Corrugation Strength Research Articles

Plastic behavior of metal sandwich beams with foam-filled sinusoidal corrugation

In this paper, the plastic behavior of metal sandwich beams with foam-filled sinusoidal corrugation is studied theoretically and numerically. The yield criterion of foam-filled sinusoidal corrugation sandwich cross-section is established, considering the effects of metal foam strength and sinusoidal corrugation strength. Based on the yield criterion, an analytical model for the plastic behavior of fully clamped foam-filled sinusoidal corrugation sandwich beams under transverse loading is developed, considering the interaction of axial force and bending moment. Finite element calculations are carried out to verify the analytical model. The influences of geometrical and material parameters on the load-carrying capacity and energy absorption of foam-filled sinusoidal corrugation sandwich beams are discussed. The results show that, with the increase of foam strength, face-sheet thickness, sinusoidal corrugation strength, sinusoidal corrugation sheet thickness, sinusoidal amplitude, sinusoidal half wavelength and punch width, the load-carrying capacity and energy absorption of foam-filled sinusoidal corrugation sandwich beams increase. In addition, when the loading position moves from the midspan to the clamped ends, the load and absorbed energy for the same deflection increase obviously.

Finite-temperature phase diagram and critical point of the Aubry pinned-sliding transition in a two-dimensional monolayer

The Aubry unpinned--pinned transition in the sliding of two incommensurate lattices occurs for increasing mutual interaction strength in one dimension ($1D$) and is of second order at $T=0$, turning into a crossover at nonzero temperatures. Yet, real incommensurate lattices come into contact in two dimensions ($2D$), at finite temperature, generally developing a mutual Novaco-McTague misalignment, conditions in which the existence of a sharp transition is not clear. Using a model inspired by colloid monolayers in an optical lattice as a test $2D$ case, simulations show a sharp Aubry transition between an unpinned and a pinned phase as a function of corrugation. Unlike $1D$, the $2D$ transition is now of first order, and, importantly, remains well defined at $T>0$. It is heavily structural, with a local rotation of moir\'e pattern domains from the nonzero initial Novaco-McTague equilibrium angle to nearly zero. In the temperature ($T$) -- corrugation strength ($W_0$) plane, the thermodynamical coexistence line between the unpinned and the pinned phases is strongly oblique, showing that the former has the largest entropy. This first-order Aubry line terminates with a novel critical point $T=T_c$, marked by a susceptibility peak. The expected static sliding friction upswing between the unpinned and the pinned phase decreases and disappears upon heating from $T=0$ to $T=T_c$. The experimental pursuit of this novel scenario is proposed.

Superlubric-pinned transition in sliding incommensurate colloidal monolayers

Two-dimensional (2D) crystalline colloidal monolayers sliding over a laser-induced optical lattice providing the periodic ``corrugation'' potential recently emerged as a new tool for the study of friction between ideal crystal surfaces. Here, we focus in particular on static friction, the minimal sliding force necessary to depin one lattice from the other. If the colloid and the optical lattices are mutually commensurate, the colloid sliding is always pinned by static friction; however, when they are incommensurate, the presence or absence of pinning can be expected to depend upon the system parameters, like in one-dimensional (1D) systems. If a 2D analogy to the mathematically established Aubry transition of one-dimensional systems were to hold, an increasing periodic corrugation strength ${U}_{0}$ should turn an initially free-sliding, superlubric colloid into a pinned state, where the static friction force goes from zero to finite through a well-defined dynamical phase transition. We address this problem by the simulated sliding of a realistic model 2D colloidal lattice, confirming the existence of a clear and sharp superlubric-pinned transition for increasing corrugation strength. Unlike the 1D Aubry transition, which is continuous, the 2D transition exhibits a definite first-order character, with a jump of static friction. With no change of symmetry, the transition entails a structural character, with a sudden increase of the colloid-colloid interaction energy, accompanied by a compensating downward jump of the colloid-corrugation energy. The transition value for the corrugation amplitude ${U}_{0}$ depends upon the misalignment angle $\ensuremath{\theta}$ between the optical and the colloidal lattices, superlubricity surviving until larger corrugations for angles away from the energetically favored orientation, which is itself generally slightly misaligned, as shown in recent work. The observability of the superlubric-pinned colloid transition is proposed and discussed.

