Nearest-neighbor Jumps Research Articles

Diffusion of O Atoms on a CO-Covered Ru(0001) Surface─A Combined High-Speed Scanning Tunneling Microscopy and Density Functional Theory Study at an Enhanced CO Coverage

The diffusion of adsorbed O atoms on a CO-covered Ru(0001) surface has recently been explained by a “door-opening” mechanism which is driven by fluctuations in the CO layer. Here, we analyze how this mechanism changes at a higher CO coverage than the 0.33 monolayers applied in the previous study and, therefore, lower concentrations of empty sites. High-speed scanning tunneling microscopy was used to track the O atoms. A statistical model based on nearest-neighbor jumps and uniform hopping probabilities into the six equivalent directions of the Ru(0001) lattice describes the data well. Surprisingly, the hopping rates, which involve site exchanges with CO molecules, are higher than the site exchanges at 0.33 monolayers. Density functional theory calculations were performed to explain these observations. The configurations of the CO molecules around the adsorbed O atoms obtained at the higher CO coverage are disordered. Displacements of CO molecules cost less energy than displacements in the ordered (3×3)R30° structure of the previous study. In addition, the activation energies for the jumps of the O atoms are lowered by enhanced O/CO repulsions. The atomic processes are thus faster at the higher coverage, but the general features of the door-opening mechanism remain valid.

THE AVERAGE TRAPPING TIME WITH NON-NEAREST-NEIGHBOR JUMPS ON THE LEVEL-3 SIERPINSKI GASKET

In this paper, we consider the trapping problem on the level-3 Sierpinski gasket [Formula: see text] when both nearest-neighbor (NN) and non-nearest-neighbor (NNN) jumps are included. Based on the topological structure of network and the method of probability generation function, we get the analytical expression of the average trapping time (ATT). Therefore, compared with the case where only NN jumps are allowed, we modify the specific value of ATT. Our results prove the exponent of the scaling expression has nothing to do with the NNN jump probability [Formula: see text], i.e. the scaling expression of ATT still scales superlinearly with the large network size. According to the analytical expression, we do numerical simulations of ATT with respect to parameters [Formula: see text] and [Formula: see text] (the number of generations of the network). The results show that the ATT will decrease with the increase of [Formula: see text]. These also indicate that NNN jump is helpful to improve the efficiency of random walk on network [Formula: see text].

Microscopic origin of diffusive dynamics in the context of transition path time distributions for protein folding and unfolding.

Experimentally measured transition path time distributions are usually analyzed theoretically in terms of a diffusion equation over a free energy barrier. It is though well understood that the free energy profile separating the folded and unfolded states of a protein is characterized as a transition through many stable micro-states which exist between the folded and unfolded states. Why is it then justified to model the transition path dynamics in terms of a diffusion equation, namely the Smoluchowski equation (SE)? In principle, van Kampen has shown that a nearest neighbor Markov chain of thermal jumps between neighboring microstates will lead in a continuum limit to the SE, such that the friction coefficient is proportional to the mean residence time in each micro-state. However, the practical question of how many microstates are needed to justify modeling the transition path dynamics in terms of an SE has not been addressed. This is a central topic of this paper where we compare numerical results for transition paths based on the diffusion equation on the one hand and the nearest neighbor Markov jump model on the other. Comparison of the transition path time distributions shows that one needs at least a few dozen microstates to obtain reasonable agreement between the two approaches. Using the Markov nearest neighbor model one also obtains good agreement with the experimentally measured transition path time distributions for a DNA hairpin and PrP protein. As found previously when using the diffusion equation, the Markov chain model used here also reproduces the experimentally measured long time tail and confirms that the transition path barrier height is ∼3kBT. This study indicates that in the future, when attempting to model experimentally measured transition path time distributions, one should perhaps prefer a nearest neighbor Markov model which is well defined also for rough energy landscapes. Such studies can also shed light on the minimal number of microstates needed to unravel the experimental data.

