J. Phys. Chem. B 1998, 102, 795-803
795
Independent and Interdependent Atomistic Structural Features of Pd Clusters Supported on the MgO(001) Surface Ryo Yamauchi, Momoji Kubo, and Akira Miyamoto* Department of Materials Chemistry, Graduate School of Engineering, Tohoku UniVersity, Sendai 980-77, Japan
Rajappan Vetrivel Catalysis DiVision, National Chemical Laboratory, Pune 411008, India
Ewa Broclawik Institute of Catalysis, Polish Academy of Sciences, ul. Niezapominajek, 30-239, Krakow, Poland ReceiVed: June 23, 1997; In Final Form: September 16, 1997
Pd particles supported on the MgO(001) surface were simulated by the molecular dynamics (MD) method. The surface and inner structures of the particles as well as the interaction sites of the Pd atoms were investigated by using computer graphics (CG) techniques. The numerical features of the surface atomic rows, the inplane symmetric configurations, the height deviation of the layer, and the lattice length defined by the distance between near neighboring rows were estimated. The dependency and the interdependence of these atomistic characteristics were evaluated. The findings on the lattice spaces were compared with the experimental and other theoretical calculation results.
1. Introduction The small metal particles on a substrate have stimulated the interest of researchers because of the significance of their applicative and fundamental meanings; active species of catalysts1-4 and initial products during the particle formation.5 The unfavorable phenomenon in the supported metal catalysts is the deactivation of catalysis caused by the growth of the particle,6 and the important phenomenon in the successive cluster formation is the occurrence of the core particle at the initial stage of the process. In both cases, the degree of stability of the particle influences the frequency of the occurrence of the incidents;5,7 if the metal particle is weakly stabilized on the substrate, which means not only the interatomic interactions but also the effect of the geometrical fit between the particle and the substrate, the coalescence more easily takes place, and the particle cannot play the role of the core. Although the change of the degree of stability occurs as the result of the external effects such as temperature and the structure is formed as the result of the transfer from initial to final states, the indication and the directionality of the migration influenced by the degree of stability seem to be correlated to the three-dimensional atomic configuration of the inner and outer atoms of the particle. Furthermore, the surfaces of the supported particle supply sites for the adsorption and the dissociation of organic molecules and transacts the oxidative and reductive catalytic reactions. Therefore the clarification of the details of the structural features of the small particles on the support is meaningful, and the accumulation of the knowledge from the findings is important for the organization of the further systematic technology based on a definite foundation. The development of spectroscopic techniques has contributed to resolving the various kinds of structural characteristics, e.g., scanning tunneling microscopy (STM) to evaluate the diameter of the particle8,9 and transmission electron microscopy (TEM)
to understand the interface structure,10,11 which supply the actual image to perceive the atomic configuration, and extended X-ray absorption fine structure (EXAFS) spectroscopy to estimate radial structure,12,13 which gives the local atomistic image including the inner part of particle. However, in investigating the structure of ultrafine metal particles, these spectroscopic techniques do not supply quantitatively satisfiable structural information because of the insufficient resolution of atomistic images and the shortage of analyzing methods in the present stage, although workers make much effort to improve the performance and to achieve greater precision. The substitutive technique as the replacement accomplishing spectroscopical analysis of the fine particles lies in computer chemistry. A typical computer simulation technique to analyze atomistic phenomena in finite temperature is the molecular dynamics (MD) method, which enhances the degree of understanding of the structure.14,15 The condition of the system of the simulation is usually restricted in the ideal situation without the mixture of internal (e.g., point defects and stacking faults) and external (electric field, magnetic field, etc.) factors; namely, the simulation supplies the essence of the phenomena because of the flexibility of the exclusion of the influence of the internal and external factors. The effects of the temperature and the surface morphology of the support in the system of Pd/MgO(100) were studied by utilizing the MD method and computer graphics (CG) techniques, from the viewpoint of the design of the supported metal catalysts.16 The usefulness of the MD simulation for the system was ascertained, and the effectiveness of the atomic holes in the support surface in preventing the Pd particles from coalescence was shown. In this report, structural characteristics of the different Pd clusters supported on the MgO(100) surface were investigated by performing MD simulations. The combined use of empirical and nonempirical potential parameters
S1089-5647(97)02035-X CCC: $15.00 © 1998 American Chemical Society Published on Web 01/07/1998
796 J. Phys. Chem. B, Vol. 102, No. 5, 1998 was adopted for the description of the dynamics of the atoms in order to satisfy the higher degree of clarification of the interaction potentials. The surface, interface, and inner structures of the clusters were investigated in detail, using various CG techniques.17 The perception manner depending on the view enhances the recognition of the mutual correlation among individual atomic configurations and gives the directionality for the quantitative estimation of the local atomistic phenomena such as structural disorder. The quantitative analysis of the structural disorder was attained by creating programs; the identification analysis was adopted for the estimation of the structural correlation between in-plane pair atoms, and the analysis of the deviation of both the row and height was applied for the evaluation of the properties as line and plane, respectively. The dilation and the contraction of the lattice spaces of the inner and outer parts of the clusters were also investigated. The findings on the dependency and the interdependence of the quantitative and qualitative results were extracted. 