Chapter 1: X-ray Fluorescence (XRF) and Particle-Induced X-ray Emission (PIXE)

1-Introduction

X-ray Fluorescence (XRF) and Particle-Induced X-ray Emission (PIXE) techniques are powerful tools for
rapid multielement nondestructive analyses and enable simultaneous detection of many elements in a
solid or liquid with highdetection sensitivities, even in those cases where only small sample amounts are
available.

The fluoresced X-rays from the sample are collected and displayed with either energy dispersive or
wavelength dispersive detector systems.

materials. Handling of samples is greatly simplified by the open-air nature of the instrument used for XRF
studies.

The elements are identified by the wavelengths (qualitative) of the emitted Xrays while the
concentrations of the elements are determined by the intensity of those X-rays (quantitative).

XRF and PIXE techniques are similar in their fundamental approach and are based on the common fact
that when an electron is ejected from an inner shell of an atom, an electron from a higher shell drop into
this lower shell to fill the hole left behind. This results in the emission of an X-ray photon equal in energy
to the energy difference between the two shells.

the difference between the two techniques: In the XRF technique, high-energy X-ray photons are
directed at the sample and this ejects the inner shell electrons while in the PIXE technique, the inner-
shell electrons are ejected when protons or other charged particles, like He-ions, are made to impinge
on the sample.

2- Principle of XRF and PIXE Techniques

The principle of both of these techniques is to excite the atoms of the substance to be analyzed by
bombarding the sample with sufficiently energetic X-rays/γrays or charged particles.

The ionization of inner shell electrons is produced by the photons and charged particles.

The excess energy is taken away by either photon (characteristic X-rays) – when an electron from a
higher-level fall into the inner-shell vacancy or Auger (higher-shell) electrons – when the energy released
during the process of hole being filled by the outer shell electron, is transferred to another higher-shell
electron.

The Auger effect is most common with low-Z elements.

when exciting the K-shell (1s1/2), the hole can be filled from LIII(2p3/2) or LII(2p1/2) subshells, leading to
Kα1 and Kα2 lines.

Electrons cannot come from the L1(i.e. 2s1/2) sub-shell, because a change in angular momentum is
required in the quantum transition.

The next shell with electrons is the valence band (n = 3) that gives rise to the widely separated and weak
Kβ lines.
Apart from the characteristic X-ray lines called the diagram lines, non-diagram lines (satellite, hyper
satellite and RAE) also appear in the complex K X-ray spectrum.

The X-ray lines arising out of the multiply ionized atoms are termed K satellite (KLn) and K-hyper satellite
lines (K2Ln), where KmLn denotes the vacancy from the de-excitation of the double K vacancies and were
observed in ion-atom collisions for the first time by Richard et al. (1972)

The double K vacancies are usually filled by the independent transitions of two electrons accompanied
by the emission of two photons or Auger electrons. The Kα satellite lines will be represented as Kα(2p)5,
Kα(2p)4, Kα(2p)3, … meaning that 5, 4, 3, ... electrons remain intact in the 2p shell while Kα(2p)6 will
represent the Kα principal line with all the six 2p electrons intact. Similar terminology is also used for Kẞ
satellite lines.

Another category in which electron and photon are simultaneously emitted (known as the Radiative
Auger effect RAE lines)

In the RAE process, the decay of a K-shell vacancy proceeds as a normal K Auger process except that
there is emission of a photon along with an electron in addition to an electron filling the K-shell vacancy.
Instead of the initial hole being filled with emission of either a full energy Kα photon or a full energy
Auger electron, there is simultaneous emission of a lower-energy photon hν and excitation of an L-
shell/M-shell electron

3-Theory and Concept

According to the quantum theory, every electron in a given atom moves on in an orbital that is
characterized by four quantum numbers:

– Principal (shell) quantum number (n): n is a positive integer 1, 2, 3, 4, . . . that designates the K, L, M, N,
. . . shells, respectively

– Azimuthal (subshell) quantum number (l): l can take all integral values between 0 and (n − 1); l = 0
corresponds to a spherical orbital while l = 1 corresponds to a polar orbital. A value of l = 0 corresponds
to s, l = 1 is p, l = 2 is d, and so forth.

– Magnetic quantum number (m): can take all the integer values between −l to +l

– Spin quantum number (s): can only take two possible values +1/2 and -1/2

The number of orbitals in a shell is the square of the principal quantum number (n)

The number of orbitals in a subshell is given by (2l + 1).

