Ab initio calculations of energies and self-diffusion on flat and stepped surfaces of Al and their implications on crystal growth

First-Principles Studies on the Atomistic Properties of Metallic Magnesium as Anode Material in Magnesium-Ion Batteries

Rechargeable magnesium-ion batteries (MIBs) are a promising alternative to commercial lithium-ion batteries (LIBs). They are safer to handle, environmentally more friendly, and provide a five-time higher volumetric capacity (3832 mAh cm^-3 ) than commercialized LIBs. However, the formation of a passivation layer on metallic Mg electrodes is still a major challenge towards their commercialization. Using density functional theory (DFT), the atomistic properties of metallic magnesium, mainly well-selected self-diffusion processes on perfect and imperfect Mg surfaces were investigated to better understand the initial surface growth phenomena. Subsequently, rate constants and activation temperatures of crucial diffusion processes on Mg(0001) and Mg(10 1 ‾ 1) were determined, providing preliminary insights into the surface kinetics of metallic Mg electrodes. The obtained DFT results provide a data set for parametrizing a force field for metallic Mg or performing kinetic Monte-Carlo simulations.

Tailoring magnetic anisotropy by graphene-induced selective skyhook effect on 4f-metals

From macroscopic heavy-duty permanent magnets to nanodevices, the precise control of the magnetic properties in rare-earth metals is crucial for many applications used in our daily life. Therefore, a detailed understanding and manipulation of the 4f-metals' magnetic properties are key to further boosting the functionalization and efficiency of future applications. We present a proof-of-concept approach consisting of a dysprosium-iridium surface alloy in which graphene adsorption allows us to tailor its magnetic properties. By adsorbing graphene onto a long-range ordered two-dimensional dysprosium-iridium surface alloy, the magnetic 4f-metal atoms are selectively lifted from the surface alloy. This selective skyhook effect introduces a giant magnetic anisotropy in dysprosium atoms as a result of manipulating its geometrical structure within the surface alloy. Introducing and proving this concept by our combined theoretical and experimental approach provides an easy and unambiguous understanding of its underlying mechanism. Our study sets the ground for an alternative path on how to modify the crystal field around 4f-atoms and therefore their magnetic anisotropies.

Free Energy Surfaces and Barriers for Vacancy Diffusion on Al(100), Al(110), Al(111) Reconstructed Surfaces

Metadynamics is a popular enhanced sampling method based on the recurrent application of a history-dependent adaptive bias potential that is a function of a selected number of appropriately chosen collective variables. In this work, using metadynamics simulations, we performed a computational study for the diffusion of vacancies on three different Al surfaces [reconstructed Al(100), Al(110), and Al(111) surfaces]. We explored the free energy landscape of diffusion and estimated the barriers associated with this process on each surface. It is found that the surfaces are unique regarding vacancy diffusion. More specically, the reconstructed Al(110) surface presents four metastable states on the free energy surface having sizable and connected passage-ways with an energy barrier of height 0.55 eV. On the other hand, the reconstructed Al(100)/Al(111) surfaces exhibit two/three metastable states, respectively, with an energy barrier of height 0.33 eV. The findings in this study can help to understand surface vacancy diffusion in technologically relevant Al surfaces.

First-principles calculations for understanding microstructures and mechanical properties of co-sputtered Al alloys

