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Quantitative Analysis in the AEM
The corrections normally associated with the analysis of thick SEM specimens
do not apply to thin TEM specimens. Consequently, quantitation may be
performed by using a simple ratio technique first developed by Cliff and
Lorimer at the University of Manchester Institute of Science and Technology
(UMIST) in the early 1970’s (Cliff and Lorimer 1975).
Cliff and Lorimer observed that matrix corrections are not needed when
analyzing very thin films because self absorption in the film is negligible.
In this case, peak intensities are proportional to concentration and
specimen thickness. They removed the effects of variable specimen thickness
by taking ratios of intensities for elemental peaks and introduced a
“k-factor” to relate the intensity ratio to concentration ratio:
CA/CB = KAB.IA / IB
Where IA = Peak intensity for element A and CA
is concentration in weight % or mass fraction. Each pair of elements
requires a different k-factor which depends on detector efficiency,
ionization cross section and fluorescence yield of the two elements
concerned.
An individual k-factor relates the concentration of two elements to their
X-ray peak intensities. Where more than two elements are to be analyzed, a
number of k- factors may be derived by using external standards to relate
known concentrations with measured intensities. If all ratios are taken with
respect to a single element (this is called the ratio standard element), a
sensitivity response curve may be drawn for any given detector/ microscope
analytical system (Figure 5).
Theoretical k factor values may be determined using the X-ray line type (K
series, L series, etc) for the ratio standard you select. For a given X-ray
line, A, and ratio standard line, R, the k factor kAR is calculated as
follows:
kAR = AA wR QB aR
eR / AR wA QA aA eA
where A = atomic weight; w = fluorescent yield; Q =
ionisation cross section; a = the fraction of the total line, e.g. Kα
/ (Kα +Kβ ) for a Ka line, and e = the absorption due to the detector
window at that line energy.
Once k factors are known relative to the ratio standard, any other k factors
can be calculated using the formula
kAB = kAR / kBR
Any element can be selected as the ratio standard element (R) if
theoretically derived k factors are employed. Conventionally, Si is
selected, but other elements such as Fe may be used instead. This selection
usually depends upon the type of sample that is commonly analyzed in the
microscope.
k factors may also be derived experimentally. A variety of standards have
been used to generate these curves and it is important that the composition
of the materials used is accurately known, that they are insensitive to the
electron beam, and thin enough to conform to the requirements of thin film
analysis. It is also necessary to make a number of measurements per standard
to take into account sample inhomogeneity and statistical variation in
counts.
It must be noted that empirically derived k- factors are system specific in
the sense that they are derived for specific beam energy and EDS window
thickness. Also, both theoretically and empirically derived k- factors are
kV dependent.
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