Each orbital can accommodate two electrons (one with spin up (s = +1/2) and one with spin down (s =
−1/2)

The most important of the forbidden transitions are the magnetic dipole (M1) transitions for which Δl=0;
Δj = 0 or ±1 and the electric quadrupole (E2) transitions for which Δl = 0, ±2; Δj = 0, ±1, or ±2

The emission of X-rays is governed by the following selection rules for allowed electric dipole (E1)
transitions:
Δn 1, Δl±1, Δj = 0, +1

4-Instrumentation/Experimentation

Modes of Excitation for XRF Analysis

X-ray fluorescence spectroscopy can be accomplished using

(a) radioactive sources as exciters

(b) X-ray tube as exciter.

Radioactive Sources as Exciters

A radioactive source (preferably monochromatic) can be used as an exciter

The sources of 55Fe, 109Cd and 241Am of a few milli Curie activity are used as primary sources.

For more energies however, the secondary exciters using Cu, Se, Y, Mo, Sn, Sm and Dy can be used with
Am241 as a primary source.

5-Radioactive Sources as Exciters

X-rays from the primary source are directed at a selectable secondary exciter target, usually Tin (Sn).

The characteristic X-rays from that exciter target are aimed at the unknown sample. This causes emission
(fluorescence) of characteristic X-rays from the sample.

These X-rays from the sample are captured in a Si(Li) detector and analyzed by computer

The energy spectrum of these X-rays can be used to identify the elements found in the sample.

6-X-ray Tube as Exciter

X-ray tubes offer greater analytical flexibility at a cost of more complexity

Electrons “boil” off the cathode when the filament is heated by a current. A high voltage between
cathode and anode causes the electrons to accelerate toward the anode, which rotates to avoid
overheating of the target. When the electrons strike the anode's target area, X-rays are emitted.

X-ray tubes usually have a power output of 3kW and may be either a side window or end-window type.
The low-power X-ray tube could be used for EDXRF while power of the tube for WDXRF is 3–4 kW. Direct
excitation using a high-power X-ray tube and EDXRF allow to reach detection limits in the parts per
billion or picogram range.

7-End window X-Ray Tube

More power = lower detection limits

Anode selection determines optimal source excitation (application specific)

8- X-ray Detection and Analysis in XRF

The X-rays detection and analysis is usually carried out in two modes:

– Wavelength dispersive X-ray spectroscopy (WDS) uses the reflection of X-rays off of a crystal at a
characteristic angle to detect X-rays of specific wavelength.

– Energy dispersive X-ray spectroscopy (EDS) works on the principle of separating and detecting X-rays of
specific energy and displays them as histograms. Imaging of lements is also possible using this capability.

Wavelength Dispersive (WD) X-ray Spectrometry

Wavelength dispersive X-ray fluorescence relies on a diffractive device such as a crystal, to isolate the
peak corresponding to an analytical line since the diffracted wavelength is much more intense than other
wavelengths that scatter of the device.

The excitation in WDXRF is carried by X-ray tube

The detection and measurement of intensity is based on the principle of X-ray diffraction i.e., the
characteristic X-rays of each element have a distinct wavelength, and by adjusting the tilt of the crystal in
the spectrometer, at a specific angle it will diffract the wavelength of specific element’s X-rays

9- Wavelength Dispersive (WD) X-ray Spectrometry

Wavelength Dispersive XRF relies on a diffractive device such as crystal or multilayer to isolate a peak,
since the diffracted wavelength is much more intense than other wavelengths that scatter of the device.

The two most common diffraction devices used in WDX instruments are the crystal and multilayer. Both
works according to the following formula.

nλ = 2d ´ sinΦ

n = integer

d = crystal lattice or multilayer spacing

Φ = The incident angle

λ = wavelength

10- Energy Dispersive X-Ray Fluorescence

Source Modifiers

Collimators (usually circular or a slit whose sizes range from approximately 10 microns to several
millimeters) are used between the excitation source (X-ray tube or radioactive source) and the sample to
restrict the size or shape of the source beam for exciting small areas

Collimator sizes range from 12 microns to several mm

The detector as usual detects the X-rays from the sample. Because simple collimation blocks unwanted
X-rays, it happens to be a highly inefficient method

