X-ray fluorescence

A Philips PW1606 X-ray fluorescence spectrometer with automated sample feed in a cement
plant quality control laboratory

X-ray fluorescence (XRF) is the emission of characteristic "secondary" (or fluorescent) X-

rays from a material that has been excited by bombarding with high-energy X-rays or gamma
rays. The phenomenon is widely used for elemental analysis and chemical analysis,
particularly in the investigation of metals, glass, ceramics and building materials, and for
research in geochemistry, forensic science and archaeology.
Physics of X-ray fluorescence, in a schematic representation.

When materials are exposed to short-wavelength X-rays or to gamma rays, ionisation of their
component atoms may take place. Ionisation consists of the ejection of one or more electrons
from the atom, and may take place if the atom is exposed to radiation with an energy greater
than its ionisation potential. X-rays and gamma rays can be energetic enough to expel tightly
held electrons from the inner orbitals of the atom. The removal of an electron in this way
renders the electronic structure of the atom unstable, and electrons in higher orbitals "fall"
into the lower orbital to fill the hole left behind. In falling, energy is released in the form of a
photon, the energy of which is equal to the energy difference of the two orbitals involved.
Thus, the material emits radiation, which has energy characteristic of the atoms present. The
term fluorescence is applied to phenomena in which the absorption of radiation of a specific
energy results in the re-emission of radiation of a different energy (generally lower).

Figure 1: Electronic transitions in a calcium atom. Remember, when electrons are jumping
down, one of the electrons in the lower orbital is missing.
Figure 2: Typical energy dispersive XRF spectrum

Figure 3: Spectrum of a rhodium target tube operated at 60 kV, showing continuous spectrum
and K lines

[edit] Characteristic radiation

Each element has electronic orbitals of characteristic energy. Following removal of an inner
electron by an energetic photon provided by a primary radiation source, an electron from an
outer shell drops into its place. There are a limited number of ways in which this can happen,
as shown in figure 1. The main transitions are given names: an L→K transition is traditionally
called Kα, an M→K transition is called Kβ, an M→L transition is called Lα, and so on. Each
of these transitions yields a fluorescent photon with a characteristic energy equal to the
difference in energy of the initial and final orbital. The wavelength of this fluorescent
radiation can be calculated from Planck's Law:

The fluorescent radiation can be analysed either by sorting the energies of the photons
(energy-dispersive analysis) or by separating the wavelengths of the radiation (wavelength-
dispersive analysis). Once sorted, the intensity of each characteristic radiation is directly
related to the amount of each element in the material. This is the basis of a powerful technique
in analytical chemistry. Figure 2 shows the typical form of the sharp fluorescent spectral lines
obtained in the wavelength-dispersive method (see Moseley's law).

[edit] Primary radiation

In order to excite the atoms, a source of radiation is required, with sufficient energy to expel
tightly held inner electrons. Conventional X-ray generators are most commonly used, because
their output can readily be "tuned" for the application, and because higher power can be
deployed relative to other techniques. However, gamma ray sources can be used without the
need for an elaborate power supply, allowing an easier use in small portable instruments.
When the energy source is a synchrotron or the X-rays are focused by an optic like a
polycapillary, the X-ray beam can be very small and very intense. As a result, atomic
information on the sub-micrometer scale can be obtained. X-ray generators in the range 20–60
kV in order to the K line, which allows excitation of a broad range of atoms. The continuous
spectrum consists of "bremsstrahlung" radiation: radiation produced when high energy
electrons passing through the tube are progressively decelerated by the material of the tube
anode (the "target"). A typical tube output spectrum is shown in figure 3.

[edit] Dispersion

In energy dispersive analysis, the fluorescent X-rays emitted by the material sample are
directed into a solid-state detector which produces a "continuous" distribution of pulses, the
voltages of which are proportional to the incoming photon energies. This signal is processed
by a multichannel analyser (MCA) which produces an accumulating digital spectrum that can
be processed to obtain analytical data. In wavelength dispersive analysis, the fluorescent X-
rays emitted by the material sample are directed into a diffraction grating monochromator.
The diffraction grating used is usually a single crystal. By varying the angle of incidence and
take-off on the crystal, a single X-ray wavelength can be selected. The wavelength obtained is
given by the Bragg Equation:

where d is the spacing of atomic layers parallel to the crystal surface.

