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The random deposition model must be enhanced to reflect the variety of surface roughness due to some material characteristics of the film growing by vacuum deposition or sputtering. The essence of the computer simulation in this case is to account for possible surface migration of atoms just after the deposition, in connection with the binding energy between atoms (as the mechanism provoking the diffusion) and/or diffusion energy barrier. The interplay of these two factors leads to different morphologies of the growing surfaces, from flat and smooth ones to rough and spiky ones. In this paper, we extended our earlier calculation by applying an extra diffusion barrier at the edges of terrace-like structures, known as the Ehrlich–Schwoebel barrier. It is experimentally observed that atoms avoid descending when the terrace edge is approached, and these barriers mimic this tendency. Results of our Monte Carlo computer simulations are discussed in terms of surface roughness, and compared with other model calculations and some experiments from literature. The power law of the surface roughness σ against film thickness t was confirmed. The nonzero minimum value of the growth exponent β near 0.2 was obtained which is due to the limited range of the surface diffusion and the Ehrlich–Schwoebel barrier. Observations for different diffusion ranges are also discussed. The results are also confirimed with some deterministic growth models.

In this paper we present a generalization of a simple solid-on-solid epitaxial model of thin film growth, when surface morphology anisotropy is provoked by anisotropy in the model control parameters of binding energy and/or diffusion barrier. The anisotropy is discussed in terms of the height–height correlation function. It was experimentally confirmed that the difference in diffusion barriers yields anisotropy in morphology of the surface. We obtained antisymmetric correlations in the two in-plane directions for antisymmetric binding.

Langevin simulation is performed to investigate the diffusion coefficient of a Brownian particle subjected to an external harmonic noise in a two-dimensional coupled periodic potential. Resonant diffusion phenomenon is observed as a result of the coupling between the central frequency of the spectral density of the harmonic noise and the frequency of the potential well bottom. The diffusion coefficient presents approximately linear functions of the strengths of the internal and external noises for low values of the strengths, these functions can be understood by the local linearization approximation of the potential force. The damping coefficient dependence of the diffusion coefficient in lower damping is well fitted by a negative power function, as an internal Gaussian white noise case does, but with a power whose absolute value is larger than 1.

By using the Stillinger–Weber atomic interactional potential, we have carried out molecular dynamics simulations of single Si adatom diffusing on the Si(001) surface and single-layer Si(001) steps at temperatures ranging from 1000 K to 1300 K. We have presented one new diffusion pathway of a single Si adatom diffusing on the Si(001) along the direction perpendicular to dimer rows, that can weaken the diffusion anisotropy. We have investigated the process of the single Si adatom diffusing across single-layer Si(001) steps as well and given adatom diffusion pathways of step-flow and transformation of single-layer into double-layer steps. Our results show that the exchange between an adatom and a surface atom plays an important role in the adatom diffusion process above 1000 K.

In this paper, the dynamic properties of a single adatom subject to a two-dimensional periodic potential of square symmetry are investigated. This problem is addressed through the strong-collision model, where the dynamical interaction of the adatom with the substrate is modeled by well-separated collisions that thermalize the velocity. By means of molecular dynamics simulations, we calculate the jump-length probability distribution and the diffusion coefficient as a function of x–y coupling term and of the collision frequency $\eta$. Our numerical results show that the x–y coupling always suppresses a large proportion of long jumps, inducing thus a decrease of the diffusion coefficient for all values of $\eta$. Implications of these findings are briefly discussed.

As regards the copper oxide nanowire growth process, our experiment was consistent with the proposal of copper ions surface diffusion on a nanowire. Simply in the atmospheric pressure it is possible to synthesize CuO nanowires by annealing a copper sheet. Under a general copper oxide nanowires occurring condition, pouring the flow rate of a slight amount of air into an enclosed electric furnace in the atmospheric pressure, copper oxide nanowires adhering copper particles were synthesized on copper sheet successfully. In the growth process of the CuO wire, when the Cu substrate was heated in the air, stresses caused grain boundaries of Cu₂O and CuO layers in the Cu substrate. Ultimately Cu ions formed a wire tip diffusing on the surface of a CuO wire in the vertical direction to the top surface of the CuO layer, while assembling to the tip. In this report, we describe characteristics of the structure of the CuO nanowire obtained by lowering the air flow rate.

We study the effects of surface stress on the dynamics of a solid interface which evolves by surface diffusion. In the absence of surface stress, it is known that a flat interface is unstable for long wavelength perturbations and that in the nonlinear regime this instability develops into the formation of a sharp cusp. We compute the stability spectrum for a circular pore and for a flat interface considering the surface stress contribution, and analyze its effect on the process of formation of the cusp. Analyzing the length scales involved in the problem, we show that, within the context of continuum elasticity theory, surface stress does not suppress the singularity formation.

