Scanning Electron Microscopy and X-Ray Microanalysis

405 23

radiation at 6.40  keV is sufficiently energetic that it under-
goes relatively little absorption in the bulk case so that the
modification of the absorption path length by particle sur-
face curvature produces a negligible effect. However, the
lower energy characteristic photons such as O K-L 2
(0.525 keV) and Mg K-L2,3 (1.254 keV) in K411 suffer signifi-
cant absorption in a flat bulk target, so that when these pho-
tons are generated in a spherical particle, the reduced
absorption path in the direction toward the EDS leads to an
increase in X-ray emission compared to a flat bulk target.

. Figure 23.32 shows that as the particle diameter increases
from zero, the k-ratios for O K-L 2 and Mg K-L2,3 initially
increase similarly to FeKα as a result of the particle mass
effect. However, for larger particles the reduced absorption
path of the curved particle surface causes the emitted O
K-L 2 k-ratio to actually exceed unity (i.e., higher emission
than bulk behavior) for a particle diameter of 1.6 μm, reach-
ing a maximum of 1.35 relative to bulk at a particle diameter
of 2.8 μm. For Mg K-L2,3, the emission exceeds unity for a
particle diameter of 2 μm and reaches a maximum of 1.17 at
a diameter of 3.0 μm. For particle diameters beyond the
intensity maxima, the O K-L 2 and Mg K-L2,3 k-ratios gradu-
ally decrease with increasing particle diameter, asymptoti-
cally approaching the equivalent of bulk behavior at 25 μm
diameter for O K-L 2 , and 18 μm diameter for Mg K-L2,3.
Thus, for spherical particles of the K-411 composition mea-
sured with E 0 = 20 keV, effectively bulk behavior is observed
for all characteristic X-ray energies for particles with diame-
ters greater than 25 μm for a beam position at the top center
of the particle (detector take-off angle 40°). As demonstrated
in. Fig. 23.23, deviations in the beam placement either
toward the EDS or away have significant effects due to the

modification of the absorption path. Particle geometry and

its impact on X-ray absorption must be considered when

selecting beam locations on a particle for analysis. It is criti-

cal that the analyst always be aware of the position of the EDS

detector relative to the X-ray source, as demonstrated in

. Fig. 23.24, to minimize the effects of particle geometry.

23.6.5 Uncertainty in Quantitative Analysis

of Particles

Quantitative analysis of particles is performed by following

the same k-ratio/matrix correction protocol used for flat, bulk

specimens. However, it must be recognized that particle

geometry modification of the interaction of beam electrons

and the subsequent propagation of X-rays introduce factors

which violate the fundamental assumption of the bulk quan-

tification method, namely that the only reason the X-ray

intensities measured in the target being analyzed are different

from the standards is that the composition(s) is different.

Thus, with the impact of the geometric factors, the analytical

accuracy of the conventional k-ratio/matrix correction proto-

col is inevitably compromised. The critical question to con-

sider is the degree to which the uncertainty budget is increased

by the systematic error contribution of the particle effects.

The Analytical Total Reveals the Impact

of Particle Effects

The analytical total is the sum of the calculated concentra-

tions, including oxygen by stoichiometry if calculated.

. Table 23.3 shows the results of the analysis of K411 glass in
the form of a flat, bulk target. The beam energy was

Monte Carlo calculations of K411 Spheres (E 0 = 20 keV)

1.6

1.8

1.2

1.0

0.8

0.6

0.4

0.2

0.0

024

Diameter (micrometers)

6810

k-ratio (K411 bulk)

O

Mg

FeK

. Fig. 23.32 Emission of Fe
K-L2,3, O K-L 2 and Mg K-L2,3 (nor-
malized to O K-L 2 and Mg K-L2,3
from bulk K411); note excursion
in the O K-L2,3 and Mg K-L2,3
above unity (i.e., exceeding the
emission from a flat, bulk target)

23.6 · Particle Analysis