Coupled molecular and cantilever dynamics model for frequency-modulated atomic force microscopy.

A molecular dynamics model is presented, which adds harmonic potentials to the atomic interactions to mimic the elastic properties of an AFM cantilever. It gives new insight into the correlation between the experimentally monitored frequency shift and cantilever damping due to the interaction between tip atoms and scanned surface. Applying the model to ionic crystals with rock salt structure two damping mechanisms are investigated, which occur separately or simultaneously depending on the tip position. These mechanisms are adhesion hysteresis on the one hand and lateral excitations of the cantilever on the other. We find that the short range Lennard-Jones part of the atomic interaction alone is sufficient for changing the predominant mechanism. When the long range ionic interaction is switched off, the two damping mechanisms occur with a completely different pattern, which is explained by the energy landscape for the apex atom of the tip. In this case the adhesion hysteresis is always associated with a distinct lateral displacement of the tip. It is shown how this may lead to a systematic shift between the periodic patterns obtained from the frequency and from the damping signal, respectively.

Dissipation signals due to lateral tip oscillations in FM-AFM.

We study the coupling of lateral and normal tip oscillations and its effect on the imaging process of frequency-modulated dynamic atomic force microscopy. The coupling is induced by the interaction between tip and surface. Energy is transferred from the normal to the lateral excitation, which can be detected as damping of the cantilever oscillation. However, energy can be transferred back into the normal oscillation, if not dissipated by the usually uncontrolled mechanical damping of the lateral excitation. For certain cantilevers, this dissipation mechanism can lead to dissipation rates larger than 0.01 eV per period. The mechanism produces an atomic contrast for ionic crystals with two maxima per unit cell in a line scan.

Coexistence and transition between shear zones in slow granular flows.

We report experiments on slow granular flows in a split-bottom Couette cell that show novel strain localization features. Nontrivial flow profiles have been observed which are shown to be the consequence of simultaneous formation of shear zones in the bulk and at the boundaries. The fluctuating band model based on a minimization principle can be fitted to the experiments over a large variation of morphology and filling height with one single fit parameter, the relative friction coefficient µ(rel) between wall and bulk. The possibility of multiple shear zone formation is controlled by µ(rel). Moreover, we observe that the symmetry of an initial state, with coexisting shear zones at both side walls, breaks spontaneously below a threshold value of the shear velocity. A dynamical transition between two asymmetric flow states happens over a characteristic time scale which depends on the shear strength.

Long-range interactions in randomly driven granular fluids.

We study the long-range spatial correlations in the nonequilibrium steady state of a randomly driven granular fluid with the emphasis on obtaining the explicit form of the static structure factors. The presence of immobile particles immersed in such a fluidized bed of fine particles leads to the confinement of the fluctuation spectrum of the hydrodynamic fields, which results in effective long-range interactions between the intruders. The analytical predictions are in agreement with the results of discrete element method simulations. By changing the shape and orientation of the intruders, we address how the effective force is affected by small changes in the boundary conditions.

Evolution of the force distributions in jammed packings of soft particles.

The evolution of the force distributions during the isotropic compression of two-dimensional packings of soft frictional particles is investigated numerically. Regardless of the applied deformation, the normal contact force distribution P(f(n)) can be fitted by the product of a power law, and a stretched exponential, while the tangential force distribution P(f(t)) is fitted well by a Gaussian. With increasing strain, the asymptotic behavior at large forces does not change, but both P(f(n)) and P(f(t)) exhibit a broadening, even though, when scaled with the average forces, their widths decrease. Furthermore, the distribution of friction mobilization P(η) is a decreasing function of η=|f(t)|/(µf(n)), except for an increased probability of fully mobilized contacts (η=1). The excess coordination number of the packings increases with the applied strain, indicating that the more a packing is compressed the more stable it becomes.

A three-dimensional self-learning kinetic Monte Carlo model: application to Ag(111).

The reliability of kinetic Monte Carlo (KMC) simulations depends on accurate transition rates. The self-learning KMC method (Trushin et al 2005 Phys. Rev. B 72 115401) combines the accuracy of rates calculated from a realistic potential with the efficiency of a rate catalog, using a pattern recognition scheme. This work expands the original two-dimensional method to three dimensions. The concomitant huge increase in the number of rate calculations on the fly needed can be avoided by setting up an initial database, containing exact activation energies calculated for processes gathered from a simpler KMC model. To provide two representative examples, the model is applied to the diffusion of Ag monolayer islands on Ag(111), and the homoepitaxial growth of Ag on Ag(111) at low temperatures.

Shear flow of dense granular materials near smooth walls. I. Shear localization and constitutive laws in the boundary region.

