23.6 · Particle Analysis

. Fig. 23.33  Relative errors observed for various sizes of spherical particles of K411 glass measured with a fixed beam placed at the center of the particle image

Relative Error (%)

40

30

20

10

0

-10

-20

Analysis of K411 Spheres (E0 = 20 keV)

Mg

Si

Ca

Fe

is the case for a flat, bulk target. When these raw concentrations are normalized, the relative errors for Mg and Si are reduced, but the relative errors for Ca and Fe are increased after normalization.

These examples demonstrate the complex interplay of X-ray generation and propagation as influenced by particle geometry. While normalization of the raw calculated concentrations is necessary to put particle analyses on a realistic concentration basis, the uncertainty budget for particle analysis is substantially increased compared to that for the ideal flat target. .  Figure 23.33 plots the relative error envelope for normalized concentrations as a function of particle diameter for spherical particles of K411 glass. For particles whose dimensions are substantially smaller than the bulk interaction volume, the relative errors in the normalized concentrations are large and increase as the particle size decreases. The relative errors decrease as the particle diameter increases, eventually converging with the flat bulk case for particles above approximately 25-μm diameter.

Normalization is most successful when applied to compositions where the measured characteristic X-rays have similar

energies, for example, Mg K-L2,3, Al K-L2,3 and Si K-L2,3. Although low atomic number elements such as oxygen can be

measured directly, the high absorption of the low energy photons of the characteristic X-ray significantly increases the effect of the particle absorption effect, so that normalization introduces large errors and effectively transfers increased

error to the other higher atomic number constituents. In the case of oxygen, the method of assumed stoichiometry is generally much more effective.

Does Overscanning Help?

Because of the difficulty in analyzing particles, overscanning the particle during EDS collection is thought to obtain a spectrum that averages particle effects. In reality, even for homogeneous particles, overscanning does not decrease the relative uncertainties but can actually cause an increase.

.  Figure 23.34a plots the relative errors in the normalized concentrations for the analysis of Mg and Fe in K411 spheres of various sizes, comparing point beam analyses centered on the particle image with continuous overscanning during EDS collection. Mg and Fe are chosen because the large separation in characteristic X-ray energy provides sensitivity to the action of the particle mass effect, which is the only significant influence on energetic Fe K-L2,3, while both the mass effect and the absorption effect influence Mg K-L2,3. While the error range for point beam analysis is substantially larger than the ideal error histogram for flat bulk target analysis, the effect of overscanning is actually to shift the distribution of results to even more severe relative errors. This is a result of the non-linear nature of X-ray absorption, which can be seen in the beam placement measurements shown in .  Figs. 23.24 and 23.25. A similar effect is seen for irregular shards in

.  Fig. 23.34b.