Recent experimental studies show that co-sputtering solutes with Al, together, can refine columnar grain size around few tens of nanometers and promote the formation and enhance the stability of planar defects such as stacking faults (SFs) and grain boundaries (GBs) in Al alloys. These crystal defects and fine columnar grains result in high strength, enhanced strain hardening and thermal stability of Al alloys. Using first-principles density-functional theory (DFT) calculations, we studied the role of eleven solutes in tailoring kinetics and energetics of adatoms and clusters on Al {111} surface, stable and unstable stacking fault energies, and kinetic energy barriers for the migration of defects. The calculations show that most solutes can effectively refine columnar grain size by decreasing the diffusivity of adatoms and surface clusters. These solutes do not necessarily decrease the stacking fault energy of Al alloys, but reduce the formation energy of faulted surface clusters and increase the energy barriers for the recovery of faulted surface clusters. Correspondingly, the formation of SFs is kinetically promoted during sputtering. Furthermore, solutes are segregated into the core of Shockley partial dislocations and play a pinning effect on SFs, SF arrays and twin boundaries, enhancing the thermal stability of these crystal defects. These findings provide insights into the design of high-strength Al alloys for high-temperature applications.

Morphology evolution of magnesium facets: DFT and KMC simulations

One of the crucial steps for the development of batteries is understanding the interface stability and morphological changes occurring during continuous stripping and deposition.

The first stages of oxide growth at the low index Al surfaces (100), (110), (111): clusters and stripes vs. homogeneous growth

We performed a density functional theory (DFT) investigation of the mechanisms of oxide growth at Al(100), Al(110) and Al(111) up to 1 monolayer (ML) coverage of O-atoms with 0.125 ML increments. We found that the surface binding site preferences of O-atoms are largely affected by the presence of neighboring O-atoms. Based on this we constructed two oxide growth models: the formation of clusters that evolve to stripes with increasing coverage and the formation of a more homogeneous distribution of O-atoms. While the former model is characterized by a lower symmetry of distribution of O-atoms at the surfaces, the latter corresponds to higher symmetries. We found that the prevalence of each oxide growth mode depends on the coverage of O-atoms and that this dependency is different for each surface. For Al(100) and Al(110), up to coverages of 1 ML the oxide grows preferably via the formation of clusters that evolve to stripes with increasing coverage, while for Al(111) the stripes and clusters are the preferred growth mode for coverages up to 0.375 ML, beyond which the homogeneous growth mode is energetically favored. The calculated Al-O pair distribution functions show that the formation of clusters and stripes leads to shorter Al-O bond lengths when compared to the homogeneous growth. The oxides formed at Al(100) and Al(110) have Al-O bond lengths and geometries typical of the shorter bonds of α-alumina while at Al(111) the bond lengths are typical of γ-alumina and β-alumina. These results suggest that for low coverages, the oxides formed at Al(100) and Al(110) are resemblant of defective α-alumina while the oxide formed at Al(111) is similar to less disordered γ-alumina and β-alumina. For Al(111), the small energy difference between the growth of clusters and stripes and homogeneous growth does not exclude the coexistence of both growth modes; this could lead to the formation of a defective or amorphous oxide.

Growth of Pd Nanoclusters on Single-Layer Graphene on Cu(111)

We report scanning tunneling microscopy results on the nucleation and growth of Pd nanoclusters on a single layer of graphene on the Cu(111) surface. The shape, organization, and structural evolution of the Pd nanoclusters were investigated using two different growth methods, continuous and stepwise. The size and shape of the formed nanoclusters were found to greatly depend on the growth technique used. The size and density of spherical Pd nanoclusters increased with increasing coverage during stepwise deposition as a result of coarsening of existing clusters and continued nucleation of new clusters. In contrast, continuous deposition gave rise to well-defined triangular Pd clusters as a result of anisotropic growth on the graphene surface. Exposure to ethylene caused a decrease in the size of the Pd clusters. This is attributed to the exothermic formation of ethylidyne on the cluster surfaces and an accompanying weakening of the Pd-Pd bonding.

Vacancy patterning and patterning vacancies: controlled self-assembly of fullerenes on metal surfaces

A density functional theory study accounting for van der Waals interactions reveals the potential of metal surface vacancies as anchor points for the construction of user-defined 2D patterns of adsorbate molecules via a controlled self-assembly process. Vice versa, energetic criteria indicate the formation of regular adsorbate-induced vacancies after adsorbate self-assembly on clean surfaces. These processes are exemplified by adsorbing C₆₀ fullerene on Al(111), Au(111), and Be(0001) surfaces with and without single, triple, and septuple atom pits. An analysis of vacancy-adatom formation energetics precedes the study of the adsorption processes.

