Investigation of surface topology of printed nanoparticle layers using wide‐angle low‐Q scattering

A new small‐angle scattering technique in reflection geometry is described which enables a topological study of rough surfaces. This is achieved by using long‐wavelength soft X‐rays which are scattered at wide angles but in the low‐Q range normally associated with small‐angle scattering. The use of nanometre‐wavelength radiation restricts the penetration to a thin surface layer which follows the topology of the surface, while moving the scattered beam to wider angles preventing shadowing by the surface features. The technique is, however, only applicable to rough surfaces for which there is no specular reflection, so that only the scattered beam was detected by the detector. As an example, a study of the surfaces of rough layers of silicon produced by the deposition of nanoparticles by blade‐coating is presented. The surfaces of the blade‐coated layers have rough features of the order of several micrometers. Using 2 nm and 13 nm X‐rays scattered at angular ranges of 5°≤θ≤ 51° and 5°≤θ≤ 45°, respectively, a combined range of scattering vector of 0.00842 Å^?1≤Q≤ 0.4883 Å^?1 was obtained. Comparison with previous transmission SAXS and USAXS studies of the same materials indicates that the new method does probe the surface topology rather than the internal microstructure.     

Study on the shadowing effect for optical wave scattering from randomly rough surface

Based on the Kirchhoff approximation for rough surface scattering and by calculating the shadowing function of the rough surface, the formula of the scattering cross section of the dielectric rough surface is presented with consideration of the shadowing effect for the optical wave incidence. It is obtained that in comparison with the conventional Kirchhoff solution, the shadowing effect should not be neglected for the optical wave scattering from the rough surface. The influence of the shadowing effect for different incidence angle, surface root mean square slope, and surface roughness on the scattering cross section is discussed in detail.     

Effect of gamma radiation on the permittivity and electrical conductivity of TlGaS<Subscript>2</Subscript> crystals

The effect of gamma radiation on the permittivity ? and the electrical conductivity σ of TlGaS₂ crystals is investigated at frequencies of 0.1, 1, and 10 kHz and 1 MHz in the temperature range 200–370 K. It is shown that an increase in the temperature leads to an increase in the permittivity ? and the electrical conductivity σ. The electrical conductivity σ of TlGaS₂ samples irradiated with a dose of 10 MR and then measured at all frequencies and the permittivity ? of samples irradiated with a dose of 1 MR and then measured at frequencies of 10 kHz and 1 MHz increase, whereas further accumulation of the dose results in a decrease in the values of ? and σ. The parameters studied are characterized by a considerable dispersion: as the frequency increases, the permittivity ? decreases and the electrical conductivity σ increases.     

Absence of renormalization group pathologies near the critical temperature. Two examples

We consider real-space renormalization group transformations for Ising-type systems which are formally defined by $$\exp \left[ { - H'(\sigma ')} \right] = \sum\limits_\sigma {T(\sigma ,\sigma ')} \exp \left[ { - H(\sigma )} \right]$$ whereT(σ, σ′) is a probability kernel, i.e., ∑_σ′ T(σ,σ′) = 1 for every configuration σ. For each choice of the block spin configuration σ′, let σ′, let μ_σ′ be the measure on spin configurations σ which is formally given by taking the probability of σ to be proportional toT(σ, σ′) exp[?H(σ)]. We give a condition which is sufficient to imply that the renormalized HamiltonianH′ is defined. Roughly speaking, the condition is that the collection of measures μ_σ′ is in the high-temperature phase uniformly in the block spin configuration σ′. The proof of this result uses methods of Olivieri and Picco. We use our theorem to prove that the first iteration of the renormalization group transformation is defined in the following two examples: decimation with spacingb = 2 on the square lattice with β < 1.36β _c and the Kadanoff transformation with parameterp on the trian gular lattice in a subset of the β,p plane that includes values of β greater than β _c .     

