Transcript Quantitative X-Ray Analysis Introduction:

Quantitative X-Ray Analysis
Introduction:
• It is extremely important to grasp the underlying physical
principles to become a sophisticated analyst rather than a mere
user.
• The x-ray microanalysis software often presents choices of datacorrection procedures for the user to make, and an optimal
choice obviously depends on proper knowledge of the relative
merits of each approach.
• With the proper experimental setup and data-reduction
procedures, the measured x rays can be used to quantitatively
analyze chemical composition with an accuracy and precision
approaching 1%.
• The EDX analysis in general is nondestructive with regard to the
specimen so that it can be reexamined using other techniques.
Some key points :
• As shown in Chapter 3, x rays can be generated depending
on the initial electron-beam energy and atomic number,
from volumes with linear dimensions as small as 1
micrometer.
• This means that, typically, a volume as small as 10-12 cm3
can be analyzed. Assuming a typical density of 7 g/cm3 for
a transition metal, the composition of 7 x 10-12 g of material
can be determined.
• From this small mass of the sample selected by the
electron x-ray interaction volume, elemental consitituents
can be determined to concentrations ranging as low as
0.01% (100 ppm), which corresponds to limits of detection
in terms of mass of 10-16 to 10-15 g. For instance, a single
atom of iron weighs about 10-22 g, so the limit of detection
corresponds to only a few million atoms.
Basic Procedures for the Quantitative X-Ray
Analysis
1. Obtain the x-ray spectrum of the specimen
and standards under defined and reproducible
conditions.
2. Measure standards containing the elements
that have been identified in the specimen (a
homogeneous steel sample characterized by
bulk analytical chemistry procedures is ok,
but a simple stoichiometric compound such
as GaP is even better).
3. For the new EDX software, no need to remove
the background since the computer will do it
automatically for you.
4. Perform quanta calibration: This procedure is to
develop the x-ray intensity ratios using the
specimen intensity and the standard intensity for
each element present in the sample and carry out
matrix corrections to obtain quantitative
concentration values.
The First Approximation to Quantitative Analysis
• The assumption that ratio of the measured unknown-tostandard intensities, Ii/I(i) and the ratio of concentrations
between the specimen and the standard should be equal is the
basic experimental measurement that underlies all quantitative
x-ray microanalysis and is called the “k-value”,
i.e. Ci/C(i) = Ii/I(i) = k
• However, careful measurements performed on homogeneous
substances of known multi-element composition compared to
pure element standards reveal that there are significant
systematic deviations between the ratio of measured intensities
and the ratio of concentrations.
• Therefore, to achieve this assumption the quanta calibration
has to be performed so that it would correct the matrix or interelement effects.
Deviations between the Ratio of
Measured Intensities and the Ratio of Concentrations
ZAF Matrix Correction
• In mixtures of elements, matrix effects arise
because of differences in elastic and inelastic
scattering processes and in the propagation of x
rays through the specimen to reach the detector.
For conceptual as well as calculation reasons, it
is convenient to divide the matrix effects into
those due to atomic number, Zi; x-ray absorption,
Ai; and x-ray fluorescence, Fi.
ZAF Matrix Correction
Using these matrix effects, the most common form of the
correction equation is
Ci/C(i) = [ZAF]i Ii/I(i) = [ZAF]i ki
Where Ci is the weight fraction of the element I of interest in
the sample and C(i) is the weight fraction of i in the standard.
This equation must be applied separately for each element
present in the sample. The Z. A. and F effects must therefore
be calculated separately for each element.
Above equation is used to express the matrix effects and is the
common basis for x-ray microanalysis in the SEM.
Effect of Atomic Number
• The x-ray generation volume decreases with increasing
atomic number. This is due to an increase in elastic
scattering with atomic number, which deviates the electron
path from the initial beam direction, and an increase in
critical excitation energy Ec, with a corresponding decrease
in overvoltage (U=Eo/Ec) with atomic number.
• The decrease in U decreases the fraction of the initial
electron energy available for the production of
characteristic x rays and the energy range over which x
rays can be produced.