[edit] Detection

In energy dispersive analysis, dispersion and detection are a single operation, as already
mentioned above. Proportional counters or various types of solid state detectors (PIN diode,
Si(Li), Ge(Li), Silicon Drift Detector SDD) are used. They all share the same detection
principle: An incoming X-ray photon ionises a large number of detector atoms with the
amount of charge produced being proportional to the energy of the incoming photon. The
charge is then collected and the process repeats itself for the next photon. Detector speed is
obviously critical, as all charge carriers measured have to come from the same photon to
measure the photon energy correctly (peak length discrimination is used to eliminate events
that seem to have been produced by two X-ray photons arriving almost simultaneously). The
spectrum is then built up by dividing the energy spectrum into discrete bins and counting the
number of pulses registered within each energy bin. EDXRF detector types vary in resolution,
speed and the means of cooling (a low number of free charge carriers is critical in the solid
state detectors): proportional counters with resolutions of several hundred eV cover the low
end of the performance spectrum, followed by PIN diode detectors, while the Si(Li), Ge(Li)
and Silicon Drift Detectors (SDD) occupy the high end of the performance scale.

In wavelength dispersive analysis, the single-wavelength radiation produced by the

monochromator is passed into a photomultiplier, a detector similar to a Geiger counter, which
counts individual photons as they pass through. The counter is a chamber containing a gas
that is ionised by X-ray photons. A central electrode is charged at (typically) +1700 V with
respect to the conducting chamber walls, and each photon triggers a pulse-like cascade of
current across this field. The signal is amplified and transformed into an accumulating digital
count. These counts are then processed to obtain analytical data.

[edit] X-ray intensity

The fluorescence process is inefficient, and the secondary radiation is much weaker than the
primary beam. Furthermore, the secondary radiation from lighter elements is of relatively low
energy (long wavelength) and has low penetrating power, and is severely attenuated if the
beam passes through air for any distance. Because of this, for high-performance analysis, the
path from tube to sample to detector is maintained under high vacuum (around 10 Pa residual
pressure). This means in practice that most of the working parts of the instrument have to be
located in a large vacuum chamber. The problems of maintaining moving parts in vacuo, and
of rapidly introducing and withdrawing the sample without losing vacuum, pose major
challenges for the design of the instrument. For less demanding applications, or when the
sample is damaged by a vacuum (e.g. a volatile sample), a helium-swept X-ray chamber can
be substituted, with some loss of low-Z (Z = atomic number) intensities.

[edit] Chemical analysis

The use of a primary X-ray beam to excite fluorescent radiation from the sample was first
proposed by Glocker and Schreiber in 1928[1]. Today, the method is used as a non-destructive
analytical technique, and as a process control tool in many extractive and processing
industries. In principle, the lightest element that can be analysed is beryllium (Z = 4), but due
to instrumental limitations and low X-ray yields for the light elements, it is often difficult to
quantify elements lighter than sodium (Z = 11), unless background corrections and very
comprehensive interelement corrections are made.

Figure 4: Schematic arrangement of EDX spectrometer

[edit] Energy dispersive spectrometry

In energy dispersive spectrometers (EDX or EDS), the detector allows the determination of
the energy of the photon when it is detected. Detectors historically have been based on silicon
semiconductors, in the form of lithium-drifted silicon crystals, or high-purity silicon wafers.
Figure 5: Schematic form of a Si(Li) detector

[edit] Si(Li) detectors

These consist essentially of a 3–5 mm thick silicon junction type p-i-n diode (same as PIN
diode) with a bias of -1000 V across it. The lithium-drifted centre part forms the non-
conducting i-layer, where Li compensates the residual acceptors which would otherwise make
the layer p-type. When an X-ray photon passes through, it causes a swarm of electron-hole
pairs to form, and this causes a voltage pulse. To obtain sufficiently low conductivity, the
detector must be maintained at low temperature, and liquid-nitrogen must be used for the best
resolution. With some loss of resolution, the much more convenient Peltier cooling can be
employed.[2]

[edit] Wafer detectors

More recently, high-purity silicon wafers with low conductivity have become routinely
available. Cooled by the Peltier effect, this provides a cheap and convenient detector,
although the liquid nitrogen cooled Si(Li) detector still has the best resolution (i.e. ability to
distinguish different photon energies).