2. Description of Interactions The electrostatic and exchange-repulsive potentials were used to describe the interactions acting on ionic atoms. The Morse potential was used to describe the central parts of metal-metal and metal-substrate interactions. The mathematical description of these potentials and the detailed MD methodology were described elsewhere.18 The potential parameters of Mg and O atoms were optimized to reproduce the bulk MgO structure (NaCl type) substantially. The equilibrium bond distances (r*ij) and the interaction energy values (Dij) of Pd-O, Pd-Mg, and Pd-Pd pairs were derived from the results of quantum chemical calculations based on density functional theory19,20 using cluster models and nonlocal approximations.21,22 The estimated Morse potential parameters were 2.10 Å, 2.45 Å, 8.09 kcal/mol, and 10.75 kcal/mol, for r*Pd-O, r*Pd-Mg, DPd-O, and DPd-Mg, respectively. The bond distance and the electronic structure of the Pd2 dimer were reported by Nakao et al.23 and Harata and Dexpert.24 Their results indicated that the equilibrium bond distance of the Pd2 dimer was shorter than that of bulk Pd crystal (2.75 Å). The shortening of the bond length between metal atoms was also reported for other clusters.24-27 These results lead to finding the directionality of the evaluation manner of the parameters of Pd-Pd interactions. In this work, the parameters of the Morse potential for Pd atoms were estimated from the results of the Pd2 dimer by using two kinds of approximations; the equilibrium bond length (r*Pd-Pd) optimized at the local level was 2.69 Å, and the interaction energy value (DPd-Pd) was 14.02 kcal/mol at the nonlocal level (the use of the different calculation levels is due to the fact that the optimization at the local level gives a reasonable structure and the nonlocal calculation is adequate for estimating the energy value). Since the only use of the Morse potential in the MD simulation of the bulk Pd crystal did not give perfect consistency of the equilibrium bond length, the repulsive potential was utilized for compensating the shortage of the mutual interactions which should be included in the system of the higher coordination state. The lattice parameter of the simulated bulk Pd crystal was consistent with the actual bulk Pd crystal within 0.0006 Å. The geometric structures of Pdn (n ) 1-6) clusters were reported by Valerio and Toulhoat.28 It was indicated that the bond length between the Pd atoms increased with the increase of the numbers constituting the cluster, approaching the bond distance of the bulk Pd crystal, which supports the reasonableness of the adoption of the repulsive potential reflecting the structural features of the bulk crystal. The surface energy of
Yamauchi et al. TABLE 1: Surface Energy of the Relaxed (100) Face of Pd Crystal surface energy (eV/atom) MD EAM FP-LMTO FPTE experimental (average face)
0.85 0.5 0.89 1.00 0.74
the (100) plane of the Pd crystal obtained from the MD simulation using the Pd-Pd potentials described above is shown in Table 1. For the comparison of the MD result with other reported results, the surface energies obtained from EAM (embedded atom method),29 FP-LMTO (full-potential linearmuffin-tin-orbital) method,30 and FPTE (first-principles totalenergy) calculation31 are also shown. The surface energy evaluated from the MD calculations is close to the FP-LMTO result and is similar to the FPTE result and the experimental result.32 Although direct comparison with the experimental results does not have a tight relation because the kinds of planes could not be specified, the coincidence found in the comparison with the theoretical results, though showing a small difference, indicates the applicapability of the inclusion of the repulsive term in describing the metal-metal interactions. 3. Simulation Procedure The precise extraction of the similarity and the difference of atomistic phenomena occurring in supported particles needs attention focused on the exclusion of the intricate incidents. The avoidance of the intricacies is enhanced by the introduction of the regularity into the aspect of the aggregate; for the bulk and slab crystals, the regularity ensuring the compensation of the occurrence of the intricate events corresponds to the periodicity in the long range, and for the cluster, the symmetric particle structure satisfies the aim. In designing the cluster, the parameter reflecting the regularity is the shape; the specification of the shape defines the kinds of side and top surfaces. The consecutive definition of the size gives the plane structure of the interface layer. The truncated pyramid shape, which seems to be reasonable as the symmetric particle shape that contributes to the decrease of the intricacies because the planes of the low index numbers appear on the outside of the cluster, was adopted for all Pd clusters. The relative atomic configurations in the cluster were motivated by the application of the face centered cubic (fcc) structure of the structural property of the bulk Pd crystal. The 〈001〉 direction of the cluster was parallel to the 〈001〉 direction of the substrate; this relation of the directionality also seems to contribute to the enhancement of the lessening of the intricacies, and the formation of the epitaxially supported particles in the experiments33,34 possibly occurred as the results of the compensation of the atomistic intricacies. Two types of plane structure, corresponding to the atomic configurations of the (001) and (002) planes of the fcc crystal, turn up as the structure of the interface layer repeatedly, according to the change of the cluster size. Thus the contrasting points about the aspect of the designed clusters are perceived as the kinds of plane of the interface layer. To encourage the decrease of the intricate incidents, the individual systems undergo simulation conditions for 1000 cycles with a time step of 0.1 × 10-15 at 300 K. Successive MD simulations for the detailed analysis were carried out under the conditions for 20 000 cycles with a time step of 2.5 × 10-15 s at 300 K. These MD calculations were performed by utilizing the MXDORTO program developed by Kawamura et al.35
Pd Clusters Supported on MgO(001) Surface
Figure 1. Top view of the 20 000th time step of the MD calculations (a) and numerical scheme of the side surfaces (b) of Pd127 cluster supported on the MgO(001) surface at 300 K.