We report on a numerical study of the shear flow of a simple two-dimensional model of a granular material under controlled normal stress between two parallel smooth frictional walls moving with opposite velocities ± V. Discrete simulations, which are carried out with the contact dynamics method in dense assemblies of disks, reveal that, unlike rough walls made of strands of particles, smooth ones can lead to shear strain localization in the boundary layer. Specifically, we observe, for decreasing V, first a fluidlike regime (A), in which the whole granular layer is sheared, with a homogeneous strain rate except near the walls, then (B) a symmetric velocity profile with a solid block in the middle and strain localized near the walls, and finally (C) a state with broken symmetry in which the shear rate is confined to one boundary layer, while the bulk of the material moves together with the opposite wall. Both transitions are independent of system size and occur for specific values of V. Transient times are discussed. We show that the first transition, between regimes A and B, can be deduced from constitutive laws identified for the bulk material and the boundary layer, while the second one could be associated with an instability in the behavior of the boundary layer. The boundary zone constitutive law, however, is observed to depend on the state of the bulk material nearby.

Shear flow of dense granular materials near smooth walls. II. Block formation and suppression of slip by rolling friction.

The role of rotational degrees of freedom and of microscopic contact properties at smooth walls in two dimensional planar shear has been investigated by contact dynamics simulations of round hard frictional particles. Our default system setup consists of smooth frictional walls, giving rise to slip. We show that there exists a critical microscopic friction coefficient at the walls, above which they are able to shear the granular medium. We observe distinctive features at this critical point, which to our knowledge have not been reported before. Activating rolling friction at smooth walls reduces slip, leading to similar shear behavior as for rough walls (with particles glued on their surface). Our simulations with rough walls are in agreement with previous results, provided the roughness is strong enough. In the limit of small roughness amplitude, however, the distinctive features of shearing with smooth walls are confirmed.

Nonadditivity of fluctuation-induced forces in fluidized granular media.

We investigate the effective long-range interactions between intruder particles immersed in a randomly driven granular fluid. The effective Casimir-like force between two intruders, induced by the fluctuations of the hydrodynamic fields, can change its sign when varying the control parameters: the volume fraction, the distance between the intruders, and the restitution coefficient. More interestingly, by inserting more intruders, we verify that the fluctuation-induced interaction is not pairwise additive. The simulation results are qualitatively consistent with the theoretical predictions based on mode coupling calculations. These results shed new light on the underlying mechanisms of collective behaviors in fluidized granular media.

Strongly anisotropic nonequilibrium phase transition in Ising models with friction.

The nonequilibrium phase transition in driven two-dimensional Ising models with two different geometries is investigated using Monte Carlo methods as well as analytical calculations. The models show dissipation through fluctuation induced friction near the critical point. We first consider high driving velocities and demonstrate that both systems are in the same universality class and undergo a strongly anisotropic nonequilibrium phase transition, with anisotropy exponent θ=3. Within a field theoretical ansatz the simulation results are confirmed. The crossover from Ising to mean field behavior in dependency of system size and driving velocity is analyzed using crossover scaling. It turns out that for all finite velocities the phase transition becomes strongly anisotropic in the thermodynamic limit.

Influence of polydispersity on micromechanics of granular materials.

We study the effect of polydispersity on the macroscopic physical properties of granular packings in two and three dimensions. A mean-field approach is developed to approximate the macroscale quantities as functions of the microscopic ones. We show that the trace of the fabric and stress tensors are proportional to the mean packing properties (e.g., packing fraction, average coordination number, and average normal force) and dimensionless correction factors, which depend only on the moments of the particle-size distribution. Similar results are obtained for the elements of the stiffness tensor of isotropic packings in the linear affine response regime. Our theoretical predictions are in good agreement with the simulation results.

Magnetic friction in Ising spin systems.

A new contribution to friction is predicted to occur in systems with magnetic correlations: Tangential relative motion of two Ising spin systems pumps energy into the magnetic degrees of freedom. This leads to a friction force proportional to the area of contact. The velocity and temperature dependence of this force are investigated. Magnetic friction is strongest near the critical temperature, below which the spin systems order spontaneously. Antiferromagnetic coupling leads to stronger friction than ferromagnetic coupling with the same exchange constant. The basic dissipation mechanism is explained. A surprising effect is observed in the ferromagnetically ordered phase: The relative motion can act like a heat pump cooling the spins in the vicinity of the friction surface.

Fractal substructure of a nanopowder.

The structural evolution of a nanopowder by repeated dispersion and settling can lead to characteristic fractal substructures. This is shown by numerical simulations of a two-dimensional model agglomerate of adhesive rigid particles. The agglomerate is cut into fragments of a characteristic size l, which then are settling under gravity. Repeating this procedure converges to a loosely packed structure, the properties of which are investigated: (a) The final packing density is independent of the initialization, (b) the short-range correlation function is independent of the fragment size, (c) the structure is fractal up to the fragmentation scale l with a fractal dimension close to 1.7, and (d) the relaxation time increases linearly with l.

