Case study about the accuracy behavior of three different T-matrix methods

In this paper we discuss the influence of two different sets of weighting functions on the accuracy behavior of T-matrix calculations for scalar scattering problems. The first set of weighting functions is related to one of Waterman's original approaches. The other set results into a least-squares scheme for the transmission problem. It is shown that both sets of weighting functions produce results with a converse accuracy behavior in the near and far fields. Additional information, such as reciprocity and the fulfillment of the boundary condition, are needed to choose the set of weighting functions that is most appropriate for a certain application. The obtained criteria are applied afterward to an iterative T-matrix approach we developed to analyze scattering on regular particle geometries with an impressed but slight surface irregularity. However, its usefulness is demonstrated in this paper by analyzing the far-field scattering behavior of Chebyshev particles of higher orders.     

Implementing the near- to far-field transformation in the finite-difference time-domain method

When the finite-difference time-domain (FDTD) method is applied to light-scattering computations, the far fields can be obtained by means of integrating the near fields either over the volume bounded by the particle's surface or on a regular surface encompassing the scatterer. For light scattering by a sphere, the accurate near-field components on the FDTD-staggered meshes can be computed from the rigorous Lorenz-Mie theory. We investigate the errors associated with these near- to far-field transform methods for a canonical scattering problem associated with spheres. For a scatterer with a small refractive index, the surface-integral approach is more accurate than its volume counterpart for computation of the phase functions and extinction efficiencies; however, the volume-integral approach is more accurate for computation of other scattering matrix elements, such as P12, P32, and P43, especially for backscattering. If a large refractive index is involved, the results computed from the volume-integration method become less accurate, whereas the surface method still retains the same order of accuracy as in the situation for the small refractive index.     

Scattering of a plane harmonic SH wave by a completely embedded corrugated scatterer

Anti‐plane‐strain model for steady‐state scattering of elastic waves by a rough inclusion or a cavity embedded in a half space is considered by using a direct boundary integral equation method. The roughness of the scatterer is assumed to be periodic with arbitrary amplitude and period. Detailed testing of the numerical results is presented. The motion along the half‐space surface is evaluated for different corrugations, frequencies and impedance contrast of the materials. The importance of the scatterer roughness upon the displacement field is clearly demonstrated. It was shown that larger corrugation amplitudes, shorter corrugation periods and higher frequencies may produce significant change in the displacement field when compared with the corresponding smooth scatterer result. This effect strongly depends upon the impedance contrast of the materials. Copyright © 2008 John Wiley & Sons, Ltd.     

Ray model of light scattering by flake pigments or rough surfaces with smooth transparent coatings

We derive expressions for the intensity and polarization of light singly scattered by flake pigments or a rough surface beneath a smooth transparent coating using the ray or facet model. The distribution of local surface normals is used to calculate the bidirectional reflectance distribution function (BRDF). We discuss the different distribution functions that can be used to characterize the distribution of local surface normals. The light-scattering model is validated by measurements of the BRDF and polarization by a metallic flake pigmented coating. The results enable the extraction of a slope distribution function from the data, which is shown to be consistent over a variety of scattering geometries. These models are appropriate to estimate or predict the appearance of flake pigment automotive paints.     

A generalized layerwise higher-order shear deformation theory for laminated composite and sandwich plates based on isogeometric analysis

This paper presents a generalized layerwise higher-order shear deformation theory for laminated composite and sandwich plates. We exploit a higher-order shear deformation theory in each layer such that the continuity of the displacement and transverse shear stresses at the layer interfaces is ensured. Thanks for enforcing the continuity of the displacement and transverse shear stresses at an inner-laminar layer, the minimum number of variables is retained from the present theory in comparison with other layerwise theories. The method requires only five variables, the same as what obtained from the first- and higher-order shear deformation theories. In comparison with the shear deformation theories based on the equivalent single layer, the present theory is capable of producing a higher accuracy for inner-laminar layer shear stresses. The free boundary conditions of transverse shear stresses at the top and bottom surfaces of the plate are fulfilled without any shear correction factors. The discrete system equations are derived from the Galerkin weak form, and the solution is obtained by isogeometric analysis (IGA). The discrete form requires the C¹ continuity of the transverse displacement, and hence NURBS basis functions in IGA naturally ensure this condition. The laminated composite and sandwich plates with various geometries, aspect ratios, stiffness ratios and boundary conditions are studied. The obtained results are compared with the 3D elasticity solution, the analytical as well as numerical solutions based on various plate theories.     

