Equilibrium shape of nickel crystal

The equilibrium shape of pure nickel and the effect of carbon on changes in the equilibrium shape at 1200°C were investigated. A statistical observation on the size-dependent, time-dependent and carbon-induced morphological evolution of crystallites suggested that the equilibrium crystal shape (ECS) of pure nickel is a polyhedron consisting of {111}, {100}, {110} and {210} surfaces. However, crystals with an extensive proportion of {320} surfaces were also frequently observed. The appearance of {320} surfaces was interpreted as kinetically stabilized metastable surfaces, which survived during the thermal equilibrating process, possibly due to a high nucleation energy barrier for their removal. On the other hand, the ECS of pure nickel was observed to change dramatically into a spherical shape with facets of {111}, {100}, {110} and {210} without exception under a carburized atmosphere, which indicates that carbon not only facilitates surface diffusion by which energetically more stable surfaces can be easily developed but also decreases the surface energy anisotropy. Together with X-ray photoelectron spectroscopy studies, it was proposed that the carbon-induced changes in the ECS are possibly due to a solid solution effect, which could lead to a reduction in the binding energy among atoms in the bulk as well as on the surfaces.     

The three-dimensional equilibrium crystal shape of Pb: Recent results of theory and experiment

The three-dimensional equilibrium crystal shape (ECS) is constructed from a set of 35 orientation-dependent surface energies of fcc Pb which are calculated by density functional theory in the local-density approximation and distributed over the [110] and [001] zones of the stereographic triangle. Surface relaxation has a pronounced influence on the equilibrium shape. The (111), (100), (110), (211), (221), (411), (665), (15,1,1), (410) and (320) facets are present after relaxation of all considered surfaces, while only the low-index facets (111), (100) and (110) exist for the unrelaxed ECS. The result for the relaxed Pb crystal state is in support of the experimental ECS of Pb at 320–350 K. On the other hand, approximating the surface energies of vicinal surfaces by assuming a linear relationship between the Pb(111) first-principles surface energy and the number of broken bonds of surface atoms leads to a trivial ECS that shows only (111) and (100) facets, with a sixfold symmetric (111) facet instead of the correct threefold symmetry. It is concluded that the broken bond rule in this simple linear form is not a suitable approximation for obtaining the proper three-dimensional ECS and correct step formation energies. PACS 05.70.Np; 61.50.Jr; 68.35.Md; 71.15.Mb     

Effect of coverage by carbon on the possibility of forming an interstitial solid solution in Fe(001) and Fe(111) subsurface layers

The interaction between carbon adatoms as a function of the coverage of the Fe(001) and Fe(111) surfaces by carbon has been theoretically investigated using first-principles calculations in terms of the density functional theory. It has been established for the first time that the sequential filling of the upper surface layer by carbon atoms leads to the embedding of a part of atoms in the subsurface iron layer due to the their collective interaction, which provides the possibility of forming the interstitial solid solution. It has been demonstrated that the high coverage of the (001) surface by carbon leads to a considerable decrease in the energy barrier to the diffusion of carbon atoms into the subsurface layer as compared to the diffusion barrier for single atoms.     

Diffusion of Al dimers on the surface of Mg clusters

The surface diffusion of Al dimmers on Mg clusters with hexahedral structure was studied using the combination of quenched molecular dynamics and the embedded atom method. The system energy barriers of typical minimum energy diffusion paths for Al dimers on the Mg clusters were calculated using the Nudged Elastic Band method. In our study range (153–4061 atoms), the binding energies on the (0001) facets and the (1\(\hbox{$\overline 1 $}\)01) facets differed, the binding energy on the former was lower than that on the latter. Moreover, cluster size only slightly influenced the binding energy values. Two possible diffusion paths were studied. Results showed that the diffusion of the dimer on the (0001) facet easily occurred at low temperatures. Furthermore, the interaction between the two atoms of the dimer facilitated the dimer crossing of the step edge between the (1\(\hbox{$\overline 1 $}\)01) facets by hopping mechanism.     