[edit] Amplifiers

The pulses generated by the detector are processed by pulse-shaping amplifiers. It takes time
for the amplifier to shape the pulse for optimum resolution, and there is therefore a trade-off
between resolution and count-rate: long processing time for good resolution results in "pulse
pile-up" in which the pulses from successive photons overlap. Multi-photon events are,
however, typically more drawn out in time (photons did not arrive exactly at the same time)
than single photon events and pulse-length discrimination can thus be used to filter most of
these out. Even so, a small number of pile-up peaks will remain and pile-up correction should
be built into the software in applications that require trace analysis. To make the most
efficient use of the detector, the tube current should be reduced to keep multi-photon events
(before discrimination) at a reasonable level, e.g. 5–20%.
[edit] Processing

Considerable computer power is dedicated to correcting for pulse-pile up and for extraction of
data from poorly resolved spectra. These elaborate correction processes tend to be based on
empirical relationships that may change with time, so that continuous vigilance is required in
order to obtain chemical data of adequate precision.

[edit] Usage

EDX spectrometers are superior to WDX spectrometers in that they are smaller, simpler in
design and have fewer engineered parts. They can also use miniature X-ray tubes or gamma
sources. This makes them cheaper and allows miniaturization and portability. This type of
instrument is commonly used for portable quality control screening applications, such as
testing toys for Lead (Pb) content, sorting scrap metals, and measuring the lead content of
residential paint. On the other hand, the low resolution and problems with low count rate and
long dead-time makes them inferior for high-precision analysis. They are, however, very
effective for high-speed, multi-elemental analysis. Field Portable XRF analysers currently on
the market weigh less than 2 kg, and have limits of detection on the order of 2 parts per
million of Lead (Pb) in pure sand.

Figure 6: Schematic arrangement of wavelength dispersive spectrometer

Chemist operates a goniometer used for X-ray fluorescence analysis of individual grains of
mineral specimens, U.S. Geological Survey, 1958.
[edit] Wavelength dispersive spectrometry

In wavelength dispersive spectrometers (WDX or WDS), the photons are separated by

diffraction on a single crystal before being detected. Although wavelength dispersive
spectrometers are occasionally used to scan a wide range of wavelengths, producing a
spectrum plot as in EDS, they are usually set up to make measurements only at the
wavelength of the emission lines of the elements of interest. This is achieved in two different
ways:

 "Simultaneous" spectrometers have a number of "channels" dedicated to analysis of

a single element, each consisting of a fixed-geometry crystal monochromator, a
detector, and processing electronics. This allows a number of elements to be measured
simultaneously, and in the case of high-powered instruments, complete high-precision
analyses can be obtained in under 30 s. Another advantage of this arrangement is that
the fixed-geometry monochromators have no continuously moving parts, and so are
very reliable. Reliability is important in production environments where instruments
are expected to work without interruption for months at a time. Disadvantages of
simultaneous spectrometers include relatively high cost for complex analyses, since
each channel used is expensive. The number of elements that can be measured is
limited to 15–20, because of space limitations on the number of monochromators that
can be crowded around the fluorescing sample. The need to accommodate multiple
monochromators means that a rather open arrangement around the sample is required,
leading to relatively long tube-sample-crystal distances, which leads to lower detected
intensities and more scattering. The instrument is inflexible, because if a new element
is to be measured, a new measurement channel has to be bought and installed.

 "Sequential" spectrometers have a single variable-geometry monochromator (but

usually with an arrangement for selecting from a choice of crystals), a single detector
assembly (but usually with more than one detector arranged in tandem), and a single
electronic pack. The instrument is programmed to move through a sequence of
wavelengths, in each case selecting the appropriate X-ray tube power, the appropriate
crystal, and the appropriate detector arrangement. The length of the measurement
program is essentially unlimited, so this arrangement is very flexible. Because there is
only one monochromator, the tube-sample-crystal distances can be kept very short,
resulting in minimal loss of detected intensity. The obvious disadvantage is relatively
long analysis time, particularly when many elements are being analysed, not only
because the elements are measured in sequence, but also because a certain amount of
time is taken in readjusting the monochromator geometry between measurements.
Furthermore, the frenzied activity of the monochromator during an analysis program is
a challenge for mechanical reliability. However, modern sequential instruments can
achieve reliability almost as good as that of simultaneous instruments, even in
continuous-usage applications.

