Atomistic simulation of point defects at low-index surfaces of noble metals

The formation energies and the migration energies of an isolated vacancy and adatom formed on low-index surfaces are calculated with MAEAM for three noble metals Cu, Ag and Au. The results indicate that the formation energies of an isolated vacancy or adatom increase with increasing atom density in the sequence (1 1 0) → (1 0 0) → (1 1 1), and it is more difficult to form an adatom than to form a vacancy at the same surface. For the mobility of an isolated vacancy, the migration energy grows in the sequence (1 0 0) → (1 1 0) → (1 1 1) for each noble metal. However, a much less migration energy is obtained for the migration of an adatom on (1 1 1) surface.     

Ab-initio pseudopotential study of electronic structure and chemisorption of oxygen on aluminium surface

Chemisorption of oxygen atom on aluminium (1 1 1), (1 1 0) and (1 0 0) surfaces is studied using ab-initio plane wave pseudopotential method based on density functional theory (DFT). Oxygen atom chemisorbed on three different high symmetry sites; top, short-bridge and hollow sites on the aluminium surfaces are examined. It has been found that the O-adatom adsorbed at the hollow site on aluminium (1 1 1), (1 1 0) and (1 0 0) plane yield energetically most stable structure. Calculation of chemisorption energies of O-adatom on aluminium surfaces shows that oxygen is most strongly bound to aluminium atoms on Al(1 1 1) plane and the calculated value of the chemisorption energy of O-adatom at the hollow site on Al(1 1 1) surface is 4.8 eV. In this work, the chemisorption energies calculated for O-adatom on Al(1 1 0) and Al(1 0 0) surfaces are reported for the first time. The electronic structures and the electronic charge density distributions of the oxygen chemisorbed aluminium surfaces are also investigated. Calculations show that for aluminium, p orbitals also contribute significantly along with the s orbitals during the bond formation with oxygen atom. Therefore, the possibilities of hybridizations lead to the strong bonding configurations.     

Calculation of the surface energy of bcc transition metals by using the second nearest-neighbor modified embedded atom method

The surface energies for 24 surfaces of all bcc transition metals Fe, Cr, Mo, W, V, Nb and Ta have been calculated by using the second nearest-neighbor modified embedded atom method. The results show that, for all bcc transition metals, the order among three low-index surface energies E_(1 1 0) < E_(1 0 0) < E_(1 1 1) is in agreement with experimental results and E_(1 1 0) is also the lowest surface energy for various surfaces. So that from surface energy minimization, the (1 1 0) texture should be favorable in the bcc films. This is also consistent with experimental results. The surface energy for the other surfaces increases linearly with increasing angle between the surfaces (h k l) and (1 1 0). Therefore, a deviation of a surface orientation from (1 1 0) can be used to estimate the relative values of the surface energy.     

The calculation of the surface energy of high-index surfaces in metals at zero temperature

We used the molecular dynamics simulation with interatomic potentials of the embedded atom method to calculate the high-index surface energies of the surfaces containing the 〈0 0 1〉 axis or 〈−1 1 0〉 axis in f.c.c. metal Al, Cu and Ni at zero temperature. We generalized an empirical formula based on structural unit model for high-index surfaces and present some new formulas that can be used to estimate the surface energy and structural feature of high-index surfaces very well. The results show that the closest surfaces have the lowest surface energy and the surface energies of the closest (1 1 1) surface and the next closest (1 1 0), (1 0 0) surfaces are the extremum on the curve of surface energy versus orientation angle. We also calculated the b.c.c. metal Fe and obtained a similar result. The difference is that in the b.c.c. metal the surface energies of the closest (1 1 0) surface and the next closest (1 0 0), (1 1 2) surfaces are the extremum on the curve of surface energy versus orientation angle. The results of theoretical simulation and the empirical formula consist well with the experiment data.     

Ab initio comparative study of C54 and C49 TiSi2 surfaces

A theoretical comparison of C54 and C49 TiSi₂ surfaces is presented, using ab initio plane-wave ultrasoft pseudopotential method based on generalized gradient approximation (GGA). The different surface energies of TiSi₂ have not only been calculated out, but the preferential formation of C49 phase in solid-state reaction could be explained by smaller surface energies and Poisson's ratio of C49 TiSi₂ as well. As for polar C54 TiSi₂(1 0 0) and C49 TiSi₂(0 1 0) surfaces, the Si termination surfaces are more stable.     

