New developments in theory of fast electron scattering in solids: Applications to microbeam analysis

The study of fast electron interaction with solids in the energy range from 100 eV to several tens of keV is prompted by quickly developing microbeam analysis techniques such as electron probe microanalysis, scanning electron microscopy, electron energy loss spectroscopy and so on. It turned out that for random solids the electron transport problem might be solved on the basis of the generalized radiative field similarity principle. The latter states that the exact differential elastic cross section in the kinetic equation may be replaced by an approximate one provided the conditions of radiative field similarity are fulfilled. Application of the generalized similarity principle to electron scattering in solids has revealed many interesting features of electron transport. Easy to use and effective formulae have been obtained for the angular and energy distribution of electrons leaving a target, total yields of characteristic photons and slow electrons escaping from a sample bombarded by fast primaries, escape probability of Auger electrons as a function of depth etc. The analytical results have been compared with Monte Carlo calculations and experiments in a broad range of electron energies and scattering properties of solids and good agreement has been observed.     

弹性散射法研究间规聚苯乙烯的冷结晶行为

用弹性光散射方法研究了间规聚苯乙烯(s-PS)的非等温冷结晶行为和等温结晶动力学.结果表明,弹性散射信号对s-PS的冷结晶过程中的构象变化非常敏感.弹性散射法所得的大分子链玻璃化转变温度Tg以及冷结晶温度Tc与DSC的测量结果一致.此外,通过散射强度随温度的变化可以更为清晰地分辨出冷结晶过程中各个阶段,包括晶体成核期,晶核生长期以及二次结晶期.通过等温弹性散射测试,同时结合Arrhenius方程,计算得到s-PS冷结晶表观活化能Ea为309 kJ/mol.     

第一性原理的形变势理论研究声学声子散射对电荷传输的影响

本文应用密度泛函理论和玻尔兹曼方程,在形变势理论的框架和驰豫时间近似下,研究了分子晶体中电子与声学声子散射对电荷传输的影响.针对蒽、萘、丁省和并五苯的计算表明,非局域化电子的传输过程主要受到来自于声学声子的散射.对于蒽晶体,与以前的Holstein-Peierls模型计算结果相比,发现纵向声学声子对空穴的散射强度是光学声子的3倍,所得到的空穴迁移率更接近超纯单晶样品的实验测量结果.同时,我们发现电子的本征迁移率比空穴还要大,应用前线轨道交叠分析可以合理地解释这一结果.     

动态光散射对良溶剂中酚醛型聚醚砜的研究

用动态光散射方法研究了酚酞型聚醚砜(PES-C)在良溶剂DMF中的稀溶液性质。在稀溶液中,PES-C分子由于内旋转发生链折叠,整体上表现出柔性链的性质,较好的符合球形模型;而分子链的局部刚性结构又使分子尺寸稳定;它的扩散行为随温度的变化符合Arrehnius方程。表征了PES-C分子在稀溶液中的形态结构,且给出了PES-C分子在DMF中的扩散系数、扩散活化能、无限稀时的扩散系数和流体力学半径等重要特征参数。     

Thermal waves scattering by a subsurface sphere in a semi-infinite exponentially graded material using non-Fourier's model

In this study, the multiple scattering of thermal waves and temperature distribution resulting from a subsurface sphere in a semi-infinite exponentially graded material are investigated, and the analytical expression of the temperature at the surface of the graded material is obtained. Non-Fourier heat conduction equation is applied to solve the temperature at the surface, and the image method is used to satisfy the semi-infinite boundary condition of graded material. The thermal wave fields are expressed using wave function expansion method, and the expanded mode coefficients are determined by satisfying the boundary condition of the sphere. According to the wave equation of heat conduction, a general solution of scattered thermal waves is presented for the first time. The temperature distribution and phase difference at the surface of the semi-infinite material with different parameters are graphically presented. Analyses show that the hyperbolic heat conduction equation cannot be regarded as a continuation of the parabolic heat conduction equation at very short time scale. The effects of the incident wave number, the structural and physical parameters on the distribution of temperature and phase difference in the semi-infinite material are also examined.     

光散射技术在蛋白质晶体生长研究中的应用和进展

光散射技术广泛应用于生物大分子的晶体生长研究中,它包括静态光散射和动态光散射两种。利用静态光散射可以测定蛋白质溶液渗透的第二维里系数;利用动态光散射可以测定蛋白质溶液的平动扩散系数,获得溶液中蛋白质粒子的流体力学半径及分布情况,分离蛋白质结晶的成核与生长过程,研究大分子的聚集行为和晶体生长的动力学。借助光散射技术可以实现蛋白质晶体生长过程的动态控制。近些年光散射仪器向着小型化、轻便化的方向发展,光散射技术不断得到改进,日益完善,不仅用于地面实验,也应用于空间领域蛋白质晶体生长的研究中。     

Elastic electron scattering by argon in the vicinity of the high-energy critical minimum

Differential cross sections (DCSs) for elastic electron scattering by argon in the vicinity of the high-energy critical minimum are presented. DCSs were measured as a function of both incident electron energy (90 –150 eV) and scattering angle (40°–126°). The absolute calibration was achieved via normalization to a single point. The positions of high angle DCS minimum versus incident electron energy were obtained. The experimentally obtained results are compared to the relativistic ab initio calculations based on the Dirac–Hartree–Fock method.     