Filters (between the X-ray source and the sample or between sample and the detector) perform one of
two functions: background reduction and improved fluorescence. The filter absorbs the low-energy X-
rays (below the absorption edge energy of the filter element) while higher energy X-rays are transmitted

Focusing optics like polycarpellary devices (used in microbeam XRF) have been developed so that the
beam could be redirected and focused on a small spot (less than 100 μm spot size)

Secondary Target

A. The x-ray tube excites the secondary target

B. The Secondary target fluoresces and excites the sample

C. The detector detects x-rays from the sample

Improved Fluorescence and lower background

The characteristic fluorescence of the custom line source is used to excite the sample, with the lowest
possible background intensity. It requires almost 100x the flux of filter methods but gives superior results

11- Source of Excitation and X-ray Detection in PIXE Analysis

The PIXE technique is similar to EDXRF (described in “Energy Dispersive X-ray Fluorescence (EDXRF)”)
except that the exciter source in this case is beam of proton, α-particles, or heavy ions of 1–3MeVamu−1.

The energy of the proton beam in PIXE is ≈3MeV because the X-ray production has maximum cross-
section at ≈3MeV.

The charged particles obtainable from particle accelerator (Pelletron, cyclotron, Van de Graaff
accelerator), lose energy while traversing through sample material.

In the energy range under consideration, the energy loss is mainly due to the interaction of those
particles with the electrons in the material causing excitation and ionization

the principle of PIXE

This ionization is followed by a rearrangement of the electronic architecture with emission of

The detection of this radiation is realized by Si(Li) or intrinsic Ge semiconductor detectors.

The characteristics of the PIXE technique are

(1) nondestructiveness (2) rapidity (±15 min) (3) easy preparation of the sample (4) determination of
most of elements with Z > 13 with a good sensibility (ppm or sub ppm) and with a good confidence

12- Scattering Chamber, Target Holder, and Samples

Scattering chamber encloses the evacuated area where the ion beam strikes the target.

The targets are usually placed at 45◦ to the beam direction

A Faraday cup is housed behind the target at the end of the chamber window

The thin targets are mounted on the target ladder placed at the center of the chamber

The target ladder can be maneuvered vertically and about its axis externally.

The surface barrier detectors, needed to yield information about the scattered charged particles are also
arranged inside the chamber in the forward or in the backward direction

The Si(Li) detector is placed at 90◦ to the beam direction to collect the characteristic X-rays of the target

The target holder assembly usually is a ladder type made of stainless steel with equidistant holes in it.
The position of the target can be well determined from the position of a pointer attached to the target
holder shaft from outside which slides over a vertically fixed scale. The ladder could also be manually
rotated from outside in order to orient the targets at the desired angle with respect to the beam
direction.

The samples in PIXE analyses are usually self-supporting or are sputtered or coated on a thin-foil or on a
thick backing containing no detectable amount of the element of interest. Most samples are analyzed in
their original state; aerosol filter, archaeological samples, soil, biological samples, etc. However, as PIXE
technique is probing only top 10–50 μm of the sample (depending on the material, energy of incident
beam and most importantly on the energy of characteristic X-rays), it is very important that the
area/volume irradiated by the beam (usually a circular area with the diameter of 1– 10mm) is
representative of the whole sample

13- Detection system

In PIXE analysis, the X-rays are detected by a Si(Li) energy dispersive system that includes a pre-amplifier
(to optimize the coupling of the detector output to the amplifier) and an amplifier (to amplify the signal
after shaping the pulses). The analog signal from the amplifier is fed into an analog to digital converter
(ADC), which is then transferred into the memory of the on-line computer via a CAMAC interface. The X-
ray spectrum can be viewed on multichannel analyzer (MCA) terminal and the analysis can be carried out
using the computer. The Kα, Kβ (or/and their components) lines of various elements as seen from the
spectrum are compared with the standard X-ray fluorescence lines from the table

14- Some Other Aspects Connected with PIXE Analysis

Choice of Beam/PIXE Using Heavy Ion Beams

PIXE work is normally carried out with protons of 2–3 MeV. Two aspects are important for consideration
i.e., (a) PIXE using low energy protons and (b) PIXE using heavy charged particles/ ions like deuterons, α-
particles and heavy ions like 3He+, 3He2+, C+, N+, O+, Ne+, etc.

