting the almost triangular pyramidal morphology of this particular MgO crystallite. To aid clarity of the figure the MgO cluster exhibiting this pyramidal morphology is colored purple. Magnesium ions are colored yellow; oxygen, red; and barium, blue.

Figure 6. Sphere model representation of an enlarged segment (top region of Figure 4a), depicting two MgO crystallites (colored blue and yellow), which intersect the main plateau region of the MgO cluster (red) resulting in the formation of complex grain-boundary structures. Barium ions are colored blue.

An enlarged segment of the bottom part of the MgO cluster (Figure 4a) is presented in Figure 8. Here, one sees a domain, which has rotated by ca. 30° about the BaO(100) with respect to the main body of the cluster. Again, the cluster in this region attempts to evolve a trigonal pyramidal morphology. The angles are calculated to be ca. 20, 68, and 83° for the MgO{100} planes relative to the BaO(100), respectively. An additional striking feature associated with this MgO cluster is the presence of many Ba ions (Figure 4a), which have migrated from the surface of the BaO support occupying positions around the edges of the MgO cluster. As far as we know there have been, as yet, no studies reporting the structure of MgO clusters supported on BaO(100) presenting atomistic detail such that a comparison can be made between the experimental and simulation results. However a related paper of Mestle et al. in studying the decomposition

of NO over BaO supported on MgO (the “inverse” of the system considered in this present study), found the BaO to be “ill defined crystallographically” and containing lattice defects.47 (c) Interfacial Structures. Figure 9a depicts a plan view of part of the interfacial BaO(100) plane lying directly below the MgO cluster. Clearly, the region is highly defective and includes many voids. Surprisingly, Mg ions, which have migrated from the overlying MgO cluster, comprise 30% of the total cations within this region. The calculated average Ba-O and Mg-O bond distances are 2.6 Å (range 2.4-2.9 Å) and 1.95 Å (range 1.8-2.1 Å), respectively. The significant reduction in both the BaO and MgO bond distances compared with the parent oxides can be attributed to the internal surface contraction of the (small) BaO and MgO oxide domains in response to the voids present within the layer.

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Figure 7. Sphere model representation of a cleaved segment of the crystallite (colored yellow in Figure 6) showing the MgO(111) surface terminated by magnesium ions. Magnesium is colored yellow; oxygen, red; and barium, blue.

Figure 8. Sphere model representation of an enlarged segment (bottom region of Figure 4(a)) of the MgO cluster showing an MgO crystallite (colored gray), which has rotated by about 30° with respect to the main body (plateau region, colored red) of the MgO cluster. The crystallite again demonstrating an almost triangular pyramidal morphology. Barium ions are colored blue.

One might suggest that the interfacial BaO(100) plane is too defective and arises as a consequence of the considerable energy introduced into the system in order to generate an amorphous structure. However, this is not the case. Inspection of the system after amorphization reveals the interfacial BaO(100) layer to be free of defects. It is only during recrystallization that defects evolve within the system. We suggest that the considerable perturbation and defective nature of the interfacial BaO(100) plane is a consequence of the high lattice misfit associated with this system. Previous analogous simulations on the SrO/MgO(100) system, which is associated with a much lower misfit, reveals that the substrate is much less defective compared with the system considered in this present study.16 Moreover, preliminary studies on SrO, CaO and MgO nanoparticles, supported on