Reconstructed (1 1 0) surfaces of FCC transition metals

The energies of the ideal, missing row (MR) and missing column (MC) (1 1 0) surfaces have been calculated by using modified embedded atom method (MEAM) for seven face centered cubic (FCC) transition metals Au, Pt, Ag, Pd, Rh, Cu and Ni. The results, that the MC reconstruction can not be formed for all metals, while the MR reconstruction can be formed naturally for Au and Pt, inductively for Ag, Pd, Rh and Cu and difficultly for Ni, are better than EAM calculated results in comparing with experimental results. In addition to the surface energy explanation, the results are also related to the surface topography and valence electron structure.     

Surface structure and solidification morphology of aluminum nanoclusters

Classical molecular dynamics simulation with embedded atom method potential had been performed to investigate the surface structure and solidification morphology of aluminum nanoclusters Al_n (n=256, 604, 1220 and 2048). It is found that Al cluster surfaces are comprised of (1 1 1) and (0 0 1) crystal planes. (1 1 0) crystal plane is not found on Al cluster surfaces in our simulation. On the surfaces of smaller Al clusters (n=256 and 604), (1 1 1) crystal planes are dominant. On larger Al clusters (n=1220 and 2048), (1 1 1) planes are still dominant but (0 0 1) planes cannot be neglected. Atomic density on cluster (1 1 1)/(0 0 1) surface is smaller/larger than the corresponding value on bulk surface. Computational analysis on total surface area and surface energies indicates that the total surface energy of an ideal Al nanocluster has the minimum value when (0 0 1) planes occupy 25% of the total surface area. We predict that a melted Al cluster will be a truncated octahedron after equilibrium solidification.     

Usage of pattern recognition scheme in kinetic Monte Carlo simulations: Application to cluster diffusion on Cu(1 1 1)

We have invoked a simple pattern recognition scheme in kinetic Monte Carlo simulations of post-deposition evolution of two dimensional islands on fcc(1 1 1) surfaces. On application of the technique to the diffusion of small Cu clusters (8-100 atoms) on Cu(1 1 1) we find that, at room temperature, clusters with certain magic numbers show stick-slip type of motion with striking patterns rather than the random paths followed by the others. At higher temperatures all clusters display random motion. The calculated diffusion coefficients show dependence on size and temperature with an effective barrier ranging between 0.62 eV and 0.84 eV. Small asymmetries in diffusion barriers lead to a large difference in the frequencies of adatom diffusion along the two types of micro-facetted steps on Cu(1 1 1) leading to consequences in their shape evolution. The pattern recognition scheme revealed 49 basic periphery single atom diffusion processes whose activation energy barriers were calculated using the nudged elastic band technique and interatomic potentials from the embedded atom method.     

Dynamic study of W atoms and clusters on W (1 1 1) surfaces

Using a field ion microscope, the diffusion behaviors and atomic processes of W atoms and clusters on W (1 1 1) surfaces were observed directly. The activation energy of W clusters diffusion on W (1 1 1) as a function of cluster size has an oscillatory and increasing behavior. But, the activation energy of a single W atom is especially high. The compact geometric structures are more stable and have higher activation energies of surface diffusion than structures with extra atoms at the periphery. Besides the terrace diffusion, other atomic processes such as the ascending, descending, detachment motion on W (1 1 1) surfaces were also observed. Unlike the general systems, their occurrence temperatures are quite near. These experimental results were used to discuss the formation mechanism of single atom W tips.     

Theoretical studies on the adsorption and decomposition of H2O on Pd(1 1 1) surface

To provide information about the chemistry of water on Pd surfaces, we performed density functional slab model studies on water adsorption and decomposition at Pd(1 1 1) surface. We located transition states of a series of elementary steps and calculated activation energies and rate constants with and without quantum tunneling effect included. Water was found to weakly bind to the Pd surface. Co-adsorbed species OH and O that are derivable from H₂O stabilize the adsorbed water molecules via formation of hydrogen bonds. On the clean surface, the favorable sites are top and bridge for H₂O and OH, respectively. Calculated kinetic parameters indicate that dehydrogenation of water is unlikely on the clean regular Pd(1 1 1) surface. The barrier for the hydrogen abstraction of H₂O at the OH covered surface is approximately 0.2-0.3 eV higher than the value at the clean surface. Similar trend is computed for the hydroxyl group dissociation at H₂O or O covered surfaces. In contrast, the O-H bond breaking of water on oxygen covered Pd surfaces, H₂O_ad + O_ad → 2OH_ad, is predicted to be likely with a barrier of ∼0.3 eV. The reverse reaction, 2OH_ad → H₂O_ad + O_ad, is also found to be very feasible with a barrier of ∼0.1 eV. These results show that on oxygen-covered surfaces production of hydroxyl species is highly likely, supporting previous experimental findings.     