Determination of the fiber-size distribution function in polydisperse dielectric fibrous materials

A simple method has been proposed for determining the average fiber length in unit volume of a polydisperse fibrous material as depending on fiber diameter. The method consists in the measurement of light attenuation as a function of the distance from an examined sample. The method entails comparison of the measured energy fluxes that reach a detector before and after scattering by an examined fibrous material sample and uses an integral relation that expresses the intensity of light transmitted through a random medium via the electric-field correlation function. Formulas have been found for the electric-field correlation function after the passage through a layer of a polydisperse fibrous material with random arrangement and orientation of fibers. The obtained correlation function enables one to derive an integral equation that expresses the logarithmic ratio of the energy fluxes reaching the radiation detector before and after the passage through a scattering medium via the fiber size-distribution function. Solution of this integral equation makes it possible to determine the fiber-size distribution function from the light attenuation measured as depending on the distance from the point of observation. Experiments have been carried out for several fibrous filters and relevant calculations have been presented. The results of the solution of the integral equation agree with the data obtained by other experimental methods and with visual processing of electron micrographs.     

Obtaining quantitative information on surface excitations from reflection electron energy‐loss spectroscopy (REELS)

A new analysis of reflection electron energy‐loss spectroscopy (REELS) spectra is presented. Assuming inelastic scattering in the bulk to be quantitatively understood, this method provides the distribution of energy losses in a single surface excitation in absolute units without the use of any fitting parameters. For this purpose, REELS spectra are decomposed into contributions corresponding to surface and volume excitations in two steps: first the contribution of multiple volume excitations is eliminated from the spectra and subsequently the distribution of energy losses in a single surface scattering event is retrieved. This decomposition is possible if surface and bulk excitations are uncorrelated, a condition that is fulfilled for medium‐energy electrons because the thickness of the surface scattering layer is small compared with the electron elastic mean free path. The developed method is successfully applied to REELS spectra of several materials. The resulting distributions of energy losses in an individual surface excitation are in good agreement with theory. In particular, the so‐called begrenzungs effect, i.e. the reduction of the intensity of bulk losses due to coupling with surface excitations near the boundary of a solid‐state plasma, becomes clearly observable in this way. Copyright © 2003 John Wiley & Sons, Ltd.     

The role of acoustic phonon scattering in charge transport in organic semiconductors: a first-principles deformation-potential study

The electron-acoustic phonon scattering for charge transport in organic semiconductors has been studied by first-principles density functional theory and the Boltzmann transport equation with relaxation time approximation. Within the framework of deformation-potential theory, the electron-longitudinal acoustic phonon scattering probability and the corresponding relaxation time have been obtained for oligoacene single crystals (naphthalene, anthracene, tetracene and pentacene). Previously, the electron-optic...     

Evaluation of elastic‐scattering cross sections for electrons and positrons over a wide energy range

Quantification of surface‐ and bulk‐analytical methods, e.g. Auger‐electron spectroscopy (AES), X‐ray photoelectron spectroscopy (XPS), electron‐probe microanalysis (EPMA), and analytical electron microscopy (AEM), requires knowledge of reliable elastic‐scattering cross sections for describing electron transport in solids. Cross sections for elastic scattering of electrons and positrons by atoms, ions, and molecules can be calculated with the recently developed code ELSEPA (Elastic Scattering of Electrons and Positrons by Atoms) for kinetic energies of the projectile from 10 eV to 50 eV. These calculations can be made after appropriate selection of the basic input parameters: electron‐density distribution, a model for the nuclear‐charge distribution, and a model for the electron‐exchange potential (the latter option applies only to scattering of electrons). Additionally, the correlation‐polarization potential and an imaginary absorption potential can be considered in the calculations. We report comparisons of calculated differential elastic‐scattering cross sections (DCSs) for silicon and gold at selected energies (500 eV, 5 keV, 30 keV) relevant to AES, XPS, EPMA, and AEM, and at 100 MeV as a limiting case. The DCSs for electrons and positrons differ considerably, particularly for medium‐ and high‐atomic‐number elements and for kinetic energies below about 5 keV. The DCSs for positrons are always monotonically decreasing functions of the scattering angle, while the DCSs for electrons have a diffraction‐like structure with several minima and maxima. A significant influence of the electron‐exchange correction is observed at 500 eV. The correlation‐polarization correction is significant for small scattering angles at 500 eV, while the absorption correction is important at energies below about 10 keV. Copyright © 2005 John Wiley & Sons, Ltd.     

Analytic correlated wave functions in momentum space and related properties of helium like ions

We obtain analytic correlated wave functions in momentum space as the Fourier transform of correlated wave functions which are able to incorporate almost all of the correlation energy for the ground-state of two-electron atoms. Then we study the atomic momentum-density, the Compton profile and the elastic and inelastic scattering factors for this kind of wave functions. The scattering factors are also compared with the ones provided by a more accurate correlated wave function. All the calculations can be analytically performed, provided the correlated wave function in position space has been determined.     

