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

There are two “zero-th level” assumptions that underpin the basis for quantitative electron-excited X-ray microanalysis: \1.\ The only reason that the measured X-ray intensity differs between the unknown and the standard(s) is that the composition is different. No other factors such as the

specimen shape, orientation, or size influence the measured X-ray spectrum.

\2.\ The specimen is homogeneous in composition over the volume excited by the electron beam from which the characteristic and continuum X-rays are emitted, including the secondary radiation induced by absorption of the primary electron-excited radiation.

When either of these conditions is not met, a significant increase in the overall uncertainty budget of the analysis can occur beyond the ideal situation in which the uncertainties arise from counting statistics and from uncertainties in the calculated matrix correction factors.

Considering “zeroth-level” assumption 1, sample geometry can significantly modify the measured X-ray intensity. The ideal specimen is flat and placed at known angles to the incident beam and the X-ray detector(s). Topographic features on bulk specimens (defined as those for which the thickness is much greater than the electron range) or unusual geometric shapes, such as particles with dimensions similar to the electron range, can strongly affect the measured X-rays by modifying X-ray generation and by affecting the loss of X-rays due to absorption. In severe cases, the impact of “geometric factors” on the final concentrations becomes so large as to render the compositional results, as calculated with the conventional standards-based/matrix corrections protocol or the standardless protocol, nearly worthless.

Cu E0 = 20 keV

. Fig. 23.1  Backscatter coefficient η vs. surface tilt θ (inclination) for Cu at E0 = 20 keV as calculated with the Monte Carlo electron trajectory simulation embedded in NIST DTSA-II

is at a minimum, BSEs carry off energy which would have gone to cause additional inner shell ionization events followed by subsequent X-ray emission had those electrons remained in the specimen. As the local surface inclination (tilt) increases, backscattering increases and more X-ray generation is lost compared to normal beam incidence situation.

.  Figure 23.2 shows Monte Carlo calculations of the Cu K-L2,3 X-ray intensity emitted from a flat, bulk copper specimen, expressed as a “k-ratio,” where the denominator is the intensity emitted from copper at zero tilt (normal beam incidence). As the local surface inclination (tilt angle) increases above zero degrees, the X-ray production decreases with

23.1\ The Origins of “Geometric Effects”:

Bulk Specimens

The ideal sample is compositionally homogeneous on a microscopic scale, has a flat surface, and is set at known angles to the incident electron beam and the X-ray spectrometer. Compared to the X-ray spectrum measured from this ideal spectrum, geometric effects occur when the size and shape of the specimen (1) modify the interaction of the electrons with the specimen so as to affect the generated X-ray intensity and (2) alter the length of the absorption path along which the generated X-rays travel to escape the specimen and reach the detector so as to affect the measured X-ray intensity.

Because electron backscattering depends on the local surface inclination to the incident beam, tilted samples generate fewer X-rays compared to a sample at normal beam incidence (0° tilt). An illustration of this effect for bulk copper, as

23 calculated with the Monte Carlo simulation embedded in NIST DTSA-II, is shown in .  Fig. 23.1. Even at normal beam incidence where the backscattered electron (BSE) coefficient

Cu K-L2,3 emission vs. Tilt (E0 = 20 keV)

0.2

0.0

. Fig. 23.2  Emitted Cu K-L2,3 X-ray intensity calculated as the k-ratio relative to the intensity at a tilt of 0°, vs. surface tilt θ (inclination), for Cu at E0 = 20 keV as calculated with the Monte Carlo electron trajectory simulation embedded in NIST DTSA-II

23.1 · The Origins of “Geometric Effects”: Bulk Specimens

. Fig. 23.3  Schematic illustration of the effects of surface topography on the X-ray absorption path length within the specimen

Normal flat bulk target absorption path

Standard

Geometric Effects: surface roughness affects local absorption path to reach detector

I/I0 = exp[-(µ/ρ)ρs]

ψ

scratch

increasing tilt due to the increased backscattering seen in

.  Fig. 23.1. There is a relatively small decrease in the k-ratio at low tilt angles, but the k-ratio decreases rapidly for tilt angles above approximately 40°. Because of the high photon energy of Cu K-L2,3 (8.04 keV) and the relative transparency of any material to its own X-rays, there is no significant absorption so that the behavior shown in .  Fig. 23.2 is almost entirely due to the modification of the production of X-rays due to backscatter loss.