4. Visualized Images and Numerical Results 4.1. Surface Atomic Rows. The phenomenological recognition on the surface structure of the particle is meaningful for the analysis of catalytic reaction and particle growth as the fundamental knowledge. Figure 1a shows the CG pictures of a Pd127 cluster (2 nm) supported on the MgO(001) surface, which corresponds to the configuration of the 20 000th time step at 300 K. All atoms of the MgO and the Pd cluster are represented by a sphere-shaped model with ionic or metallic radii, respectively. The Pd127 cluster slightly migrated on the MgO(001) surface, chiefly along the 〈110〉 direction of the MgO substrate; for example, the displaced distance of the center atom of the interface Pd layer was 1.563 Å. Regarding the configurations of the surface atoms as the rows, it is recognized that Pd atoms on the top and side surfaces of the cluster formed a structure similar to the (001) and (111) planes of a fcc crystal, respectively. Thus, based on the recognition of the structural features of the particle perceived from the visualized images, it is noted that the bulklike planes can be retained in such a small cluster surface. The manner of the sight analysis along the outline and ridge of the cluster gives the apparent recognition of the disorder; though the structure of the four corners of the lowest Pd layer was the same initially and showed symmetry four times, the equilibrium structure around two corners was disordered and the Pd rows corresponding to the ridges of the cluster were not straight. The numerical structural characteristics of the side surfaces of the cluster were estimated from the arrangements of the atomic rows projected in the xy-plane, which gives a quantitative perception of the qualitatively perceived features of the top image. Here the atomic rows taken into consideration are the surface Pd rows along 〈220〉 and 〈22h0〉 directions of the MgO substrate. Each atomic row was mathematically approximated by linear equations including gradient and intercept as variables.
J. Phys. Chem. B, Vol. 102, No. 5, 1998 797 The equations were obtained from x and y coordinates, except for z coordinates; each equation is equivalent to the image of the atomic row projected in the xy-plane and indicates that the interval distance between neighboring liner equations corresponds to the lattice space of the (220) and (22h0) planes of the cluster. After calculating the linear equations using the coordinates obtained in each MD cycle, both the gradients and the intercepts were averaged by the number of MD cycles. The difference between actual and ideal (1.0 or -1.0) gradient values ranged from 0.0006 to 0.0062. This small diversity of the gradient ensures the validity of the linear approximation of the rows and enables us to define lattice space as the distance between neighboring rows. The values of both lattice length and row deviation of the Pd127 cluster, obtained from the above procedure, are shown in Figure 1b. Here, the increase of the number assigned to a surface Pd row corresponds to the increase of the height value of the row. The larger deviation was found in the slopes: the first and third rows in slope A (0.075 and 0.069 Å2) and the first row in both slope B and slope C (0.048 and 0.044 Å2). These findings indicate that the structural property of the surface atomic row as a line is relatively irregular, especially for the first rows. The surface lattice length ranged from 0.764 to 1.668 Å, and these lattice spaces were distributed on the slopes unsymmetrically. In slope A, the lattice space between the second and third surface rows was elongated (+0.293 Å) and the space between the third and fourth rows was shortened (-0.330 Å), comparing with lattice spaces of the (220) and (22h0) planes expected from bulk Pd crystal (both are 1.375 Å). This large difference between actual and ideal lattice spaces can be found in other slopes. The increase of the lattice length occurred between the third and fourth rows in slope B (+0.217 Å), between the second and third rows in slope C (+0.116 Å), and between the second and third rows in slope D (+0.205 Å). The large decrease of the lattice space between the first and second rows occurred in both slope B (-0.336 Å) and slope C (-0.611 Å). Although the distribution of these marked change of space between the surface atomic rows was not regular, the occurrence of the difference larger than about 0.3 Å in absolute value was correlated with the position of the surface row. The top image of the Pd82 cluster (1.7 nm) supported on the MgO(001) surface at 300 K is shown in Figure 2a. This image obtained by CG techniques corresponds to the atomic configurations of the 20 000th cycle of the MD calculations. The slight migration observed in the case of the Pd127 cluster did not occur. This lack of migration indicates that the atomic arrangement of the (002) plane of the interface layer may be suitable for the plane structure of the MgO(001) surface. In this cluster size, the atomic arrangement similar to the (001) and the (111) planes of the fcc crystal is also recognized on the top and the side surfaces of the cluster. The shape of the cluster was more symmetric than the Pd127 cluster. However, from the concentrated sight analysis of Figure 2a, it is recognized that Pd atoms forming the cluster surface slightly changed equilibrium positions, which is clearly found in the ridges and the outline of the cluster. The estimated values of the lattice space and the row deviation of the surface Pd rows of the Pd82 cluster along the 〈220〉 and 〈22h0〉 directions of the MgO substrate are schematically shown in Figure 2b. The degree of deviation was not so remarkable as that of the Pd127 cluster, which means the more regular property of the surface atomic rows as a line. Although the values of the lattice space of the Pd82 cluster are distributed in the narrow range 1.255-1.552 Å, the arrangement of the spaces
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Figure 3. Side images of Pd127 (a) and Pd82 (b) clusters on the MgO(001) surface at the 20000th time step of the MD simulation at 300 K.