TRAPPING PROBLEM OF THE WEIGHTED SCALE-FREE TRIANGULATION NETWORKS FOR BIASED WALKS

In this paper, we study the trapping problem in the weighted scale-free triangulation networks with the growth factor [Formula: see text] and the weight factor [Formula: see text]. We propose two biased walks, one is standard weight-dependent walk only including the nearest-neighbor jumps, the other is mixed weight-dependent walk including both the nearest-neighbor and the next-nearest-neighbor jumps. For the weighted scale-free triangulation networks, we derive the exact analytic formulas of the average trapping time (ATT), the average of node-to-trap mean first-passage time over the whole networks, which measures the efficiency of the trapping process. The obtained results display that for two biased walks, in the large network, the ATT grows as a power-law function of the network size [Formula: see text] with the exponent, represented by [Formula: see text] when [Formula: see text]. Especially when the case of [Formula: see text] and [Formula: see text], the ATT grows linear with the network size [Formula: see text]. That is the smaller the value of [Formula: see text], the more efficient the trapping process is. Furthermore, comparing the standard weight-dependent walk with mixed weight-dependent walk, the obtained results show that although the next-nearest-neighbor jumps have no main effect on the trapping process, they can modify the coefficient of the dominant term for the ATT. The smaller the value of probability parameter [Formula: see text], the more efficient the trapping process for the mixed weight-dependent walk is.

Atomic self-diffusion in TiNi

The projector augmented wave method was applied to investigate the energetics of point defect formation at finite temperatures and the Ni-vacancy jumps in the intermetallic B2-TiNi alloy. It was shown that the effective formation energy of the Ni-vacancy (1.14 eV) is significantly lower than that of Ti-vacancy (1.74 eV); however, the antistructural atoms are dominant defects irrespective of alloy composition. The obtained results reveal that the migration barrier of the Ni-vacancy to the nearest-neighbor site is less (0.19 eV) than that for the Ni-vacancy jump to the next-nearest-neighbor site (1.64 eV). The Ni-vacancy implements two sequential nearest-neighbor jumps with short-lived intermediate configuration and some of such jumps initiate six-jump cycles of the Ni-vacancy along [0 0 1] and [1 1 0] directions with [0 0 1] bent mechanism as preferential one. In the latter case the calculated migration barrier of 0.82 eV is found to be in good agreement with experiment. The energy barrier for four-jump cycle flat mechanism is calculated by 0.27 eV higher. It is shown that the Ni-vacancy diffusion in B2-TiNi is strongly dominated by both six-jump cycle [0 0 1] bent and flat mechanisms at low temperatures but the contribution of the next-nearest-neighbor jumps become important with temperature increase.

Diffusion in B2 NiAl and FeAl Intermetallics and Their Alloys

Both FeAl and NiAl with B2 crystal structure are envisaged for their usage in high temperature applications and hence, availability of diffusion data in these intermetallics is crucial in designing their alloys and processes as well as deciding their in-service performance. A comprehensive overview of diffusion data available in B2 FeAl and NiAl and their alloys is provided in this article. Nearest neighbor vacancy jumps in B2 intermetallic lead to a local disorder in the lattice and hence it is not necessarily the unit step of diffusion in these structures. Several mechanisms of diffusion proposed in the literature are discussed including nearest neighbor jumps, next nearest neighbor jumps, six-jump vacancy cycle, triple defect and antisite bridge. Relevance of these mechanisms in FeAl and NiAl is discussed. An overview is given on the self-and solute diffusion and interdiffusion data available in both binary FeAl and NiAl. Due to wide solubility range of both FeAl and NiAl as well as their alloying requirements for improved properties, it becomes pertinent to study the multicomponent diffusion in the alloys based on these B2 itnermetallics. Hence, in the latter part of the article, various methods used for determining multicomponent diffusion data are reviewed. A detail overview is also provided on the diffusion studies available in literature on ternary alloys based on FeAl and NiAl with an emphasis on highlighting the diffusional interactions observed in these systems.

Metastability in the reversible inclusion process

We study the condensation regime of the finite reversible inclusion process, i.e., the inclusion process on a finite graph $S$ with an underlying random walk that admits a reversible measure. We assume that the random walk kernel is irreducible and its reversible measure takes maximum value on a subset of vertices $S_\star\subset S$. We consider initial conditions corresponding to a single condensate that is localized on one of those vertices and study the metastable (or tunneling) dynamics. We find that, if the random walk restricted to $S_\star$ is irreducible, then there exists a single time-scale for the condensate motion. In this case we compute this typical time-scale and characterize the law of the (properly rescaled) limiting process. If the restriction of the random walk to $S_\star$ has several connected components, a metastability scenario with multiple time-scales emerges. We prove such a scenario, involving two additional time-scales, in a one-dimensional setting with two metastable states and nearest-neighbor jumps.