Superlubricity through graphene multilayers between Ni(111) surfaces

A single graphene layer placed between two parallel Ni(111) surfaces screens the strong attractive force and results in a significant reduction of adhesion and sliding friction. When two graphene layers are inserted, each graphene is attached to one of the metal surfaces with a significant binding and reduces the adhesion further. In the sliding motion of these surfaces the transition from stick-slip to continuous sliding is attained, whereby non-equilibrium phonon generation through sudden processes is suppressed. The adhesion and corrugation strength continues to decrease upon insertion of the third graphene layer and eventually saturates at a constant value with increasing number of graphene layers. In the absence of Ni surfaces, the corrugation strength of multilayered graphene is relatively higher and practically independent of the number of layers. Present first-principles calculations reveal the superlubricant feature of graphene layers placed between pseudomorphic Ni(111) surfaces, which is achieved through the coupling of Ni-3d and graphene-$\pi$ orbitals. The effect of graphene layers inserted between a pair of parallel Cu(111) and Al(111) surfaces are also discussed. The treatment of sliding friction under the constant loading force, by taking into account the deformations corresponding to any relative positions of sliding slabs, is the unique feature of our study.

Haze and Polarization Scrambling of Nonlinearly Scattered Light From Antiglare Si Nanorod Surface

The scattering angle, the Haze ratio, and the field polarization factor of the frequency-doubled Nd:YAG laser nonlinearly scattered from the semiconductor nanorod surface are investigated. Both the scattering angle and the reflected Haze ratio of the laser beam reflected from Si nanorod surface present a nonlinearly increasing trend with nanorod length. As the nanorod lengthens from 190 to 2760 nm, the scattering angle broadens from 2.5° to 25° and from 2.5° to 24°. Concurrently, the reflected Haze ratio increases from 5% to 22% and 3% to 21% under TE and TM-mode incidences, respectively. A significant polarization scrambling transfers the linearly polarization into an elliptical polarization, and the field polarization factor increases from 0.54 to 0.86 and from 0.42 to 0.84 under TE- and TM-mode incidences with an enlarging nanorod length from 190 to 2760 nm. The reflected Haze ratio is linearly proportional with the broadened scattering angle. However, the field polarization factor shows a gradually saturating effect at larger scattering angle. The theoretical calculation is used to quantitatively analyze the polarization scrambling effect, which demonstrates that the scattered wave nonlinearly depends on the surface corrugation and can be expressed by the second-order function of the surface corrugation strength. The strong correlations of the TE-mode scattering with the nanorod length and the TM-mode scattering with the laser incident angle are observed. The polarization of the reflected laser beam eventually transfers from a linear to an elliptical one with a nanorod length exceeding over 1 μm.

Plasmons at the interface between a corrugated semiconductor film and a binary metallic superlattice

We investigate the minigaps of the dispersion relation of plasmon polaritons that propagate at the interface between a corrugated semiconductor film and a binary metallic superlattice. Minima of the reflectivity for p-polarized light are calculated and their frequencies are used to obtain the ‘optical’ dispersion relations which are compared with the corresponding electromagnetic dispersion curves, in the effective medium theory. Results show that the minigap enlarges with the corrugation strength.

Effects of defects on friction for a Xe film sliding on Ag(111)

The effects of a step defect and a random array of point defects (such as vacancies or substitutional impurities) on the force of friction acting on a xenon monolayer film as it slides on a silver (111) substrate are studied by molecular-dynamics simulations and compared with the results of lowest-order perturbation theory in the substrate corrugation potential. For the case of a step, the magnitude and velocity dependence of the friction force are strongly dependent on the direction of sliding respect to the step and the corrugation strength. When the applied force F is perpendicular to the step, the film is pinned for F less than a critical force ${F}_{c}.$ Motion of the film along the step, however, is not pinned. Fluctuations in the sliding velocity in time provide evidence of both stick-slip motion and thermally activated creep. Simulations done with a substrate containing a 5% concentration of random point defects for various directions of the applied force show that the film is pinned for the force below a critical value. The critical force, however, is still much lower than the effective inertial force exerted on the film by the oscillations of the substrate in experiments done with a quartz-crystal microbalance (QCM). Lowest-order perturbation theory in the substrate potential is shown to give results consistent with the simulations, and it is used to give a physical picture of what could be expected for real surfaces which contain many defects.