Hydrogen adsorption,absorption and diffusion on and in transition metal surfaces: A DFT study

Periodic, self-consistent DFT-GGA(PW91) calculations are used to study the interaction of hydrogen with different facets of seventeen transition metals—the (100) and (111) facets of face-centered cubic (fcc) metals, the (0001) facet of hexagonal-close packed (hcp) metals, and the (100) and (110) facets of body-centered cubic (bcc) metals. Calculated geometries and binding energies for surface and subsurface hydrogen are reported and are, in general, in good agreement with both previous modeling studies and experimental data. There are significant differences between the binding on the close-packed and more open (100) facets of the same metal. Geometries of subsurface hydrogen on different facets of the same metal are generally similar; however, binding energies of hydrogen in the subsurface of the different facets studied showed significant variation. Formation of surface hydrogen is exothermic with respect to gas-phase H₂ on all metals studied with the exception of Ag and Au. For each metal studied, hydrogen in its preferred subsurface state is always less stable than its preferred surface state. The magnitude of the activation energy for hydrogen diffusion from the surface layer into the first subsurface layer is dominated by the difference in the thermodynamic stability of these two states. Diffusion from the first subsurface layer to one layer further into the bulk does not generally have a large thermodynamic barrier but still has a moderate kinetic barrier. Despite the proximity to the metal surface, the activation energy for hydrogen diffusion from the first to the second subsurface layer is generally similar to experimentally-determined activation energies for bulk diffusion found in the literature. There are also some significant differences in the activation energy for hydrogen diffusion into the bulk through different facets of the same metal.     

Double rotation mechanism in small Cu clusters concerted diffusion over Cu{1 1 1} surfaces

In this work, we study the role of the double rotation mechanism in the concerted diffusion of two-dimensional small Cu clusters (up to 10 atoms) over Cu{1 1 1} surfaces. Our results show that the necessary energy to diffuse the cluster on any direction over the surface (overall activation energy) increases proportionally to the cluster size. However, the minimum energy necessary to just move the cluster center of mass presents a nonmonotonic increase. The reason for this behavior relies on the double rotation mechanism, which is observed in some clusters with diamond shape configuration. Consequently, clusters as big as hexamers can be expected to be surprisingly mobile with activation energies around 0.15 eV.     

Diffusion mechanisms for iron on tungsten

Diffusion of iron atoms on clean W(1 0 0) and W(1 1 0) as well as on Fe/W(1 0 0) and Fe/W(1 1 0) surfaces was investigated by means of exhaustive first-principle calculations. Comparison of the activation energy barriers obtained for hopping and exchange migration processes shows that the surface diffusion proceeds via jumps to the nearest sites. The activation energies are higher for Fe adatom on clean tungsten than those for Fe adatoms moving on iron-covered tungsten. The magnetism of the underlying Fe/W(1 0 0) films has a pronounced influence on the diffusion, as evidenced not only by a reduced activation energy barrier but also by a change of the stable adsorption place. Fe atoms reaching step edges are trapped there and eventually diffuse along the steps more slowly than the adatoms on the terraces. The rate of diffusion increases upon depositing a row of Fe atoms along steps.     

First-principles study of C chemisorption and diffusion on the surface and in the subsurfaces of Ni(1 1 1) during the growth of carbon nanofibers

First-principles calculations based on density functional theory and the generalized gradient approximation have been used to study the C chemisorption and diffusion on the surface and in the subsurfaces of Ni(1 1 1). The threefold Hcp site is observed to be preferred by the C adsorption on Ni(1 1 1) surface while in the subsurfaces, the octahedral site is more energetically favorable than the tetrahedral site and all surface adsorption sites. The calculated binding energies have been compared with the previous experimental and theoretical results and good agreement is found. Minimum energy paths for the C diffusion between different adsorption sites are also investigated using the nudged elastic band method. It is predicted that if the C surface diffusion rate is higher than the production rate of C atoms during the growth of carbon nanofibers and the C concentration is low at the Ni surface, the generated C atoms are likely to diffuse on the catalyst surface predominantly because of the lowest energy barrier, while if the generated C production rate is higher and some adsorption sites are blocked by the accumulated carbon, the C atoms may diffuse both on the surface and in the subsurfaces simultaneously.     

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.     