Elastic scattering of gamma rays and X-rays

Studies of elastic gamma ray scattering were pursued independently by the groups of Prof. Ghose and the author for several decades in spite of somewhat meagre support. Several techniques for such studies developed by the two groups and some of the results obtained in the energy range from tens of keV to about 1.5 MeV are described briefly. The theoretical background necessary for understanding these results is also outlined. The results showed the importance of Modified Relativistic Form Factor (MRFF) approximation in the explanation of atomic Rayleigh scattering cross sections in the small angle regime and the necessity for an inclusion of real Delbrück scattering amplitudes at large scattering angles. Dispersion corrections to form factor amplitudes or the so-called anomalous scattering factors are shown to be needed at photon energies close to electron binding energy thresholds. A few promising future extensions of such studies are indicated at the end.     

Bound and scattering states for a hyperbolic‐type potential in view of a new developed approximation

A new developed approximation is used to obtain the arbitrary l‐wave bound and scattering state solutions of Schrödinger equation for a particle in a hyperbolic‐type potential. For bound state, the energy eigenvalue equation and unnormalized wave functions in terms of Jacobi polynomials are achieved using the Nikiforov–Uvarov (NU) method. Besides, energy eigenvalues are calculated numerically for some states and compared with those given in the literature to check accuracy of our results. For scattering state, the wave function is found in terms of hypergeometric functions. Furthermore, scattering amplitude and phase shifts are achieved using scattering solutions. Also it is shown that the energy eigenvalue equation obtained from analytic property of scattering amplitude is same with one obtained using NU method. © 2015 Wiley Periodicals, Inc.     

DYNAMIC LIGHT SCATTERING STUDY ON TRANSLATION DIFFUSION OF 8-ARM STAR POLYSTYRENE IN GOOD AND THETA SOLVENTS

The technique of dynamic light scattering has been used to investigate the translation diffusion behavior of 8-arm star polystyrene (SPS)in a good solvent, tetrahydrofuran (THF) or benzene (BZ) and a theta solvent, cyclohexane (CH), by homodyne photon correlation spectroscopy .The intensityintensity autocorrelation function was analyzed by the method of cumulant. The translation diffusion coefficients have been obtained as a function of temperature and concentration. Under theta condition ,the non-concentration dependence of diffusion coefficient showed the unperturbed Gaussian state o the SPS molecular chain. The different hydrodynamic radii estimated from Stokes- Einstein equation reflected the stretch extent of the arm chain for regular star polymer. The data of diffusion activation energy of SPS in THF, BZ and CH were also obtained respectively.     

准弹性光散射研究苯乙烯-二乙烯基苯共聚超微粒的溶液性质

本文用光子相关光谱技术研究了聚苯乙烯-二乙烯基苯(PSt-DVB)共聚超微粒的溶液性质.该微粒的浓度涨落时间相关函数在波矢为q时,有指数衰减形式,其衰减速率г=q~2D_t.在精确的实验误差范围内,衰减速率的变化率为零。用累积量方法解析散射场的一阶时间相关方程,得到了作为浓度和温度函数的微粒扩散常数.与流体办学方程结合,计算出了微粒的流体力学尺寸.通过实验也确定了微粒在良溶剂中的分子形态.     

Incorporation of the electron energy-loss straggling into the Fermi–Eyges equation

A modified Fermi–Eyges equation has been derived from the linear Boltzmann equation by including a term for describing electron energy-loss straggling. The solution has been obtained by the use of a generalized Eyges' method, yielding the electron energy distribution expressed with moments method in addition to Eyges' original solution. The first- and second-order approximations of the spectrum give the well-known continuous-slowing-down approximation (CSDA) and Gaussian distribution, respectively. Inclusion of the third-order moment in the spectrum yields the Vavilov distribution approximated with the Airy function. The higher order approximations can be evaluated numerically.     

An analysis of the siegert eigenvalue problem for autoionizing states

We show that the divergent integrals which appear in a direct matrix solution to the Siegert problem for autoionizing (or electron scattering) state energies and widths can be cancelled exactly. When this is done the Siegert problem becomes essentially a bound state problem. We also show that the resulting non-hermitian secular equation which requires several non-hermitian diagonalizations in the iterative solution for the complex energy can be exactly reduced by a partitioning technique to a single hermitian diagonalization (for a single open channel) with the subsequent iterative solution of a simple algebraic equation.     

Field-theoretical approach to vibrational excitation in atom—diatom collinear collisions

The field-theoretical atom—diatom scattering equations of Csanak have been tested numerically, assuming a collinear collision model, with an exponential repulsive interaction potential and with a harmonic oscillator approximation for the molecule. Dyson's equation, in its integral form, has been solved obtaining orbitals representing the elastic scattering of an atom off the target and these Dyson's orbitals have been used to evaluate a matrix element containing a transition potential. This has been obtained by approximating Bethe—Salpeter's equation and yields directly the transition amplitudes for inelastic scattering. The results for single and multiple-jumps compare favourably with the exact values of Secrest and Johnson, and refinements of the model are suggested for further improvements.