Figure 2. Top image of the 20 000th cycle of the MD simulation (a) and schematic diagram of the side atomic rows (b) of the Pd82 cluster supported on the MgO(001) surface at 300 K.
on the side surfaces was not a symmetrical distribution, similar to the unsymmetric distribution of the Pd127 cluster. These findings on the clusters suggest that the relatively irregular distribution of the lattice length can occur on the metal particle surface and this occurrence does not depend on the structural property of the surface atomic row as a line, although the degree of the row deviation influences not the occurrence but the degree of the lattice length, as found in the Pd127 cluster. The length difference between the actual and ideal lattice spaces was smaller than that of the Pd127 cluster; enumerating the chief values of the difference, the space between the first and second rows was elongated in slope A (+0.154 Å), was elongated in slope B (+0.177 Å), and was shortened in slope C (-0.120 Å); the space between the second and third rows was elongated in slope A (+0.119 Å), was elongated in slope B (+0.119 Å), was shortened in slope D (-0.100 Å), and was shortened in slope C (-0.086 Å); and the space between the third and fourth rows was shortened in slope D (-0.103 Å). Although the antisymmetric relation between slope A and slope C seems to be recognized from the distribution of the marked values of the difference, the overall aspect of the difference between the actual and ideal values was not regular. This relatively irregular distribution of the difference was also recognized in the Pd127 cluster. Therefore it is concluded that elongation and contraction of the spaces can occur on the metal particle surface irregularly, and this occurrence of the irregular fluctuation of the spaces is independent of the occurrence of the slight migration of the particle, though the degree of the irregularity of the distribution seems to be contributed by the migration of the cluster and the plane structure of the interface layer. 4.2. Height Characteristics of the Layers. The side view of the Pd127 cluster is shown in Figure 3a. The clearly outlined atomistic images on the MgO substrate correspond to the Pd atoms composing the side surfaces of the cluster. From the recognition of the structure of the particle in the direction parallel to the substrate surface, it is found that the equilibrium positions of the Pd atoms are not perfectly the same in each layer, although it is obviously recognized that the atoms constituting
Figure 4. Numerical schematics of height deviation (noted as H dev. in Å2), lattice length (Å), and identification difference (noted as ID diff. in Å2), corresponding to Pd127 (a) and Pd82 (b) clusters on the MgO(001) surface at 300 K, respectively.
the inner and outer parts of the cluster form the planar layer because the Pd atoms were not displaced drastically. Figure 3b displays the side image of the Pd82 cluster on the substrate. Similar to the Pd127 cluster, the height disunity of the atoms occurred in each layer of the Pd82 cluster. However, from the symmetrical comparison of the positions of the atoms belonging to the individual layers, the diversity of the degree of the disorder is perceived; the lateral atomic configurations of the Pd82 cluster were not as irregular as those of the Pd127 cluster. The quantitative perception of the side view is attained by evaluating the height deviation of the layer and the length of the interlayer. Here, the height deviation is defined as the measure of the structural disorder of the layer as a plane. The estimation of the height deviation was performed by making a program in which the input data were the coordinates of the atoms obtained from the MD calculations. The procedure to obtain the height deviation values using the data in one cycle of MD calculation is as follows: defining the height of the layer as the average height by dividing the sum of the height value of the atoms by the number of atoms composing the layer, cumulating the square number of the difference between the height of the layer and the height of the atom, and dividing the cumulated value by the number of atoms composing the layer. Simultaneously, the length of the interlayer was evaluated from the use of the value of the layer height, on average. The height deviation and the interlayer length of the Pd127 cluster are shown in Figure 4a. The time-averaged values of the height deviation of each layer were 0.010, 0.017, 0.016, 0.012, and 0.009 Å2, for the first, second, third, fourth, and fifth
Pd Clusters Supported on MgO(001) Surface layers, respectively. Here, the assigned numbers for the layers correspond to the order of the smallness of the height of the layer assuming the substrate surface as the criterion of height. The degree of deviation of these values the atomic height enables one to view the layer as a line. Apparently, the height disunity of the atoms belonging to the layer tended to decreas with the increase of the layer height. However, the height deviation of the interface (first) layer was smaller than the second layer. This discontinuity of the change of the deviation suggests the less uniform conjunction of the interface and second layers. The interlayer distance estimated from the average layer heights were 2.113, 1.988, 1.972, and 1.999 Å, for the first-second, secondthird, third-fourth, and fourth-fifth interlayers, respectively. Since the lattice length of the Pd(002) plane expected from the bulk a Pd crystal with Pd-Pd distance of 2.7504 Å is given as 1.945 Å, the elongated lengths were 0.168, 0.043, 0.027, and 0.054 Å, for the first-second, second-third, third-fourth, and fourth-fifth interlayers, respectively. The dilation of the cluster averaged 0.073 Å (3.8%). A relatively wider space between the first and second layers indicates the possibility of the occurrence of the different structural feature in the xy-plane of the first and second layers. In the upper interlayers, the degree of the dilation decreased with the increase of the value of the height of the layer. However the lattice expansion increased again in the top interlayer. Figure 4b shows the height deviation and the interlayer length of the Pd82 cluster. The calculated values of the height deviation of the Pd82 cluster were 0.004, 0.006, 0.005, and 0.004 Å2, corresponding to the first, second, third, and fourth layers, respectively. Although the deviation of each layer of the Pd82 cluster was less than the Pd127 cluster, the decreasing trend of the height deviation and the smaller height deviation of the first layer were the same characteristics found in the Pd127 cluster. This similarity gives the interpretation that the manner of the distribution of the height deviation does not depend on the occurrence of a slight migration. The time-averaged lattice spaces between the first and second layers, between the second and third layers, and between the third and fourth layers were 1.995, 1.952, and 1.987 Å, respectively. These values were relatively smaller than those of the Pd127 cluster. The values of the elongated lengths were 0.050, 0.007, and 0.042 Å, for the first-second, second-third, and third-fourth interlayers, respectively. The increase of the dilation rate in the top interlayer was consistent with the results of the Pd127 cluster. The lattice expansion of the Pd82 cluster averaged 0.033 Å (1.7%). This smaller lattice expansion as an average suggests that the in-plane structure of the Pd82 cluster is not so similar to that of the Pd127 cluster. 