Numerical experiments on low-energy ion scattering at a surface containing adsorbed impurity atoms

The energy distributions of Cs⁺ and W⁺ ions scattered, respectively, at Mo and W single crystals, the surfaces of which contain adsorbed oxygen, nitrogen, and cesium atoms, are calculated via the molecular dynamics method. It is demonstrated that the energy spectra are sensitive to the impurity atoms of a surface. When compared with the energy distributions corresponding to a pure surface, even a partial monolayer of these atoms can modify their shape. A peak in the scattered-ion intensity is commonly shifted to the lowerenergy region if the adsorbate is light and to higher energies if the adsorbate is heavy.     

Carbon diffusion between the volume and surface of (100) molybdenum

The diffusion of carbon atoms between the volume and the surface of (100) molybdenum is directly studied at temperatures between 1400 and 2000 K (i.e., at process temperatures) for the first time. The balance of carbon atoms in the system is determined. The difference in the activation energies of carbon dissolution and precipitation, ΔE=E s 1-E1s, is found for the case when the diffusion fluxes of dissolved and precipitated carbon atoms are in equilibrium. This difference defines the enrichment of the surface by carbon relative to the bulk. The experimentally found activation energy of carbon dissolution is Es1=3.9 eV. The activation energy of carbon precipitation is estimated at E 1 s=1.9 eV. The latter value is close to the energy of bulk diffusion of carbon in molybdenum.     

Structural, electronic, and magnetic properties of bcc iron surfaces

Trends in atomic multilayer relaxations, surface energy, electronic work function, and magnetic structure of several low-Miller-index surfaces of iron are investigated employing density functional theory total energy calculations. The calculated topmost layer relaxations reproduce well the experimental contractions and their variation with the surface crystallographic orientation, and surface roughness. The multilayer relaxation sequences correlate with the reduced coordination in surface layers and can be explained in terms of a simple electrostatic picture. The surface energies scale almost linearly with the surface roughness. They agree well with the experimental surface tensions and show a small anisotropy in agreement with predictions based on measurements for other metals. The equilibrium shape of a bcc Fe crystal is determined and discussed. The work function anisotropy is calculated and rationalized in terms of changes in the valence charge distribution. Significantly increased local magnetic moments of atoms in the surface region are determined. The correlation between the anisotropy of the surface magnetic moments and atomic coordination in the outermost layers is demonstrated to follow a simple rule.     

Ab initio investigation of the clustering of carbon adatoms on Fe(001) and Fe(111) surfaces

A theoretical investigation of the interaction between carbon adatoms on the Fe(001) and Fe( 111 ) surfaces is performed using ab initio calculations in terms of density functional theory. Calc ulations of the adsorption energy demonstrate the existence of a strong bonding between single carbon adatoms and the iron surface. An analysis of the calculated energies of the interaction between carbon adatoms reveals for the first time that the repulsion between the carbon adatoms located at the nearest neighbor sites on the Fe(001) surface occurs and that clusters with a looser packing are formed on the surface.     

Growth of carbon nanotubes on metal nanoparticles: a microscopic mechanism from ab initio molecular dynamics simulations

We report on ab initio molecular dynamics simulations of the early stages of single-walled carbon nanotube (SWCNT) growth on metal nanoparticles. Our results show that a sp2 bonded cap is formed on an iron catalyst, following the diffusion of C atoms from hydrocarbon precursors on the nanoparticle surface. The weak adhesion between the cap and iron enables the graphene sheet to "float" on the curved surface, as additional C atoms covalently bonded to the catalyst "hold" the tube walls. Hence the SWCNT grows capped. At the nanoscale, we did not observe any tendency of C atoms to penetrate inside the catalyst, consistent with total energy calculations showing that alloying of Fe and C is very unlikely for 1 nm particles. Root growth was observed on Fe but not on Au, consistent with experiment.     

