Calculation of the formation energies of isolated vacancy and adatom-vacancy pair at low-index surfaces of fcc metals with MAEAM

The formation energies of isolated vacancy and adatom-vacancy pair (where the two are separated by a large distance) at low-index surfaces of fcc metals calculated by using the modifies analytical embedded atom method (MAEAM). The results predict the prevailing formation of vacancies on the surfaces (1 1 1), (1 0 0) (but Pd), Cu and Ni on the (1 1 0) surfaces at low temperature, and the defect formation energies consistently create in the sequence (1 1 0) → (1 0 0) → (1 1 1). With good accuracy, the calculated energy values coincide with those obtained by the embedded atom methods (EAM) and from experiments. The correctness of the method by which calculated the formation energies of point defects on the surface was proved.     

Atomistic simulation of the self-diffusion in Fe (1 1 1) surface

The formation energies, the intra- and inter-layer self-diffusion activation energies of a single vacancy in Fe (1 1 1) surface have been investigated with the modified analytical embedded-atom method (MAEAM). The results show that the effect of the surface is down to the sixth layer for the formation and intra-layer migration of the vacancy. It is easier for a vacancy to form and to migrate in intra-layer in the first (especially), the second and the third layer. For inter-layer migration, a single vacancy in each of the first six layers is favorable to migrate to the upper layers. On the contrary, a single vacancy in the seventh, the eighth and the ninth layers is favorable to migrate to the lower layers.     

Study on low-energy bombardment of Au (1 1 1) by noble metal atoms with molecular dynamics simulations

The low-energy bombardment of Au (1 1 1) surface by noble metal atoms is studied with molecular dynamics (MD) simulations. With the incident-energy dependence of adatom yields, sputtering yields, and vacancy yields for different projectiles, we find that the implantation of projectiles in shallow layers below surface can be distinguished by subplantation (in the first and second layers) and implantation (deeper than the third layer). The transition from subplantation to implantation occurs at the incident energy of about 45 eV for the low-energy bombardment of noble metal atoms on Au (1 1 1). The incident-energy dependence of defect yields is obviously different for the subplantation and implantation of projectiles. Based on our MD simulations, we discuss the influence of low-energy bombardment on film growth and the guide to the search for optimum deposition parameters.     

Diffusion of single adatom Cu on Cu (0 0 1) and (1 1 0) surfaces

With static relaxation, the surface diffusion activation energies of a single Cu adatom migrated by both atomic exchange and hopping mechanisms and the forces acted on the diffusing adatom from other atoms of Cu (0 0 1) or (1 1 0) surface are calculated by using the MAEAM. When adatom migrated on Cu (0 0 1) or (1 1 0) surface, the increment curves of the system energy by hopping mechanism are symmetrical and the saddle points are in the midpoints of the migration path, but the ones by the exchange mechanism are dissymmetrical and the saddle points are always close to the initial hole positions of the adatom and away from the initial equilibrium positions of the exchanged atom. From minimization of both the diffusion activation energy and the force acted on the diffusing adatom from other atoms, we found that, on Cu (0 0 1) surface the favorable diffusion mechanism is hopping mechanism, however, on Cu (1 1 0) surface, hopping via long bridge is easier than the exchange mechanism but the hopping via short bridge is more difficult than the exchange mechanism.     

Atomistic simulation of the vacancy in Ni (1 1 0) surface

Both the formation energies and the intra- and inter-layer diffuse activation energies of a vacancy in the first six atomic planes of Ni (1 1 0) surface have been investigated by means of molecular dynamics (MD) in conjunction with the semi-experiential many-body potential of the modified analytical embedded-atom method (MAEAM). The results show that the effect of the surface is only down to the fifth-layer. It is easer for a vacancy in the first or second layer to form and to migrate in intra-layer. For the inter-layer migration, a vacancy in the second or third layer is favorable to migrate to the upper layer, this is not the case for a vacancy in the fourth or fifth layer.     

First principles calculations of the adsorption and diffusion of Y on the Si(0 0 1)-c(4 × 2) surface

We have studied the adsorption and diffusion of yttrium on the Si(0 0 1)-c(4 × 2) surface in the early stages of growth. Our first principles total energy calculations are based on the density functional theory as implemented in the SIESTA code. The exchange and correlation energies are treated within the generalized gradient approximation according to the Perdew, Burke and Ernzerhof parametrization. Our results demonstrate that the most favorable adsorption site is in the trench between two silicon dimer rows, identified as valley-bridge (V). Our studies show that the diffusion of an Y adatom on Si(0 0 1)-c(4 × 2) surface presents an anisotropic behavior. We found two values for the barriers along the valley (0.54 and 1.07 eV) and one of 1.24 eV in the perpendicular direction, showing that diffusion along the valley is more probable. The analysis of the Mulliken overlap populations shows that the bonding between an Y adatom and the surface is partially covalent. Two Y atoms on the surface do not form dimers instead they are adsorbed as adatoms.     