Application of the boundary-element method to the interaction of light with single and coupled metallic nanoparticles

The boundary-element method is applied to the interaction of light with resonant metallic nanoparticles. At a certain wavelength, excitation of a surface plasmon takes place, which leads to a resonantly enhanced near-field amplitude and a large scattering cross section. The resonance wavelength for different scatterer geometries is determined. Alteration of the scattering properties in the presence of other metallic nanoparticles is discussed. To treat this problem, a novel formulation of the boundary-element method is presented that solves the interaction problem for all the coupled particles.     

Angular distribution of light scattered from a sinusoidal grating

The angular distributions of light scattered by gold-coated and aluminum-coated gratings with amplitudes of ~90 nm and periods of 6.67 mum were measured and calculated for light incident from a He-Ne laser at an angle of 6 degrees . Experimental results are compared with predictions of Beckmann's scalar theory and Rayleigh's vector theory. The measured scattering pattern has a background of scattered light due mainly to residual surface roughness. Also the power in the higher-order peaks is larger by several orders of magnitude than the computed one, which can be attributed mainly to the low-order contributions of the harmonics in the profile.     

Wall-slip effects in SnAgCu solder pastes used in electronics assembly applications

Solder paste is the most important strategic bonding material used in the assembly of surface mount components in electronics manufacturing. As the trend towards miniaturisation of electronic products continues, there is an increasing demand for better understanding of the flow and deformation that is, the rheological behaviour of solder paste formulations. Wall slip plays an important role in characterising the flow behaviour of solder paste materials. The problem of wall slip arises due to the various attractive and repulsive forces acting between the solder particles and the walls of the measuring geometry. These interactions could lead to the presence of a thin solvent layer adjacent to the wall, which gives rise to slippage. In rheological measurements, slip effects can generally be avoided by using roughened surfaces for measuring geometries. In this paper, a novel technique is developed to study the effect of wall slip in the rheological measurements of lead-free solder paste. The viscosity and oscillatory data obtained for three different solder paste samples (from measuring geometries of different surface roughness) have been analysed and compared. In viscosity measurements, slip effects were dominant at low shear rates and the use of serrated surfaces was found to be quite effective in minimizing slip effects. Oscillatory measurements were also affected by roughening the surfaces of measuring geometries.     

Numerical study on optimization of ejector primary nozzle geometries

In an ejector refrigeration system (ERS), ejector acts as a compressor but without using any moving parts. To some extent, ejector performances are subjected to primary nozzle's geometries with the action of shock waves. In this paper, CFD simulation was conducted to improve the ejector performance by varying the following ejector primary nozzle's geometries and surface roughness: two angles of convergent and divergent portion, three lengths and surface roughness of throat, convergent and divergent portion. The CFD model was validated with the test results of an ERS experimental rig with working fluid of R134a. The optimum geometric parameters and surface roughness of the primary nozzle were obtained with the CFD analysis. The simulation results revealed that the throat and divergent portion of the primary nozzle should be paid more attention when designing ejector since the entrainment ratio of the ejector is rather sensitive to the length and surface roughness of these two portions.     

抛光液组分对硬盘盘基片超光滑表面抛光的影响

在硬盘盘基片的最终抛光中,研究SiO2溶胶颗粒、氧化剂、络合剂和润滑剂对盘基片Ni—P材料抛光性能的变化规律,获得较高的材料去除速率（MRR）和原子级光滑表面,以满足下一代硬盘盘基片制造的更高要求．结果表明,采用平均粒径25nm的SiO2溶胶颗粒,易减少微划痕等缺陷;以过氧化氢为氧化剂,可大幅提高MRR;加入有机酸络合剂后,MRR显著增大,其中含有水杨酸的抛光液MRR最大,并讨论不同络舍剂对盘基片去除的影响机理;丙三醇润滑剂的引入,使抛光中摩擦系数减小,盘基片的表面粗糙度得到明显降低．采用原子力显微镜（AFM）、光学显微镜和ChapmanMP2000＋表面形貌仪来考察盘基片抛光后的表面质量,基于抛光液各组分的影响作用,最终获得表面粗糙度尺。为0．08nm的盘基片表面,且MRR达到0．132μm／min．     

Surface roughness and material removal in fluid jet polishing

Based on experiments, the dependence of material removal and surface roughness on the characteristics of abrasive particles, on the workpiece, and on other process parameters such as working pressure and incidence angle in fluid jet polishing (FJP) technology were investigated. Experimental results show a volume removal rate that is approximately proportional to the square root of the Young's modulus (E) and inversely proportional to the square of the Knoop hardness (Hk) of glass. Similarly, surface roughness is also determined in FJP by elastic stiffness E and plastic parameter Hk. The influence of the incidence angle on surface roughness and material removal were studied, and a linear dependence of material removal on the working pressure was obtained. Further, it was found that an optical-quality surface can be achieved by use of Cerox 1650 abrasive particles in FJP and can satisfy the requirements of modern optical manufacturing.     