氧原子在Zr(0001)表面附近的扩散

在密度泛函理论计算的基础上,利用微动弹性带（nudged elastic band）方法研究了氧原子在Zr（0001）表面附近的扩散.首先计算了氧原子从稳定的表面面心立方（SFCC）位置向表面六角密排位置的扩散激活能（0.77 eV）;然后计算了氧原子从稳定的SFCC位置扩散到表面下第1层与第2层之间的八面体间隙位置,再继续向表面下第2层与第3层之间的八面体间隙位置扩散的激活能,在此过程中氧原子需克服两个能垒,其激活能分别为2.14和2.57 eV.结果表明,氧原子在Zr（0001）表面上方的扩散比较容易,而氧原子向Zr（0001）表面下的扩散相对较难. 关键词： Zr（0001）表面 微动弹性带 氧的扩散     

Monte Carlo simulation of surface segregation phenomena in extended and nanoparticle surfaces of Pt-Pd alloys

The surface segregation phenomena in the extended and nanoparticle surfaces of Pt-Pd alloys have been studied using the Monte Carlo (MC) simulation method and the modified embedded-atom method (MEAM) potentials developed for Pt-Pd alloys. The MEAM potentials were fitted to reproduce the experimental values of the lattice parameters, cohesive energies and surface energies of pure Pt and Pd metals, as well as the density functional theory calculation results of the lattice parameters and heat of formation of L1(2) Pt(3)Pd, L1(0) PtPd and L1(2) PtPd(3) crystal. Using the MC method and the developed MEAM potentials, we calculated the Pt concentrations in the outermost three layers of the equilibrium (111), (100) and (110) extended surfaces as well as the outermost surfaces of the equilibrium cubo-octahedral nanoparticles of Pt-Pd alloys. Our simulation results showed that the Pd atoms would segregate into the outermost layers of the extended surfaces and the Pt concentration would increase monotonically from the extended surfaces into the bulk. The equilibrium Pt-Pd nanoparticles were found to have Pd-enriched shells and Pt-enriched cores. In the shell of the Pt-Pd nanoparticles, the Pd atoms were predicted to preferably segregate to the (100) facets rather than the (111) facets.     

Mechanisms of the oxidation of defect-free surfaces of carbon nanostructures: the influence of surface curvature

This work is concerned with reaction paths in the interaction of carbon defect-free nanostructures with different surface curvatures (graphene, tubulenes, and fullerene C₆₀) with atomic and molecular oxygen. The interaction energies of atoms were calculated by the density functional theory method using the basis set of plane waves and the VASP package. The potential surface of reactions with molecular oxygen was studied by the nudged elastic band method. The energy parameters of the reaction (released energy and barrier) strongly depended on the curvature of carbon structure surfaces. The interaction of atomic oxygen in the ground state with the surface of carbon nanostructures is an exothermic reaction. The barrier to the reaction with molecular oxygen (0.5–2.5 eV) decreases as the curvature of nanostructure surfaces increases. The calculation results are in agreement with the experimental data and other ab initio calculations.     

A systematic DFT study of hydrogen diffusion on transition metal surfaces

Density functional theory calculations of the diffusion of hydrogen atoms on 23 transition metal surfaces in their closed-packed structure have been carried out. The d-metals chosen are all the metals in the 4th, 5th and 6th periods, from Sc to Au, except Mn, Tc, and Hf. Potential energy surfaces of H atom on these metals are constructed and the diffusion barrier from one minima to another is compared with nudged elastic band calculations. Most of the minimum energy paths have a single activation barrier, except on two surfaces where a dip in the bridge position (W and Pt) is observed. Trends in the adsorption and activation energies are observed where the former is explained with the d-band model. All the activation energies for diffusion are relatively low, or from 0.04 eV for Pt to 0.28 eV on Y and Zr. Finally, we estimate the temperature where tunneling effects should start to take place.     

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.     

Adsorptions and diffusions of carbon atoms on the surface and in the subsurface of Co （200）： A first-principles density-functional study

First-principles calculations based on density functional theory are used to investigate the adsorptions and diffusions of carbon atoms on the surface and in the subsurface of Co(200). The preferred site for the carbon atom on the surface is the hollow site, and the preferred site in the subsurface is the octahedral site. There is charge transfer from the surface to the adsorbed carbon atom, and for the most favorable adsorbed structure the charge transfer is largest. Moreover, the energy barriers for the diffusions of carbon atoms on the surface and from the surface into the subsurface and then back to the surface are calculated in detail. The results indicate that the energy barrier for the diffusion of carbon atoms on the surface is comparable to that from the subsurface to the surface. The results imply that both the direct surface nucleation and the surface segregation from Co bulk can be observed in the chemical vapor deposition growth of graphene on Co(200)substrate, which can gain a new insight into the growth mechanism of graphene.