407 23
is the case for a flat, bulk target. When these raw concentra-
tions 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 concen-
trations is necessary to put particle analyses on a realistic
concentration basis, the uncertainty budget for particle anal-
ysis 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 interac-
tion volume, the relative errors in the normalized concentra-
tions 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 compo-
sitions 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 pho-
tons 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 gen-
erally much more effective.Does Overscanning Help?
Because of the difficulty in analyzing particles, overscan-
ning 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 separa-
tion in characteristic X-ray energy provides sensitivity to
the action of the particle mass effect, which is the only sig-
nificant 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.
Analysis of K411 Spheres (E 0 = 20 keV)
40302010Relative Error (%) 0-10-20
0246
Diameter (micrometers)81012141618Mg
Si
Ca
Fe. 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 par-
ticle image
23.6 · Particle Analysis