Frequency domain analysis of elastic bounded domains using a new semi-analytical method

In this paper, a new semi-analytical method is developed for solving two-dimensional elastodynamic problems in the frequency domain, employing Fast Fourier Transform. Using specific non-isoparametric elements, the boundary of the problem’s domain is discretized. By employing higher-order Chebyshev mapping functions, special shape functions, Clenshaw–Curtis quadrature, and implementing a weak form of weighted residual method, coefficient matrices of equation system become diagonal. This fact results in a set of decoupled Bessel differential equations to be used for solving the whole system. This means that the governing Bessel differential equation for each degree of freedom (DOF) becomes independent from other DOFs of the domain. For each DOF, the Bessel differential equation is solved for a specific frequency. Finally, the time history of responses may be obtained by using Inverse Fast Fourier Transform. Three numerical examples are presented to demonstrate the accuracy of the present new method.     

Plasmonic properties of polycrystalline hollow Au nanoparticles: a surface roughness effect

Hollow Au nanoparticles with a 25 nm polycrystalline shell and a 50 nm hollow core were produced in large amounts by using electrochemically evolved hydrogen nanobubbles as templates and reducing agents for electroless deposition from a Na3Au(SO3)2 electrolyte. The surface roughness of these nanoparticles can be tuned by adding NaSO3 into the electrolyte. Different surface roughnesses can be readily obtained for sub-100 nm particles with the same size. As surface roughness increases, surface plasmon resonance (SPR) peaks shift to longer wavelengths. Particles with an 8 nm roughness have a SPR peak centered at 750 nm, which is particularly attractive for in vivo diagnostic and therapeutic applications. A three-dimensional finite difference time domain (FDTD) simulation confirms that the red-shifts of SPR peaks are mainly caused by their surface roughness, and the hollow nature of these particles plays only a minor role. This unique plasmonic property of hollow Au nanoparticles opens up the possibility to maintain the desirable optical properties after loading other substances into the hollow core to form multifunctional core-shell nanoparticles.     

Crossed source-detector geometry for a novel spray diagnostic: Monte Carlo simulation and analytical results

Sprays and other industrially relevant turbid media can be quantitatively characterized by light scattering. However, current optical diagnostic techniques generate errors in the intermediate scattering regime where the average number of light scattering is too great for the single scattering to be assumed, but too few for the diffusion approximation to be applied. Within this transitional single-to-multiple scattering regime, we consider a novel crossed source-detector geometry that allows the intensity of single scattering to be measured separately from the higher scattering orders. We verify Monte Carlo calculations that include the imperfections of the experiment against analytical results. We show quantitatively the influence of the detector numerical aperture and the angle between the source and the detector on the relative intensity of the scattering orders in the intermediate single-to-multiple scattering regime. Monte Carlo and analytical calculations of double light-scattering intensity are made with small particles that exhibit isotropic scattering. The agreement between Monte Carlo and analytical techniques validates use of the Monte Carlo approach in the intermediate scattering regime. Monte Carlo calculations are then performed for typical parameters of sprays and aerosols with anisotropic (Mie) scattering in the intermediate single-to-multiple scattering regime.     

Light scattering from particles located under a rough dielectric layer

A discussion is presented of the effect of roughness on the detectability of subsurface particles by means of the light-scattering method. We have studied the scattering of light by calibrated spheres located under a slightly rough dielectric surface both experimentally and theoretically. In our experiments, the scattering from slightly rough layers with nonresonant particles was dominated by the roughness, and the scattering diagram did not bear any discernible indications of the spheres. However, at resonance, the subsurface particles manifested themselves by an increase in the total scattered intensity and by well-pronounced maxima in the angular dependence of both the scattering diagram and the backscattered intensity. Theoretical calculations show that the angular positions of the maxima in the scattering diagram are essentially determined by the interference of fields scattered by the particles and by the surface, whereas the contribution of the multiple interparticle scattering is negligible. By contrast, the oscillations in the angular dependence of the backscattered intensity are due primarily to the scattering between neighboring spheres.     