Local stability of Kolmogorov forward equations for finite state nonlinear Markov processes

The focus of this work is on local stability of a class of nonlinear ordinary differential equations (ODE) that describe limits of empirical measures associated with finite-state weakly interacting N-particle systems. Local Lyapunov functions are identified for several classes of such ODE, including those associated with systems with slow adaptation and Gibbs systems. Using results from [5] and large deviations heuristics, a partial differential equation (PDE) associated with the nonlinear ODE is introduced and it is shown that positive definite subsolutions of this PDE serve as local Lyapunov functions for the ODE. This PDE characterization is used to construct explicit Lyapunov functions for a broad class of models called locally Gibbs systems. This class of models is significantly larger than the family of Gibbs systems and several examples of such systems are presented, including models with nearest neighbor jumps and models with simultaneous jumps that arise in applications.

Moments and Lyapunov exponents for the parabolic Anderson model

We study the parabolic Anderson model in $(1+1)$ dimensions with nearest neighbor jumps and space-time white noise (discrete space/continuous time). We prove a contour integral formula for the second moment and compute the second moment Lyapunov exponent. For the model with only jumps to the right, we prove a contour integral formula for all moments and compute moment Lyapunov exponents of all orders.

First-principles study of self- and solute diffusion mechanisms inγ′-Ni3Al

Multiple, competing diffusion mechanisms have been postulated in L1${}_{2}$ ordered compounds such as Ni${}_{3}$Al due to the presence of two distinct sublattices for self- and solute diffusion. They involve intrasublattice, intersublattice, two-pair vacancies, the six-jump cycle, and the antisite assisted jumps. In this work we systematically study these diffusion paths in L1${}_{2}$ ordered Ni${}_{3}$Al, postulated from three decades of experiments, by coupling density functional theory and the nudged elastic band methods. We determine activation barriers for self-diffusion (Ni and Al) atoms and solute diffusion (Cr, Co, and Ti) atoms, and also explore how solutes influence self-diffusion activation barriers. These calculations reveal that Ni vacancies mediate both self- and solute diffusion in ordered Ni${}_{3}$Al. Other findings include: (i) Ni atoms diffuse in their own sublattice via nearest neighbor jumps, (ii) Al atoms also preferentially diffuse in the Ni sublattice, (iii) solutes in the proximity of vacancies strongly affect the formation and also the migration energies in problems studied here, and (iv) diffusion mechanism(s) of solutes depend strongly on whether they occupy a Ni or Al site. This site occupancy is predicted by our activation barrier calculations and agrees with experiments. Our calculations reveal that antisite assisted solute diffusion has the lowest activation barrier. However, experiments report a higher activation barrier that correspond to the barriers for the six jump cycle mechanism determined by our calculations. Thus, our calculations together with published experimental work point to multiple, competing mechanisms driving the diffusion of ternary elements in Ni${}_{3}$Al.

Structural properties and diffusion processes of the Cu 3Au (0 0 1) surface

The surface relaxation and surface energy of both the mixed AuCu and pure Cu terminated Cu 3Au (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 Cu 3Au (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.

Localized Relaxational Dynamics of Succinonitrile

Succinonitrile (N≡C—CH2—CH2—C≡N) is a good ionic conductor, when doped with an ionic compound, at room temperature, where it is in its plastic crystalline phase (Long et al. Solid State Ionics 2003, 161, 105; Alarco et al. Nat. Mater. 2004, 3, 476). We report on the relaxational dynamics of the plastic phase near the two first-order phase transitions and on the effect of dissolving a salt in the plastic matrix by quasi-elastic neutron scattering. At 240 K, the three observed relaxations are localized and we can describe their dynamics (τ ≈ 1.7, 17, and 140 ps) to a certain extent from a model using a single molecule that was proposed by Bée et al. allowing for all conformations in its unit cell (space group IM3M). The extent of the localized motion as observed is however larger than that predicted by the model and suggests that the isomerization of succinonitrile is correlated with a jump to the nearest neighbor site in the unit cell. The salt containing system is known to be a good ionic conductor, and our results show that the effect of the ions on the succinonitrile matrix is homogeneous. Because the isomerizations and rotations are governed by intermolecular interactions, the dissolved ions have an effect over an extended range. Due to the addition of the salt, the dynamics of one of the components (τ ≈ 17 ps) shows more diffusive character at 300 K. The calculated upper limit of the corresponding diffusion constant of succinonitrile in the electrolyte is a factor 30 higher than what is reported for the ions. Our results suggest that the succinonitrile diffusion is caused by nearest neighbor jumps that are localized on the observed length and time scales.

