Anisotropy of diffusion along steps on the (111) faces of gold and silver

Crystal plane orientation-dependent surface atom diffusion in sub-10-nm Au nanocrystals

Surface atom diffusion is a ubiquitous phenomenon in nanostructured metals with ultrahigh surface-to-volume ratios. However, the fundamental atomic mechanism of surface atom diffusion remains elusive. Here, we report in situ atomic-scale observations of surface pressure-driven atom diffusion in gold nanocrystals at room temperature using high-resolution transmission electron microscopy with a high-speed detection camera. The topmost layer of atoms on (001) plane initially diffuse in a column-by-column manner. As diffusion proceeds, the remaining atomic columns collectively inject into adjacent underlayer, accompanied by nucleation of a surface dislocation. In comparison, atoms on (111) plane directly diffuse to the base without collective injection. Quantitative calculations indicate that these crystal plane orientation-dependent atom diffusion behaviors contribute to the larger diffusion coefficient of (111) plane compared to (001) plane in addition to the effect of diffusion activation energy. Our findings provide valuable insights into atomic mechanisms of diffusion-dominant morphology evolution of nanostructured metals and guide the design of nanostructured materials with enhanced structural stability.

Controlling the Shape of Small Clusters with and without Macroscopic Fields

Despite major advances in the understanding of the formation and dynamics of nanoclusters in the past decades, theoretical bases for the control of their shape are still lacking. We investigate strategies for driving fluctuating few-particle clusters to an arbitrary target shape in minimum time with or without an external field. This question is recast into a first passage problem, solved numerically, and discussed within a high temperature expansion. Without field, large-enough low-energy target shapes exhibit an optimal temperature at which they are reached in minimum time. We then compute the optimal way to set an external field to minimize the time to reach the target, leading to a gain of time that grows when increasing cluster size or decreasing temperature. This gain can shift the optimal temperature or even create one. Our results could apply to clusters of atoms at equilibrium, and colloidal or nanoparticle clusters under thermo- or electrophoresis.

Effects of boron defects on mechanical strengths of TiB2 at high temperature: ab initio molecular dynamics studies

We report the determination of diffusion paths and potential barriers of boron point defects in TiB2 calculated using the climbing image nudged elastic band method at T = 0 K, and ab initio molecular dynamics studies on the structural stabilities, diffusion behavior of boron point defects and mechanical strengths of TiB2 at elevated temperatures. In contrast to the previous conjecture that TiB2 with boron vacancies are thermodynamically unstable based on the calculations at T = 0 K that boron vacancies have positive formation energies and shift electronic Fermi energies from the pseudogap valleys to the bonding states, our results show that boron vacancies in TiB2 are very robust and they have negligible effects on the structural stabilities and mechanical strengths of TiB2 at least up to 2000 K within the vacancy concentration we studied (<2.5 at%). On the other hand, our results reveal that the boron interstitials can diffuse easily in TiB2 at a moderately high temperature (1000 K) or under large shear and tensile deformations, which give rise to significant deteriorations (more than 50% reduction) in the mechanical strength of TiB2 at a high temperature (2000 K) with a boron interstitial density below 2.5 at%. Under all the shear and tensile deformations we applied, the boron interstitials in TiB2 eventually diffuse into the boron layers, causing deformations of these boron layers, which weakens their interactions with metal layers nearby and consequently reduces the mechanical strengths of the materials as temperature and boron interstitial density increase. The present findings expand our understandings on the material strength of TiB2 at high temperatures with boron point defects, and offer new insights for its applications as a high-strength ultra-high temperature ceramic.

Computing long time scale biomolecular dynamics using quasi-stationary distribution kinetic Monte Carlo (QSD-KMC)

It is a challenge to obtain an accurate model of the state-to-state dynamics of a complex biological system from molecular dynamics (MD) simulations. In recent years, Markov state models have gained immense popularity for computing state-to-state dynamics from a pool of short MD simulations. However, the assumption that the underlying dynamics on the reduced space is Markovian induces a systematic bias in the model, especially in biomolecular systems with complicated energy landscapes. To address this problem, we have devised a new approach we call quasistationary distribution kinetic Monte Carlo (QSD-KMC) that gives accurate long time state-to-state evolution while retaining the entire time resolution even when the dynamics is highly non-Markovian. The proposed method is a kinetic Monte Carlo approach that takes advantage of two concepts: (i) the quasistationary distribution, the distribution that results when a trajectory remains in one state for a long time (the dephasing time), such that the next escape is Markovian, and (ii) dynamical corrections theory, which properly accounts for the correlated events that occur as a trajectory passes from state to state before it settles again. In practice, this is achieved by specifying, for each escape, the intermediate states and the final state that has resulted from the escape. Implementation of QSD-KMC imposes stricter requirements on the lengths of the trajectories than in a Markov state model approach as the trajectories must be long enough to dephase. However, the QSD-KMC model produces state-to-state trajectories that are statistically indistinguishable from an MD trajectory mapped onto the discrete set of states for an arbitrary choice of state decomposition. Furthermore, the aforementioned concepts can be used to construct a Monte Carlo approach to optimize the state boundaries regardless of the initial choice of states. We demonstrate the QSD-KMC method on two one-dimensional model systems, one of which is a driven nonequilibrium system, and on two well-characterized biomolecular systems.

