X-Ray Fluorescence (XRF)
Becoming the most widely used
method for elemental analysis of
solids
ADVANTAGES AND
DISADVANTAGES
Advantages of X-Ray Spectrometry
* Simple spectra
* Spectral positions are almost independent of
the chemical state of the analyte
* Minimal sample preparation
* It is non-destructive
* Applicable over a wide range of
concentrations
* Good precision and accuracy
Disadvantages of X-Ray Spectrometry
* X-ray penetration of the sample is limited to
the top 0.01 - 0.1 mm layer
* Light elements (below 22Ti) have very limited
sensitivity although C is possible on new
instruments
* Inter element (MATRIX) effects may be
substantial and require computer correction
* Limits of detection are only modest
* Instrumentation is fairly expensive
NOMENCLATURE
Simplified spectral lines observed in x-ray
spectra (each energy shell actually comprises
several energy levels, thus transitions are
more numerous than shown).
PRINCIPLES OF X-RAY
FLUORESCENCE
X-Ray Excitation
Electron
Excitation
AUGER ELECTRON EMISSION
(internal photoionisation)
The Auger effect is more common in elements
of low Z because their atomic electrons are
more loosely bound and their characteristic Xrays more readily absorbed.
X-RAY FLUORESCENCE YIELD
The yield of X-ray photons is reduced by the
Auger effect. The fluorescence yield ( ) is the
ratio of X-ray photons emitted from a given
shell to the number of vacancies created in
that shell.
Since production of Auger electrons is the only
other competing reaction the ratio of Auger
electrons to vacancies must be 1- .
X-RAY ABSORPTION AND
SCATTERING IN CONDENSED
PHASES
The probability of X-ray absorption as a
function of path length through the sample is
given by Beer's law for X-rays:
I/I0 = exp(-µm
d)
where I/I0 is the fraction of X-rays transmitted
through a thickness d of a material of density
. The parameter µm is the mass absorption
coefficient which is a function of the atomic
number Z and the energy (wavelength) of the
X-ray.
The mass absorption coefficient for a complex
sample is the weighted average of the
coefficients for the constituent atoms.
X-RAY MASS ABSORPTION
COEFFICIENTS
A plot of mass absorption coefficient vs energy
of the X-ray photon for 82Pb.
Abrupt changes are observed corresponding to
absorption edges for K, L and M electrons. At
the energy (wavelength) of the edge, the
photons first become sufficiently energetic to
eject K, L and M photoelectrons.
X-RAY SOURCES
The X-ray tube is energised by a high-voltage
power supply with an output of 0.5 to 50 kV.
The head of the vacuum tube consists of a
target (anode), which is often made of
tungsten and chromium. As accelerated
electrons strike the target, X-rays are emitted.
The tube also forms the X-rays into a beam
through a Beryllium window.
In the target the 74W is used to excite L and
K lines of higher Z atoms and the 24Cr is
used to excite atoms of 22Ti and below.
Spectral Output
X-ray spectrum produced by electron
bombardment of a tungsten target:
Continuum Spectrum: The continuum results
from deceleration of electrons by the atoms in
the target. The German term "bremsstrahlung"
means "braking radiation."
Characteristic Spectra: Electron
bombardment also produces characteristic
peaks K and K provided the accelerating
potentials are sufficiently high.
DETECTORS
X-ray photons (as well as other energetic
particles) can be measured using the following
types of detectors:
* gas-filled detectors register a current pulse
from the collection of electron-ion pairs
formed;
* a semiconductor detector register a current
pulse from the formation of electron-hole
pairs;
* a scintillation detector counts light pulses
created when an X-rays passes through a
phosphor;
* a photographic plate.
Gas-Proportional Counters
A gas-proportional counter is filled with P90
gas (90% argon, 10% methane). X-rays ionise
the gas, leaving electrons that migrate to the
anode and positive ions that move to the case.