[edit] Sample presentation

In order to keep the geometry of the tube-sample-detector assembly constant, the sample is
normally prepared as a flat disc, typically of diameter 20–50 mm. This is located at a
standardized, small distance from the tube window. Because the X-ray intensity follows an
inverse-square law, the tolerances for this placement and for the flatness of the surface must
be very tight in order to maintain a repeatable X-ray flux. Ways of obtaining sample discs
vary: metals may be machined to shape, minerals may be finely ground and pressed into a
tablet, and glasses may be cast to the required shape. A further reason for obtaining a flat and
representative sample surface is that the secondary X-rays from lighter elements often only
emit from the top few micrometers of the sample. In order to further reduce the effect of
surface irregularities, the sample is usually spun at 5–20 rpm. It is necessary to ensure that the
sample is sufficiently thick to absorb the entire primary beam. For higher-Z materials, a few
millimetres thickness is adequate, but for a light-element matrix such as coal, a thickness of
30–40 mm is needed.

Figure 7: Bragg diffraction condition

[edit] Monochromators

The common feature of monochromators is the maintenance of a symmetrical geometry

between the sample, the crystal and the detector. In this geometry the Bragg diffraction
condition is obtained.

The X-ray emission lines are very narrow (see figure 2), so the angles must be defined with
considerable precision. This is achieved in two ways:

 Flat crystal with Soller collimators

The Soller collimator is a stack of parallel metal plates, spaced a few tenths of a millimetre
apart. To improve angle resolution, one must lengthen the collimator, and/or reduce the plate
spacing. This arrangement has the advantage of simplicity and relatively low cost, but the
collimators reduce intensity and increase scattering, and reduce the area of sample and crystal
that can be "seen". The simplicity of the geometry is especially useful for variable-geometry
monochromators.
Figure 8: Flat crystal with Soller collimators

Figure 9: Curved crystal with slits

 Curved crystal with slits

The Rowland circle geometry ensures that the slits are both in focus, but in order for the
Bragg condition to be met at all points, the crystal must first be bent to a radius of 2R (where
R is the radius of the Rowland circle), then ground to a radius of R. This arrangement allows
higher intensities (typically 8-fold) with higher resolution (typically 4-fold) and lower
background. However, the mechanics of keeping Rowland circle geometry in a variable-angle
monochromator is extremely difficult. In the case of fixed-angle monochromators (for use in
simultaneous spectrometers), crystals bent to a logarithmic spiral shape give the best focusing
performance. The manufacture of curved crystals to acceptable tolerances increases their price
considerably.

[edit] Analysis Lines

The spectral lines used for chemical analysis are selected on the basis of intensity,
accessibility by the instrument, and lack of line overlaps. Typical lines used, and their
wavelengths, are as follows:

tabel

Other lines are often used, depending on the type of sample and equipment available.

[edit] Crystals

The desirable characteristics of a diffraction crystal are:

 High diffraction intensity

 High dispersion
  Narrow diffracted peak width

 High peak-to-background

 Absence of interfering elements

 Low thermal coefficient of expansion

 Stability in air and on exposure to X-rays

 Ready availability

 Low cost

Crystals with simple structure tend to give the best diffraction performance. Crystals
containing heavy atoms can diffract well, but also fluoresce themselves, causing interference.
Crystals that are water-soluble, volatile or organic tend to give poor stability.

Commonly used crystal materials include LiF (lithium fluoride), ADP (ammonium
dihydrogen phosphate), Ge (germanium), graphite, InSb (indium antimonide), PE (tetrakis-
(hydroxymethyl)-methane: penta-erythritol), KAP (potassium hydrogen phthalate), RbAP
(rubidium hydrogen phthalate) and TlAP (thallium(I) hydrogen phthalate). In addition, there
is an increasing use of "layered synthetic microstructures", which are "sandwich" structured
materials comprising successive thick layers of low atomic number matrix, and monoatomic
layers of a heavy element. These can in principle be custom-manufactured to diffract any
desired long wavelength, and are used extensively for elements in the range Li to Mg.