If heavy ions are used for bombardment in PIXE studies, a more complex spectrum is caused because of
the following two reasons – first, the projectile has a greater mass and charge and would therefore be
expected to exert a more disruptive effect on the target atom; and secondly, the projectile has an
electronic level structure of its own, causing multiple ionization i.e., that one or more L electrons are
ejected simultaneously with a K shell electron or double K ionization takes place. Due to appearance of
the new set of lines (satellite and hyper-satellite), the principle X-ray lines get broadened and shifted to
the higher energy side when observed by a Si(Li) detector. However, the complexity of the spectrum is
very much visible when observed through a crystal spectrometer (energy resolution ≈1–2 eV).

Limitations of Heavy-Ions for PIXE Analysis

1. The interaction of heavy charged particles tend to destroy target by sputtering

2. The projectile X-rays are also produced, which may interfere/overlap with target (sample) X-rays

Charging/Sparking/Heating in PIXE

The main difficulty in PIXE analysis is the collection of beam charges from insulating targets. For this
purpose, the targets can be sprayed with electrons from electron gun integrated with the faraday cup.
Charging effects might be responsible for local electrical potential producing the acceleration of
secondary electrons resulting in intense Bremsstrahlung spectra. This effect can also be reduced by
carbon shadowing or by covering the sample with a metal grid

15-Charging/Sparking/Heating in PIXE

A potential problem in PIXE analysis of thick nonconducting samples is one of the charge build-up and
subsequent sparking which can cause large spikes in the spectrum and/or may deflect the proton beam
resulting in poor precision. Spikes have the effect of irreproducible increasing the background over a
large but random portion of the spectrum. Techniques such as spraying the sample with electrons from
an electron gun or increasing the pressure in the target chamber can solve the problem

The very high-energy ion beam can also cause heat-up of the sample unless the current is kept low.
These temperatures can cause damage to the sample and/or loss of volatiles, which may change the
sample composition. In order to reduce the high-energy Bremsstrahlung component due to the target
charge-up, the use of electron gun, the foil technique, the poor vacuum, and helium filled chamber can
be made.

16-Applications of XRF and PIXE Techniques

In Biological Sciences

In Criminology

In Material Science

Pollution Analysis

For Archaeological Samples

For Chemical Analysis of Samples

For Analysis of Mineral Samples

17- Comparison Between EDXRF and WDXRF Techniques

Resolution

The resolution of the WDXRF system, which is dependent on the crystal and optics design, particularly
collimation, spacing and positional reproducibility, varies from 2 to 10 eV at 5.9 keV. While the resolution
in WDXRF depends on the diffracting crystal, the resolution of the EDX system is dependent on the
resolution of the detector. This can vary from 150–200 eV for Si(Li) and HpGe and about 600 eV or more
for gas filled proportional counter at 5.9 keV

Simultaneity

EDXRF has the capability to detect a group of elements all at once while it is not possible with the
WDXRF system

Spectral Overlaps

Since the resolution of a WDXRF spectrometer is relatively high, spectral overlap corrections are not
required. However, with the EDXRF analyzer, some type of deconvolution method must be used to
correct for spectral overlaps as it has poor resolution

Background

Since a WDXRF system usually uses direct radiation flux, the background in the region of interest is
directly related to the amount of continuum radiation. However, the EDXRF system uses filters and/or
targets to reduce the amount of continuum radiation in the region of interest, which is also resolution
dependent, while producing a higher intensity X-ray peak to excite the element of interest. Thus,
although the WDXRF has an advantage due to resolution yet it suffers due to large background i.e., if a
peak is one tenth as wide, it has one tenth the background. However, EDXRF counters with filters and
targets can reduce the background intensities by a factor of ten or more
Excitation Efficiency

Excitation efficiency is the main factor for determining detection limits, repeatability, and reproducibility.
The relative excitation efficiency is improved by having more source X-rays closer to but above the
absorption edge energy for the element of interest WDXRF generally uses direct unaltered X-ray
excitation, which contains a continuum of energies with most of them not optimal for exciting the
element of interest. However, EDXRF analyzers may use filter to reduce the continuum energies at the
elemental lines, and effectively increase the percentage of X-rays above the element absorption edge.

