Nonequilibrium effects in diffusion of interacting particles on vicinal surfaces

We study the influence of nonequilibrium conditions on the collective diffusion of interacting particles on vicinal surfaces. To this end, we perform Monte Carlo simulations of a lattice-gas model of an ideal stepped surface, where adatoms have nearest-neighbor attractive or repulsive interactions. Applying the Boltzmann–Matano method to spreading density profiles of the adatoms allows the definition of an effective, time-dependent collective diffusion coefficient DtC(θ) for all coverages θ. In the case of diffusion across the steps and strong binding at lower step edges we observe three stages in the behavior of the corresponding Dtxx,C(θ). At early times when the adatoms have not yet crossed the steps, Dtxx,C(θ) is influenced by the presence of steps only weakly. At intermediate times, where the adatoms have crossed several steps, there are sharp peaks at coverages θ1−1∕L, where L is the terrace width. These peaks are due to different rates of relaxation of the density at successive terraces. At late stages of spreading, these peaks vanish and Dtxx,C(θ) crosses over to its equilibrium value, where for strong step edge binding there is a maximum at θ=1∕L. In the case of diffusion in direction along the steps the nonequilibrium effects in Dtyy,C(θ) are much weaker, and are apparent only when diffusion along ledges is strongly suppressed or enhanced.Peer reviewe

Interplay between steps and nonequilibrium effects in surface diffusion for a lattice-gas model of O/W(110)

The authors consider the influence of steps and nonequilibrium conditions on surfacediffusion in a strongly interactingsurfaceadsorbate system. This problem is addressed through Monte Carlo simulations of a lattice-gas model of O∕W(110), where steps are described by an additional binding energy EB at the lower step edge positions. Both equilibrium fluctuation and Boltzmann-Matano spreading studies indicate that the role of steps for diffusion across the steps is prominent in the ordered phases at intermediate coverages. The strongest effects are found in the p(2×1) phase, whose periodicity Lp is 2. The collective diffusion then depends on two competing factors: domain growth within the ordered phase, which on a flat surface has two degenerate orientations [p(2×1) and p(1×2)], and the step-induced ordering due to the enhanced binding at the lower step edge position. The latter case favors the p(2×1) phase, in which all adsorption sites right below the step edge are occupied. When these two factors compete, two possible scenarios emerge. First, when the terrace width L does not match the periodicity of the ordered adatom layer (L/Lp is noninteger), the mismatch gives rise to frustration, which eliminates the effect of steps provided that EB is not exceptionally large. Under these circumstances, the collective diffusion coefficient behaves largely as on a flat surface. Second, however, if the terrace width does match the periodicity of the ordered adatom layer (L/Lp is an integer), collective diffusion is strongly affected by steps. In this case, the influence of steps is manifested as the disappearance of the major peak associated with the ordered p(2×1) and p(1×2) structures on a flat surface. This effect is particularly strong for narrow terraces, yet it persists up to about L≈25Lp for small EB and up to about L≈500Lp for EB, which is of the same magnitude as the bare potential of the surface. On real surfaces, similar competition is expected, although the effects are likely to be smaller due to fluctuations in terrace widths. Finally, Boltzmann-Matano spreading simulations indicate that even slight deviations from equilibrium conditions may give rise to transient peaks in the collective diffusion coefficient. These transient structures are due to the interplay between steps and nonequilibrium conditions and emerge at coverages, which do not correspond to the ideal ordered phases.Peer reviewe

Diffusion processes and growth on stepped metal surfaces

We study the dynamics of adatoms in a model of vicinal (11m) fcc metal surfaces. We examine the role of different diffusion mechanisms and their implications to surface growth. In particular, we study the effect of steps and kinks on adatom dynamics. We show that the existence of kinks is crucially important for adatom motion along and across steps. Our results are in agreement with recent experiments on Cu(100) and Cu(1,1,19) surfaces. The results also suggest that for some metals exotic diffusion mechanisms may be important for mass transport across the steps.Comment: 3 pages, revtex, complete file available from ftp://rock.helsinki.fi/pub/preprints/tft/ or at http://www.physics.helsinki.fi/tft/tft_preprints.html (to appear in Phys. Rev. B Rapid Comm.

Width Distributions and the Upper Critical Dimension of KPZ Interfaces

Simulations of restricted solid-on-solid growth models are used to build the width-distributions of d=2-5 dimensional KPZ interfaces. We find that the universal scaling function associated with the steady-state width-distribution changes smoothly as d is increased, thus strongly suggesting that d=4 is not an upper critical dimension for the KPZ equation. The dimensional trends observed in the scaling functions indicate that the upper critical dimension is at infinity.Comment: 4 pages, 4 postscript figures, RevTe

Two-Loop Renormalization Group Analysis of the Burgers-Kardar-Parisi-Zhang Equation

A systematic analysis of the Burgers--Kardar--Parisi--Zhang equation in $d+1$ dimensions by dynamic renormalization group theory is described. The fixed points and exponents are calculated to two--loop order. We use the dimensional regularization scheme, carefully keeping the full $d$ dependence originating from the angular parts of the loop integrals. For dimensions less than $d_c=2$ we find a strong--coupling fixed point, which diverges at $d=2$, indicating that there is non--perturbative strong--coupling behavior for all $d \geq 2$. At $d=1$ our method yields the identical fixed point as in the one--loop approximation, and the two--loop contributions to the scaling functions are non--singular. For $d>2$ dimensions, there is no finite strong--coupling fixed point. In the framework of a $2+\epsilon$ expansion, we find the dynamic exponent corresponding to the unstable fixed point, which describes the non--equilibrium roughening transition, to be $z = 2 + {\cal O} (\epsilon^3)$, in agreement with a recent scaling argument by Doty and Kosterlitz. Similarly, our result for the correlation length exponent at the transition is $1/\nu = \epsilon + {\cal O} (\epsilon^3)$. For the smooth phase, some aspects of the crossover from Gaussian to critical behavior are discussed.Comment: 24 pages, written in LaTeX, 8 figures appended as postscript, EF/UCT--94/3, to be published in Phys. Rev. E

