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.