The properties and structures of the mono- and the di- vacancy in Cu crystal

The structures and energies of formation and migration of the mono- and di-vacancy in Cu crystal have been described and calculated with modified analytical embedded atom method (MAEAM). The lattice relaxation is considered with molecular dynamics (MD) method at T=0 K. The results show the FN di-vacancy is the most stable and likely occurs in practice from the energy minimization. Compared with the mono-vacancy, the formation energy of the FN di-vacancy is higher than that of a mono-vacancy, but lower than that of two isolated mono-vacancy. The preferred migration mechanism of the FN di-vacancy is multi-jump of either vacancy (rotating the di-vacancy). The calculated migration energy of the FN di-vacancy is lower than that of a mono-vacancy, so the FN di-vacancy is easier to migrate. All of the calculated results are in good agreement with the experimental values.     

Surface structure and energy of B2 type intermetallic compound NiAl

The surface structure and energies for 22 surfaces of NiAl, an ordered intermetallic compound of B2 structure, have been studied by using embedded atom method. The results show that, for alternating Ni and Al surfaces with odd numbers of the sum of their three Miller indices, the energy difference between the Ni terminated surface and Al terminated surface increase linearly with increasing the interlayer distance. So from surface energy minimization, the Al terminated surface is favorable for each alternating Ni and Al surface. This is in agreement with experimental results. However, the energy of the (1 1 0) surface belonged to the other kind of the surface consisted of stoichiometric atomic layers and with even numbers of the sum of their three Miller indices, is the lowest in all two kinds of the surfaces. Therefore the (1 1 0) texture of NiAl appears mostly in the experiments.     

Anisotropy analysis of the surface energy of hcp (c/a < 1.633) metals

In this paper, anisotropy of the surface energy of 5 hcp metals Be, Hf, Ru, Ti and Y have been analyzed. The surface energies of three kinds of representative surfaces, (h 0 l), (h h l) and (h k 0) belong to [0 1 0], [] and [0 0 1] crystal band, respectively, have been calculated using the modified embedded atom method. For all 5 hcp metals, the (1 1 0) plane has the minimum surface energy in all 35 surfaces studied. Considering surface energy minimization solely, the (1 1 0) texture should be favorable in the hcp films. The fact that the short termination corresponds to much lower surface energy than long one implies the former is more stable for those surfaces having two possible terminations. Such as the prism plane (1 0 0), only the short termination was observed in experiment.     

Interactions of H with tungsten carbide surfaces: An ab initio study

Adsorption of atomic hydrogen at several coverages on three WC surfaces with occupation of W and C sites is studied using a DFT formalism and generalized gradient approximation. In all three cases, at low coverage, the H adsorption over the W on top site is clearly favoured. Beyond this coverage, the surface occupation of both W and C sites become possible. The calculated adsorption energies ΔE indicate chemisorption. The evolution of the DOS with the coverage is reported. Our results are complemented by determination of surface energies for the (0 0 0 1), (1 0 −1 0) and (1 1 −2 0) surfaces.     

A theoretical study of the water gas shift reaction mechanism on Cu(1 1 1) model system

The water gas shift (WGS) reaction is an important reaction system and has wide applications in several processes. However, the mechanism of the reaction is still in dispute. In this paper we have investigated the reaction mechanism on the model Cu(1 1 1) system using the density functional method and slab models. We have characterized the kinetics and the thermodynamics of the four reaction pathways containing 24 elementary steps and computed the reaction potential energy surfaces. Calculations show that the formate (HCOO) intermediate mechanism (CO + OH → HCOO → CO₂ + H) and the associative mechanism (CO + OH → CO₂ + H) are kinetically unlikely because of the high formation barrier. On the other hand, the carboxyl (HOCO) intermediate mechanism (CO + OH → HOCO → CO₂ + H) and the redox mechanism (CO + O → CO₂) are demonstrated to be feasible. Our calculations also indicate that surface oxygen atoms can reduce the barriers of both water dissociation and HOCO decomposition significantly. The calculated potential energy surfaces show that the water dissociation which produces OH groups is the rate-determining step at the initial stage of the reaction or in the absence of surface oxygen atoms. With the development of the reaction or in the presence of oxygen atoms on the surface, CO + OH → HOCO and CO + O → CO₂ become the rate-limiting step for the carboxyl and redox mechanisms, respectively.     