Shear zones in granular media: three-dimensional contact dynamics simulation.

The properties of shear zones forming in slow three-dimensional granular flow are investigated. We simulate a straight version of the split-bottom shear cell. It is shown that the same type of wide shear zones is obtained in the presence as well as in the absence of gravity. We investigate the relaxation of the material toward stationary flow and analyze the stress and the velocity fields. A functional form of the widening of the shear zone inside the bulk is given. We discuss the growth of the region where the material is in the critical state. The growth of this critical zone turns out to be responsible for the initial transient of the shear zone.

Macroscopic diagnostics of microscopic friction phenomena.

We show that the static friction force which must be overcome to render a sticking contact sliding is reduced if an external torque is also exerted. As a test system we study a planar disk lying on a horizontal flat surface. We perform experiments and compare with analytical results to find that the coupling between static friction force and torque is nontrivial: It is not determined by the Coulomb friction laws alone, instead it depends on the microscopic details of friction. Hence, we conclude that the macroscopic experiment presented here reveals details about the microscopic processes lying behind friction.

Force indeterminacy in the jammed state of hard disks.

Granular packings of hard disks are investigated by means of contact dynamics which is an appropriate technique to explore the allowed force realizations in the space of contact forces. Configurations are generated for given friction coefficients, and then an ensemble of equilibrium forces is found for fixed contacts. We study the force fluctuations within this ensemble. In the limit of zero friction, the fluctuations vanish in accordance with the isostaticity of the packing. The magnitude of the fluctuations has a nonmonotonous friction dependence. The increase for small friction can be attributed to the opening of the angle of the Coulomb cone, while the decrease as friction increases is due to the reduction of connectivity of the contact network, leading to local, independent clusters of indeterminacy. We discuss the relevance of indeterminacy to packings of deformable particles and to the mechanical response properties.

Self-focusing dynamics in monopolarly charged suspensions.

The Smoluchowski equation for irreversible aggregation in suspensions of equally charged particles is studied. Accumulation of charges during the aggregation process leads to a crossover from power-law to sublogarithmic cluster growth at a characteristic time and cluster size. For larger times the suspension is usually called stable, although aggregation still proceeds slowly. In this regime the size distribution evolves towards a universal scaling form, independent of any parameter included in the theory. The relative width falls off to a universal value sigma(infinity)(r) approximately 0.2017 that is much smaller than in the uncharged case. We conjecture that sigma(infinity)(r) is a lower bound for the asymptotic relative width for all physical systems with irreversible aggregation.

Interfacial mixing in heteroepitaxial growth.

We investigate the growth of a film of some element B on a substrate made of another substance A in a model of molecular beam epitaxy. A vertical exchange mechanism (partial surfactant behavior) allows the A atoms to stay on the growing surface with a certain probability. Using kinetic Monte Carlo simulations as well as scaling arguments, the incorporation of the A 's into the growing B layer is investigated. Moreover, we develop a rate equation theory for this process. The concentration of A impurities decays in the B -film like (distance from the interface)(-1-beta), where beta approximately 0.5 for two-dimensional surfaces, approximately 0.8 in the one-dimensional case, and 1 in mean-field approximation. The power law is cut off exponentially at a characteristic thickness of the interdiffusion zone that depends on the rate of exchange of a B adatom with an A atom in the surface and on the diffusion length. Under certain conditions the interdiffusion zone is predicted to become narrower, if the growth temperature is increased.

Frictional coupling between sliding and spinning motion.

The tangential motion at the contact of two solid objects is studied. It consists of a sliding and a spinning degree of freedom (no rolling). We show that the friction force and torque are inherently coupled. As a simple test system, a sliding and spinning disk on a horizontal flat surface is considered. We calculate, and also measure, how the disk slows down and find that it always stops its sliding and spinning motion at the same moment. We discuss the impact of this coupling between friction force and torque on the physics of granular materials.

Epitaxial growth with pulsed deposition: submonolayer scaling and Villain instability.

It has been observed experimentally that under certain conditions, pulsed laser deposition (PLD) produces smoother surfaces than ordinary molecular beam epitaxy (MBE). So far, the mechanism leading to the improved quality of surfaces in PLD is not yet fully understood. In the present work, we investigate the physical properties of a simple model for PLD, in which the transient mobility of adatoms and diffusion along edges is neglected. Analyzing the crossover from MBE to PLD, the scaling properties of the time-dependent nucleation density as well as the influence of Ehrlich-Schwoebel barriers, we find that there is indeed a range of parameters, where the surface quality in PLD is better than in MBE. However, since the improvement is weak and occurs only in a small range of parameters we conclude that deposition in pulses alone cannot explain the experimentally observed smoothness of PLD-grown surfaces.