Bistatic scattering and depolarization by randomly rough surfaces: application to the natural rough surfaces in X-band

Abstract

The scattering of waves by random rough surfaces has important applications in the remote sensing of oceans and land. The problem of developing a model for rough surfaces is very difficult since, at best, the scattering coefficient σ⁰ is dependent upon (at least) the radar frequency, geometrical and physical parameters, incident and observation angles, and polarization. The problem of electromagnetic scattering from a randomly rough surface is analysed using the Kirchhoff approximation (stationary phase, scalar approximation), the small-perturbation model and the two-scale models. A first major new consideration in this paper is the polarimetric signature calculations as a function of the transmitter location and receiver location for a bistatic radio-link. We calculate the like- and cross-polarized received power directly using the scattering coefficients, without calculating the Mueller matrix. Next, a study of the regions of validity of the Kirchhoff and small-perturbation rough surface scattering models (in the bistatic case) is presented. Comparisons between the numerical calculations and the models are made for various surface rms heights and correlation lengths both normalized to the incident wavenumber (denoted by σ and L, respectively). By using these two parameters to form a two-dimensional space, the approximate regions of validity are then established. The second major new consideration is the development of a theoretical two-scale model describing bistatic reflectivity as well as the numerical results computed for the bistatic radar cross section from rough surfaces especially from the sea and snow-covered surfaces. The results are used to show the Brewster angle effect on near-grazing angle scattering.     

On the surface energy of compressible nuclei

The specific nuclear surface energy σ as a function of the central density n_c is shown to behave in a way opposite to that of the saturation curve; in particular, σ is maximum at the saturation density. Starting from the energy of a compressible nucleus, we find after deriving a simple expression for the second derivative of σ, a formula for thecompressibility modulus K_A of finite nuclei which contains, besides the saturation density and the bulk value K_∞, only some well-known surface parameters.     

Picosecond three-color holographic digital interferometry

The possibilities of multicolor digital holographic interferometry are experimentally studied upon measuring displacements of a surface in radiation of a picosecond Nd:YAG laser with the radiation frequency conversion into harmonics (λ₁ = 1.06 μm, λ₂ = 0.53 μm, and λ₃ = 0.35 μm). It is shown that three-color digital holographic interferometry makes it possible to increase the measurement accuracy of displacements. The peculiarities of multicolor digital holographic interferometry by picosecond pulses are discussed.     

Microwave sea return at moderate to high incidence angles

Abstract

Bragg scattering is widely recognized as the dominant mechanism by which the ocean surface backscatters microwave radiation, but efforts to identify other, non-Bragg sources of this scattering have been pursued for many years. Non-Bragg backscattering from the sea surface is known to occur at incidence angles close to 0° and 90°. In this paper Bragg scattering is shown to explain most features of sea surface backscatter for incidence angles between about 20° and 80°, except when it predicts very small mean cross sections. The often-quoted evidence for non-Bragg scattering in this incidence angle range is that σ _o (HH) is occasionally found to be larger than or equal to σ _o (VV) for short integration times. We show that because of fading this is not evidence of non-Bragg scattering. For incidence angles up to about 50°, standard Bragg/composite surface scattering theory yields probabilities of finding σ _o (HH)>σ _o (VV) that are only slightly smaller than those found experimentally. As the incidence angle increases, greater differences between theoretical and experimental probabilities are found. The addition of Bragg scattering from bound, tilted waves brings theory into excellent agreement with experiment at incidence angles near 45° but still cannot account adequately for the probability of σ _o (HH)>σ _o (VV) or observed σ _o (HH) cross sections at higher incidence angles. We show that the addition of a small, non-Bragg cross section that is independent of the incidence angle and polarization, brings simulated cross sections and probability distributions into good agreement with data. A possible source of this small, non-Bragg sea return is sea spray just above the air/sea interface.     

Electrode reaction at Pt,O2(g)/stabilized zirconia interfaces. Part I: Theoretical consideration of reaction model

This study aims to make clear the reaction kinetics at Pt, O₂(g)/zirconia electrodes in the oxygen partial pressure, P_O2, of ∼ 10⁻⁴ − 1 atm at ∼ 400–∼800°C. By a critical review on the preceding studies, problems were pointed out in the application of the Langmuir adsorption isotherm to the P_O2 dependence of electrode conductance, in the assumption of electric double layer at the electrode interface, and of the inconsistency between the recent reaction model of surface diffusion controlled kinetics and the absolute rate theory. It was shown that the charge transfer kinetics cannot be the rate determining step (RDS) of the electrode reaction. The possible RDS was concluded to be either (i) dissociative adsorption of oxygen molecules on the Pt surface or (ii) surface diffusion of O_ad atoms on the Pt surface to the Pt/zirconia contact. The diffusion of O_ad atoms on the Pt surface was considered to be proportional to θ(1−θ)(∂μ_O/∂x), where θ is the occupancy of O_ad atoms on Pt and μ_O is the oxygen chemical potential on the Pt surface. The rate equation, current-potential relationship, and the electrode conductivity, σ_E, were calculated for the cases the RDS is (i) and (ii), respectively. By comparing the calculated σ_E versus log P_O2 relationship with the reported ones, it was shown that the RDS is (i) for T ≲ 500°C and is (ii) for T ≳ 600°C. In the former case, σ_E is essentially constant irrespective to P_O2, and in the latter case, σ_E maximum appears on the σ_E versus log P_O2 relations.     