Proportional counters use gas amplification:
the detector voltage is raised to 500 to 700 V
so that the primary electrons and ions, first
formed, are accelerated to produce secondary
electrons and ions when they collide with gas
atoms. This yields a greatly increased signal
which is, nevertheless, proportional to the
energy of the original x-ray.
Solid-State Detectors
When an electron enters the crystal it ejects a
high-energy photoelectron which ultimately
dissipates its energy in multiple interactions
which promote valence band electrons to the
conduction band, leaving holes in the valence
band. The electron-hole pairs are then
collected by biasing the detector at -1000 V,
giving rise to a current pulse for each x-ray
entering the detector. Charge collection is
much more efficient than in a gas.
Lithium-Drifted Si(Li) Detectors
A lithium-drifted Si(Li) detector is
manufactured from high-purity p-type silica.
However, p-type silica of sufficiently high
purity is difficult to fabricate. Most Si crystals
contain extrinsic holes, caused by impurities,
which allow significant "leakage" of current at
the required bias voltage. In order to
compensate for these extrinsic holes, lithium,
an n-type dopant, is diffused into the material
at 350 - 450ºC under an electrical gradient.
The lithium atoms compensate for the extrinsic
charge-carriers in the p-type silicon and
provide a wide "intrinsic" region of high
resistance.
Si(Li) detectors are operated at 77 K with a
liquid N2 cryostat to prevent further diffusion
and to reduce the level of random noise due to
the thermal motion of charge carriers.
WAVELENGTH DISPERSIVE XRF
SPECTROSCOPY
Instrumentation
In wavelength dispersive spectrometers, the
several x-ray lines emitted from the sample
are dispersed spatially by crystal diffraction on
the basis of wavelength. The detector then
receives only one wavelength at a time.
The crystal and detector are made to
synchronously rotate through angles of θ and
2θ respectively.
Bragg Diffraction
Wavelength dispersive X-ray spectrometers
function by separating the X-rays of interest
using diffraction from a crystal. This follows
from the Bragg equation:
n = 2 d sin( )
where n is the diffraction order, d is the
interplanar spacing of the atomic layer and
the angle of incidence.
Crystals
Crystal
Primary Range
LiF
0.025 - 0.272 nm
Si
0.055 - 0.598 nm
pentaerythritol 0.076 - 0.834 nm
CaSO4.2H2O 0.132 - 1.45 nm
KAP*
0.232 - 2.54 nm
lead stearates 6 - 15 nm
is
*Potassium hydrogen phthalate
ENERGY DISPERSIVE XRF
SPECTROSCOPY
The primary X-ray beam excites several
spectral lines from the sample. In energy
dispersive XRF all wavelengths enter the
detector at once. The detector registers an
electric current having a height proportional to
the photon energy. These pulses are then
separated electronically, using a pulse
analyser.
WAVELENGTH AND ENERGY
DISPERSION COMPARED
Advantages of Energy Dispersion:
* simplicity of instrumentation - no moving
parts
* simultaneous accumulation of the entire Xray spectrum
* qualitative analysis can be performed in 30 s,
or so
* a range of alternative excitation sources can
be used in place of high-power x-ray tubes
with their large, heavy, expensive and powerconsuming supplies
* alternative sources include, low power x-ray
tubes, secondary monochromatic radiators,
radioisotopes and ion beams.
Advantages of Wavelength Dispersion:
* resolution is better at wavelengths longer
than 0.08 nm
* higher individual intensities can be measured
because only a small portion of the spectrum is
admitted to the detector
* with multichannel analysers sensitivity for
weak lines in the presence of strong lines is
limited because the strongest line determines
the counting time
* lower detection limits are possible
SAMPLE PREPARATION
Reproducible sample preparation methods are
essential. Samples must be in a form that are
similar to available standards in terms of
matrix, density and particle size.
* Solids, generally solids must be polished as
surface roughness may give erratic results.
