Modeling of the bremsstrahlung radiation produced in pure-element targets by 10–40 keV electrons

Abstract

A new global relationship has been developed for predicting electron-excited bremsstrahlung intensities over a wide range of accelerating voltages 10–40 keV, atomic numbers 4–92, and x-ray energies 1.5–20 keV. The new relationship was determined empirically from the mathematical modeling of extensive data and is designed for calculating bremsstrahlung intensities in analytical procedures, such as those requiring peak-to-background measurements, where the direct measurement of the bremsstrahlung intensities is impracticable. The distribution of errors between the data and the model is symmetrical, centered around zero error with 63% of the values falling between ±10% relative error.

Simulation of electron‐excited X‐ray spectra with NIST–NIH Desktop Spectrum Analyzer (DTSA)

“…To complete the spectral simulation for subsequent application to the problem of determining the success of spectrum deconvolution tools, the X-ray background was modeled with the empirical continuum expression of Small et al, 16 which is based upon extensive experimental measurements.…”

The prediction of thick target electron bremsstrahlung spectra in the 0.25–50 keV energy range

“…Small et al [74] observed that discrepancies between the existent models for bremsstrahlung and experimental values were about 50% or even 100%. For this reason they developed an expression by fitting a large set of experimental data:…”

“…Several authors tried to find analytical expressions for the continuum background so that only one parameter remained undetermined [73][74][75][76][77]. This scaling factor depends on the particular detection geometry and must be fitted for each equipment -but not for each spectrum because it is not related neither to the sample composition nor to the excitation conditions.…”

“…Mass absorption coefficients were calculated with the expression given by Heinrich [81]. This approach involves the assumption of considering the depth distribution of continuum xray production similar to that of characteristic radiation, as also considered in previous predictions [73,74]. Although characteristic radiation is isotropically emitted, this is a reasonable approximation: even when each bremsstrahlung photon preferably follows the forward electron direction (particularly for high energies), after a few interactions the electron path looses correlation with the incidence direction.…”

“…A large set of spectra was involved in the fitting process in order to achieve a reliable Table 1 Global χ 2 values for the comparison performed by Trincavelli et al [75]. Reed's model [52] with coefficients given by Statham [65] and the expression given by Small et al [74] were also assessed expression for the continuum function which describes properly the bremsstrahlung spectrum for photon energies ranging from 0.25 to 20 keV and atomic numbers between 4 and 83, at beam energies ranging from 5 to 38 keV. The expression obtained in this work is Fig.…”