Examination of surface roughness on light scattering by long ice columns by use of a two-dimensional finite-difference time-domain algorithm

Natural particles such as ice crystals in cirrus clouds generally are not pristine but have additional microroughness on their surfaces. A two-dimensional finite-difference time-domain (FDTD) program with a perfectly matched layer absorbing boundary condition is developed to calculate the effect of surface roughness on light scattering by long ice columns. When we use a spatial cell size of 1/120 incident wavelength for ice circular cylinders with size parameters of 6 and 24 at wavelengths of 0.55 and 10.8 microm, respectively, the errors in the FDTD results in the extinction, scattering, and absorption efficiencies are smaller than approximately 0.5%. The errors in the FDTD results in the asymmetry factor are smaller than approximately 0.05%. The errors in the FDTD results in the phase-matrix elements are smaller than approximately 5%. By adding a pseudorandom change as great as 10% of the radius of a cylinder, we calculate the scattering properties of randomly oriented rough-surfaced ice columns. We conclude that, although the effect of small surface roughness on light scattering is negligible, the scattering phase-matrix elements change significantly for particles with large surface roughness. The roughness on the particle surface can make the conventional phase function smooth. The most significant effect of the surface roughness is the decay of polarization of the scattered light.     

Controlled formation of dielectric chain aggregates on material surfaces

This paper investigated the formation of chain aggregates from fine particles suspended in gas stream onto material surfaces under the action of electric field. The results showed that the shape of aggregate formed on material surface was greatly influenced by the field intensity and the surface condition of materials. In a weak electric field without corona discharge, particles tended to form clustered aggregates on a metal plate with smooth surface, but on a metal mesh and a porous alumina substrate, to form chain aggregate. On the other hand, in a corona discharge field, these surfaces were coated uniformly. Consequently, for forming chain aggregates on material surface, an electric field without corona discharge and a rough surface are necessary conditions. On rough surface, chain aggregates of dielectric particles or conductive particles grew from the protrusions of the surface and could form a rough and porous layer. When the external electric field was removed, the chain aggregates remained long time due to the Van der Waals forces. After sintered at proper temperature, the chain aggregates became fiber-like. The results indicate that the formation of chain aggregate can be controlled by electrostatic force, and sintering can be used as a method for increasing their mechanical strength.     

Computer Reconstruction of a Random Rough Surface in the Presence of Higher Diffraction Orders

Abstract

The profile of a random rough surface (RRS), whose mean roughness R_a is greater than the light wavelength, is visualized by computer processing. The surface is presented as a sum of sinusoidal gratings. The light diffracted from this surface field is registered by a photodiode array. The second and third diffraction orders from each grating are taken into account in computer processing of the diffracted field and the mixing field–the field obtained at the mixing of the reference and the diffraction fields. The criterion for taking into account higher diffraction orders is the asymmetry of the diffraction pattern to the left and to the right relative to the central peak (the field of zero diffraction orders obtained from each grating) The number of the diffraction orders higher than the first is defined from the average intensity distribution between the central peak and the diffraction orders to the left and to the right at arbitrary light wavelength. The surface profile is reconstructed by a computer program and the mean roughness R_a is calculated. The obtained value of R_a is in satisfactory agreement with that measured by the contact pin method.     

Guided self-assembly of nanostructured titanium oxide

A series of nanostructured titanium oxide particles were synthesized by a simple wet chemical method and characterized by means of small-angle x-ray scattering (SAXS)/wide-angle x-ray scattering (WAXS), atomic force microscope (AFM), scanning electron microscope (SEM), transmission electron microscope (TEM), thermal analysis, and rheometry. Tetrabutyl titanate (TBT) and ethylene glycol (EG) can be combined to form either TiO(x) nanowires or smooth nanorods, and the molar ratio of TBT:EG determines which of these is obtained. Therefore, TiO(x) nanorods with a highly rough surface can be obtained by hydrolysis of TBT with the addition of cetyl-trimethyl-ammonium bromide (CTAB) as surfactant in an EG solution. Furthermore, TiO(x) nanorods with two sharp ends can be obtained by hydrolysis of TBT with the addition of salt (LiCl) in an EG solution. The AFM results show that the TiO(x) nanorods with rough surfaces are formed by the self-assembly of TiO(x) nanospheres. The electrorheological (ER) effect was investigated using a suspension of titanium oxide nanowires or nanorods dispersed in silicone oil. Oil suspensions of titanium oxide nanowires or nanorods exhibit a dramatic reorganization when submitted to a strong DC electric field and the particles aggregate to form chain-like structures along the direction of applied electric field. Two-dimensional SAXS images from chains of anisotropically shaped particles exhibit a marked asymmetry in the SAXS patterns, reflecting the preferential self-assembly of the particles in the field. The suspension of rough TiO(x) nanorods shows stronger ER properties than that of the other nanostructured TiO(x) particles. We find that the particle surface roughness plays an important role in modification of the dielectric properties and in the enhancement of the ER effect.