* Powders and pellets, powdered samples are
often pressed into pellets, suspensions may
also be analysed
* Fusions, with potassium pyrophosphate
(K2P2O7) or a tetraborate (Na2B4O7 or Li2B4O7)
present a homogenised sample which can often
be analysed directly
* Liquids and solutions, a x-ray transparent
cover and sample cup must be provided to
prevent volatility under vacuum conditions
* support media, such as filter paper, millipore
filters, ion-exchange membranes
MATRIX EFFECTS
Types of Matrix Effects
In XRF absorption-enhancement effects arise
from the following phenomena:
1. The matrix absorbs primary x-rays
(primary-absorption effect); it may have a
larger or smaller absorption coefficient than
the analyte for primary source x-rays
2. The matrix absorbs the secondary analyte xrays (secondary-absorption effect); it may
have a larger or smaller absorption coefficient
for the analyte-line radiation
3. The matrix elements emit their own
characteristic lines, which may lie on the short
wavelength side of the analyte absorption
edge, thereby exciting the analyte to emit
additional radiation to that excited by the
primary source of X-rays alone (enhancement)
Absorption-Enhancement Effects
Absorption-enhancement effects can be
positive or negative on the basis of their effect
upon analyte intensity.
In the positive absorption effect, the matrix
has a smaller absorption coefficient than the
analyte for the primary and analyte-line
radiation, and the analyte-line radiation is
higher than would be predicted.
In the negative absorption effect, the matrix
has a larger absorption coefficient than the
analyte, and the analyte-line intensity is lower
than expected.
In the enhancement effect, one or more
spectral lines of the matrix elements excite
analyte-line emission). This enhancement may
take two forms: direct enhancement (
C
both excite
A)
B
and the third element
and
enhancement (
excites
C
excites
B
which in turn
A).
QUANTITATIVE ANALYSIS
1. Calibration-Standard Methods. The analyteline intensity from samples is compared with
that from standards having the same form as
the samples and, nearly as possible, the same
matrix.
2. Internal Standardisation. The calibrationstandard method is improved by quantitative
addition to all samples of an internal standard
element having excitation, absorption and
enhancement characteristics similar to those of
the analyte in the particular matrix. The
calibration function involves measuring the
intensity ratio of the analyte and internal
standard lines.
3. Matrix-Dilution Methods. The matrix of all
samples is diluted to a composition such that
the effect of the matrix is determined by the
diluent rather than the matrix.
4. Thin-Film Methods. The samples are made
so thin that absorption-enhancement effects
substantially disappear.
5. Standard Addition and Dilution Methods. The
analyte concentration is altered quantitatively
in the sample itself. The sample is subjected to
one or more quantitative incremental
concentrations or dilutions of the analyte. The
intensity of the analyte lines is measured for
effectively the same matrix in each case.
6. Mathematical Corrections. Absorptionenhancement effects are corrected
mathematically by the use of influence
coefficients for each element present (these
are derived experimentally from reference
samples). The basic approach is that the XRF
intensity at a particular wavelength will in
some way be affected by each element in the
sample.
Calibration
Quantitative XRF analyses require calibration of
the measuring arrangement, which may be
performed by two major approaches:
empirical calibration
fundamental
parameters
(FP)
calibration.
The empirical calibration is based on the
analysis of standards with known elemental
compositions. To produce a reliable calibration
model, the standards must be representative
of the matrix and target element concentration
ranges of the sample to be analyzed.
Maintaining the same sample morphology
(particle size distribution, heterogeneity and
surface
condition)
and
source/sample
geometry for both standard and sample
measurements is essential in empirical
calibrations.
Alternatively, “standardless” FP techniques
may be used, which rely on built-in
mathematical algorithms that describe the
physics of the detector’s response to pure
elements. In this case, the typical composition
of the sample must be known, while the
calibration model may be verified
optimized by one single standard sample.
and
Detection limits
Two types of detection limits
considered in XRF analysis:
should
be
a) instrument detection limits, which represent
the threshold concentration of a given element
that a particular instrument can resolve and
b) method detection limits, related to sample
preparation and analysis time. Depending on
the element to be analyzed and the sample
matrix, typically achieved detection limits vary
between 10 and 100 ppm.