Universality and scaling in two-step epitaxial growth in one dimension

Irreversible one-dimensional (1D) epitaxial growth at small coverages via the recently suggested two-step growth protocol [Tokar and Dreyssé, Surf. Sci. 637-638, 116 (2015)] has been studied with the use of the kinetic Monte Carlo and the rate-equation techniques. It has been found that similar to the two-dimensional (2D) case the island capture zones could be accurately approximated with the Gamma probability distribution (GD). Coverage independence of the average island sizes grown at the first step that was also found in two dimensions was observed. In contrast to 2D case, the shape parameter of the GD was also found to be coverage-independent. Using these two constants as the input, an analytical approach that allowed for the description of the commonly studied statistical distributions to the accuracy of about 2% has been developed. Furthermore, it was established that the distributions of the island sizes and the interisland gaps grown via the two-step protocol were about 50% narrower than in the case of nucleation on random defects, which can be of practical importance. Equivalence between the GD shape of the island size distribution in the scaling regime and the linear dependence of the capture numbers on the island size in the rate-equation approach has been proved.

Analytical approach for collective diffusion: one-dimensional homogeneous lattice

Diffusion of particles adsorbed on the homogeneous one-dimensional chain was investigated using a theoretical approach and kinetic Monte Carlo simulations. The concentration dependencies of the center-of-mass and Fickian diffusion coefficients have been calculated for some representative values of lateral interactions between adsorbed particles. The analytical dependencies have been compared with the numerical data. The perfect coincidence of the data obtained by the two quite different methods clearly demonstrates that the analytical expressions for the diffusion coefficients derived in the framework of the approach based on the non-equilibrium statistical operator exactly describe the particle migration in the lattice gas systems.

Quantitative measurement of the surface self-diffusion on Au nanoparticles by aberration-corrected transmission electron microscopy

We present a method that allows for a quantitative measurement of the surface self-diffusion on nanostructures, such as nanoparticles, at the atomic scale using aberration-corrected high-resolution transmission electron microscopy (HRTEM). The diffusion coefficient can be estimated by measuring the fluctuation of the atom column occupation at the surface of Au nanoparticles, which is directly observable in temporal sequences of HRTEM images. Both a Au icosahedron and a truncated Au octahedron are investigated, and their diffusion coefficients are found to be in the same order of magnitude, D = 10(-17) to 10(-16) cm(2)/s. It is to be assumed that the measured surface diffusion is affected by the imaging electron beam. This assumption is supported by the observed instability of a (5 × 1) surface reconstruction on a {100} Au facet.

How Far to Use Tight-Binding Potentials for Bimetallic Surface Modelling?

Modelling in a realistic way both equilibrium and dynamical processes on bimetallic surfaces requires the availability of interatomic potentials sufficiently simple (i.e. analytical) although derived from the electronic structure. This is possible in the framework of Tight-Binding formalism. We present here a review of the applications of such potentials, together with some reflexions about their limitations.

Anisotropic diffusion of n-butane and n-decane on a stepped metal surface

The diffusion of single n-butane and n-decane molecules on a model stepped surface, Pt655, and on a corresponding flat surface, Pt111, is investigated using molecular-dynamics simulations and anisotropic united atom model. The surface step on Pt655 causes the alkane molecules to adsorb on the lower terrace in all-trans conformations with their long molecular axes adjacent and parallel to the step edge, and to diffuse anisotropically along the surface step via a constant wiggly motion without rotation or marked deviation from the parallel adsorption configuration. At relatively high temperatures, the alkane molecules can temporarily break away from the step edge but cannot migrate across the step edge in either the downstair or upstair direction. In comparison with the diffusion on Pt111, the diffusivity of n-decane is reduced by the surface step but its diffusion barrier is hardly affected. In the case of the shorter n-butane, however, the surface step significantly reduces the diffusion energy barrier and gives rise to higher diffusion coefficients at lower temperatures. Important implications of the simulation results are discussed.