Upper critical dimension, dynamic exponent and scaling functions in the mode-coupling theory for the Kardar-Parisi-Zhang equation

We study the mode-coupling approximation for the KPZ equation in the strong coupling regime. By constructing an ansatz consistent with the asymptotic forms of the correlation and response functions we determine the upper critical dimension d_c=4, and the expansion z=2-(d-4)/4+O((4-d)^2) around d_c. We find the exact z=3/2 value in d=1, and estimate the values 1.62, 1.78 for z, in d=2,3. The result d_c=4 and the expansion around d_c are very robust and can be derived just from a mild assumption on the relative scale on which the response and correlation functions vary as z approaches 2.Comment: RevTex, 4 page

Stretched exponential relaxation in the mode-coupling theory for the Kardar-Parisi-Zhang equation

We study the mode-coupling theory for the Kardar-Parisi-Zhang equation in the strong-coupling regime, focusing on the long time properties. By a saddle point analysis of the mode-coupling equations, we derive exact results for the correlation function in the long time limit - a limit which is hard to study using simulations. The correlation function at wavevector k in dimension d is found to behave asymptotically at time t as C(k,t)\simeq 1/k^{d+4-2z} (Btk^z)^{\gamma/z} e^{-(Btk^z)^{1/z}}, with \gamma=(d-1)/2, A a determined constant and B a scale factor.Comment: RevTex, 4 pages, 1 figur

Developmental Toxicity of Surface-Modified Gold Nanorods in the Zebrafish Model

Background: nanotechnology is one of the fastest-growing areas, and it is expected to have a substantial economic and social impact in the upcoming years. Gold particles (AuNPs) offer an opportunity for wide-ranging applications in diverse fields such as biomedicine, catalysis, and electronics, making them the focus of great attention and in parallel necessitating a thorough evaluation of their risk for humans and ecosystems. Accordingly, this study aims to evaluate the acute and developmental toxicity of surfacemodified gold nanorods (AuNRs), on zebrafish (Danio rerio) early life stages. Methods: in this study, zebrafish embryos were exposed to surface-modified AuNRs at concentrations ranging from 1 to 20 μg/mL. Lethality and developmental endpoints such as hatching, tail flicking, and developmental delays were assessed until 96 h post-fertilization (hpf). Results: we found that AuNR treatment decreases the survival rate in embryos in a dose-dependent manner. Our data showed that AuNRs caused mortality with a calculated LC50 of EC50,24hpf of AuNRs being 9.1 μg/mL, while a higher concentration of AuNRs was revealed to elicit developmental abnormalities. Moreover, exposure to high concentrations of the nanorods significantly decreased locomotion compared to untreated embryos and caused a decrease in all tested parameters for cardiac output and blood flow analyses, leading to significantly elevated expression levels of cardiac failure markers ANP/NPPA and BNP/NPPB. Conclusions: our results revealed that AuNR treatment at the EC50 induces apoptosis significantly through the P53, BAX/BCL-2, and CASPASE pathways as a suggested mechanism of action and toxicity modality.This research was funded by the Qatar University–internal grant, grant number QUCP-CHS-2022-483 for M.A. and financial funding of the Deanship of Scientific Research at the Al-Zaytoonah University of Jordan (2020-2019/12/28) for N.M

Self-diffusion of adatoms, dimers, and vacancies on Cu(100)

We use ab initio static relaxation methods and semi-empirical molecular-dynamics simulations to investigate the energetics and dynamics of the diffusion of adatoms, dimers, and vacancies on Cu(100). It is found that the dynamical energy barriers for diffusion are well approximated by the static, 0 K barriers and that prefactors do not depend sensitively on the species undergoing diffusion. The ab initio barriers are observed to be significantly lower when calculated within the generalized-gradient approximation (GGA) rather than in the local-density approximation (LDA). Our calculations predict that surface diffusion should proceed primarily via the diffusion of vacancies. Adatoms are found to migrate most easily via a jump mechanism. This is the case, also, of dimers, even though the corresponding barrier is slightly larger than it is for adatoms. We observe, further, that dimers diffuse more readily than they can dissociate. Our results are discussed in the context of recent submonolayer growth experiments of Cu(100).Comment: Submitted to the Physical Review B; 15 pages including postscript figures; see also http://www.centrcn.umontreal.ca/~lewi

Nonlinear Measures for Characterizing Rough Surface Morphologies

We develop a new approach to characterizing the morphology of rough surfaces based on the analysis of the scaling properties of contour loops, i.e. loops of constant height. Given a height profile of the surface we perform independent measurements of the fractal dimension of contour loops, and the exponent that characterizes their size distribution. Scaling formulas are derived and used to relate these two geometrical exponents to the roughness exponent of a self-affine surface, thus providing independent measurements of this important quantity. Furthermore, we define the scale dependent curvature and demonstrate that by measuring its third moment departures of the height fluctuations from Gaussian behavior can be ascertained. These nonlinear measures are used to characterize the morphology of computer generated Gaussian rough surfaces, surfaces obtained in numerical simulations of a simple growth model, and surfaces observed by scanning-tunneling-microscopes. For experimentally realized surfaces the self-affine scaling is cut off by a correlation length, and we generalize our theory of contour loops to take this into account.Comment: 39 pages and 18 figures included; comments to [email protected]