Growth and Structure of Metallic Barrier Layers and Interconnect Films II: Atomistic Simulations of Film Deposition onto Inclined Surfaces

We present three dimensional lattice Monte Carlo simulations of sputter deposition onto inclined surfaces. For this purpose, we use a model of an fcc material and we vary the substrate inclination, the texture, and the atomic mobility. In this way we can examine different conditions and mechanisms involved in depositing barrier layer and interconnect films. We obtain results on the density and the roughness of the films. We find that the film texture has dramatic effects on the film density and smoothness. Surprisingly, we find that the surface diffusion coefficients may not be critical parameters; changes in the coefficients by several orders of magnitude may cause only a small change in the film morphology when depositing onto non-wetting substrates.

Multiscale Modeling of Au-Island Ripening on Au(100)

We describe a multiscale modeling hierarchy for the particular case of Au-island ripening on Au(100). Starting at the microscopic scale, density functional theory was used to investigate a limited number of self-diffusion processes on perfect and imperfect Au(100) surfaces. The obtained structural and energetic information served as basis for optimizing a reactive forcefield (here ReaxFF), which afterwards was used to address the mesoscopic scale. Reactive force field simulations were performed to investigate more diffusion possibilities at a lower computational cost but with similar accuracy. Finally, we reached the macroscale by means of kinetic Monte Carlo (kMC) simulations. The reaction rates for the reaction process database used in the kMC simulations were generated using the reactive force field. Using this strategy, we simulated nucleation, aggregation, and fluctuation processes for monoatomic high islands on Au(100) and modeled their equilibrium shape structures. Finally, by calculating the step line tension at different temperatures, we were able to make a direct comparison with available experimental data.

Electronic nature of step-edge barriers against adatom descent on transition-metal surfaces

By studying a series of adatoms on representative transition-metal surfaces through first-principles calculations, we establish a clear correlation between the preferred mechanism and activation energy for adatom descent at a step and the relative degree of electronic shell filling of the adatom and the substrate. We also find an approximate linear relation between the adatom step-edge hopping barriers and the adatom-surface bonding strength with slope roughly proportional to the number of the adatom's nearest neighbors initially. These results may serve as simple guiding rules for predicting precise atomic surface morphologies in heteroepitaxial growth, as in formation of nanowires.

Diffusion mechanisms taking place at the early stages of cobalt deposition on Au(111)

In the present work a detailed atomic-level analysis of some of the main diffusion mechanisms which take place during cobalt adatom deposition are studied within atom dynamics (AD) and the nudged elastic band (NEB) method. Our computer simulations reveal a very fast exchange between Co and Au atoms when the deposit is a single cobalt adatom. However, when the nucleus size increases, a decrease in the exchange probability is observed. Activation energies for different transitions are obtained using AD in combination with the NEB method.

Equilibrium structures and shapes of clusters on metal fcc(111) surfaces

Using embedded-atom-method potentials, the lower-energy structures (LESs) of adatom clusters are obtained directly on a series of metal fcc(111) surfaces by the method based on the genetic algorithm. The structural features, energy distributions, number of LESs and their differences on different surfaces are discussed and explained in terms of the nearest-neighbor and next-nearest-neighbor (NN, NNN) adatom-adatom interactions, and the edge-type difference. When the energetic preference for one edge type over another is slight, e.g., on Ag(111), only one type of structure is included, and it does not change with the increment of cluster size. However, when there is a strong energetic preference for one of the edge types, e.g., on Pt(111), an interesting phenomenon of structure replacement is revealed, by which the structures in the LES group deviate more and more from the configuration with the maximum number of NN bonds as the cluster size increases. The structure replacement also finally leads to the shape of the two-dimensional island on Pt(111) being quite distinct from that on Ag(111). Based on these results, the general trend of the variation of lower-energy structures with cluster size is discussed further for other metal fcc(111) surfaces.

