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

. Table 23.7  Relative Deviation from Expected Value (RDEV) observed with peak-to-background corrections compared to the raw

concentrations and normalized concentrations after conventional k-ratio/matrix corrections

	Cbulk	Craw	RDEV(%)	CN	RDEV(%)	CP/B	RDEV(%)
Al	0.0603	0.0201	−67%	0.0241	−60%	0.0552	−8%
Mo	0.0353	0.0194	−45%	0.0233	−34%	0.0437	+24%
Ti	0.0519	0.0406	−22%	0.0487	−6%	0.0480	−7%
Cr	0.0965	0.0788	−18%	0.0945	−2%	0.0996	+3%
Co	0.155	0.139	−11%	0.166	+7%	0.156	+1%
Ni	0.601	0.536	−11%	0.643	+7%	0.598	−0.5%

Spherical particle: IN-100 alloy, 88 μm diameter, with beam placed at 22 μm from the top center on the backside of particle

standard identical in composition to the unknown object is generally not available. However, an estimate of the concentrations of elements in the unknown object is always available in the ZAF procedure, including the first step, where

Ci = ki /Σk. The value of IB,bulk can therefore be estimated from the background measured on pure element standards:

	IB,bulk = ∑CjIj,B,std		(23.6)
	j	\
	where Ij,B,std is the pure element bremsstrahlung at the energy
	of interest and Cj	is the concentration of element j. An exam-
	ple of an analysis of a complex IN-100 particle with conven-
	tional k-ratio/matrix corrections (including normalization of
	the raw values) and using the k-ratio/matrix corrections aug-
	mented with the P/B method is given in .  Table 23.7. The
	relative deviation from the expected value (RDEV) for each
	element is reduced compared with the simple normalization
	procedure, especially for Al, which is highly absorbed when
	measured on the backside of the particle.
	The special advantage of the P/B method is that it can be
	applied to spectra obtained with a focused probe directed at
	a specific location on a particle. Thus, particles that have a
	chemically heterogeneous sub-structure can be directly stud-
	ied. To be effective, the P/B method requires spectra with
	high counts. Because the ratio of background intensities is
	used to scale the particle peak intensities, the statistical
	uncertainty in the background ratio propagates into the error
	in each concentration value in addition to the statistics of the
	characteristic peak. Even more importantly, the P/B method
	depends on the background radiation originating in the
	excited volume of the specimen only, and not in the sur-
	rounding substrate. When an irregularly shaped object such
	as a particle becomes small relative to the bulk interaction
	volume, the penetration of the beam into the substrate means
	that the continuum continues to be produced, even if the
23	substrate is a low atomic number element such as carbon. As
	noted above, the energy-dispersive X-ray		spectroscopy

collimator has a large acceptance area at the specimen. To minimize the extraneous background contributions, the small particles should be mounted on a thin (approximately 10–20 nm) carbon film supported on a metal grid (typically copper, as used in the transmission electron microscope) and mounted over a blind hole drilled into a carbon block. The continuum contribution from such a thin film is negligible relative to particles as small as approximately 250 nm in diameter.

23.7\ Summary

\1.\ Particle analysis is inevitably compromised compared to analysis of ideal flat samples, leading to an increased error budget.

\2.\ Careful attention must be paid to optimizing particle sample preparation to minimize substrate contributions to the spectrum and to reduce contributions from nearby particles.

\3.\ Quantitative analysis of particles follows the k-ratio/ matrix correction protocol. The analytical total that results from this procedure is an indication of the magnitude of particle geometry effects (mass effect and absorption effect).

\4.\ Normalization of the raw concentrations (including oxygen by stoichiometry, if appropriate) is necessary to place the calculated composition on a realistic basis.

\5.\ Large relative errors, exceeding 10%, are encountered after normalization. The analytical errors are exacerbated when low and high photon peaks must be used for analysis.

\6.\ The analytical errors generally increase as the particle size decreases.

\7.\ Overscanning does not decrease the analytical errors, and may well increase the errors depending on the particular combination of elements being analyzed.

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