O-vacancy and surface on CeO2: A first-principles study

Atomic and electronic structures of CeO₂ (1 1 1), (1 1 0) and (1 0 0) surfaces are investigated using the first-principles density functional theory taking into account the on-site Coulomb interaction. Both the stoichiometric and O-deficient surfaces are examined in order to clarify the overall features. The CeO₂ (1 1 1) is found to be the most stable surface, followed by the (1 1 0) and (1 0 0) surfaces, consistent with experimental observations. Three surfaces exhibit different features of relaxation. Large relaxations are found at the (1 1 0) and (1 0 0) surfaces, while very small changes are observed at the (1 1 1) surface. It is found that the O-vacancy occurs more readily at the (1 1 0) surface as compared with the (1 1 1) surface. Furthermore, the formation energies of the O-vacancy in the surfaces are lower than that in the bulk. The energetically favorable O-vacancy locates in the second O-atomic layer for the (1 1 1) while at the surface layer for the (1 1 0). The excess electrons left with the removal of the O atom are distributed in the first two layers with certain (a considerable) fraction filling the Ce-4f states.     

Anharmonicity in Al vicinal surfaces of (1 0 0) with (1 1 1) step

Molecular dynamics simulations incorporating an analytic embedded atom potential have been used to investigate the atomic structure and surface order of the Al vicinal surfaces for the temperature up to 900 K. The relaxation, mean square vibrational amplitude, and structure factor as a function of temperature, and of the terrace width for the p(1 0 0) × (1 1 1) surfaces (2 ≤ p ≤ 10) are discussed. The obtained structure factor indicates that the anharmonic effect reduces with increasing terrace widths. The decrease of surface energy with increasing terrace width also supports this conclusion.     

Adsorption of SO2 on Li atoms deposited on MgO (1 0 0) surface: DFT calculations

The adsorption of sulfur dioxide molecule (SO₂) on Li atom deposited on the surfaces of metal oxide MgO (1 0 0) on both anionic and defect (F_s-center) sites located on various geometrical defects (terrace, edge and corner) has been studied using density functional theory (DFT) in combination with embedded cluster model. The adsorption energy (E_ads) of SO₂ molecule (S-atom down as well as O-atom down) in different positions on both of O⁻² and F_s sites is considered. The spin density (SD) distribution due to the presence of Li atom is discussed. The geometrical optimizations have been done for the additive materials and MgO substrate surfaces (terrace, edge and corner). The oxygen vacancy formation energies have been evaluated for MgO substrate surfaces. The ionization potential (IP) for defect free and defect containing of the MgO surfaces has been calculated. The adsorption properties of SO₂ are analyzed in terms of the E_ads, the electron donation (basicity), the elongation of S-O bond length and the atomic charges on adsorbed materials. The presence of the Li atom increases the catalytic effect of the anionic O⁻² site of MgO substrate surfaces (converted from physisorption to chemisorption). On the other hand, the presence of the Li atom decreases the catalytic effect of the F_s-site of MgO substrate surfaces. Generally, the SO₂ molecule is strongly adsorbed (chemisorption) on the MgO substrate surfaces containing F_s-center.     

Bulk and surface properties of spinel Co3O4 by density functional calculations

DFT calculations are employed to bulk and surface properties of spinel oxide Co₃O₄. The bulk magnetic structure is calculated to be antiferromagnetic, with a Co²⁺ moment of 2.631 μ_B in the antiferromagnetic state. There are three predicted electron transitions O(2p) → Co²⁺(t_2g) of 2.2 eV, O(2p) → Co³⁺(e_g) of 2.9 eV and Co³⁺(t_2g) → Co²⁺(t_2g) of 3.3 eV, and the former two transitions are close to the corresponding experimental values 2.8 and 2.4 eV. The naturally occurring Co₃O₄ (1 1 0) and (1 1 1) surfaces were considered for surface calculations. For ideal Co₃O₄ (1 1 0) surfaces, the surface relaxations are not significant, while for ideal Co₃O₄ (1 1 1) surfaces the relaxation of Co²⁺ cations in the tetrahedral sites is drastic, which agrees with the experiment observation. The stability over different oxygen environments for possible ideal and defect surface terminations were explored.     

Ab initio studies of hydrogen desorption from low index magnesium hydride surface

The low index Magnesium hydride surfaces, MgH₂(0 0 1) and MgH₂(1 1 0), have been studied by ab intio Density Functional Theory (DFT) calculations. It was found that the MgH₂(1 1 0) surface is more stable than MgH₂(0 0 1) surface, which is in good agreement with the experimental observation. The H₂ desorption barriers vary depending on the crystalline surfaces that are exposed and also the specific H atom sites involved - they are found to be generally high, due to the thermodynamic stability of the MgH₂ system, and are larger for the MgH₂(0 0 1) surface. The pathway for recombinative desorption of one in-plane and one bridging H atom from the MgH₂(1 1 0) surface was found to be the lowest energy barrier amongst those computed (172 KJ/mol) and is in good agreement with the experimental estimates.