Roughness Correlation Function Research Articles

Effects of soldering and wear of die-casting die during ejection: Surface roughness and casting temperature

In the process of high pressure die casting, the soldering of aluminum alloy to dies is a concern. This soldering behavior will cause surface abrasion during the ejection of the casting by ejector rods, which deteriorates the surface quality of the casting and the die. Although the soldering can be mitigated by mold release agents and coating technologies, the die surface roughness and casting temperature also have a significant impact on the soldering problem. This study evaluates the soldering tendency for different casting temperatures and surface roughness by measuring the force of pulling the samples out of the casting, aiming to thoroughly investigate the effects of casting temperatures and die surface roughness on the soldering and wear during ejection for die-casting dies. After casting, the aluminum alloy and the sample surface interlocked. With the surface roughness increased from Ra 0.6 μm to Ra 1.2 μm, the maximum extraction force increased by 26.4 % in the 5th pullout. The high roughness surface induced the formation of surface cracks during the pullout process, which damaged the surface quality of the sample. As the casting temperature increased from 650 °C to 750 °C, the growth rate of maximum extraction force was 8.1 % in the 10th pullout. The severity of surface damage is related to the sample hardness. Therefore, the low surface roughness and casting temperature are beneficial to reduce the soldering and wear of the aluminum alloy on the die. Finally, the correlation function of surface roughness and the number of pullouts to maximum extraction force was obtained.

Coherent reflection recovery in forward scattering from random rough surfaces with non-Gaussian correlation functions

The coherence between incident and reflected acoustic waves, with wavenumber k, scattered from a random rough surface, with root-mean-square roughness height h, decreases exponentially as khcosθ increases. The incidence angle, θ, and the surface roughness properties are set by the geometry and characteristics of the environment while the wavenumber range is governed by the signal bandwidth. The frequency-difference autoproduct is a nonlinear field construction capable of recovering reflected-field coherence by downshifting recorded frequencies, effectively decreasing the wavenumber. However, due to the quadratic nature of the frequency-difference autoproduct, dependence on the surface correlation function is introduced. This effect, and other relevant features, appear in the analytic form of the frequency-difference autoproduct derived for Gaussian-distributed surface roughness and surface correlation function. Previous results from simulated isotropic Gaussian surfaces and simple laboratory experiments verify the validity of this form. This presentation provides new results for autoproduct-based coherence recovery in fields scattered from surfaces exhibiting non-Gaussian correlation functions. Coherence recovery is quantified by the coherent surface reflection coefficient (ensemble-average reflected-field amplitude divided by flat-surface reflected-field amplitude), and comparisons are made to the Gaussian-based theory. Experimental results may be provided. [Work supported by ONR and an NDSEG Fellowship.]

Surface roughness mediated specularity parameter of thin Cu films

Roughness-induced resistivity variation of thin metal films is conveniently described by the Fuchs–Sondheimer model, where the phenomenological parameter p is used to quantify the extent of specular scattering at surfaces. However, p is a lumped parameter and does not include microscopic information that characterizes roughness, viz., auto-correlation function, root-mean-square height, and correlation length. In this work, we extract these roughness parameters for Cu films of thickness ranging from 31 nm to 95 nm. We find that the roughness–roughness correlation function is an exponential with a characteristic correlation length that increases monotonically with the film thickness. Using this, we predict the roughness parameter-dependent specularity coefficient, which has an implicit thickness dependency. This alters the resistivity scaling compared to the prevailing model of resistivity scaling, where p is assumed to be a constant.

Measurement Accuracy Problems of the Surface Texture Parameters

In this scientific article the recommendations for a three-dimensional surface roughness parameters determination of mechatronics elements are developed. First of all, the measurements for surface with irregular roughness were made, what led to the determination of a 3D roughness correlation function. On that basis correlation interval in two perpendicular treatment directions was calculated and associated with number of surface roughness uncorrelated points. Secondly, the surface roughness step parameters evaluation precision in two mutually perpendicular directions was analysed. Particular attention was paid to the roughness average step RSm in the treatment longitudinal direction. As a result, the recommendations for a 3D roughness parameters determination were prepared.