XRF applications
During the last two decades, the development
in X-ray detectors has established the XRF
method as a powerful technique in a number
application fields, including:
Ecology and environmental management:
measurement of heavy metals in soils,
sediments, water and aerosols
Geology and mineralogy: qualitative and
quantitative analysis of soils, minerals, rocks
etc.
Metallurgy and chemical industry: quality
control of raw materials, production processes
and final products
Paint industry: analysis of lead-based paints
Jewelry: measurement of precious metals
concentrations
Fuel industry: monitoring the amount of
contaminants in fuels
Food chemistry: determination of toxic metals
in foodstuffs
Agriculture: trace metals analysis in soils and
agricultural products
Art Sciences: study of paintings, sculptures
etc. in order to make an expertise
EDX Microanalysis As the name suggests, this refers to the
analysis of a sample on a microscopic scale,
resulting in structural, compositional and
chemical information about the sample.
There exists a whole host of analytical
techniques that exploit the many signals which
may be generated within the sample. X-ray
microanalysis specifically gives information
about the elemental composition of the
specimen, in terms of both quantity and
distribution.
K X-rays
L X-rays
On entering a sample, the energetic incident
electrons undergo a number inelastic and
elastic scattering events resulting in a zig-zag
path into the sample until they either come to
rest or are backscattered out of the surface.
The distribution of trajectories is contained
within the so called ‘interaction volume’, the
shape and dimensions of which are strongly
affected by both:
- the atomic number and the incident energy of
the electrons.
At any point along a given trajectory,
characteristic X-rays can be produced provided
that the energy of the electron or indeed X-ray
is greater than the absorption edge associated
with that characteristic emission line.
The volume of the sample from which X-rays
are produced is known as the X-ray production
volume or X-ray generation volume, the size
and dimensions of which depends on the X-ray
line being excited and the density of the
material. For example, in the case of lead, the
sample volume producing the higher energy L
series X-rays will be smaller and nearer to the
surface than the volume from which M series
X-ray lines are generated.
J(rz)
Depth
(microns)
0
The typical features of the j(rz) curve are
shown in the adjacent figure. Near the surface,
X-ray production is greater than for a thin
unsupported film because of scattered
electrons travelling up from below being able
to generate X-rays and therefore resulting in
the value of j(rz) being greater than one.
After initially rising to a maximum, the curve
decreases due to scattering and deceleration of
the electrons, eventually falling to zero.
Geometry
The position of the front end of the detector in
relation to the surface of the sample is
important in order to optimise the collection of
X-rays.
Detector
Working
distance
Entrance
angle
Sample at ideal working distance
for X-ray microanalysis
Sample at incorrect working
distance for X-ray microanalysis
EDX-Mapping
The X-ray spectrum detected by EDX can be
used to construct a true color response that
would be obtained if the human visual
sensitivity to the electromagnetic spectrum
could be offset to the X-ray wavelength region.
This color input is then used to augment a
conventional electron image. In this way the
detail of the original electron image is retained
whilst portraying the underlying elemental
composition because the spectrum from each
compound gives it a characteristic color. Thus
topographic and compositional information
from all elements is compressed into a single
view giving the analyst a useful 'first look' to
guide further microanalysis.
Quantitative microanalysis
Quantitative analysis of elements in any
sample, requires an accurate measure of the
intensity of peaks, before the concentration of
elements in a sample can be calculated. In
determining peak areas in spectra, two
problems arise,
1) a typical spectrum contains characteristic
peaks, which are superimposed on a slowly
varying background, which is 'noisy' because
of statistical variations. This background
contribution needs to be carefully subtracted
from the spectrum.
