40623
E 0 = 20 keV, and the standards used pure elements Mg, Si, and
Fe, while SRM 470 K412 glass was used as the Ca standard.
The analytical total was 0.9789 (the sum of the SRM certifi-
cate values is 0.9886), and the relative errors were all well
within the ±5 % error envelope, with the largest error at
−2.2 % relative for Ca.. Table 23.4 gives the results of applying the k-ratio/
matrix correction factor protocol to the analysis of a
1.3-μm-diameter spherical particle of K411 glass, with the
EDS spectrum collected with the beam placed at the center of
the particle image. The intensity of each elemental constitu-
ent has been measured relative to the same suite of standards:
pure elements Mg, Si, and Fe, and CaF 2 as the Ca standard.
Oxygen has been calculated by the method of assumed stoi-
chiometry. The analytical total is 0.3480, and the relative
errors for the raw calculated concentrations are large and
negative, for example, − 70 % relative for Mg and − 56 % rela-
tive for Fe. These large negative relative errors (a negative
relative error indicates that the calculated concentration
underestimates the true concentration) for both the low pho-
ton energy peaks (e.g., Mg K-L2,3 and Si K-L2,3) and the high
photon energy peaks (e.g., Ca Kα and Fe Kα) are a result of
the particle mass effect reducing all X-ray intensities com-
pared to bulk behavior. Clearly, these raw concentrations
have such large systematic errors as to offer no realistic
meaning. To compensate for the mass effect and thus place
the concentrations on a meaningful basis, internal normal-
ization can be applied:CCni()= ii/ΣC
(23.3)Note that normalization is only useful if all constituents pres-
ent in the analyzed volume are included in the total, includ-
ing any such as oxygen that are calculated by assumed
stoichiometry rather than measured directly. After normal-
ization, the relative errors are reduced in magnitude, as given
in. Table 23.4, but the values for Mg (− 14 %) and Fe (+26 %)
remain well outside the bulk analysis error histogram.. Table 23.5 presents similar measurements and calcula-
tions for a 6.1-μm-diameter K411 particle for which the ana-
lytical total is 1.091. This particle diameter is sufficiently large
so that the X-ray production for the higher energy photons,
Ca K-L2,3 and Fe K-L2,3, has nearly reached equivalence to the
flat, bulk target, resulting in relative errors of − 5 % or less.
For this particle size, the lower energy photon peaks, Mg
K-L2,3 and Si K-L2,3, are still strongly influenced by the parti-
cle absorption effect, causing relative errors that are large and
positive, since more of these low energy photons escape than
. Table 23.4 Analysis of a 1.3-μm-diameter spherical particle of K411 glass with fixed beam located at particle center (standards: Mg, Si,
CaF 2 , Fe; oxygen by stoichiometry)
Element SRM value Analysis Rel error (%) Normalized Rel error (%)O 0.4236 0.1470 − 65 0.4224 −0.3
Mg 0.0885 0.0265 − 70 0.0761 − 14
Si 0.2538 0.0884 − 65 0.2541 +0.1
Ca 0.1106 0.0370 − 67 0.1064 −3.8
Fe 0.1121 0.0491 − 56 0.1410 +26
Raw analytical total 0.3480. Table 23.5 Analysis of a 6.1-μm-diameter spherical particle of K411 glass with fixed beam located at particle center (standards: Mg, Si,
Ca [K412 glass], Fe; oxygen by stoichiometry)
Element SRM value Analysis Rel error (%) Normalized Rel error (%)O 0.4236 0.4748 +12 0.4353 +2.8
Mg 0.0885 0.1110 +25 0.1018 +15
Si 0.2538 0.2874 +13 0.2636 +3.9
Ca 0.1106 0.1062 −4.0 0.0974 − 12
Fe 0.1121 0.1112 −0.8 0.1019 −9.1
Raw analytical total 1.091Chapter 23 · Analysis of Specimens with Special Geometry: Irregular Bulk Objects and Particles