Sayle and Watson BaO(100), revealed that the perturbation and concentration of defects within the interfacial BaO(001) layer of the substrate increases with the misfit associated with the system. Specifically, for the SrO/BaO(100) system (-6% misfit), there is almost no perturbation of the interfacial BaO(100) layer. Figure 9b shows a 2.5 Å slice cut parallel to the BaO(100) through the interfacial region of the MgO cluster and again shows a reduced ionic density compared with a perfect crystal. In addition, the voids are populated by Ba ions, which have migrated from the surface of the support and comprise ca. 16% of the total cations within this region. The calculated average Ba-O and Mg-O bond distances are 2.6 Å (range 2.4-2.9 Å) and 2.02 Å (range 1.8-2.3 Å), respectively. A 2.5 Å slice above that shown in Figure 9b is depicted in Figure 9c. Here, the concentration of both migrated Ba ions and voids is lower compared with the slice below (Figure 9b) as the MgO crystal densifies further from the interfacial region. Specifically, the slice comprises only 4% Ba ions, which occupy positions at grain boundaries (intersections between regions colored blue, yellow, and red in Figure 6) and within small cavities that have formed within the MgO cluster. The calculated Mg-O bond distance is 2.07 Å (range 1.9-2.2 Å). A study by Chern and Cheng, who fabricated MgO, SrO, and NiO thin films supported on MgO(001) and SrTiO3, using molecular beam epitaxy, suggests that the lattice parameters for the thin films are slightly compressed in the first few layers but then relax back to the bulk lattice parameters further from the interfacial plane.48 Tasker and Stoneham have suggested that reduced interfacial densities enhance the stability.21 Since the methodology employed here was designed to generate low-energy cluster configurations, our simulation supports such arguments as the resulting interfacial densities of our interfaces are much reduced owing to the multitude of voids present within the interfacial regions. We also suggest that the high migration of Ba and Mg across the interfacial planes facilitates a strain gradient across the interfacial planes (as opposed to an abrupt 27% change in lattice parameter). The calculated pseudo-lattice parameters based upon the proportion of Ba and Mg in each plane are calculated to be 2.75, 2.56 (Figure 9a), 2.20 (Figure 9(b)), 2.13 (Figure 9c), and 2.08 Å (based upon lattice parameters of 2.75 and 2.1 Å for BaO and MgO, respectively) as one proceeds from the underlying BaO support to the MgO. In addition, the increased relaxational freedom, arising from the voids within the thin film as one traverses the interface, will reduce further the discontinuity. An experimental study by Lind et al. on the Fe2O3/NiO system49 showed interdiffusion between the Fe2O3 and NiO of the order of 1 or 2 atomic layers. Imaduddin and Lad50 and Imaduddin et al.51 used MBE to grow MgO on NiO(001) at growth temperatures of 100-250 °C. High-quality crystalline layers were reported at this temperature, although growth did not proceed in a layer-by-layer fashion. The threshold temperature for interdiffusion was found to be 750 °C. (d) Dislocations within the MgO Cluster. Analysis of the MgO thin film, using graphical techniques, revealed the presence of dislocations within the MgO cluster, which were only observed within the “plateau” region of the MgO cluster (Figure 4a). The core structure of one particular dislocation is presented in Figure 10a and shows that the dislocation has mixed screwedge character. In previous simulations of MgO supported on BaO, mixed screw-edge as opposed to either pure-edge or purescrew dislocations were observed.19 In Figure 10b, part of the MgO lattice surrounding the dislocation core is shown to aid interpretation. One interesting feature associated with this

Atomistic Structure of an MgO Cluster

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Figure 9. Sphere model representations depicting the calculated atom positions of (a) part of the interfacial BaO plane underlying the MgO cluster; (b) a 2.5 Å slice cut parallel to the interfacial plane through the interfacial region of the MgO cluster; and (c) a 2.5 Å slice above that in (b). Magnesium ions are colored yellow; oxygen, red; and barium, blue.

Figure 10. (a) Ball and stick model representation of the core structure of a mixed screw-edge dislocation identified within the MgO cluster. Magnesium is colored yellow; oxygen, red; and barium, blue.; (b) stick model representation of the dislocation core (colored purple) depicting also part of the surrounding MgO lattice (colored gray).

dislocation is that at about 8 Å from the surface of the MgO cluster, a void or cavity has evolved within the MgO, which is enveloped by the spiral of Mg and O ions comprising the core of the screw-edge dislocation. Within each MgO plane, there are ca. 12 vacancies in each of four planes parallel to the interfacial plane; the dislocation core encloses an area of approximately 90 Å2 within each plane. Such a defect may have pinned the dislocation preventing it from annealing out of the structure. It is also clear from Figure 10a that there are three oxygen ions, two magnesium, and a barium that are located at the side of this void. Further inspection of the MgO cluster revealed two additional dislocations, again accommodating screw-edge character, which are presented in Figure 11. Interestingly, the dislocations lie at 90° to one another with overlapping core structures. Analysis using graphical techniques of the ‘interconnecting’ grains comprising the MgO cluster (colored blue, yellow, gray, and purple in Figures 5-8) did not reveal the presence of dislocations within these regions. Experimentally, owing to the difficulty in characterizing the atomistic structure of dislocations within supported oxides, there is very little experimental data with which to compare our simulated models and therefore our simulations must, at present, take a predictive role. Misfit dislocation core structures have been reported within R-Cr2O3(0001)/R-Al2O3(0001)6 and SrZrO3/ SrTiO3(001)52 depicting edge character.

Figure 11. Ball and stick representation of the core structures of two interconnecting screw-edge dislocations identified within the MgO cluster. Magnesium is colored blue and yellow, and oxygen is red.

(e) Epitaxy. In previous studies of supported thin films, we have attempted to rationalize the structure of the overlying thin film by assigning various epitaxial relationships that exist between the thin film and underlying support to some near coincidence site lattice53,54 thereby enabling an associated (local)

