23.4 · Useful Indicators of Geometric Factors Impact on Analysis

measurement conditions, but a low total can also reveal the presence on an unexpected elemental constituent that is not in the list of elements analyzed. For example, an oxidized inclusion in a metallic alloy will typically have an oxygen mass fraction of approximately 0.3, leading to a sharp decrease in the analytical total to ~ 0.7 (70 %) if oxygen is not recognized and included in a standards-based analysis of that location compared to the surrounding metallic region. Thus, even for conventional analysis of ideal specimens, the raw analytical total conveys useful information and should always be inspected.

When a specimen deviates from the ideal flat condition and geometric factors affect the analysis, the raw analytical total gives a direct indication, providing a standards-based–matrix correction factor protocol is being used. Note that “standardless analysis” does not provide this critical information on the raw analytical total if this protocol reqwuires a forced normalization to unity mass fraction (100 wt %) since the electron dose information is not considered. “Standardless analysis” schemes that use a locally measured elemental spectrum to establish the dose relationship to the vendor’s standard intensity database or which use the peak-to-background method (see below) can provide a meaningful analytical total.

.  Figures 23.11a, b shows the calculated normalized concentrations as a function of the raw analytical total for Mg and Fe in

K411 from the suite of spectra obtained from the various

geometric shapes. Note that for this data set, the raw analytical total varies from 0.03 to 1.30 mass fraction (3–130 weight wt %). For this particular composition (K411 glass), the RDEV for Mg and Fe is within a range of 10% relative when the analytical total is in the range 0.8–1.2 mass fraction (80–120 wt %). Different compositions are likely to have different sensitivities to deviations in accuracy, but the general experience is that when the raw analytical total ranges from 0.9 to 1.1 mass fraction (90–110 wt %), the impact of the geometric factors on the analysis will be minimized.

23.4.2\ The Shape of the EDS Spectrum

A second powerful indicator that can alert the careful analyst to the possible impact of geometric factors on an analysis is the shape of the EDS spectrum. The shape of the X-ray continuum

(bremsstrahlung) background from an ideal flat specimen has distinctive properties. Consider the spectrum of pure boron, selected because of the absence of significant characteristic peaks above the energy of boron (0.185 keV), as shown in

.  Fig. 23.12. A small peak of oxygen that arises from the inevitable surface oxide on the boron can be seen in this spectrum, as well as the artifact silicon peak from the absorption and internal fluorescence of the silicon window support grid and the silicon dead layer of the detector. Otherwise, the spectrum consists

. Fig. 23.11  Calculated normalized concentrations as a function of the raw analytical total from the suite of spectra obtained from the various geometric shapes: a Fe, b Mg

Raw analytical total (weight percent)

Raw analytical total (weight percent)

only of the X-ray bremsstrahlung that occurs at all photon energies, Eν, up to the incident beam energy, E0 (Duane–Hunt limit). Inspecting this spectrum starting at high photon energy, as the photon energy Eν decreases, the intensity of the continuum, Icm, increases, a consequence of the physics of the generation of the bremsstrahlung, which has the following form:

where iB is the beam current, and Ż is the average atomic number of the target. For a given material, the mass

absorption coefficient increases as the photon energy decreases. Absorption is an exponential effect, so that eventually the increased absorption overwhelms the increase in the continuum intensity so that the intensity reaches a maximum. For boron with E0 = 20 keV this maximum occurs at approximately 1.3 keV. Because of the effect on the electron range and the subsequent X-ray absorption, the exact location of the maximum in bremsstrahlung intensity depends on beam energy as well as the specific element(s) acting as the absorber. Moreover, for complex compositions the numerous characteristic peaks are superimposed on the