This paper addresses the approximation of surface diffusion flow using Cahn–Hilliard-type models. We introduce and analyze a new variational phase field model that associates the classical Cahn–Hilliard energy with two degenerate mobilities and guarantees a second-order accuracy in the approximation of the sharp limit. We also introduce simple and efficient numerical schemes to approximate the solutions to three Cahn–Hilliard-type models for surface diffusion flow, including the one we propose, and we provide 2D and 3D numerical experiments that illustrate the advantages of our approach.

A better comprehension of the behavior of shale gas transport in shale gas reservoirs will aid in predicting shale gas production rates. In this paper, an analytical apparent permeability expression for real gas is derived on the basis of the fractal theory and Fick’s law, with adequate consideration of the effects of Knudsen diffusion, surface diffusion and flexible pore shape. The gas apparent permeability model is found to be a function of microstructural parameters of shale reservoirs, gas property, Langmuir pressure, shale reservoir temperature and pressure. The results show that the apparent permeability increases with the increase of pore area fractal dimension and the maximum effective pore radius and decreases with an increase of the tortuosity fractal dimension; the effects of Knudsen diffusion and surface diffusion on the total apparent permeability cannot be ignored under high-temperature and low-pressure circumstances. These findings can contribute to a better understanding of the mechanism of gas transport in shale reservoirs.

In this work, a new gas transport model for shale reservoirs is constructed by embedding randomly distributed roughened tree-like bifurcation networks into the matrix porous medium. We constructed apparent permeability models for different shale gas flow mechanisms based on fractal theory, taking into account the effects of relative roughness and surface diffusion. The effects of bifurcation structure parameters as well as shale gas parameters on different apparent permeabilities are systematically analyzed. It is found that the permeability generally shows a decreasing trend with the increase in pore pressure, but the effect on viscous flow is inconsiderable. In addition, larger porosity, fractal dimension and bifurcation levels lead to increased permeability of different mechanisms. Whereas, the increase in the bifurcation levels implies a greater flow resistance, resulting in a decreased permeability. In addition, The relative roughness hinders the development of total permeability but favors surface diffusion permeability. Moreover, larger length ratios and diameter ratios are beneficial to the shale gas flow.

The adsorption of Ni atom on the Mo(110) surface has been studied within the density functional theory framework. It turned out that Ni–Mo surface alloy was formed with Ni atoms substituting Mo atom in the outermost layer. The subsurface site adsorption was found to be not preferred. Geometric analysis showed that the rumpling between substitutional Ni and Mo in the first alloy layer was about 0.108 Å at medium and low coverage (Θ). In addition, the diffusion of Ni on bare and Ni-substitutional Mo(110) surface has been investigated. It was shown that the diffusion energy barrier was reduced as the increase of coverage on bare Mo(110) surface, which supports the switch of growth mode layer-by-layer to Stranski–Krastanov as the function of coverage. Substitutional Ni atom only slightly increases the energy barrier for Ni diffusion on Mo(110) surface.

We apply a first-principles molecular-dynamics method based on the density functional theory to calculate several initial configurations of an O₂ molecule adsorbed on a Si(001) surface. The bonding processing, adsorption energy, dynamic track, and diffusion coefficient are investigated. The results indicate that the adsorption process may be divided into four stages: physical adsorption, chemical adsorption early stage, chemical adsorption late stage, and the superficial stable state. The Si=O structure, the Si–O–Si surface oxygen-bridge structure, and the Si–O–Si oxygen-bridge structure where oxygen atoms are inserted into the backbonds between the surface and the second layer of silicon atoms in the stable adsorption structures, are beneficial to the formation of the silica tetrahedral structure. We conclude that the remarkable difference between the diffusion coefficients during the physical adsorption stage leads to different diffusion paths, which results in the formation of two concomitant stable structures in the early process of silicon surface oxidation.

We performed STM measurements on the K/GaAs(110) surface with high K coverage. The K atoms gradually disappeared while scanning the tip over the surface at negative sample bias voltage. The phenomenon strongly occurred over the scanning area and can be explained by the field-induced surface diffusion from the scanning area to radial direction. Considering the interaction between the dipole moment of the adsorbed K atoms and the electric field, we discuss the relationship between the static and induced dipole moment of K atoms on a GaAs(110) surface.

Concepts, recent developments and achievements in investigations addressing the mobility of complex organic molecules on welldefined metal surfaces are reviewed.

A class of algorithms for computing high order geometric motions of planar curves is developed. The algorithms alternate between two simple steps—a convolution step and a "thresholding" step—to evolve planar curves according to combinations of Willmore flow, surface diffusion flow, and more general curvature dependent flows. When a closed curve is represented by a level set function and the thresholding step is replaced by redistancing the level set function according to its zero level contour, the proposed algorithm provide efficient and accurate computations of these geometric motions on uniform grids.