3924 J. Phys. Chem. B, Vol. 106, No. 15, 2002 lattice misfit to be estimated. For example for SrO supported on MgO, it was observed that eight lattice spacings for the overlying SrO were lattice matched with 10 from the underlying MgO support. This configuration was calculated to be associated with a -2.3% misfit (compared with a bulk lattice misfit of +20% between the parent oxides). However, owing to the complexity of the cluster, it is difficult to assign any epitaxial relationships that exist between the MgO cluster and BaO support. Moreover, the ill-defined orientations of various regions of the cluster in conjunction with the observed curvature of the lattice planes helps to compound this difficulty. Consequently, we have been unable to determine effectively any geometrical relationships. Indeed, attributing epitaxial relationships to the structure may prove misleading. However, it was observed that the central MgO plateau region appears to have rotated by ca. 6° relative to the underlying BaO about an axis normal to the interfacial plane. Discussion An initial concern when employing the amorphization and recrystallization methodology to explore supported clusters was the possibility that tension or compression induced amorphization of a thin film was successful owing to the influence of neighboring (image) cells. For example, under compression/ tension induced amorphization for a fully covered substrate, all ions within the thin film experience (initially) the same forces in directions parallel to the interfacial plane. Conversely, for a cluster, since there are surfaces both parallel and perpendicular to the interfacial plane, the forces generated within the cluster parallel to the interfacial plane will be different for surface or near surface regions. This also raises the question of whether the cluster has suitably amorphized. However, it is clear from the MSD (Figure 1), RDF (Figure 3b), and structure (Figure 3a) that at 1 ps the cluster does go amorphous. In addition, these properties are very similar to those calculated previously for a fully covered thin film16 indicating a completely amorphized structure has been achieved. Moreover, the final structure reveals a fully crystalline cluster that has no structural similarities (density, orientation, nor surface area) to the starting structure indicating that our initial structure has not influenced the final structure (a major objective of the amorphization and recrystallization approach). A possible reason for this success is that in previous studies the degree of compression/tension for rocksalt-structured oxides did not prove critical to the successful amorphization and recrystallization of the thin film. Conversely, for alternative systems such as CeO2/YSZ (yttrium-stabilized zirconia) the success of the methodology was critically dependent upon the degree of compressive strain imposed upon the supported CeO2 prior to amorphization.55 For example, when the compressive strain was too small, the CeO2 did not amorphize; under more but still inadequate strain the CeO2 did amorphize, although recrystallization was incomplete resulting in interconnecting regions of amorphous and crystalline CeO2. With too high a compression, the simulation failed catastrophically. It is likely therefore, that for CeO2 clusters, the amorphization will need to be carefully controlled and the compression/tension required to amorphize a complete thin film may not correspond to those values required to amorphize a CeO2 cluster. Accordingly, the amorphization and successful recrystallization of materials other than binary oxides considered here may prove more problematic. In a previous study, a thin film of MgO, supported on a BaO(100) substrate, was simulated using amorphization and recrystallization (complete thin-film coverage). The final MgO

Sayle and Watson thin-film structure revealed that the MgO formed many nanocrystallites ca. 200 to 2,000 Å in size and rotated with respect to the BaO surface normal by various angles ranging from 0 to 90°. The resulting grain-boundary structures, formed at the intersections of the nanocrystallites, were similar to those observed experimentally in NiO. However, the orientation of the MgO with respect to the BaO(100) substrate was entirely MgO(100) or vicinal MgO(100) with no regions oriented at angles commensurate with those observed in this present study (such as orientations seen in Figures 6-8, tentatively, MgO(111)/BaO(100)). In this present study, since the ions comprising the cluster are much less constrained, the material has increased relaxational freedom to evolve into a low energy configuration. Conclusions We have shown that the simulated amorphization and recrystallization methodology, developed previously, and employed to generate models of supported thin-films, where the film completely covers the surface of the substrate, can be successfully applied also to generate models of clusters. Straining the MgO cluster under considerable tension, followed by the application of high-temperature dynamical simulation, was found to be a suitable mechanism for inducing amorphization on the thin film. In addition, prolonged dynamical simulation, performed on this amorphous cluster, resulted in complete recrystallization. The duration of the dynamical simulation to effect recrystallization of the MgO (855ps) was found to be commensurate with previous studies, suggesting that the procedure is computationally no more demanding than that required to amorphize a thin film, which completely covers the surface of the substrate. The final configuration of the cluster includes many structural features one might expect of a supported thin film as the material attempts to relive the strain associated with the lattice misfit between the parent oxides. One important feature was the evolution of various crystallographic orientations of the MgO with respect to the underlying BaO thin film. Specifically, the cluster comprises a central plateau (MgO(100)/BaO(100)) intersected by misorientated crystallites at each corner, which display (loosely) triangular pyramidal morphologies. However, owing to the significant curvature of the MgO, characterization of the specific orientation of the various crystallites is difficult and may prove misleading, although there is strong evidence to suggest the existence of the ‘dipolar’ MgO(111)/BaO(100). In addition, the sides of this particular region (colored yellow in Figure 6) comprises a complex combination of mono-, di, and tri atomic steps. Structural analysis, using graphical techniques, revealed that the crystallites are free of dislocations, although three mixed screw-edge dislocations were observed to have evolved within the central plateau region. In accord with previous studies, at the interfacial region, the cluster comprises a reduced density of ions, with significant intermixing of Ba and Mg species. We suggest that the driving force to such behavior is to facilitate a strain gradient at the interfacial region thereby reducing the strain discontinuity. In addition, significant migration of Ba ions from the support were observed with the ions occupying positions around the sides of the cluster. In summary, the various crystallographic orientations, surface steps, ledges, grain-boundaries, dislocations, and defects, present within this model, provide a wealth of potential nucleation sites, which can be explored further to help understand the growth process. And while, the size of the particular cluster, considered

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