Surface characterization of magnesium fluoride thin films prepared by a fluorine trapping based non-reactive sputtering technique

Successful deposition of magnesium fluoride thin films by a non-conventional magnetron sputtering technique is reported here followed by the analysis of their optical, morphological and structural properties. The drawback in the external supply of health hazardous fluorinated gases in the context of fabricating fluoride films by conventional sputtering processes was completely eliminated by trapping the dissociated fluorine gas inside the chamber during deposition. The dependencies of basic thin film properties stated above on magnetron energizing power were investigated. Qualities of surface structures were analyzed on the basis of surface roughness and surface correlation function parameters. A qualitative correlation of film morphology with optical properties of such fluoride films was observed in the present study. Film growth rates were found to have great importance in deciding the surface topography of the films. Careful investigation of film structure clearly revealed a remarkable increase in crystallite size with the increase in sputtering power. The composition of the film is maintained throughout the studied power range as seen by X-ray photoelectron spectroscopy. Finally, optimum sputtering power for film deposition was decided by taking into consideration the quality in surface structure together with optical quality of the films.

Analysis of surface roughness correlation function by X‐ray reflectivity

X‐ray reflectivity (XRR) is a powerful tool for the analysis on surface and interface roughness. In the conventional XRR analysis, the reflectivity was calculated based on the Parratt formalism, accounting for the effect of roughness by the theory of Nevot–Croce. We have developed an improved XRR formalism which derives more accurate surface and interface roughness. In this study, we introduced the effective roughness depending on the incidence angle of X‐rays. The newly developed XRR formalism, which derives more accurate surface and interface roughness, is found to be dependent on the size of coherent X‐rays probing area, and further derives the roughness correlation function as well as the lateral correlation length. Copyright © 2016 John Wiley & Sons, Ltd.

Recent Developments in the X-ray Reflectivity Analysis

X-ray reflectivity (XRR) is a powerfull tool for investigations on surface and interface structures of multilayered thin film materials. In the conventional XRR analysis, the X-ray reflectivity has been calculated based on the Parratt formalism, accounting for the effect of roughness by the theory of Nevot-Croce conventionally. However, the calculated results have shown often strange behaviour where interference effects would increase at a rough surface. The strange result had its origin in a serious mistake that the diffuse scattering at the rough interface was not taken into account in the equation. Then we developed new improved formalism to correct this mistake. However, the estimated surface and interface roughnesses from the x-ray reflectivity measurements did not correspond to the TEM image observation results. For deriving more accurate formalism of XRR, we tried to compare the measurements of the surface roughness of the same sample by atomic force microscopy (AFM), high-resolution Rutherford backscattering spectroscopy (HRBS) and XRR. The results of analysis showed that the effective roughness measured by XRR might depend on the angle of incidence. Then we introduced the effective roughness with depending on the incidence angle of X-ray. The new improved XRR formalism derived more accurate surface and interface roughness with depending on the size of coherent X-rays probing area, and derived the roughness correlation function and the lateral correlation length. In this review, an improved XRR formalism, considering the diffuse scattering and the effective roughness, is presented. The formalism derives an accurate analysis of the x-ray reflectivity from a multilayer surface of thin film materials.