The effect of bombardment with neutralized neon ions on the roughness of a fused silica and beryllium surface

The effect of Ne ion beam etching on the roughness of materials for optical substrates—fused silica and beryllium—is studied. It is shown that the treatment of a fused silica surface by neutralized Ne ions with an energy of 400–800 eV makes it possible to smooth roughnessed in the range of higher spatial frequencies of 3–63 μm^–1 at an incidence angle of 0°–30°. For beryllium, the possibility of smoothing the surface roughness at an ion energy of 400 eV is found.     

Effect of accumulation on the formation of multiply charged ions in solids under grazing incidence of multiple laser radiation

The effect of accumulation on the formation of multiply charged ions in optically opaque solids as a function of the number and the angle of incidence of laser pulses is investigated by mass spectrometry. It is revealed that the accumulation effect manifests itself at prethreshold power densities q = 10⁸–10⁹ W/cm² irrespective of the angle of incidence of laser radiation α = 18°–85° and at subthreshold power densities q > 10¹⁰ W/cm² in the case of grazing incidence of laser radiation at an angle α = 85°. The accumulation effect brings about an increase in the maximum charge multiplicity Z _max of tungsten ions and a decrease in the number of impurity ions and in their intensity. No accumulation effect is observed at subthreshold power densities when laser radiation is incident at an angle α = 18°.     

Dynamic thermometry of a solid via optical diffraction method at pulsed irradiation

A method for the fast measurement of the temperature of solids under the action of a high-power light pulse is proposed and demonstrated. This method is based on the application of the Fraunhofer diffraction and is implemented for silicon samples heated to melting temperatures T _melt = 1412°C by a high-power light pulse. The current silicon temperature was determined by measuring the varying diffraction angle of the probing laser beam. The diffraction angle was varied over time because the period of the diffraction grating increased as a result of the dynamic thermal expansion of the crystal. An initial grating was formed on the surface of the silicon plate with a period of d = 4 μm. The radiation beam of a He-Ne laser with λ = 0.6328 μm was used as the probing beam; the measured signal was recorded in the pair of symmetric fifth-order diffraction maxima.     

Angular dependence of the scattered ion yields in 4He+ → Cu scattering spectrometry

Assuming long range charge exchange mechanisms and neglecting shadowing effects, theory predicts the variation of the scattered ion yield with the scattering angle θ and the incidence angle ψ for some well defined experimental conditions. Such measurements were performed for ⁴He⁺ scattering on polycrystalline copper at incident energies ranging from 0.5 to 1.25 keV and at scattering angles from 20° to 130°. It is suggested that shadowing effects should be taken into account in order to explain the observed behaviour.     

Grain size, stress, and creep in polycrystalline solids

If a stress σ is applied to a polycrystal of grain size L, the mode of creep deformation depends on the answers to the following questions: (I) Does σ exceed the Peierls stress σ_p; (II) Does L exceed the dislocation spacing in a Taylor lattice stabilized by σ_p; (III) Does Lσ exceed the value required for a Frank-Read or Bardeen-Herring source to operate within the grain? (IV) Does L ^1/2σ exceed the Hall-Petch value required for slip to propagate across a grain boundary? The (L, σ) plane is thus partitioned into regions in which different creep modes predominate.     

Electrical conductivity of N-methyl phenazinium tetracyanoquinodimethanide, (NMP) (TCNQ)

New conductivity, σ, vs. temperature, T, measurements on numerous (NMP)-(TCNQ) samples, as well as older data, can all be fit, in the range 65K<T<400K, by the simple expression σ = σ_oT^-αexp(-900/T). σ_o and α(3<α<4) are sample-dependent constants. We interpret this as representing an activated carrier concentration and strongly T-dependent mobility, μ. We can account for the magnitude and T-dependence of μ by a model involving interaction with the molecular vibrations through the known electron-phonon coupling constants of TCNQ^-.     

