Quantitative XRay Analysis

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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 data-correction 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.

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• 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.

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Basic Procedures for the Quantitative X-Ray
Analysis

• Obtain the x-ray spectrum of the specimen and
  standards under defined and reproducible
  conditions.
• 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).
• For the new EDX software, no need to remove the
  background since the computer will do it
  automatically for you.

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• 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.

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The First Approximation to Quantitative Analysis

• The assumption that ratio of the measured
  unknown-to-standard 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 inter-element effects.

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Deviations between the Ratio of Measured
Intensities and the Ratio of Concentrations
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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.

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ZAF Matrix Correction

• Using these matrix effects, the most common form
  of the correction equation is
• Ci/C(i) ZAFi Ii/I(i) ZAFi 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.

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• 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 (UEo/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 x-rays generated in
  specimens. The effects are even more complex when
  considering the more interesting multi-element
  samples as well as in the generation of L and M
  shell x-ray radiation.

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Effects of Varying the Initial Electron-Beam
Energy
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• ?(?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.

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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.

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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-atomic-number 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.

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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.

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Interaction Volumes of Materials with
Different Density
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Take-Off Angle and Path Length (PL)
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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-atomic-number target is about 0.1eV/nm, so
  that only 10-100eV is lost through a 100-nm
  section.

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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.

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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 dont 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.

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Light-Element Analysis

• Quantitative x-ray analysis of the low-energy
  (lt0.7 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.

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Operation Conditions for Light-Element Analysis

• One can reduce the effect of x-ray absorption by
  analyzing at high take-off angles ? and low
  electron-beam 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.

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