Atomistic simulation of the point defects in B2-type MoTa alloy

The formation and migration mechanisms of three different point defects (mono-vacancy, anti-site defect and interstitial atom) in B 2 -type MoTa alloy have been investigated by combining molecular dynamics (MD) simulation with modified analytic embedded-atom method (MAEAM). From minimization of the formation energy, we find that the anti-site defects Mo Ta and Ta Mo are easier to form than Mo and Ta mono-vacancies, while Mo and Ta interstitial atoms are difficult to form in the alloy. In six migration mechanisms of Mo and Ta mono-vacancies, one nearest-neighbor jump (1NNJ) is the most favorable due to its lowest activation and migration energies, but it will cause a disorder in the alloy. One next-nearest-neighbor jump (1NNNJ) and one third-nearest-neighbor jump (1TNNJ) can maintain the ordered property of the alloy but require higher activation and migration energies, so the 1NNNJ and 1TNNJ should be replaced by straight [1 0 0] six nearest-neighbor cyclic jumps (S[1 0 0]6NNCJ) or bent [1 0 0] six nearest-neighbor cyclic jumps (B[1 0 0]6NNCJ) and [1 1 0] six nearest-neighbor cyclic jumps ([1 1 0]6NNCJ), respectively. Although the migrations of Mo and Ta interstitial atoms need much lower energy than Mo and Ta mono-vacancies, they are not main migration mechanisms due to difficult to form in the alloy.

Diffusion model of solute dynamics in a membrane channel: Mapping onto the two-site model and optimizing the flux

The steady-state flux through a singly occupied membrane channel is found for both discrete and continuum models of the solute dynamics in the channel. The former describes the dynamics as nearest-neighbor jumps between N sites, while the latter assumes that the molecule diffuses in a one-dimensional potential of mean force. For both models it is shown that the flux is the same as that for a simple two-site model with appropriately chosen rate constants, which contain all the relevant information about the more detailed dynamics. An interesting consequence of single occupancy is that the flux has a maximum as a function of the channel-solute interaction. If this interaction is too attractive, the molecule will never leave the channel, thus blocking it for the passage of other molecules. If it is too repulsive, the solute molecule will never enter the channel. Thus the flux vanishes in the two limits and, hence, has a maximum somewhere in-between. In the framework of the diffusion model, we find the optimal intrachannel potential of mean force that maximizes the flux using the calculus of variations. For a symmetric channel this potential is flat and occupies the entire channel. In the general case of an asymmetric channel, the optimal potential is obtained by tilting the optimal flat potential for the corresponding symmetric channel around the channel center, so that the solute is driven towards the reservoir with the lower solute concentration by a constant force. This implies that the flux is higher when the solute binding near the channel exit is stronger than that near the entrance.

Kinetics of atom rebounding in surface self-diffusion

Self-diffusion of tungsten atoms as well as the distribution of displacements has in the past been examined on the channeled $\mathrm{W}(211)$ plane. In addition to simple nearest-neighbor jumps and double transitions, rebound jumps, in which an atom jumps but returns immediately to its starting position, have been identified. The kinetics of rebounds have now been determined. Rebounds occur on $\mathrm{W}(211)$ at temperatures as low as $300\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, with an activation energy of $1.03\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$ and a frequency prefactor of $1.40\ifmmode\times\else\texttimes\fi{}{10}^{16}\phantom{\rule{0.3em}{0ex}}{\mathrm{s}}^{\ensuremath{-}1}$; they have not been found in diffusion on $\mathrm{W}(110)$.

Euler hydrodynamics of one-dimensional attractive particle systems

We consider attractive irreducible conservative particle systems on $\mathbb{Z}$, without necessarily nearest-neighbor jumps or explicit invariant measures. We prove that for such systems, the hydrodynamic limit under Euler time scaling exists and is given by the entropy solution to some scalar conservation law with Lipschitz-continuous flux. Our approach is a generalization of Bahadoran et al. [Stochastic Process. Appl. 99 (2002) 1--30], from which we relax the assumption that the process has explicit invariant measures.