2) The energy resolution of the detector
imposes a limit on the separation of peaks.
Identification of peaks is generally not a
problem, but overlapping peaks require
deconvolution, before being able to extract
the true peak intensities relevant to the
elements present in the sample.
Once these intensities have been determined,
a comparison is then made with standards of
known composition, followed by application of
matrix corrections, before the concentration
of each element can be determined.
Background subtraction
The simple method of linear interpolation of
the background beneath a peak is not
appropriate, since the background is non
linear, both locally in the vicinity of peaks, and
over the entire energy range. There are
various schools of thought as how to best
remove this background and to separate peaks
from each other:
1) One such method relies on the fitting of a
theoretical background to the spectrum
background, and then using a least squares
fitting technique to obtain peak intensities.
However, construction of a model to fit the
background requires an accurate knowledge of
a number of physical parameters, which are
often difficult to determine precisely.
2) A second method suppresses the
background, using a filtering method which
avoids any specific shape calculation. The peak
intensities are then obtained by using a least
squares fit of standard peaks, in which the
background has also been suppressed.
Peak deconvolution
The energy resolution of an EDS imposes a
limit on the separation of peaks. There are
several examples of peak overlap which
commonly occur: the Ka peaks for Be, B, C, O,
N and F, are sufficiently close for the tails of
one peak to overlap into the neighbouring
peak. Overlaps between the Kb line of one
element and the Ka line of another, often
overlap. Examples include the V Kb and Cr Ka
(15eV apart) and overlaps between lines from
different shells e.g. between Mo La and S Ka,
can often occur.
When peaks overlap, it is possible to extract
individual peak areas, provided that the
corresponding peak shapes are accurately
known. These peak shapes or profiles are fitted
to the spectrum using the method of least
squares. Clearly the accuracy of the fitting
depends on the similarity of the peaks in the
unknown spectrum, to those of the profiles,
and this is reflected in the accuracy of the peak
intensities. This is particularly important when
small peaks and larger peaks overlap. The
fitting of profiles to the unknown spectrum
requires that the gain and the system
resolution should be matched between the two.
Optimization of spectra, in terms of gain and
resolution, can be taken into account by using
an optimization standard which produces
suitable known peaks.
Matrix corrections
Atomic number
The atomic number of the material and the
incident beam energy have a profound effect
on both the number of electrons backscattered
out of the material and the rate at which the
electrons lose their energy within the sample.
Both of these factors will have an affect on the
number of X-rays produced at a given depth in
the interaction volume and hence the shape
and area of the j(rz) curve which corresponds
to the total number of X-ray generated. The
atomic number correction is largest when
considering light elements within a heavy
sample matrix.
Fluorescence correction
Fluorescence arises as a result of the ionization
of atom shells by X-rays rather than electrons.
The result is the emission of characteristic Xrays. This contribution to the spectrum will be
in addition to those X-rays which have been
produced directly by electrons. Fluorescence
can only occur if the energy of the incident Xray is greater than the critical excitation
energy. There will be a fluorescence
contribution from both the continuum and
characteristic X-rays but the contribution from
characteristic X-rays is the most dominant.
Electron
Beam
FeK
CrK
Resolution and count rate
Energy resolution is the primary test of
detector performance, and the main
specification for an EDX detector is the
resolution at Mn. The benefits of improved
resolution, are improved detection limits,
because a narrower peak is higher above the
background. Well defined peak shapes make
peak ID faster and more reliable, and in
addition, overlapped peaks are better resolved,
leading to significantly improved detection
limits, and accuracy of routines used in
quantitative analysis.
The acquisition rate into the spectrum is
important and this is related to the input
count rate, via the deadtime and the
selected processing time.
Input rate: This shows the approximate rate
of photons striking the detector.
Acquisition rate: This shows how fast the
system is accumulating spectrum counts.
Deadtime (%): is the percentage time for
which the pulse processor is unavailable for
further counting. (see acquisition rate).