Penetration Depths and Analytical Volume

In XRFS penetration depths are relatively large, of the order of a few millimeters while in PIXE analysis,
the analytical depths are ≈10–50 μm because of the limited penetration of particles into the sample.
Therefore, PIXE analysis is essentially a surface technique even when applied to “thick” samples.

Excitation and Background Intensity

The background intensity distribution in XRF and PIXE spectra are opposite to each other due to its
dependence on the excitation cross-section

Typical background intensity distribution curves for XRF and PIXE analyses in the 0–30 keV energy range

The PIXE excitation and ionization cross-sections of various elements decrease with increasing atomic
number, while in X-ray photon excitation, the cross-section increases with increase atomic number. Since
detection limits are largely controlled by the background intensity, EDXRF is a better technique for the
determination of elements with low energy X-ray lines which fall especially in the range of 1–4 keV (Na
through Ca), while PIXE is better for elements with relatively higher characteristic X-ray energies. For
elements with atomic number greater than ≈50, both techniques are forced to use L X-ray lines in place
of K X-ray lines.

Energy Resolution

At energies lower than 20 keV, better energy resolution (FWHM) is achieved with wavelength dispersive
X-ray fluorescence (WDXRF) as compared to proton-induced Xray emission (PIXE) and energy dispersive
X-ray fluorescence (EDXRF)

Lower Limits of Detection

XRF is more favorable for elements having their absorption edges close to the exciting energies. They
provide a great advantage, e.g., in the analysis of Ba and Ti, employing a fluoresce plate of rare-earth
element heavier than Ce would yield a rather high sensitivity for Kα (Ba).

In PIXE analysis, using proton beam of 1-3MeV for most favored elements in low-Z matrices and think
targets, the best sensitivities down to 0.1 ppm have been obtained. These levels are achieved for
elements near Z = 40 using K lines and Z = 80 using L lines

Applications

XRFs has been applied in a wide variety of fields for both qualitative and quantitative analysis e.g.,
exploration, mining and processing of minerals and materials, forensic and metallurgical fields. Most
PIXE applications have been in the analysis of thin samples in which matrix effects are minimal or
nonexistent e.g., in the fields of biology, mineralogy, medicine, geochemistry, materials science,
archaeological, environment, and geology

Summery

X-ray Fluorescence (XRF) and Particle-Induced X-ray Emission (PIXE) are powerful tools for rapid
multielement nondestructive analyses, enabling simultaneous detection of many elements in solid or
liquids with high detection sensitivities. The fluoresced X-rays from the sample are collected and
displayed with either energy dispersive or wavelength dispersive detector systems.

The two techniques are similar in their fundamental approach, based on the common fact that when an
electron is ejected from an inner shell of an atom, an electron from a higher shell drop into this lower
shell to fill the hole left behind. This results in the emission of an X-ray photon equal in energy to the
energy difference between the two shells.

The principle of both XRF and PIXE techniques is to excite the atoms of the substance to be analyzed by
bombarding the sample with sufficiently energetic X-rays/γrays or charged particles. The excess energy is
taken away by either photon (characteristic X-rays) when an electron from a higher-level fall into the
inner-shell vacancy or Auger (higher-shell) electrons when the energy released during the process of
hole being filled by the outer shell electron is transferred to another higher-shell electron.

The Radiative Auger Effect (RAE) is another category in which electron and photon are simultaneously
emitted, where the decay of a K-shell vacancy proceeds as a normal K Auger process except that there is
emission of a photon along with an electron in addition to an electron filling the K-shell vacancy.

According to the quantum theory, every electron in a given atom moves on in an orbital characterized by
four quantum numbers: Principal (shell) quantum number (n), Azimuthal (subshell) quantum number (l),
Magnetic quantum number (m), and Spin quantum number (s). The emission of X-rays is governed by
the selection rules for allowed electric dipole (E1) transitions.

X-ray fluorescence spectroscopy can be performed using radioactive sources as exciters or X-ray tubes as
exciters. Primary sources include sources of 55Fe, 109Cd, and 241Am, while secondary exciters use Cu,
Se, Y, Mo, Sn, Sm, and Dy. X-rays from the primary source are directed at a selectable secondary exciter
target, usually Tin (Sn), causing emission (fluorescence) of characteristic X-rays from the sample. These X-
rays are captured in a Si(Li) detector and analyzed by computer.
X-ray tubes offer greater analytical flexibility at a cost of more complexity. They have a power output of
3kW and may be either a side window or end-window type. Direct excitation using a high-power X-ray
tube and EDXRF allows for detection limits in the parts per billion or picogram range. End window X-Ray
Tubes determine which elements can be excited, with more power resulting in lower detection limits.