壁面二次电子发射对霍尔推力器放电通道绝缘壁面双鞘特性的影响

为进一步揭示霍尔推力器放电通道绝缘壁面鞘层的特性, 利用考虑了壁面二次电子分布函数的一维稳态流体鞘层模型, 研究了壁面二次电子发射对近壁双鞘特性的影响. 分析结果表明, 由于壁面发射的二次电子对近壁鞘层中的电子密度有增加作用, 存在一个临界二次电子发射系数σ_dc使得: 当σ≤σ_dc时, 鞘层为单层的正离子鞘结构; 当σ>σ_dc时, 鞘层表现为双层的正离子鞘和电子鞘相连结构, 连接点对应于垂直于壁面方向上电势分布的拐点. 然而, 当σ进一步增大到0.999时, 鞘层转变为三层的正离子鞘-电子鞘-正离子鞘交替结构. 数值结果表明: 随着σ的增加, 电子鞘与离子鞘的连接点向远离壁面的方向移动, 电子鞘的厚度逐渐增加; 随着壁面出射电子能量系数a的增加, 近壁区鞘层的厚度也逐渐增加. 关键词： 霍尔推力器 双鞘 壁面二次电子发射     

Relationship between σxx and σyx - integral quantum hall effect

The possibility of a Kramers-Kronig relation between the longitudinal and transverse conductivities of a 2-D electron gas in the presence of a magnetic field is investigated. The longitudinal (σ_xx) and the transverse (σ_yx) conductivities are expressed as the real and imaginary part of a complex conductivity (σ). A formal expression is derived for σ within the independent particle approximation. In the classical limit, σ is analytic in the upper complex ω_c plane, where ω_c is the cyclotron frequency. Hence the usual Kramers-Kronig relation holds for σ^c. We modeled a quantum correction (σ^q) to σ and found that σ^q is non-analytic in the upper half plane, hence the total σ does not satisfy a Kramers-Kronig relation.     

Experimental studies of polarization of laser radiation in a rotating optical glass

The results of experiments on observation of rotation of the plane of polarization of coherent laser radiation with wavelength λ = 0.632991 μm after propagation through a rotating optical disk made of TF3 glass with refractive index n = 1.71250 are analyzed. The experiments were conducted at angle of ray incidence on the flat disk surface ?₀ = 60°, and the rotational speed of the disk was varied from 0 to 200 Hz in both directions. The results indicate that rotation of optically transparent, homogeneous, and isotropic dielectric causes rotation of linear polarization of the monochromatic electromagnetic plane wave by several tens of degrees. At a rotational speed of 3 Hz, the rotation of polarization reached Δφ = 70° for the vertical component of laser output polarization. The dependences of the angle of rotation of polarization and the degree of polarization of the rays on rotational speed are nonlinear and are attributed to the appearance of substantial anisotropic properties in a rotating dielectric.     

Numerical study of the extinction matrix for a plate crystal

Energy and polarization characteristics of optical radiation passed through a semitransparent plate crystal with a preset orientation in space are studied numerically within the framework of the method of physical optics. Results of calculations of the extinction matrix elements versus particle size, refractive index, crystal orientation, and incident radiation wavelength (from 0.5 to 15 μm) are presented. It is demonstrated that K₁₁, K₁₂, and K₃₄ are most informative among the elements of the extinction matrix. It is established that the first of them is most sensitive to changes in the microphysical and orientational parameters of the particle when the angle of radiation incidence on the plate changes from 0 to 20°, and the nondiagonal elements are most sensitive when the angle of radiation incidence is greater than 40°. The characteristics of the total field scattered near the forward direction are determined. It is established that their dependence on the physical parameters of the crystal is most strong at scattering angles smaller than or equal to 4° and wavelengths from the IR range (in particular, from the atmospheric transparency window).     

Parametrization of the 1S0 two nucleon transition matrix

The ¹S₀ two-nucleon transition matrix T is constructed from the symmetric part σ of its half-shell elements. The on-shell component of σ is given by the phase shift, while a wide class of parametrizations is suggested for the off-shell part. Restrictions on the off-shell part of σ arising from the short range and the proper one-pion-exchange tail of the nucleon-nucleon interaction are investigated. Using σ in the ¹S₀ and the Reid soft-core potential in the other partial waves, the binding energy per particle in nuclear matter and ¹⁶O and the ¹⁸O shell-model spectrum are computed. The sensitivity of these nuclear-structure results is tested with respect to (i) smooth off-shell changes in σ, (ii) various assumptions on the high-energy phase shift, (iii) the charge dependence of the phase shift, and (iv) experimental uncertainties in the phase shift.