Intrinsic polyatomic defects in Sc2(WO4)3

The intrinsic formation of polyatomic defects in Sc₂(WO₄)₃-type structures is studied by Mott Littleton calculations and Molecular Dynamics simulations. Defects involving the WO₄²⁻ tetrahedron are found to be energetically favorable when compared to isolated W and O defects. WO₄²⁻ Frenkel and (2Sc³⁺, 3WO₄²⁻) Schottky defects exhibit formation energies of 1.23 eV and 1.97 eV, respectively and therefore may occur as intrinsic defects in Sc₂(WO₄)₃ at elevated temperatures. WO₄²⁻ vacancy and interstitial migration processes have been simulated by classical Molecular Dynamics simulations. The interstitial defect exhibits a nearly 10 times higher mobility (with a migration energy of 0.68 eV), than the vacancy mechanism (with a slightly higher migration energy of 0.74 eV) and thus should dominate the overall ionic conduction. Still both models reproduce the experimental activation energy (0.67 eV) nearly within experimental uncertainty.     

Atomistic simulation of the vacancy diffusion in (0 0 1) surface of MoTa alloy

The formation and diffusion of a single Mo or Ta vacancy in the (0 0 1) surface of the B₂-type MoTa alloy have been investigated by using modified analytical embedded-atom method (MAEAM). The results show that the effect of the surface on the vacancy is only down to the sixth layer. It is easier for the vacancy to form in the first layer. Comparing the migration energy of the vacancy migrating in the intra-layer, to the upper layer and to the nether layer via 2NN jump, we find that the vacancy in the first or second layer is preferred to migrate in intra-layer, and that in the third or fourth layer is favorable to migrate to the upper layer. Although 1NN jump will result in an anti-site so that a disorder in the order alloy, it may also occur due to the much lower migration energy especially for the vacancy in the second and third layer to migrate to the first and second layer, respectively.     

Early stages of vanadium deposition on Si(1 1 1)-7 × 7

We investigate the low-coverage regime of vanadium deposition on the Si(1 1 1)-7 × 7 surface using a combination of scanning tunnelling microscopy (STM) and density-functional theory (DFT) adsorption energy calculations. We theoretically identify the most stable structures in this system: (i) substitutional vanadium atoms at silicon adatom positions; (ii) interstitial vanadium atoms between silicon adatoms and rest atoms; and (iii) interstitial vanadium - silicon adatom vacancy complexes. STM images reveal two simple vanadium-related features near the Si adatom positions: bright spots at both polarities (BB) and dark spots for empty and bright spots for filled states (DB). We relate the BB spots to the interstitial structures and the DB spots to substitutional structures.     

Structural properties and diffusion processes of the Cu3Au (0 0 1) surface

The surface relaxation and surface energy of both the mixed AuCu and pure Cu terminated Cu₃Au (0 0 1) surfaces are simulated and calculated by using the modified analytical embedded-atom method. We find that the mixed AuCu termination is energetically preferred over the pure Cu termination thereby the mono-vacancy diffusion is also investigated in the topmost few layers of the mixed AuCu terminated Cu₃Au (0 0 1) surface. In the mixed AuCu terminated surface the relaxed Au atoms are raised above Cu atoms for 0.13 Å in the topmost layer. All the surface atoms displace outwards, this effect occurs in the first three layers and changes the first two inter-layer spacing. For mono-vacancy migration in the first layer, the migration energies of Au and Cu mono-vacancy via two-type in-plane displace: the nearest neighbor jump (NNJ) and the second nearest neighbor jump (2NNJ), are calculated and the results show that the NNJ requires a much lower energy than 2NNJ. For the evolution of the energy requirements for successive nearest neighbor jumps (SNNJ) along three different paths: circularity, zigzag and beeline, we find that the circularity path is preferred over the other two paths due to its minimum energy barriers and final energies. In the second layer, the NN jumps in intra- and inter-layer of the Cu mono-vacancy are investigated. The calculated energy barriers and final energies show that the vacancy prefer jump up to a proximate Cu site. This replacement between the Cu vacancy in the second layer and Cu atom in the first layer is remunerative for the Au atoms enrichment in the topmost layer.     

