The Impact of Chemical Bonding on Mass Absorption Coefficients of Soft X-rays.

Accurate elemental quantification of materials by X-ray detection techniques in electron microscopes or microprobes can only be carried out if the appropriate mass absorption coefficients (MACs) are known. With continuous advancements in experimental techniques, databases of MACs must be expanded in order to account for new detection limits. Soft X-ray emission spectroscopy (SXES) is a characterization technique that can detect emitted X-rays whose energies are in the range of 10 eV to 2 keV by using a varied-line-spaced grating. Transitions producing soft X-rays can be detected and accurate MACs are required for use in quantification. This work uses Monte Carlo modeling coupled with multivoltage SXES measurements in an electron probe micro-analyzer (EPMA) to compute MACs for the L2,3-M and Li Kα transitions in a variety of aluminum alloys. Electron depth distribution curves obtained by the software MC X-ray are used in a parametrized fitting equation. The MACs are calculated using a least-squares regression analysis. It is shown that X-ray distribution cross-sections at such low energies need to take into account additional contributions, such as Coster­Kronig transitions, Auger yields, and wave function effects in order to be accurate.

Secondary Fluorescence Correction for Characteristic and Bremsstrahlung X-Rays Using Monte Carlo X-ray Depth Distributions Applied to Bulk and Multilayer Materials.

Secondary fluorescence effects are important sources of characteristic X-ray emissions, especially for materials with complicated geometries. Currently, three approaches are used to calculate fluorescence X-ray intensities. One is using Monte Carlo simulations, which are accurate but have drawbacks such as long computation times. The second one is to use analytical models, which are computationally efficient, but limited to specific geometries. The last approach is a hybrid model, which combines Monte Carlo simulations and analytical calculations. In this article, a program is developed by combining Monte Carlo simulations for X-ray depth distributions and an analytical model to calculate the secondary fluorescence. The X-ray depth distribution curves of both the characteristic and bremsstrahlung X-rays obtained from Monte Carlo program MC X-ray allow us to quickly calculate the total fluorescence X-ray intensities. The fluorescence correction program can be applied to both bulk and multilayer materials. Examples for both cases are shown. Simulated results of our program are compared with both experimental data from the literature and simulation data from PENEPMA and DTSA-II. The practical application of the hybrid model is presented by comparing with the complete Monte Carlo program.

A hydrodynamic approach to electron beam imaging using a Bloch wave representation.

Calculations of quantum trajectories associated to a propagated wave function provide new insight into quantum processes such as particle scattering and diffraction. Here, hydrodynamic calculations of electron beam imaging under conditions comparable to those of a transmission electron microscope display the mechanisms behind different commonly investigated diffraction conditions. The Bloch wave method is used to propagate the electron wave function and associated trajectories are computed to map the wave function as it is transmitted through the material. Simulations at normal incidence and of the two-beam condition are performed and electron diffraction is analyzed through a real space interpretation of the wave function. In future work, this method can be coupled with Monte Carlo modeling in order to create all encompassing simulations of electron imaging.

Wave-packet numerical investigation of thermal diffuse scattering: A time-dependent quantum approach to electron diffraction simulations.

The effects of thermal diffuse scattering on diffraction of highly-accelerated electrons by crystal lattices are investigated with a method that combines the frozen phonon approximation with an exact numerical solution of the time-dependent Schrödinger equation. The phonon configuration for each single-electron diffraction process is determined by means of Einstein's model. It is shown that this procedure provides the possibility of describing and explaining, in a natural way, after averaging over a number of electron realizations, how the typical diffraction features that characterize a fully coherent pattern are gradually suppressed by thermally-induced incoherence. This is achieved by a controlled increase of the lattice atomic vibrations and is in contrast to the use of attenuating Debye-Waller factors and complex potential absorbers. A lattice with reduced dimensionality is first considered as a working model, where the method renders results compatible with those reported in the literature. Subsequently, a full three-dimensional system is simulated and results are compared to experimental imaging displaying the method's reliability.

A universal equation for computing the beam broadening of incident electrons in thin films.

A universal equation for computing the beam broadening of incident electrons in thin films is presented. This equation is based on the concepts of anomalous diffusion with the Hurst exponent H. When the thickness to elastic mean free path ratio, t/λ, is greater than 1, the Hurst exponent goes to 0.5 and this random walk behavior leads to the Goldstein et al. [1] beam broadening equation when non-relativistic screened Rutherford elastic cross-sections are used. When t/λ≪1, the lack of elastic collisions for the electron trajectories gives an H exponent of 1 and a different beam broadening equation is obtained. A general equation to compute the beam broadening that takes into account the variation of H with t/λ is presented and this equation was fitted and validated with Monte Carlo simulations of electron trajectories in thin films.