A Simplified Formulation for Rough Surface Cross-Polarized Backscattering Under the Second-Order Small-Slope Approximation

We present simplified expressions for the cross-polarized backscatter of a randomly rough surface predicted by the second-order small-slope approximation (SSA2). The simplification is based on appropriate polynomial approximations of the SSA2 kernel function. We obtain numerically efficient expressions for the cross-polarized backscattering amplitude of a deterministic surface in the form of a single space integral involving only the surface elevation and the second (mixed) derivative of the surface elevation. The ensemble average normalized radar cross section is then derived under a Gaussian random process assumption for the surface. The resulting expression has the form of a Kirchhoff integral involving the roughness correlation function and its second- and fourth-order cross-derivatives. Further simplification is achieved for off-nadir observations using a high-frequency approximation; the result is an analytical formula involving only the resonant curvature and the radar-filtered mean square slope in the out-of-plane direction. A numerical validation of the simplified expressions is provided by comparison with exact SSA2 predictions in representative test cases. The dependence of cross-polarized backscattering on the incidence angle as well as wind speed and direction is then investigated for the case of a directional sea surface model. At near nadir incidence, a clear maximum in azimuth of the cross-polarized backscatter is observed for radar look directions 45 $^{\circ}$ from the wind direction.

Quantum transport equation for systems with rough surfaces and its application to ultracold neutrons in a quantizing gravity field

We discuss transport of particles along random rough surfaces in quantum size effect conditions. As an intriguing application, we analyze gravitationally quantized ultracold neutrons in rough waveguides in conjunction with GRANIT experiments (ILL, Grenoble). We present a theoretical description of these experiments in the biased diffusion approximation for neutron mirrors with both one- and two-dimensional (1D and 2D) roughness. All system parameters collapse into a single constant which determines the depletion times for the gravitational quantum states and the exit neutron count. This constant is determined by a complicated integral of the correlation function (CF) of surface roughness. The reliable identification of this CF is always hindered by the presence of long fluctuation-driven correlation tails in finite-size samples. We report numerical experiments relevant for the identification of roughness of a new GRANIT waveguide and make predictions for ongoing experiments. We also propose a radically new design for the rough waveguide.

Perturbative roughness corrections to electromagnetic Casimir energies

Perturbative corrections to the Casimir free energy due to macroscopic roughness of dielectric interfaces are obtained in the framework of an effective low-energy field theory. It describes the interaction of electromagnetic fields with materials whose plasma frequency ${\ensuremath{\omega}}_{p}$ determines the low-energy scale. The na\"{\i}ve perturbative expansion of the single-interface scattering matrix in the variance of the profile is sensitive to short-wavelength components of the roughness correlation function. We introduce generalized counterterms that subtract and correct these high-momentum contributions to the loop expansion. To leading order, the counterterms are determined by the phenomenological plasmon model. The latter is found to be consistent with the low-energy description. The proximity force approximation is recovered in the limit of long correlation length and gives the upper limit for the roughness correction to the Casimir force. The renormalized low-energy theory is insensitive to the high-momentum behavior of the roughness correlation function. Predictions at zero temperature of the improved theory are compared with those of the unrenormalized model and with experiment. The Casimir interaction of interfaces with low levels of roughness is found to be well reproduced by that of flat parallel plates with the measured reflection coefficients at a distance that is slightly less than the mean separation of the rough surfaces.

Rough Mirror as a Quantum State Selector: Analysis and Design

We report analysis of rough mirrors used as the gravitational state selectors in neutron beam and similar experiments. The key to mirror properties is its roughness correlation function (CF) which is extracted from the precision optical scanning measurements of the surface profile. To identify CF in the presence of fluctuation-driven fat tails, we perform numerical experiments with computer-generated random surfaces with the known CF. These numerical experiments provide a reliable identification procedure which we apply to the actual rough mirror. The extracted CF allows us to make predictions for ongoing GRANIT experiments. We also propose a radically new design for rough mirrors based on Monte Carlo simulations for the 1D Ising model. The implementation of this design provides a controlled environment with predictable scattering properties.

Quantized Ultracold Neutrons in Rough Waveguides: GRANIT Experiments and Beyond

We apply our general theory of transport in systems with random rough boundaries to gravitationally quantized ultracold neutrons in rough waveguides as in GRANIT experiments (ILL, Grenoble). We consider waveguides with roughness in both two and one dimensions (2D and 1D). In the biased diffusion approximation the depletion times for the gravitational quantum states can be easily expressed via each other irrespective of the system parameters. The calculation of the exit neutron count reduces to evaluation of a single constant which contains a complicated integral of the correlation function of surface roughness. In the case of 1D roughness (random grating) this constant is calculated analytically for common types of the correlation functions. The results obey simple scaling relations which are slightly different in 1D and 2D. We predict the exit neutron count for the new GRANIT cell.