Computer simulation study of self-diffusion in Pd(0 0 1) surface

Both the formation energies and the intra- and inter-layer activation energies of self-diffusion of a single vacancy in the first six planes of Pd(0 0 1) surface have been investigated by means of molecular dynamics (MD) in conjunction with the semi-experiential many-body potential of the modified analytical embedded-atom method (MAEAM). The results show that the effect of the surface on the vacancy is only down to the fifth-layer. It is easer for a single vacancy to form and to migrate in the first layer. Furthermore, the vacancy in the second layer is favorable to migrate to the first layer. This is in agreement with the experimental results that the first layer has the highest concentration of the vacancy.     

Study of vacancy on diamond (1 0 0) (2 × 1) surface from first-principles

Structure and energy related properties of neutral and charged vacancies on relaxed diamond (1 0 0) (2 × 1) surface were investigated by means of density functional theory. Calculations indicate that the diffusion of a single vacancy from the top surface layer to the second layer is not energetically favored. Analysis of energies in charged system shows that neutral state is most stable on diamond (1 0 0) (2 × 1) surface. The multiplicity of possible states can exist on diamond (1 0 0) surface in dependence on the surface Fermi level, which supports that surface diffusion of a vacancy is mediated by the change of vacancy charge states. Analysis of density of states shows surface vacancy can be effectively measured by photoelectricity technology.     

Formation of oxygen vacancies on the TiO2(1 1 0) surfaces

Density functional theory was employed to investigate the formation and properties of the oxygen vacancies on the rutile TiO₂(1 1 0) surface. It is found that the formation of the positively charged bridging-oxygen vacancy (BOV⁺, 4.2 eV) is the most favored one, followed by the positively charged in-plane-oxygen vacancy (POV⁺, 4.5 eV). In contrast, the formation of the neutral bridging-oxygen and in-plane-oxygen vacancies (BOV and POV), and their dication oxygen vacancies (BOV²⁺ and POV²⁺) needs much higher energies (7.9 and 8.3 vs. 8.1 and 8.6 eV), respectively.     

Vacancy diffusion in Cu∑ = 5[0 0 1] twist grain boundary

Both the formation energies and the diffusive activation energy of a single vacancy migrating intra- and inter-layer in the first four atomic planes near Cu∑ = 5[0 0 1] twist GB have been investigated by means of MD in conjunction with MAEAM. The effects of the GB on the vacancy formation and migration are only to the third layer. The vacancy is favorable to be formed on the un-coincident site in the first, second and third layers near the GB plane and this case is enhanced successively following the third, second and first layers. A single vacancy either on un-coincident site or on coincident site in the forth, third and second layers is favorable to migrate to un-coincident site (its first-nearest-neighbor) in its adjacent layer near the GB. But for the first layer, the favorable migration path of the vacancy on the un-coincident site is between un-coincident sites of the first layer or to its nearest-neighbor of the first layer in the rotating grain, which is not the case for the vacancy on the coincident site ‘1’ that is migrated difficultly. So, there are collective tendency of the vacancy in the GB.     

Theoretical study of Ni adsorption on the GaN(0 0 0 1) surface

First-principles pseudo-potential calculations within density-functional theory framework are performed in order to study the structural and electronic properties of nickel adsorption and diffusion on a GaN(0 0 0 1)-2×2 surface. The adsorption energies and potential energy surfaces are investigated for a Ni adatom on the Ga-terminated (0 0 0 1) surface of GaN. This surface is also used to study the effect of the nickel surface coverage. The results show that the most stable positions of a Ni adatom on GaN(0 0 0 1) are at the H₃ sites and T₄ sites, for low and high Ni coverage respectively. In addition, confirming previous experimental results, we have found that the growth of Ni monolayers on the GaN(0 0 0 1) surface is possible.     

First-principles calculations on electronic structures of Fe-vacancy-codoped TiO2 anatase (1 0 1) surface

The electronic structures of Fe-doped TiO₂ anatase (1 0 1) surfaces have been investigated by all spin-polarized density functional theory (DFT) plane-wave pseudopotential method. The general gradient approximation (GGA)+U (Hubbard coefficient) method has been adopted to describe the exchange-correlation effects. Through the density functional calculations for the formation energies of various configurations, the complex of a substitutional Fe plus an O vacancy was found to form easily in the most range of O chemical potential. The calculated density of the states of the system of Fe-doped surface with a surface oxygen vacancy shows a band gap narrowing from 2.8 to 1.9 eV comparing with the pure surface due to the synergistic effects of surface Fe impurities with O vacancies. The system processes high visible light sensitivity and photocatalytic ability by decreasing extrinsic absorption energy. By comparing the partial DOS of some O and Ti atoms lying in the outermost and bottom layers of Fe-doped surfaces, it was found that the influence of Fe impurities on the electronic structure of the system is localized.     