Properties of commonly used crystals

min λ max λ thermal

material plane d (nm) intensity durability
(nm) (nm) expansion

LiF 200 0.2014 0.053 0.379 +++++ +++ +++

LiF 220 0.1424 0.037 0.268 +++ ++ +++

LiF 420 0.0901 0.024 0.169 ++ ++ +++

ADP 101 0.5320 0.139 1.000 + ++ ++

Ge 111 0.3266 0.085 0.614 +++ + +++

graphite 001 0.3354 0.088 0.630 ++++ + +++

InSb 111 0.3740 0.098 0.703 ++++ + +++

PE 002 0.4371 0.114 0.821 +++ +++++ +

KAP 1010 1.325 0.346 2.490 ++ ++ ++

RbAP 1010 1.305 0.341 2.453 ++ ++ ++

Si 111 0.3135 0.082 0.589 ++ + +++

TlAP 1010 1.295 0.338 2.434 +++ ++ ++

YB66 400 0.586          

6 nm LSM - 6.00 1.566 11.276 +++ + ++

[edit] Detectors

Detectors used for wavelength dispersive spectrometry need to have high pulse processing
speeds in order to cope with the very high photon count rates that can be obtained. In addition,
they need sufficient energy resolution to allow filtering-out of background noise and spurious
photons from the primary beam or from crystal fluorescence. There are four common types of
detector:

 gas flow proportional counters

 sealed gas detectors

 scintillation counters

 semiconductor detectors
Figure 10: Arrangement of gas flow proportional counter

Gas flow proportional counters are used mainly for detection of longer wavelengths. Gas
flows through it continuously. Where there are multiple detectors, the gas is passed through
them in series, then led to waste. The gas is usually 90% argon, 10% methane ("P10"),
although the argon may be replaced with neon or helium where very long wavelengths (over
5 nm) are to be detected. The argon is ionised by incoming X-ray photons, and the electric
field multiplies this charge into a measurable pulse. The methane suppresses the formation of
fluorescent photons caused by recombination of the argon ions with stray electrons. The
anode wire is typically tungsten or nichrome of 20–60 μm diameter. Since the pulse strength
obtained is essentially proportional to the ratio of the detector chamber diameter to the wire
diameter, a fine wire is needed, but it must also be strong enough to be maintained under
tension so that it remains precisely straight and concentric with the detector. The window
needs to be conductive, thin enough to transmit the X-rays effectively, but thick and strong
enough to minimize diffusion of the detector gas into the high vacuum of the monochromator
chamber. Materials often used are beryllium metal, aluminised PET film and aluminised
polypropylene. Ultra-thin windows (down to 1 μm) for use with low-penetration long
wavelengths are very expensive. The pulses are sorted electronically by "pulse height
selection" in order to isolate those pulses deriving from the secondary X-ray photons being
counted.

Sealed gas detectors are similar to the gas flow proportional counter, except that the gas does
not flow though it. The gas is usually krypton or xenon at a few atmospheres pressure. They
are applied usually to wavelengths in the 0.15–0.6 nm range. They are applicable in principle
to longer wavelengths, but are limited by the problem of manufacturing a thin window
capable of withstanding the high pressure difference.

Scintillation counters consist of a scintillating crystal (typically of sodium iodide doped with
thallium) attached to a photomultiplier. The crystal produces a group of scintillations for each
photon absorbed, the number being proportional to the photon energy. This translates into a
pulse from the photomultiplier of voltage proportional to the photon energy. The crystal must
be protected with a relatively thick aluminium/beryllium foil window, which limits the use of
the detector to wavelengths below 0.25 nm. Scintillation counters are often connected in
series with a gas flow proportional counter: the latter is provided with an outlet window
opposite the inlet, to which the scintillation counter is attached. This arrangement is
particularly used in sequential spectrometers.

Semiconductor detectors can be used in theory, and their applications are increasing as their
technology improves, but historically their use for WDX has been restricted by their slow
response (see EDX).
A glass "bead" specimen for XRF analysis being cast at around 1100 °C in a Herzog
automated fusion machine in a cement plant quality control laboratory. 1 (top): fusing, 2:
preheating the mould, 3: pouring the melt, 4: cooling the "bead"

[edit] Extracting analytical results

At first sight, the translation of X-ray photon count-rates into elemental concentrations would
appear to be straightforward: WDX separates the X-ray lines efficiently, and the rate of
generation of secondary photons is proportional to the element concentration. However, the
number of photons leaving the sample is also affected by the physical properties of the
sample: so-called "matrix effects". These fall broadly into three categories:
  X-ray absorption