Influence of surface roughness on the electrical conductivity of semiconducting thin films

The Green function solution of the Boltzmann transport equation has been applied in case of no magnetic field by ignoring any volume impurities. Gaussian, exponential and power law models for the surface roughness correlation function have been studied and the results have been compared with the ones obtained by other methods. It has been found that the electrical conductivity σ increases with increasing correlation length l for the first two models, while for the third model σ value is of the same order as the first two models. Therefore we show that the shape of the surface roughness can strongly influence the electrical properties.

Acoustic scattering strength of turbulence generated waves in a shallow water flow

This work examines an airborne method of ultrasonic characterization of the dynamically rough water surface in an shallow water flow. A new experimental setup has been developed and tested in a 12 m long, 450 mm wide laboratory flume. This equipment includes a source of a 45 kHz airborne wave, microphone array, and an array of wave probes. It has been shown experimentally and theoretically that the directivity of the ultrasonic wave scattered by the dynamically rough water surface can be related directly to the roughness correlation function which can be measured non-acoustically. It is shown that the form of the roughness correlation function is determined unambiguously by the scale and intensity of the turbulence processes in the flow. The proposed acoustic method is accurate, remote, and rapid. It can be used to relate the spectral and statistical characteristics of the rough flow surface to the scale and intensity of the turbulent flow structures which cause the water surface to appear rough.

Grazing-incidence small-angle X-ray scattering from a random rough surface: a self-consistent wavefunction approximation

An attempt is made to go beyond the distorted-wave Born approximation addressed to the grazing-incidence small-angle X-ray (GISAX) scattering from a random rough surface. The integral wave equation adjusted with the Green function formalism is applied. To find out an asymptotic solution of the non-averaged integral wave equation in terms of the Green function formalism, the theoretical approach based on a self-consistent approximation for the X-ray wavefunction is elaborated. Such an asymptotic solution allows one to describe the reflected X-ray wavefield everywhere in the scattering (θ, ϕ) angular range, in particular below the critical angle θ(cr) for total external reflection (θ is the grazing scattering angle with the surface, ϕ is the azimuth scattering angle; θ(0) is the grazing incidence angle). Analytical expressions for the reflected GISAX specular and diffuse scattering waves are obtained using the statistical model of a random Gaussian surface in terms of the r.m.s. roughness and two-point cumulant correlation function. For specular scattering the conventional Fresnel expression multiplied by the Debye-Waller factor is obtained. For the reflected GISAX diffuse scattering the intensity of the R(dif)(θ, ϕ) scan is written in terms of the statistical scattering factor eta(theta, theta0) and Fourier transform of the two-point cumulant correlation function. To be specific for isotropic solid surfaces, the statistical scattering factor eta(theta, theta0) and Fourier transform of the two-point cumulant correlation function parametrically depend on the root-mean-square roughness σ [eta(theta, theta0) = 0 for σ = 0] and cumulant correlation length ℓ, respectively. The reflected R(dif)(θ, ϕ) scans are numerically simulated for the typical-valued {θ(0), σ, ℓ} parameters array.

Influence of interface roughness scattering on electronic magnetotransport in a quantum well

By assuming several different analytical forms of correlation function for the interface roughness in a quantum well, the influence of interface roughness scattering on the electronic transport in the presence of a magnetic field is investigated. It is found that the roughness-limited conductivities are mainly determined by the behaviour of the correlation functions in Fourier space within the range of inverse magnetic length. Thus the electronic magnetotransport property sensitively depends on the detail of the roughness correlation function in the case of a large magnetic field. On the other hand, when the magnetic length is much larger than the roughness correlation length, which usually corresponds to the case of a relatively weak magnetic field, the conductivities calculated by different forms of roughness correlation function do not show a notable difference from each other.