Effects of metal-support interactions on the electronic structures of metal atoms adsorbed on the perfect and defective MgO(1 0 0) surfaces

The electronic structures of Ni, Pd, Pt, Cu, and Zn atoms adsorbed on the perfect MgO(1 0 0) surface and on a surface oxygen vacancy have been studied at the DFT/B3LYP level of theory using both the bare cluster and embedded cluster models. Ni, Pd, Pt, and Cu atoms can form stable adsorption complexes on the regular O site of the perfect MgO(1 0 0) surface with the binding energies of 19.0, 25.2, 46.7, and 17.3 kcal/mol, respectively, despite very little electron transfer between the surface and the metal atoms. On the other hand, adsorptions of Ni, Pd, Pt, and Cu atoms show strong interaction with an oxygen vacancy on the MgO(1 0 0) surface by transferring a significant number of electron charges from the vacancy to the adsorbed metal atoms and thus forming ionic bonds with the vacancy site. These interactions on the vacancy site for Ni, Pd, Pt, and Cu atoms increase the binding energies by 25.8, 59.7, 85.2, and 19.1 kcal/mol, respectively, compared to those on the perfect surface. Zn atom interacts very weakly with the perfect surface as well as the surface oxygen vacancy. We observed that the interaction increases from Ni to Pt in the same group and decreases from Ni to Zn in the same transition metal period in both perfect and vacancy systems. These relationships correlate well with the degrees of electron transfer from the surface to the adsorbed metal atom. The changes in the ionization potentials of the surface also correlate with the adsorption energies or degrees of electron transfers. Madelung potential is found to have significant effects on the electronic properties of metal atom adsorptions on the MgO(1 0 0) surface as well as on an oxygen vacancy, though it is more so for the latter. Furthermore, the Madelung potential facilitates electron transfer from the surface to the adsorbed metal atoms but not in the other direction.     

Surface alloying of immiscible metals induced by surface state shift

By using first principles calculations, it is found that the noble metal atoms Ag, Au and Cu would like to occupy the vacancy sites of the W(0 0 1) or Mo(0 0 1) surface to form the substitutional surface alloys, despite the fact that they do not like to form alloy in the bulk. The electronic local function (ELF) for these substitutional surface alloys shows that there is no obvious chemical bonding between the noble metals and W or Mo. The analysis of electronic structures lets us conclude that the surface alloying of immiscible metals may originate from the surface state shift of W (or Mo) induced by changes of the electronic environment of surface W (or Mo) when surface W (or Mo) atoms are alternatively replaced by Ag (Au or Cu).     

Adatom and dimer migration in heteroepitaxy: Co/Pt(1 1 1)

By means of tight-binding molecular-dynamics simulations, Co adatom and dimer migration on a Pt(1 1 1) surface is investigated. Combining static and dynamic calculations, activation energies associated to these processes are determined. Since the size mismatch between Co and Pt is large, the presented simulations provide an illustration of the way in which growth can be affected by size effects in heteroepitaxy. In particular an increase of the mobility is found for Co dimers (heteroepitaxy) relatively to Pt ones (homoepitaxy).     

Atomistic simulation of the point defects in B2-type MoTa alloy

The formation and migration mechanisms of three different point defects (mono-vacancy, anti-site defect and interstitial atom) in B₂-type MoTa alloy have been investigated by combining molecular dynamics (MD) simulation with modified analytic embedded-atom method (MAEAM). From minimization of the formation energy, we find that the anti-site defects Mo_Ta and Ta_Mo are easier to form than Mo and Ta mono-vacancies, while Mo and Ta interstitial atoms are difficult to form in the alloy. In six migration mechanisms of Mo and Ta mono-vacancies, one nearest-neighbor jump (1NNJ) is the most favorable due to its lowest activation and migration energies, but it will cause a disorder in the alloy. One next-nearest-neighbor jump (1NNNJ) and one third-nearest-neighbor jump (1TNNJ) can maintain the ordered property of the alloy but require higher activation and migration energies, so the 1NNNJ and 1TNNJ should be replaced by straight [1 0 0] six nearest-neighbor cyclic jumps (S[1 0 0]6NNCJ) or bent [1 0 0] six nearest-neighbor cyclic jumps (B[1 0 0]6NNCJ) and [1 1 0] six nearest-neighbor cyclic jumps ([1 1 0]6NNCJ), respectively. Although the migrations of Mo and Ta interstitial atoms need much lower energy than Mo and Ta mono-vacancies, they are not main migration mechanisms due to difficult to form in the alloy.