4.3. Inner Structures and Interaction Sites. The inner structure of the clusters was investigated by CG techniques, which allows visualization of the sectional plane. The heterojunction structure of the Pd127 cluster is shown in Figure 5a. The center of the interface (first) layer was constituted by one Pd atom. The structure of the interface layer was not as regular as the basal plane of the bulk Pd crystal. The interaction sites of the Pd atoms attaching to the substrate could be grouped as 4-fold sites and 3-fold sites (see Figure 6a), and the Pd atoms occupying the bridge site (between Mg and O atoms) were found. This variety of the interaction site could arise from the migration of the cluster. The structure of the second layer was more ordered than the first layer (see Figure 5b), similar to the (002) plane of the fcc crystal. Two different sites were occupied by the Pd atoms of the second Pd layer; most of the Pd atoms were on the 4-fold site, and other Pd atoms were on the 3-fold
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Figure 5. Sectional plane images of the 20 000th cycle of the MD calculations of the Pd127 cluster on the MgO(001) surface at 300 K; interface layer (a) and second layer (b), respectively.
Figure 6. Schematic illustrations of interaction sites of the Pd atoms on the MgO substrate (a) and on the Pd layer (b), respectively.
site (see Figure 6b). In the upper (third, fourth and fifth) layers, the configurations of the atoms were more regularly ordered than the second layer and the 4-fold sites were just occupied (naturally except for the atoms at each layer corner). From these findings on the structure and the interaction site of the Pd atoms, it is noted that the structural disorder in the xy-plane of the layer decreases with the decrease of the variety of the occupation site. The heterojunction structure of the Pd82 cluster is depicted in Figure 7. Around the imaginary center defined by the cross point of the long and the short axes of the interface layer, four Pd atoms lie on the substrate surface symmetrically. This means that the center of this layer is composed of four Pd atoms. The in-plane structure of the interface Pd layer was relatively symmetrically ordered. The Pd atoms directly interacting with the MgO substrate were almost completely on the center of the 4-fold site, which indicates that the occupation of the 4-fold site is one of the possible cases as the interaction site. This uniformity of the kind of interaction site of the Pd82 cluster was in contrast to the variety of the site in the Pd127 cluster. In the upper (second, third, and fourth) Pd layers, almost the same structural features were found; the Pd atoms of the upper layer
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Figure 7. Heterojunction structure of the 20 000th time step of the MD calculations of the Pd82 cluster on the MgO(100) surface at 300 K.
were placed on the 4-fold site of four Pd atoms of the lower layer, and the structure of the layer was quite similar to the atomic arrangement of the corresponding plane of the fcc crystal. 4.4. Identification Difference. Although there is no criterion to estimate the in-plane structural disorder of the particle, if the regularity is observed in the in-plane structure, the degree of the disorder can be estimated from the degree of the identity between two-dimensional positions of two atoms (host and guest atoms) which are able to be a symmetrical pair related to each other. Although the disorder of the in-plane structure is remarkable, the degree of the disorder can be defined as the number counted when no atom can be a guest atom of the host atom in finding the symmetrical pair. Here, the estimation ways along the former and the latter manners are named as the identification analysis and the guest loss analysis, respectively. The procedure of the identification analysis using MD results of one cycle of the MD calculation contains four steps. First, defining the center atom of the layer as a plane, if one atom can be found in the narrow range near the cross point of the long and short axes which are defined as the length of the layer in the x and y directions, the found atom is defined as the only center atom; if no atom can be found in the narrow area, after searching the wider area around the cross point, some atoms are defined as the center atoms. Second, the host vector is calculated from the center atom to the host atom, the expected vector is obtained from the inversion of the sign of one (x or y) component of the host vector, and the expected guest position is defined from the use of the expected vector. Third, the guest position is found by utilizing the expected vector and estimating the difference between the coordinate components of the found and the expected guest positions. Fourth, the sum of the square values of each component (x and y coordinates) difference is obtained, the square root values of the sum are accumulated, and estimating the value of the identification difference is estimated by averaging the accumulated value by the number of atoms composing the layer. To simplify the description, the results for the guest loss analysis were eliminated. The identification difference values of the Pd127 cluster (see Figure 4a), reaveraged by the cycle numbers of the MD simulation, were 0.050, 0.013, 0.008, 0.005, and 0.008 Å, for the first, second, third, fourth, and fifth Pd layers, respectively. The larger value of the first layer reflects the variety of the interaction sites. The value of the identification difference decreased in the order from the first to fourth layer and increased in the fifth layer. This tendency to decrease indicates the stepwise recovery of the degree of the symmetry of the in-plane atomic configurations. The values of the identification difference of the Pd82 cluster (see Figure 4b) were 0.011, 0.009, 0.005,