The reflectivity of a film with a grating in contact with a semi-infinite bimetallic superlattice

We study the influence of a semi-infinite bimetallic superlattice on the `excitation' of surface polaritons appearing in a film with a grating surface. The transfer-matrix formalism and the Rayleigh-Fano approach are applied to study the optical response for p-polarized light. We analyse the reflectivity and the dispersion relation of the surface plasmon-polaritons, considering Al and Mg for the semi-infinite superlattice and Mg for the film. The `optical' dispersion relation of surface plasmons is constructed using the minima of the reflectivity. This relation shows a dependence on the corrugation strength such that, as this corrugation grows, the corresponding curve shifts to lower frequencies.

Effect of substrate corrugation on the spreading of polymer droplets.

We have performed molecular dynamics simulations of chain molecules of length sixteen adsorbed on corrugated van der Waals substrates. We find that substrate corrugation qualitatively changes the motion of individual atoms during spreading. Both the corrugation strength and the degree of commensurateness affect the dynamics of spreading.

Surface-profile dependence of photon-plasmon-polariton coupling at a corrugated silver surface

The influence of the surface-profile Fourier decomposition on photon–surface-plasmon-polariton (SPP) coupling at a corrugated silver surface, as probed by changes in diffraction-order intensities, line shapes, and peak positions, is explored. The effect of higher spatial harmonics on diffraction orders is considered for coupling to the SPP in the vicinity of a grating-induced minigap as well as away from the minigap region. Numerical results are obtained with the reduced Rayleigh equations, which are accurate in the range of corrugation strengths that optimize photon–SPP coupling for silver. Under first-order-coupling conditions away from the minigap region the presence of a particular spatial harmonic in the surface profile enhances a specific diffraction order in an easily predictable way. The selectivity, sensitivity, and associated line-shape changes for enhancement are examined as a function of harmonic amplitude for several higher harmonics. In connection with recent experiments [ J. Opt. Soc. Am. B8, 1348 ( 1991)] we investigate the influence of the second and the third spatial harmonics on the propagating orders in the vicinity of the (+ 1, −2) minigap region of an 870-nm grating at 633 nm. The interaction between first- and second-order couplings to the opposite branches of the SPP dispersion relation is tuned by variation of the corrugation depth. It is found that changes in the profile Fourier decomposition with corrugation depth, which arise in the holographic fabrication of diffraction gratings, can explain the observed momentum gap in the −1 diffraction order in this case.

Extreme sensitivity of corrugation strength on diffraction resonance line-shapes for the gas-surface system He (21 meV)/Cu (115)

An example of an isolated resonance with highly non-Lorentzian line-shape has been found for the gas–surface diffraction system He(21 meV)/Cu(115 ). When the corrugation strength parameter for the surface is very slightly varied, the signature of the narrow resonance structure shifts. © 1992 John Wiley & Sons, Inc.

A theory of He diffraction and resonance scattering from Cu(115) by the complex coordinate method

Our method for computing specular elastic scattering intensities of atomic beams from a periodically corrugated solid surface, is generalized to include nonspecular diffraction intensities, and is applied to the scattering of a helium beam from the Cu(115) surface for resonance as well as off-resonance incident angles. Using a simple corrugated Morse potential with a one-dimensional corrugation function and reasonable values of its parameters, a remarkable agreement with the experimental resonance line shapes over the entire angular range is obtained for both the specular and a nonspecular diffraction channel. The line shapes are found to be extremely sensitive to the corrugation strength parameter, but quite insensitive to the shape of the surface corrugation.

Reflection of electromagnetic waves from a periodically rough multilayered surface

The analysis of Cavalcante et al.[ J. Opt. Soc. Am. B4, 1372 ( 1987)], which treats the reflectivity and polariton coupling problem of p-polarized radiation incident on a thin metallic film with a grating underlayer, is extended by considering the placement of a thin dielectric film on top of the metallic film. In general, the numerical results from the Rayleigh–Fano equations for extremely thin dielectric overlayers of the order of 100 Å are comparable with those found by Cavalcante et al., except that the field enhancement peaks and reflectivity dips are shifted slightly toward higher angles of incidence. It is observed that the two-mode polariton interaction is nearly quenched to a single mode as the thickness of the metal thin-film grating is increased and that the reflectivity dips and field enhancement peaks are decreased uniformly as the thickness of the dielectric overlayer is increased. An increased peak behavior for the reflectivity and field enhancement interactions is also found as the metal film corrugation strength or the dielectric constant of the overlayer is increased; however, a limiting behavior is observed for further increases in the dielectric constant.