 X-ray enhancement

 sample macroscopic effects

All elements absorb X-rays to some extent. Each element has a characteristic absorption
spectrum which consists of a "saw-tooth" succession of fringes, each step-change of which
has wavelength close to an emission line of the element. Absorption attenuates the secondary
X-rays leaving the sample. For example, the mass absorption coefficient of silicon at the
wavelength of the aluminium Kα line is 50 m²/kg, whereas that of iron is 377 m²/kg. This
means that a given concentration of aluminium in a matrix of iron gives only one seventh of
the count rate compared with the same concentration of aluminium in a silicon matrix.
Fortunately, mass absorption coefficients are well known and can be calculated. However, to
calculate the absorption for a multi-element sample, the composition must be known. For
analysis of an unknown sample, an iterative procedure is therefore used. It will be noted that,
to derive the mass absorption accurately, data for the concentration of elements not measured
by XRF may be needed, and various strategies are employed to estimate these. As an
example, in cement analysis, the concentration of oxygen (which is not measured) is
calculated by assuming that all other elements are present as standard oxides.

Enhancement occurs where the secondary X-rays emitted by a heavier element are
sufficiently energetic to stimulate additional secondary emission from a lighter element. This
phenomenon can also be modelled, and corrections can be made provided that the full matrix
composition can be deduced.

Sample macroscopic effects consist of effects of inhomogeneities of the sample, and

unrepresentative conditions at its surface. Samples are ideally homogeneous and isotropic, but
they often deviate from this ideal. Mixtures of multiple crystalline components in mineral
powders can result in absorption effects that deviate from those calculable from theory. When
a powder is pressed into a tablet, the finer minerals concentrate at the surface. Spherical grains
tend to migrate to the surface more than do angular grains. In machined metals, the softer
components of an alloy tend to smear across the surface. Considerable care and ingenuity are
required to minimize these effects. Because they are artifacts of the method of sample
preparation, these effects can not be compensated by theoretical corrections, and must be
"calibrated in". This means that the calibration materials and the unknowns must be
compositionally and mechanically similar, and a given calibration is applicable only to a
limited range of materials. Glasses most closely approach the ideal of homogeneity and
isotropy, and for accurate work, minerals are usually prepared by dissolving them in a borate
glass, and casting them into a flat disc or "bead". Prepared in this form, a virtually universal
calibration is applicable.

Further corrections that are often employed include background correction and line overlap
correction. The background signal in an XRF spectrum derives primarily from scattering of
primary beam photons by the sample surface. Scattering varies with the sample mass
absorption, being greatest when mean atomic number is low. When measuring trace amounts
of an element, or when measuring on a variable light matrix, background correction becomes
necessary. This is really only feasible on a sequential spectrometer. Line overlap is a common
problem, bearing in mind that the spectrum of a complex mineral can contain several hundred
measurable lines. Sometimes it can be overcome by measuring a less-intense, but overlap-free
line, but in certain instances a correction is inevitable. For instance, the Kα is the only usable
line for measuring sodium, and it overlaps the zinc Lβ (L2-M4) line. Thus zinc, if present,
must be analysed in order to properly correct the sodium value.

[edit] Other spectroscopic methods using the same principle

It is also possible to create a characteristic secondary X-ray emission using other incident
radiation to excite the sample:

 electron beam: electron microprobe (or Castaing microprobe);

 ion beam: particle induced X-ray emission (PIXE).

When radiated by an X-ray beam, the sample also emits other radiations that can be used for
analysis:

 electrons ejected by the photoelectric effect: X-ray photoelectron spectroscopy (XPS),

also called electron spectroscopy for chemical analysis (ESCA)

The de-excitation also ejects Auger electrons, but Auger electron spectroscopy (AES)
normally uses an electron beam as the probe.

Confocal microscopy X-ray fluorescence imaging is a newer technique that allow control over
depth, in addition to horizontal and vertical aiming, for example, when analyzing buried
layers in a painting.[3]

[edit] Instrument qualification

A 2001 review,[4] addresses the application of portable instrumentation from QA/QC

perspectives. It provides a guide to the development of a set of SOPs if regulatory compliance
guidelines are not available.