Yamauchi et al. and 0.008 Å, for the first, second, third, and fourth Pd layers, respectively. In contrast to the Pd127 cluster, the identification difference of the first layer was not remarkable, due to the uniformity of the interaction sites of the Pd atoms of the interface layer of the Pd82 cluster. However, the decrease trend of the identification difference and the reincrease of the difference in the topmost layer were consistent with the Pd127 cluster. Therefore it is suggested that the tendency of the change of the identification difference does not depend on the degree of the formality of the interaction sites, although the variety of the occupation site induces a larger identification difference and the formality of the site provides a smaller difference of the symmetric pair relation. Taking into consideration the results that the height deviation of the first layer was smaller than the second layer and the decrease trend of the height difference occurred from the second to the top layer, perceived in both clusters, it is obviously clarified that the relaxation of the lattice misfit between the metal particle and the substrate is achieved mainly not by the increase of the height deviation but by the decrease of the degree of the symmetry of the in-plane atomic configuration of the interface layer. In addition, it is pointed out that the height deviation of the upper layer is influenced by the in-plane structure of the lower layer, eliminating the top layer. 4.5. Lateral Characteristics of the Layers. The lattice spaces of the clusters in the direction parallel to the MgO(001) surface were evaluated from the calculation of the line equations using the x and y coordinates of the atoms in each MD cycle. The Pd atoms dislocated from the atomic rows were excluded from this evaluation. The lateral lattice length was defined as the interval distance between the near neighboring atomic rows. The estimated values of the lateral lattice spaces of the Pd127 cluster are shown in Figure 8a. The change of the lattice length of the first layer occurred contrastively; the four spaces between the lattices continuing from the edge were elongated and the successive five spaces were shortened, comparing with the (200) lattice length of the bulk Pd crystal. The occurrence of this contrastive manner of the change was due to the slight migration of the cluster. In the second layer, the three spaces from the edge were dilated. The successive five spaces were contracted, and the last space was expanded. In the upper (third, fourth, and fifth) layers, the manner of the change of the lattice space was relatively symmetric; the lattice spaces near the edges were dilated, and the spaces around the middle of the layer were contracted. Averaging the values of the lattice length in each layer gave the arranged configuration of the lattice space; the average lattice space showed a slight expansion (0.04-0.77%) in all layers and the elongated length was 0.001, 0.001, 0.015, 0.005, and 0.003 Å, for the first, second, third, fourth, and fifth Pd layers, respectively. The rate of the lattice dilation occurring in the 〈001〉 direction was 3.8%. Thus it can be specified that the anisotropic lattice expansion occurred in the Pd127 cluster. This anisotropy of the dilation is due to the occurrence of partial contraction in each layer; the partial contraction occurring in the layer contributes to the decrease of the lateral dilation on average and to the increase of the rate of the vertical expansion. The values of the lattice length of the Pd82 cluster are shown in Figure 8b. The larger and smaller values of the lateral length were more symmetrically distributed in each layer; the smaller values of the lattice spaces were distributed around the middle of the layer, and the larger values were found near the edges of the layer. In both the first and second layers, all lattice spaces were expanded. The contraction of the spaces was found around the middle of the third and fourth layer. The shortening of the
Pd Clusters Supported on MgO(001) Surface
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Figure 8. Schematic diagrams of the distribution of the lateral lattice length of Pd127 (a) and Pd82 (b) clusters on the MgO(001) surface at 300 K, respectively.
spaces in the top surface was a common characteristic of both clusters. The arrangment of the Pd82 cluster was provided by the average of the lattice length of each layer. The mean values of the lattice length showed the expansion in each layer. The rate of the lattice expansion increased with the decrease of the layer height (0.28%-1.84%); the elongated lengths were 0.036, 0.024, 0.012, and 0.005 Å, for the first, second, third, and fourth Pd layers, respectively, and averaged 0.020 Å (1.03%). Since the rate of the dilation of the Pd82 cluster in the direction perpendicular to the substrate surface was 1.7%, it is specified that the lattice spaces of the Pd82 cluster were expanded in both directions parallel and perpendicular to the substrate surface. This relatively isotropic lattice dilation of the Pd82 cluster was in contrast to the anisotropic expansion of the Pd127 cluster. As mentioned in section 4.1, a slight migration occurred in the Pd127 cluster, which induced the lattice contraction in half of the interface layer. The occurrence of this contraction induced a shortening of the spaces of the second and third layers successively. Therefore, phenomenologically speaking, the migration of the cluster on the substrate can induce anisotropic lattice dilation. On the other hand, the Pd82 cluster facing the (002) plane of the substrate did not migrate. This lack of migration enabled the dilation in all spaces of the interface layer to occur and provided the relatively well arranged in-plane atomic configurations. Thus the isotropic expansion of the metal particle presupposes the uniformity of the interaction site contributing to the regularity of the atomic configuration. The dilation of the Pd127 cluster in the direction perpendicular to the substrate surface caused by the occurrence of the in-plane contraction in each layer, especially contributed to the shortening of the lattice space of the interface layer. Taking into consideration the results that the identification difference drastically decreased between the first and second layers and the height deviation gradually decreased, it is suggested that the occurrence of the contraction contributes to the increase of the deviation of the atomic heights in the layer. Thus it is proposed that the height deviation can be a measure of the recognition of the occurrence of the dilation induced by the inplane contraction. The characteristics of the structural features of the side surfaces were little influenced by the migration of the cluster, though the degree of the structural irregularity evaluated from the space of the surface atomic row was enhanced by the