Polariton resonant absorption in a bigrating: Exact theory compared to recent experiments and to perturbation theory

A nonperturbative theory of light scattering from a bigrating, with resonant excitation of surface polaritons, has been implemented to fit the results of a recent experiment. The experiment measured light absorption in Ag, with results that showed some discrepancies with first-order perturbation theory — particularly at 2-polariton peaks. The exact theory has accounted for some but not all of the discrepancies, indicating that their cause is not entirely due to perturbation theory's underestimating higher-order processes. A comparison of the Fourier coefficients of the surface profile function as determined by the two theories indicates that perturbation theory may develop problems in dealing with the cross-terms in the expansion of 2-dimensional profiles, even for small corrugation strengths.

Quasiclassical trajectory studies of rigid rotor–rigid surface scattering. II. Corrugated surface

The quasiclassical trajectory method, previously applied to rigid rotor–rigid flat surface scattering [J. M. Bowman and S. C. Park, J. Chem. Phys. 77, 5441 (1982)] is applied to a rigid rotor–rigid corrugated surface, i.e., a N2–LiF(001), system. The mechanisms for rotational excitation at low and high collision energies are studied as well as their dependence on initial beam orientation and corrugation strength. A significant correlation between long-lived trajectories and high rotational excitation is found for low energy collisions and rotational rainbows are clearly observed in the high energy regime, although these features are broadened relative to the flat surface reported previously.

Surface plasmons on a randomly rough surface

We have studied the dispersion relation for surface plasmons on a randomly rough surface, going beyond the lowest-order approximation in the surface profile function. This improvement is required because an analysis of the expansion for the surface-plasmon dispersion relation in powers of the surface profile function shows that it contains an infinite subset of terms that are all of the same order of magnitude as the lowest-order contribution, which is the only one that has been considered in previous theoretical determinations of this dispersion relation. The indicated subset of terms is summed to yield a nonlinear integral equation for the surface-plasmon proper self-energy, in terms of which the dispersion relation is expressed. This integral equation has been solved numerically and the surface-plasmon spectral density constructed. The splitting of the surface-plasmon dispersion curve into two branches by the surface roughness, which was predicted theoretically by the lowest-order perturbation theory calculation, and which has been observed experimentally, is preserved in the results of the present calculation. However, both the magnitude of the splitting and the damping of the surface plasmon obtained from the present calculations are larger, for the same corrugation strength, than the same quantities obtained from the lowest-order perturbation calculation, for most surface-plasmon wave vectors.

Selective adsorption resonances in the scattering of helium atoms from xenon coated graphite: Close-coupling calculations and potential dependence

Accurate close-coupling calculations are carried out for the scattering of helium atoms from a monolayer of Xe on the (0001) face of graphite, using atom-surface potentials based on pairwise additivity and the (known) He–Xe pair potential. Good agreement is obtained with the selective adsorption data of Bracco et al. The potential dependence of the resonance spectrum is explored, and it is found that the data are very sensitive to fine details; two pair potentials which both reproduce the gas phase data well, give significantly different resonance spectra, and the contributions of three-body forces are also shown to be important. The resonance spectra are significantly affected by small changes in the corrugation strength as well as by the laterally averaged potential. The potential dependence becomes even more pronounced as the scattering energy is decreased.

Exact calculations of the diffraction of s-polarized electromagnetic radiation from large-amplitude dielectric gratings

On the basis of the extinction theorem form of Green's theorem we have calculated the diffraction of s-polarized electromagnetic radiation from large amplitude, dielectric gratings of several different profiles. We demonstrate the existence of Wood “anomalies” for gratings of sufficiently large amplitude, and identify them as threshold singularities. No evidence of resonance singularities due to the excitation of leaky surface waves supported by the grating is obtained for the grating profiles and corrugation strengths considered here, in contrast with earlier interpretations of analogous results. Rainbow scattering is predicted. Finally, no significant enhancement of the scattered field by the grating surface is found.