Comprehensive Understanding of Electron and Hole Mobility Limited by Surface Roughness Scattering in Pure Oxides and Oxynitrides Based on Correlation Function of Surface Roughness

A new model of the roughness correlation function S(r) has been proposed in order to explain the different behavior of high field mobility limited by surface roughness scattering, µSR, between electrons and holes in metal oxide semiconductor field effect transistors (MOSFETs) with oxynitrides. It has been shown, for the first time, that the change in electron and hole µSR associated with NO oxynitridation can be reasonably well explained by the appropriate choice of the form of S(r).

AFM study of SiN x:H surfaces treated by hydrogen plasma: modification of morphological and scaling characteristics

Exposing silicon nitride surfaces to hydrogen plasma prior to low temperature microcrystalline-Si deposition is an effective way of modifying surfaces to improve wettability and surface cleanliness. Atomic force microscopy (AFM) and Auger electron spectroscopy (AES) showed a delicate change in the morphology and a clear increase in nucleation resulting from the modification and cleaning effect of the SiN x :H surface by H 2 plasma exposure. The surface roughness correlation function measured by AFM has been shown to be in good agreement with a simple model from which the roughness exponent and lateral sizes of mountains and valleys in the surface can be deduced.

Characterization of the grinding process by acoustic emission

The properties of a ground surface can be estimated on-line during manufacturing based on the analysis of acoustic signals emitted by the grinding process. This possibility is demonstrated using an experimental system comprising an external grinding machine, a data acquisition unit and an artificial neural network. In the initial phase of system application, an empirical model of the grinding process is formed in the memory of the neural network by self-organized learning driven by empirical data consisting of the acoustic emission spectrum and a surface roughness correlation function. After learning, the system applies the model to estimate the correlation function of the surface profile from the input acoustic emission spectrum. For this purpose, non-parametric regression, based on the conditional average estimator, is utilized. Experiments were done on the grinding of hardened steel workpieces by a corundum wheel. During formation of the model, the surface profile and its correlation function were determined off-line, while in testing system performance the surface correlation function was estimated on-line from the acoustic emission spectrum. With respect to the estimation error, three characteristic periods of the process were observed corresponding to grinding with a newly dressed, slightly worn, and worn out wheel. The best estimation is obtained during grinding by a slightly worn wheel.

On bistatic sea surface scattering: Field measurements and modeling

The bistatic scattering cross section of the sea surface, σ, is studied, along with a model for σ and its comparison with field data. The data are horizontal spatial coherence and ensemble-averaged intensity, which represent integral measures of sea surface bistatic scattering, and the model for σ is used to generate these same properties for comparison with the field data. The data are from an experiment conducted in shallow waters off southern Florida, using a sound frequency of 30 kHz. Directional wave measurements were made with a wave buoy positioned within 100 m of the acoustic measurements, with the environment characterized by rms wave heights of O(10) cm and wind speeds of 1–4 m/s. In the model σ is divided into two components: σr associated with scattering from the rough, air/sea interface, and σb associated with scattering from near-surface bubbles. The second-order small slope approximation is used to compute σr, which is a much improved approach over the traditionally used composite roughness model. The primary advantage in the small slope approximation was the resulting smooth behavior in σr over a broad range of scattering angles. Directional wave data obtained by the wave buoy were converted to an estimate of the 2-D spatial correlation function of sea surface roughness, C(ξ,final_sigma), for use in the scattering calculations. An analysis of the effective correlation properties of C(ξ,final_sigma) suggested that an isotropic correlation function C(ρ), based on the directionally averaged wave-number spectrum, would be equally effective in the scattering calculations. Model-data agreement was quite satisfactory, regardless of whether C(ξ,final_sigma) or C(ρ) was used in the scattering calculations.