regularity of the inner structure of the cluster. The apparent independence of the top layer from the kind of plane structure is recognized from the similarity of the findings found in both clusters: the larger identification difference of the top layer than the underlying layer, the enhanced dilation of the top interlayer, and the manner of the change of the lateral lattice spaces. Therefore it is suggested that the unsymmetrical atomic row arrangement of the side surfaces and the lateral lattice contraction of the top surface may be reasonable as particular phenomena of the surfaces of the metal particle on the support. Assuming a the relation between the size of the particle and the directionality of the lattice dilation, it is proposed that in analyzing the detailed structural features of particles with the size distribution we have to take into consideration two presuppositions; mutual consistency (i) of the degree of the height deviation and (ii) of the degree of the in-plane symmetry of the interface layer among supported particles. If both presuppositions are observed in all particles or recognized in most of the particles, the correlation between particle size and lattice expansion is recognized in the directions parallel and perpendicular to the substrate surface. On the other hand, if the contribution of particles deviating from the presuppositions is not negligible, the correlation manner depends on the direction. 5. Discussion The structural characteristics of the simulated clusters by the MD method were compared with some valuable reports, as described below. Those results supply the abundant knowledge and enhance the improvement of the perception of the atomistic phenomena of the metal particles. However, it is not specified if the change of the lattice spaces occurred in all spaces or in some spaces of the particle. Moreover, it is not clarified that what kinds of particles contribute to the observation of the lattice expansion, since the image of the cluster, evaluated from the results such as diffraction spots, supplies the average state of particles because the actual samples are vary in size, the distribution of which was characterized in detail.8,36,37 Although the observation of the narrow area gives characterized structural features, there exists the difficulty in perceiving the actual interface layer, which seems to influence the structure of the upper layers strongly. Therefore usually the comparison of the
802 J. Phys. Chem. B, Vol. 102, No. 5, 1998 experimental results with the simulated results can make sense in a limited meaning of the qualitative recognition of the difference or the coincidence obtained from the results of the experiments and the simulations. Because a difference among the results occurs, the most important thing is the interpretation based on the accumulation of findings. However, since caution should be used when suggesting that particle size depends on the cluster shape used in analysis,38,39 the value of the diameter of the particle depends on how one measures it, which means the possibility of a difference between the particle images drawn from the experiments and those drawn from the simulations. However, if a closer correspondence between simulated image and actual statue is possible, the quatitative comparison will contribute to the improvement of the perception. In addition, note that the (100) plane is equivalent to the (010) and (001) planes and the (200) plane is equal to the (020) and (002) planes in bulk Pd crystal. The lattice parameters of Pd particles (1.6-2.7 nm) epitaxially supported on the MgO(100) surface were investigated by K. Heinemann et al.34 The measurements indicated that the Pd lattice spaces estimated from the Pd diffraction spots increased with the decrease of the mean diameter of the particles. Since the diffraction spots corresponding to the bulk lattice spaces between (200) planes of the MgO substrate were used as the standard of the evaluation, the increase trend of the Pd lattice spaces reveals the decrease trend of the lattice misfit. These lattice expansions (2-4%) corresponded to the structural feature parallel to the (100) surface of the substrate. Hence, it is possible to specify that the agreement of the trend of the lattice expansion parallel to the substrate surface was shown between their experimental results and the simulated MD results. However, the observed lattice dilation reflects the average state of the particles, and the simulation results reflect the individual state of the particle. Therefore the experiments the trend of the dilation in the direction parallel to the support surface, and the simulations supply the detailed characteristics of the structure and the possibility of such kinds of atomistic phenomena. Giorgio et al. also reported on the lattice dilation of Pd particles on small MgO cubes.40 The lattice parameters of a (200) and (020) planes of the Pd particles having the (100) orientation to the substrate (100) surface were estimated from the microdiffraction pattern produced by an electron beam with a diameter of 20 nm. The substrate diffraction spots were also used as the internal standard. It was indicated that the lattice expansion increased with the decrease of the particle size; e.g., about 1.5% and 2.8% for the 6 nm and 3 nm particles, respectively. This observed result also enables us to specify that the tendency of the lateral average lattice dilation of the MD simulations is consistent with the experiments, though containing paradoxical meanings. The trend of the dilation observed in their experiments show a uniform increase of the expansion in the parts where dilation occurs, because the structural characteristics of the particle of such a size are possibly governed by the structural property of the bulk Pd crystal predominantly, according to the increase of the number of layers. However, the MD results indicated the possibility of the weakening of the relationship between particle size and lattice dilation. Therefore the coincidence of the experimental and simulation results is recognized as the fact that the lateral dilation may be the definite phenomenon in the metal particle. In their experiments of the cross sectional observation, the diffraction patterns of the isolated particle were investigated by convergent-beam electron diffraction with a probe diameter of 4 nm. This observation indicated that both lattice parameters