Surface plasmons on a large-amplitude doubly periodically corrugated surface

On the basis of the Rayleigh hypothesis we have derived the dispersion relation for surface plasmons propagating in an arbitrary direction along a doubly periodically corrugated metal surface, and have solved it numerically. The system considered consists of a vacuum in the region ${x}_{3}>\ensuremath{\zeta}({x}_{1}, {x}_{2})$. The surface-profile function $\ensuremath{\zeta}({x}_{1}, {x}_{2})$ is periodic in both ${x}_{1}$ and ${x}_{2}$. In our numerical calculations it was chosen to have the form $\ensuremath{\zeta}({x}_{1}, {x}_{2})={\ensuremath{\zeta}}_{0}(cos(\frac{2\ensuremath{\pi}{x}_{1}}{a})$+$cos(\frac{2\ensuremath{\pi}{x}_{2}}{a}))$, while $\ensuremath{\epsilon}(\ensuremath{\omega})$ was assumed to be given by $1\ensuremath{-}(\frac{{{\ensuremath{\omega}}_{p}}^{2}}{{\ensuremath{\omega}}^{2}})$, where ${\ensuremath{\omega}}_{p}$ is the bulk-plasma frequency of the metal. The frequencies of the surface plasmons in this system were calculated for wave vectors ${\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}}_{\ensuremath{\parallel}}$ along symmetry directions in the irreducible part of the two-dimensional first Brillouin zone defined by the periodicity of $\ensuremath{\zeta}({x}_{1}, {x}_{2})$. For each value of ${\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}}_{\ensuremath{\parallel}}$ there is an infinity of branches of the dispersion curve with frequencies above and below the dispersion curve for surface plasmons on a flat surface, ${\ensuremath{\omega}}_{\mathrm{sp}}({\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}}_{\ensuremath{\parallel}})=\frac{{\ensuremath{\omega}}_{p}}{\sqrt{2}}$. We have considered corrugation strengths $\frac{{\ensuremath{\zeta}}_{0}}{a}$ up to a value of 0.25, for which the largest frequency shift with respect to ${\ensuremath{\omega}}_{\mathrm{sp}}$, at $\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}=(\frac{\ensuremath{\pi}}{a}, \frac{\ensuremath{\pi}}{a})$, is over 45%.

Propagation of Rayleigh surface waves across a large-amplitude grating

The dispersion relation for a Rayleigh surface wave propagating normal to the grooves of a diffraction grating has been obtained by two different methods. The first is based on the use of the Rayleigh hypothesis. The second uses the extinction theorem form of Green's theorem to obtain an exact pair of homogeneous linear integral equations for the boundary values of the elastic displacement field, from the solvability condition for which the Rayleigh-wave dispersion relation is obtained. When the latter pair of equations are solved by Fourier-series expansions, the dispersion relation obtained is identical with the one obtained on the basis of the Rayleigh hypothesis, in the case that the grating profile function is an even function of its argument. Numerical solutions of the dispersion relation are obtained for a sinusoidal profile and for a symmetric sawtooth profile. For the former profile, solutions are found to be convergent for corrugation strengths far beyond the value at which the Rayleigh hypothesis is known to become invalid for the scattering of a scalar plane wave from a hard sinusoidal surface. For the sawtooth profile (for which in the aforementioned problem the Rayleigh hypothesis is invalid due to the nonanalyticity of the profile) convergent results are here obtained for appreciable values of the corrugation strength. These results indicate that the Rayleigh hypothesis can be used for the calculation of the dispersion curve for a Rayleigh wave propagating across a large-amplitude grating, even when the grating profile function is not an analytic function of its argument. The dispersion curves obtained possess gaps for values of the one-dimensional wave vector, characterizing the propagation of the Rayleigh wave, corresponding to the boundaries of the one-dimensional Brillouin zones defined by the period of the grating. An analytic expression is obtained for the form of the dispersion curve in the vicinity of each gap, in the small corrugation limit, for an arbitrary grating profile. Comparison of the predictions of this analytic result with the exact numerical results allows the limits of validity of the small-amplitude approximation to be determined.