Surface topography modifies the X-ray absorption path length to the detector compared to a flat specimen at normal beam incidence. As shown schematically in .  Fig. 23.3, topographic features such as scratches and ridges can increase or decrease the absorption path length in the direction of the X-ray detector. X-ray absorption follows an exponential dependence on this path length:

where I0 is the initial intensity, I is the intensity that remains after passing through a path length s (cm), (μ/ρ) is the mass absorption coefficient (cm2/g) for the photon energy of interest that depends on the absorption contributions of all elements present, and ρ is the density (g/cm3). Considering the entire energy range of the generated X-ray spectrum, which extends from a practical minimum threshold of 100 eV to the incident beam energy, E0 (the Duane–Hunt limit), as the X-ray photon energy decreases, absorption generally increases. Absorption is especially strong if the photon energy is less than 1 keV above the critical ionization energy for any elemental constituent in the specimen. An example of this effect is shown in .  Fig. 23.4

Absorption path length (mm)

. Fig. 23.4  Absorption as a function of path length for Al K-L2,3

(1.487 keV) passing through Si (Kcrit = 1.838 keV), and Si K-L2,3 (1.740 keV) passing through Al (Kcrit = 1.559 keV)

for absorption as a function of path length for two contrasting

cases:AlK-L2,3 (1.487keV)passingthroughSi(Kcrit =1.838keV), and Si K-L2,3 (1.740 keV) passing through Al (Kcrit =1.559 keV). Because Si K-L2,3 is 0.181 keV above the critical ionization

energyforAl,SiisverystronglyabsorbedbyAl(μ/ρ=3282cm2/g) such that there is no penetration beyond approximately 6 μm. By comparison, Al K-L2,3 is below the critical ionization energy for Si, so it much less strongly absorbed (μ/ρ=535 cm2/g), with approximately 50% of Al K-L2,3 intensity still remaining after 6-μm penetration through Si.

23.2\ What Degree of Surface Finish Is

Required for Electron-Excited X-ray

Microanalysis To Minimize Geometric

Effects?

Early in the history of microanalysis by electron-excited X-ray spectrometry, it was recognized that controlling the surface condition of a specimen was critical to achieving high-accu- racy results by reducing geometric effects to a negligible level. Yakowitz and Heinrich (1968) performed a series of experiments in which the metallographic preparation sequence of grinding and polishing was interrupted at various stages. Materials examined included pure elements with two widely different characteristic peak energies, for example, Au M5-

N6,7 at 2.123 keV and Au L3-M4,5 at 9.711 keV, and homogeneous binary metal alloys with widely differing characteristic

X-ray energies. For each surface condition, the characteristic

X-ray intensity was then measured at random locations and along line traverses on the specimen surface to examine the variation in characteristic X-ray intensity that could be ascribed to surface roughness. Results for selected surface conditions for a gold target are listed in .  Table 23.1. For the Au L3-M4,5 measurements, a final polish of the surface with 0.5-μm alumina was necessary to reduce the coefficient of

variation for 20 random measurements to a level similar to the expected variation from the random counting statistics,

expressed as 3 n1/2/n. For the lower photon energy Au M5-N6,7 which suffers stronger absorption, it was necessary to improve

the surface polish to 0.1 μm alumina to achieve similar results. For even lower photon energy peaks, such as those associated with low atomic number elements with Z ≤ 9 (fluorine) for which E < 1 keV, even better surface finish is required to control the geometric effects. Newbury and Ritchie (2013a) simulated X-ray emission from crenelated surfaces with the Monte Carlo simulation embedded in NIST DTSA-II to examine the influence of surface topography on low photon energy peaks. As shown in .  Fig. 23.5 for FeO at an incident beam energy E0 = 10 keV, the depth of scratches had to be reduced below 50 nm to reduce the geometric effects on O K,

Fe L3-M4,5, and Fe K-L2,3 to a negligible level.

23.2.1\ No Chemical Etching

In addition to achieving a high degree of surface finish to minimize geometric effects, it is also important to avoid chemical or electrochemical etching of the final surface. For effective optical microscopy of microstructures, chemical

. Fig. 23.5  Plots of O K, Fe L3-

M4,5, and Fe K-L2,3 as a function of scratch depth for a crenelated

surface as calculated with the

Monte Carlo simulation embed- 1.0 ded in NIST DTSA-II (Newbury

and Ritchie 2013a,b)

0.01

FeO E0 = 10 keV

EDS

O K-L2,3 (0.523 keV)

Fe L (0.704 keV)

FeK-L2,3 (6.400 keV)

Scratch depth and period (micrometers)