Scanning Electron Microscopy and X-Ray Microanalysis

404

23

for an incident beam energy of 20 keV. For this plot, the Fe

K-L2,3 intensity emitted from the particle has been divided by

the intensity calculated for a flat bulk K411 target to deter-

mine the k-ratio. Note that as the particle diameter increases

from zero, the Fe K-L2,3 k-ratio increases and asymptotically

approaches unity (i.e., equivalent to the flat bulk target) for a

diameter of approximately 10 μm. Thus, for the case K411 at

E 0 = 20  keV, bulk behavior for Fe K-L2,3 (6.400  keV) is

observed for spherical particles with diameters of 10 μm and

gre ater.

“Particle Absorption Effect”

The surface curvature of a particle can reduce the absorption

path to the detector compared to the interaction volume in a

flat bulk target, as shown schematically in. Fig. 23.31. Since

X-ray absorption depends exponentially on the absorption

path length, surface curvature can significantly modify the

measured intensity, creating the “particle absorption effect.”

The magnitude of the particle absorption effect depends

strongly on the energy of the characteristic photons involved.

For the example shown in. Fig. 23.32, the Fe K-L2,3

1.2

1.0

0.8

0.6

0.4

0.2

0.0

01234

Sphere diameter (μm)

Monte Carlo Simulation Fe in K411 Spheres, E 0 = 20 keV

Fe

k-ratio (bulk K411)

5678910

. Fig. 23.30 Monte Carlo calculation of the emission of Fe K-L2,3 from
K411 spheres of various diameters at E 0 = 20 keV. The intensity is nor-
malized by the Fe K-L2,3 intensity calculated for a flat bulk target of K411
. Table 23.3 Composition of K411 glass and analysis of flat,
bulk target at E 0 = 20 keV (Standards: Mg, Si, CaF 2 , Fe; oxygen by
stoichiometry)

NIST SRM 470 certificate values

Element Mass

concentration

Analysis Relative

error (%)

O 0.4236 0.4192 −1.0

Mg 0.0885 0.0870 −1.7

Si 0.2538 0.2512 −1.0

Ca 0.1106 0.1082 −2.2

Fe 0.1121 0.1134 1.1

Absorption

path

in particle

Additional

absorption path

in flat bulk target

Electron

trajectory

Incident

beam

Path through vacuum

X-ray detecto

r

. Fig. 23.31 Schematic illus-
tration of the difference in the
X-ray absorption path length in
a particle and in a flat bulk target
of the same material

Chapter 23 · Analysis of Specimens with Special Geometry: Irregular Bulk Objects and Particles