The Application Of Bem In Particle Scattering And Energy Loss Spectra

In the field of nano science, the research of nanomaterials is an important issue. There exists an important material, the metal nano material which plays an important role in the modern industry and the high-tech development. Nano particles are a kind of colloidal particles, because of its unique optical properties and application value, metallic nanomaterials have attracted more and more attention. The study of optical absorption properties is the focus of our attention. With the popularization of nanomaterial, the surface properties of material surface and the environment have attracted the attention of the researchers, the research of electron energy loss spectra has been applied to a wide range of applications. When the electron beam passes through or by the metal particles, energy will be lost due to the action of the surface plasmons. The calculation of the energy loss spectra generated by the electrons passing through the metal medium is helpful for us to understand the local chemical and electronic structure. The specific research works have been carried out from the following aspects.(1) The scattering phenomena and the calculation of the electron energy loss spectra of different metal nanoparticles are studied. In this process, the calculation of the energy loss of fast electrons is also obtained by the analytical solution. Based on the formula of classical electron energy loss spectrum, an efficient computational formula is obtained by using the alternative of the induced electric field and the boundary element method. The surface modes of various particularly simple geometries have been theoretically investigated in the past without inclusion of retardation effects. Isolated spheres, two coupled spheres, cylinders, two coupled cylinders are considered. Granular materials composed of randomly distributed spheres have been studied as well using effective medium theories to find the loss function of equivalent homogeneous media.(2) Based on the boundary integral equation of the boundary element method, the boundary integral equation of particle scattering and electron energy loss spectra in the nonretarded and retarded cases is derived. In the theory, the surface charge and surface current are used to represent the potential and the magnetic potential and a series of integral equations are obtained. For the simulation of electronic energy loss spectrum, while the medium distance is far, or the electronic speed is relatively fast, the local approximation of the dielectric constant may need to make the corresponding adjustment. When the medium size is relatively small, the local approximation of the dielectric constant need to be given special attention.(3) The shape function of the boundary element method is studied, and the higher order form function has a great advantage in improving the accuracy of the solution. We use a higher order form function to deal with the discrete boundary integral equation, obtaining the concrete form of the discrete equations, the coefficient of which is a integral form of the shape function and the kernel function. The numerical solution of the equations is obtained by combining the fast algorithm, which greatly improves the accuracy of the solution. Because the quantity of the inner boundary can be expressed by the boundary variables, the amount of the inner boundary can be obtained by the numerical integration method.(4) In the numerical simulation of particle scattering and electron energy loss spectra of different shapes and numbers, the boundary element method with high order form function is used. In the process, we compare the effect of different sizes and different distances to the results, and analyze the corresponding physical phenomena. Based on the calculation of radiation decay rate and total decay rate under the excitation of metal nanoparticles in oscillating dipoles, the relationship between the wavelength of the incident wave and radiation decay rate and total decay rate is numerically simulated, and the validity of the algorithm is verified.