Monte Carlo simulation of electrodeposition of copper: a multistep free energy calculation

Electrodeposition of copper (Cu) involves length scales of a micrometer or even less. Several theoretical techniques such as continuum Monte Carlo, kinetic Monte Carlo (KMC), and molecular dynamics have been used for simulating this problem. However the multiphenomena characteristics of the problem pose a challenge for an efficient simulation algorithm. Traditional KMC methods are slow, especially when modeling surface diffusion with large number of particles and frequent particle jumps. Parameter estimation involving thousands of KMC runs is very time-consuming. Thus a less time-consuming and novel multistep continuum Monte Carlo simulation is carried out to evaluate the step wise free energy change in the process of electrochemical copper deposition. The procedure involves separate Monte Carlo codes employing different random number criterion (using hydrated radii, bare radii, hydration number of the species, redox potentials, etc.) to obtain the number of species (CuCl(2) or CuSO(4) or Cu as the case may be) and in turn the free energy. The effect of concentration of electrolyte, influence of electric field and presence of chloride ions on the free energy change for the processes is studied. The rate determining step for the process of electrodeposition of copper from CuCl(2) and CuSO(4) is also determined.

Sensing dipole fields at atomic steps with combined scanning tunneling and force microscopy

The electric field of dipoles localized at the atomic steps of metal surfaces due to the Smoluchowski effect were measured from the electrostatic force exerted on the biased tip of a scanning tunneling microscope. By varying the tip-sample bias the contribution of the step dipole was separated from changes in the force due to van der Waals and polarization forces. Combined with electrostatic calculations, the method was used to determine the local dipole moment in steps of different heights on Au(111) and on the twofold surface of an Al-Ni-Co decagonal quasicrystal.

Kinetic pathway for the formation of fe nanowires on stepped Cu111 surfaces

We report the discovery of a novel kinetic pathway for the formation of one-dimensional Fe nanowires of single atom width on stepped Cu(111) surfaces. This pathway, identified through extensive total-energy calculations within density functional theory, establishes that the stable structure involves a row of Fe atoms on the upper edge of a step. The formation of the surface wire is preceded by facile incorporation of an initial row of Fe atoms into the surface layer at one lateral lattice constant away from the step edge, which then acts as an attractor for the second exposed row of atoms. The resulting wire structure provides a natural interpretation of existing experimental results. We also explore the applicability of this mechanism in the formation of other related systems.

Adatom ascending at step edges and faceting on fcc metal (110) surfaces

Using first-principles total-energy calculations, we show that an adatom can easily climb up at monatomic-layer-high steps on several representative fcc metal (110) surfaces via a place exchange mechanism. Inclusion of such novel adatom ascending processes in kinetic Monte Carlo simulations of Al(110) homoepitaxy as a prototypical model system can lead to the existence of an intriguing faceting instability, whose dynamical evolution and kinetic nature are explored in comparison with experimental observations.

Site determination and thermally assisted tunneling in homogenous nucleation

A combined low-temperature scanning tunneling microscopy and density functional theory study on the binding and diffusion of copper monomers, dimers, and trimers adsorbed on Cu(111) is presented. Whereas atoms in trimers are found in fcc sites only, monomers as well as atoms in dimers can occupy the fcc as well as the metastable hcp site. In fact the dimer fcc-hcp configuration is only 1.3 meV less favorable with respect to the fcc-fcc configuration. This enables a confined intracell dimer motion, which at temperatures below 5 K is dominated by thermally assisted tunneling.