X-ray detection and analysis are usually carried out in two modes: Wavelength Dispersive X-ray
spectroscopy (WDS) and Energy Dispersive X-ray spectroscopy (EDS). WDS uses the reflection of X-rays
off of a crystal at a characteristic angle to detect X-rays of specific wavelength, while EDXRF works on the
principle of separating and detecting X-rays of specific energy and displays them as histograms.

Energy Dispersive X-Ray Fluorescence (EDXRF) spectrometers consist of X-ray source, sample, and
detector. Source modifiers include collimators, filters, secondary targets, collimators, and focusing optics.
Secondary targets are used to excite the sample with the lowest possible background intensity, requiring
almost 100x the flux of filter methods but providing superior results.

The PIXE technique is similar to Energy Dispersive X-ray Fluorescence (EDXRF) but uses a beam of proton,
α-particles, or heavy ions of 1–3MeVamu−1. The energy of the proton beam in PIXE is approximately
3MeV due to the maximum cross-section at ≈3MeV. The principle of PIXE involves ionizing atomic levels
using charged particles and then rearrangement of the electronic architecture with emission of
characteristic X-rays. The detection of this radiation is realized by Si(Li) or intrinsic Ge semiconductor
detectors.

The scattering chamber, target holder, and samples are essential components of PIXE analysis. The
targets are usually placed at 45◦ to the beam direction, and the thin targets are mounted on the target
ladder. Surface barrier detectors are also arranged inside the chamber to yield information about
scattered charged particles. The Si(Li) detector is placed at 90◦ to the beam direction to collect the
characteristic X-rays of the target.

The X-rays are detected by a Si(Li) energy dispersive system that includes a pre-amplifier and an
amplifier. The analog signal from the amplifier is fed into an analog to digital converter (ADC), which is
then transferred into the memory of the on-line computer via a CAMAC interface. The X-ray spectrum
can be viewed on a multichannel analyzer (MCA) terminal, and the analysis can be carried out using the
computer.

Some other aspects connected with PIXE analysis include the choice of beam/PIXE using heavy ions, such
as deuterons, α-particles, and heavy ions like 3He+, 3He2+, C+, N+, O+, Ne+, etc. If heavy ions are used
for bombardment in PIXE studies, a more complex spectrum is caused due to the projectile's greater
mass and charge and its own electronic level structure. However, the complexity of the spectrum is
visible when observed through a crystal spectrometer.

PIXE and XRF techniques are used in various fields, including biological sciences, criminalology, material
science, pollution analysis, archaeological samples, chemical analysis of samples, and mineral analysis.
The main difficulty in PIXE analysis is the collection of beam charges from insulating targets, which can
be reduced by using electron guns integrated with faraday cups or carbon shadowing.

A potential problem in PIXE analysis of thick nonconducting samples is charge build-up and sparking,
which can cause large spikes in the spectrum and/or deflect the proton beam resulting in poor precision.
Techniques such as spraying the sample with electrons from an electron gun or increasing the pressure
in the target chamber can solve this problem.

EDXRF has the capability to detect a group of elements all at once, while WDXRF is not possible.
However, EDXRF requires some type of deconvolution method to correct for spectral overlaps due to
poor resolution.

The background intensity distribution in XRF and PIXE spectra is opposite to each other due to its
dependence on the excitation cross-section. EDXRF is better for the determination of elements with low
energy X-ray lines, while PIXE is better for elements with relatively higher characteristic X-ray energies.

Energy resolution (FWHM) is achieved with wavelength dispersive X-ray fluorescence (WDXRF) at
energies lower than 20 keV. XRF is more favorable for elements having their absorption edges close to
the exciting energies, providing a great advantage. In PIXE analysis, using proton beam of 1-3MeV for
most favored elements in low-Z matrices and think targets, the best sensitivities down to 0.1 ppm have
been obtained.

XRFs have been applied in a wide variety of fields for both qualitative and quantitative analysis, such as
exploration, mining and processing of minerals and materials, forensic and metallurgical fields. Most
PIXE applications have been in the analysis of thin samples in which matrix effects are minimal or
nonexistent.