Yamauchi et al. parallel and perpendicular to the substrate surface were expanded to the same degree. In our simulations, the isotropic dilation occurred in the Pd82 cluster, and the anisotropic lattice expansion took place in the Pd127 cluster. Taking into consideration the occurrence of the migration in the simulation of the Pd127 cluster, it is suggested that the anisotropic dilation is a possible characteristics of the atomistic structure for the migrated metal particle. In their reports41,42 the lateral lattice dilation of each Pd layer of the small Pd particles (2-6 nm) was also evaluated from the results of the HRTEM. It was indicated that the lattice distance of the Pd layer was accommodated with the lattice length of the MgO at the interface and the decrease of the dilation occurred as the distance from the interface increased. MD results depicted in Figure 8 also showed the same trend in the decrease of the lateral lattice dilation. Although the qualitative coincidence was shown in comparing the MD results with the reported HRTEM results, the rate of the dilation was not perfectly the same. To supply the a quantitive explanation on this matter, a detailed investigation will be reported elsewhere. The characteristics of the interface and the sub-interface layers of metal particles were reported by T. Kizuka et al.43 Their experimental results about the system of Au(100)/MgO(100) indicated that the lattice spaces between (020) planes of the interface and the sub-interface layers of Au particles were expanded when the 〈001〉 direction of the particle was parallel to the 〈001〉 direction of the support. This observation on the lattice expansion parallel to the substrate surface proves the occurrence of expansion in the interface and the sub-interface layers of the clusters simulated in our MD calculations. Furthermore, taking into consideration the fact that Au and Pd metals are the typical kinds giving smaller (3.2%) and larger (7.6%) lattice misfits for the MgO crystal, it is proposed that metal particles having atomic configurations similar to a fcc structure undergo lateral lattice dilation in the interface and subinterface layers as a universal structural property. In their experiments it was indicated that the lattice spaces between (022) planes of the interface and the sub-interface layers were not expanded when the Au〈011〉 direction was parallel to the MgO〈001〉 direction, after the rotational movement of the particle on the MgO(100) surface occurs. Although the finding of the lattice expansion of (022) planes is more difficult than (020) planes because the lattice space of the (022) planes (1.4418 Å) is smaller than the (020) planes (2.0915 Å), if understanding the meaning phenomenologically, their observation can be the actual evidence of our finding that the slight migration of the cluster reduces the rate of lateral expansion below a perceivable degree. Moraitis et al. studied the lattice relaxation of the surface of transition metals44 by using the tight-binding scheme. Their investigation of the (100) surface of the Pd slab crystal indicated that the first interlayer space of the surface was elongated by 0.072 Å (expansion of 3.7%), compared to the corresponding lattice space of the bulk Pd crystal. Quinn et al. experimentally studied the relaxation of the Pd (100) surface,45 utilizing lowenergy electron diffraction (LEED) technique. Their measurements on the normal incidence of the primary electron beam indicated that the lattice expansion of 0.056 ( 0.03 Å (2.8 ( 1.5%) occurred in the first interlayer. In our MD results the values of the elongation of the first interlayer were 0.055 Å (2.8%) and 0.042 Å (2.1%) for the Pd127 and Pd82 clusters, respectively. The qualitative agreement among those results indicates the consistency of the directionality of the lattice change of the first interlayer. Thus it is specified that the
Pd Clusters Supported on MgO(001) Surface occurrence of the dilation of the top interlayer in our MD simulations is a positive atomistic phenomenon. Therefore, this certainty enhances the sureness of the occurrence of the lateral lattice contraction of the top layer of metal particles, as occurred in our MD simulations. Summary The structural features on the ultrafine metal Pd particles supported on MgO(001) surface were supplied by the qualitative and quantitative estimation of the results of the MD calculations. The visualized images showed the structural disorder of the surface atomic rows and distinguished the interaction sites. The numerically evaluated results enabled us to recognize atomistic phenomena such as the dilation and the contraction of the lattice spaces, the height deviation of the metal atoms constituting the layer, and the identification difference of the symmetric pair atoms. The salient findings about the similarity and the difference extracted from the evaluation of the independence and the interdependence of the atomistic characteristics can be summarized as follows: (1) The dilation and contraction of the length between the surface atomic rows can occur on the metal particle surface irregularly; these structural features of the metal surfaces did not depend on the occurrence of the slight migration of the particle and on the structural property of the row as a line. (2) The degree of both height disunity of the atoms and the lattice dilation parallel to the support surface showed the similar decrease trend, according to the increase of the layer height value; these structural characteristic were independent of the kinds of plane structures of the interface layer of the metal cluster. (3) The decreased dependency of the change of the identification difference on the formality of the occupation site and the discontinuity of the change of the height deviation suggest that the lattice misfit can be relaxed by the reduction of the degree of symmetry of the in-plane atomic configuration of the interface layer. (4) The partial lateral lattice contraction of the layer of the metal particle contributes to the rate of the reduction of the average lateral dilation of the layer and to the rate enhancement of the vertical expansion of the interlayer lattice. (5) The degree of uniformity of the kinds of interaction sites of the metal particles influences the atomistic structural characteristics of the particles as presuppositions. Furthermore the common features about the atomistic structural characters of the metal particles on the substrate were extracted from the estimation of the findings of the mutual correlations of the structural features: (1) If focusing attention on the independence of the occurrence of the lattice length change, the lateral lattice dilation of the intralayer is proposed as a universal structural feature of metal particles on the support. (2) The consistency about the directionality of the change of the lattice length of the top interlayer, recognized in comparing our results with the results of other workers, indicates that the lateral lattice contraction of the top intralayer is the particular phenomenon of the top surface of the metal particle on the support. References and Notes (1) Cordatos, H.; Bunluesin, T.; Gorte, R. J. Surf. Sci. 1995, 323, 219. (2) Garbowski, E.; Jantou, C. F.; Mouaddib, N.; Primet, M. Appl. Catal. A: General 1994, 109, 277.
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