Adatom-vacancy mechanisms for the C6)/Al111-(6 x 6) reconstruction

The irreversible (6x6) reconstruction of the C(60)/Al(111) system from the (2sqrt[3]x2sqrt[3])R30 degrees phase is studied by first-principles techniques. We find that C60 binds optimally to the surface if an Al vacancy is created directly underneath. The removed Al atoms form a (6x6) array of ad-dimers in the interstices below the C60 overlayer, to which they strongly bind. This spontaneous local process, rather than the compression state of the unreconstructed C60 overlayer, explains why one molecule out of three protrudes from the surface upon reconstruction.

Nanocrystal formation and faceting instability in Al(110) homoepitaxy: true upward adatom diffusion at step edges and island corners

Using atomic force microscopy and spot-profile analyzing low energy electron diffraction, we have observed the existence of a striking faceting instability in Al(110) homoepitaxy, characterized by the formation of nanocrystals with well-defined facets. These hut-shaped nanocrystals are over tenfold higher than the total film coverage, and coexist in a bimodal growth mode with much shallower and more populous surface mounds. We further use density functional theory calculations to elucidate the microscopic origin of the faceting instability, induced by surprisingly low activation barriers for adatom ascent at step edges and island corners.

Theoretical studies of atomic-scale processes relevant to crystal growth

The study of adsorption, diffusion, island formation, and interlayer transport of atoms on a growing surface has been an active field in the past decade, because of both experimental and theoretical advances. Experiments can give detailed images of patterns formed on growing surfaces. An important challenge to the theoretical studies is the identification of dynamical processes controlling the pattern formation and overall surface morphology. This can be achieved by accurate modeling of the atomic interactions, a thorough search for active atomic-scale processes, and simulation of the growth on the experimental timescale to allow for detailed comparison with the experimental measurements. An overview of some of the theoretical methodology used in these studies and results obtained for one of the most extensively studied systems, Pt(111), is given here. A remarkable richness of phenomena has emerged from these studies, where apparently small effects can shift the balance between competing molecular processes and thereby change the morphology of a growing surface. The article concludes with a discussion of possible future directions in this research area.

Self-diffusion of small clusters on fcc metal (111) surfaces

We use ab initio density-functional theory supplemented with the embedded-atom method to study the self-diffusion of small clusters on the (111) surface of eight fcc metals. A zigzag motion is found to be important in the dimer and tetramer diffusions. The dimer diffuses by a zigzag and concerted motion. The trimer diffuses by a concerted three-atom motion. The tetramer diffuses through a zigzag motion where only two atoms move simultaneously in each step. Thus, instead of increasing, the migration energy is lowered (or stays constant) for the tetramer as compared to that for the trimer. This novel break of the upwards trend in migration energy is predicted to be a general phenomenon.

Formation and diffusion of S-decorated Cu clusters on Cu(111)

S-decorated Cu trimers are a likely agent of S-enhanced Cu transport between islands on Cu(111). According to ab initio calculations, excellent S bonding to trimer-Cu dangling valence results in an ad- Cu(3)S(3) formation energy of only approximately 0.28 eV, compared to 0.79 eV for a self-adsorbed Cu atom, and a diffusion barrier < or =0. 35 eV.

Probability of dimer reassociation in two dimensions

We study the problem of dimer dissociation and reassociation in two dimensions through a random-walk-like calculation. In order to find the probability of dimer reassociation after a given number of hops, we give the exact analytical solution for the probability of a first return into a given region (rhombus) for a two-dimensional random walker on a squared lattice.

Dynamics of surface migration in the weak corrugation regime

We report a systematic study for metal-on-metal surface migration in the weak corrugation regime, i.e., with migration barriers falling below approximately 100 meV. The migration characteristics are elucidated by variable-temperature scanning tunneling microscopy observations in the 50-200 K temperature range, which are analyzed by means of nucleation theory. The results demonstrate that, upon entering the weak corrugation regime, the dynamics of the systems are characterized by increasingly reduced effective preexponential factors, while Arrhenius behavior prevails.