Molecular mass and dynamics of poly(methyl acrylate) in the glass-transition region

The segmental dynamics of bulk poly(methyl acrylate) (PMA) were studied as a function of molecular mass in the glass-transition region using 2H NMR and modulated differential scanning calorimetry (MDSC). Quadrupole-echo 2H NMR spectra were obtained for four samples of methyl-deuterated PMA-d3 with different molecular masses. The resulting spectra were fit using superpositions of simulated spectra generated from the MXQET simulation program, based on a model incorporating nearest-neighbor jumps from positions on the vertices of a truncated icosahedron (soccer-ball shape). The lower molecular-mass samples, influenced by the presence of more chain ends, showed more heterogeneity (broader distribution) and lower glass transitions than the higher molecular-mass samples. The MDSC experiments on both protonated and deuterated samples showed behavior consistent with the NMR results, but temperature shifted due to the different frequency range of the measurements in terms of both the position and breadth of the glass transition as a function of molecular mass.

Fractional diffusion modeling of ion channel gating

An anomalous diffusion model for ion channel gating is put forward. This scheme is able to describe nonexponential, power-law-like distributions of residence time intervals in several types of ion channels. Our method presents a generalization of the discrete diffusion model by Millhauser, Salpeter, and Oswald [Proc. Natl. Acad. Sci. U.S.A. 85, 1503 (1988)] to the case of a continuous, anomalous slow conformational diffusion. The corresponding generalization is derived from a continuous-time random walk composed of nearest-neighbor jumps which in the scaling limit results in a fractional diffusion equation. The studied model contains three parameters only: the mean residence time, a characteristic time of conformational diffusion, and the index of subdiffusion. A tractable analytical expression for the characteristic function of the residence time distribution is obtained. In the limiting case of normal diffusion, our prior findings [Proc. Natl. Acad. Sci. U.S.A. 99, 3552 (2002)] are reproduced. Depending on the chosen parameters, the fractional diffusion model exhibits a very rich behavior of the residence time distribution with different characteristic time regimes. Moreover, the corresponding autocorrelation function of conductance fluctuations displays nontrivial power law features. Our theoretical model is in good agreement with experimental data for large conductance potassium ion channels.

Ni and Fe tracer diffusion in the B2-ordered Ni 40Fe 10Al 50 ternary alloy

Ni and Fe bulk diffusion in the B2-ordered Ni 40Fe 10Al 50 ternary alloy is investigated by means of radiotracer measurements ( 63Ni and 59Fe tracers) and SIMS analysis ( 64Ni tracer) in an extended temperature interval from 1150 to 1550 K. Almost linear Arrhenius behavior was observed for both, Ni (pre-exponential factor D 0 ∗ Ni =1.3·10 −5 m 2/s and activation enthalpy Q Ni=270 kJ/mol) and Fe ( D 0 ∗ Fe =1.2·10 −4 m 2/s and Q Fe=279 kJ/mol) diffusion. The Fe diffusivity was found to be by a factor of three to five larger than that of Ni. Furthermore, Ni diffuses in Ni 40Fe 10Al 50 faster than in stoichiometric NiAl and the activation enthalpy of Ni diffusion in Ni 40Fe 10Al 50 is significantly smaller as compared to the stoichiometric binary NiAl alloy (by about 35 kJ/mol). The activation enthalpy of Ni diffusion in the Ni 50− x Fe x Al 50 ternary alloys was found to reveal a minimum for ternary compositions with about 10% of Fe addition. The apparent controversial behavior of creep resistance and self-diffusivity in the NiFeAl ternary alloys is discussed. The analysis of experimental data favors nearest-neighbor jumps (most likely the triple defect mechanism) as a dominant diffusion mechanism in the alloy.

The two internal friction peaks in rapidly cooled Fe71Al29 alloy*

Three internal friction peaks were found around 180℃ (termed as P1),340℃ (termed as P2) and 510℃(termed as P3) in rapidly cooled Fe71Al29 alloy,while only the P3 peak can be observed in slowly cooled sp ecimens.Only the P1 and P2 peaks were investigated using a computer- controlled inverted torsion pendulum in the present study.The P1 and P2 peaks in air-cooled specimens disappear during cooling or after long term ag eing at 350℃.They decline even disappear with increasing ageing time.Both the P1 and P2 peaks have relaxation features and their activation energy values are H1=1．03±0．08eVfor the P1 peak and H2=1．64±0．05eV for the P2 peak.It is suggested that P1 peak originates from the nearestneighbor jumps of Al atoms within tetrahedral lattices and P2 peak from the next-nearest-neighbor jumps of Al atoms within tetrahedral lattices in quenched alloys.