• As illustrated from the Monte Carlo simulations, the atomic
number of specimen strongly affects the distribution of xrays generated in specimens. The effects are even more
complex when considering the more interesting multielement samples as well as in the generation of L and M
shell x-ray radiation.
Effects of Varying the Initial Electron-Beam Energy
•
(z) is used to evaluated the intensity of x-ray generated with the
change of the escape depth of the x-ray. So (z) is a normalized
generated intensity. The term z is called the mass depth and is the
product of the density  of the sample and the depth dimension z; is
usually given in units of g/cm2.
X-Ray Absorption Effect
The following figure shows that Cu characteristic x-rays are
generated deeper in the specimen and the x-ray generation
volume is larger as Eo increases. This is because the energy of
the backscattered electrons increases with higher values of Eo.
Effects of Atomic Number on the Distribution of X-Ray Generation
•
•
In specimens of high
atomic number, the
electrons undergo more
elastic scattering per unit
distance and the average
scattering angle is greater,
as compared to low-atomicnumber materials. The
electron trajectories in
high-atomic-number
materials thus tend to
deviate out of the initial
direction of travel more
quickly and reduce the
penetration into the solid.
The shape of the interaction
volume also changes
significantly as a function
of atomic number.
Influence of Specimen Surface Tilt on Interaction Volume
• As the angle of tilt
of a specimen
surface increases
(i.e., the angle of
the beam relative
to the surface
decreases), the
interaction volume
becomes smaller
and asymmetric.
Interaction Volumes of Materials with Different Density
Take-Off Angle and Path Length (PL)
Thin Specimen Technique for Biological
Specimen
• Biological or polymer specimen is sensitive to the
incident beam and very likely to be damaged by
the e-beam.
• The specimen structure may be rearranged.
• The light elements may be evaporated while
heavy elements of interest in biological
microanalysis (e.g., P, S, Ca) remain.
• Thin specimen technique: is based on the fact
that the rate of energy loss in a low-atomicnumber target is about 0.1eV/nm, so that only 10100eV is lost through a 100-nm section.
Bulk Targets and Analysis of a Minor Element
• Since the density and average atomic number of
biological and many polymeric specimens is low, the
excitation volume for x-rays is large. This volume can
easily exceed 10 um in extent. Consequently, one of
the major advantages of the method is diminished,
the ability to analyze very small volumes.
• In general, the increased excitation volume is
acceptable to perform a ZAF analysis.
Analysis Geological Specimen
• Almost all specimens for geological analysis are
coated with a thin layer of C or metal to prevent
surface-charging effects. However, x-rays are
generated in depth in the specimen, and the
surface conducting layer has no influence on
electrons that are absorbed micrometers into the
specimen. Electrical fields may be built up deep in
the specimen, which can ultimately affect the
shape of the (z) Curves.
• Most geologists don’t measure oxygen directly, but
get their oxygen values by stoichiometry. If oxygen
analysis is desired, then C coatings are not optimal
because they are highly absorbing for both O and
N K x-ray.
Light-Element Analysis
Quantitative x-ray analysis of the low-energy (<0.7
keV) K lines of the light elements is difficult in the
SEM. The following table lists the low-atomic-number
elements considered in this section along with the
energies and wavelengths of the K lines. X-ray
analysis in this energy range is a real challenge for
the correction models developed for quantitative
analysis since a large absorption correction is usually
necessary. Unfortunately, the mass absorption
coefficients for low-energy x-rays are very large and
the values of many of these coefficients are still not
well known. The low-energy x-rays are measured
using large d spacing crystals in a WDS system or
thin-window or windowless EDS detector.
Operation Conditions for Light-Element
Analysis
• One can reduce the effect of x-ray absorption by
analyzing at high take-off angles  and low electronbeam energies Eo. The higher the take-off angle, the
shorter the path length for absorption within the
specimen. The penetration of the electron beam is
decreased when lower operating energies are used,
and x-rays are produced closer to the surface.Figure
9.33 shows the variation of boron K intensity with
electron-beam energy Eo, at a constant take-off angle
for boron and several of its compounds. A maximum
in the boron K intensity occurs when Eo is 5 to 15
keV, depending on the sample.