X-Ray Fluorescence (XRF) Spectrometer

X-Ray Fluorescence (XRF) Spectrometer

X-ray fluorescence (XRF) is used to detect and measure the concentration of elements in substances. Fluorescence is the phenomena of absorbing incoming radiation and reradiating it as lower-energy radiation. X-rays are part of the electromagnetic spectrum with energies ranging from 0.1 keV to 100 keV (Fig 1a). X-rays are produced by one of the three mechanisms namely (i) deceleration of high velocity electrons in the vicinity of a target nucleus, (ii) atomic transitions between discrete energy levels, and (iii) the radioactive decay of some atomic nuclei. Each mechanism leads to a typical spectrum.

Fig 1 Electromagnetic spectrum and simplified figure of an X-ray tube

X-rays can be seen as electromagnetic waves with their associated wavelengths, or as beams of photons with associated energies. Both views are correct, but one or the other is easier to understand depending on the phenomena. Other electromagnetic waves include light, radio waves and gamma-rays. Fig 1a shows that X-rays have wavelengths and energies between gamma-rays and ultra violet light. The wavelengths of X-rays are in the range from 0.01 nm (nano metre) to 10 nm, which corresponds to energies in the range from 0.125 keV to 125 keV. The wavelength of X-rays is inversely proportional to its energy.

Normally, an X-ray tube is used for the generation of X-rays by bombarding highly accelerated electrons on a heavy metal target. X-ray production in this manner results from the first two of the mechanisms listed above. A schematic for producing X-rays is shown in Fig 1b. Electrons are ejected thermally from a filament behind the cathode and accelerated towards the heavy metal anode by a high voltage (in kilovolts range). Upon hitting the target (anode), these fast electrons decelerate and lose energy in the form of high energy photons. These photons are the X-rays, with precise value of energy depending on the kind of target used.

The intensity of the X-rays produced is dependent on the number of electrons hitting the target (or tube current), which in turn depends on the temperature of the filament emitting the electrons. However, increasing the X-ray tube current at a constant X-ray tube voltage increases the X-ray intensity without affecting the energy distribution. The production of X-rays is carried out by two different atomic processes, the X-ray fluorescence and the bremsstrahlung radiation.

X-ray fluorescence is the emission of characteristic or secondary X-rays from a material which has been excited by bombarding with high energy electrons, or other X-ray or gamma-ray photons. If the incident particle has enough energy, it can knock out an orbital electron out of the inner shell of the target atom. To fill the vacancy, one of the electrons from the higher shells then jumps to the inner shell, emitting in the process, a photon with energy equal to the difference in binding energy of the two shells. The process is shown in Fig 2a, which shows the characteristic emission of K and L X-rays as a result of electronic transition from L to K and M to L shells respectively. The X-ray fluorescence produces an emission spectrum of X-rays at discrete energies. These emission spectral lines depend on the target element and hence are called characteristic or fluorescent X-rays. These spectra can be used to identify the elements by comparing the peak’s energy with the element’s binding energy.

Fig 2 Fluorescence and Bremsstrahlung radiations

Bremsstrahlung (‘Brems’ is German for decelerate, ‘strahlung’ is for radiation) is a German word for braking radiation. Accelerating charges give off electromagnetic radiation. In an X-ray tube, shown in Fig 1b, electrons travel from cathode with high speed towards the anode and penetrate the anode material. When these electrons pass in close proximity to the strong electric field of the nucleus, they get deflected and are decelerated by the attractive force from the nucleus, hence radiating X-rays, which are called braking or bremsstrahlung radiation. The production of these X-rays is shown in Fig 2b, which shows a decelerating electron emitting bremsstrahlung X-rays. This gives off a continuous distribution of radiation which becomes more intense and shifts toward higher frequencies when the energy of the bombarding electrons or the tube voltage (kV) is increased.

In case of the Bremsstrahlung spectrum, an electrostatic field exists around the nucleus in which electrons experience the braking force. The nuclear field can be imagined as a target with the actual nucleus located in the centre. An electron striking anywhere within the target experiences a braking force and produces an X-ray photon. Now, the electrons striking closest to the centre are subjected to the greatest force and lose the most energy to produce the highest energy photons while the electrons hitting the outer zones experience a weaker force and produce lower energy photons. The outer zones capture more electrons and create more photons.

There are three main interactions when X-rays contact matter. They are (i) fluorescence, (ii) Compton scatter, and (iii) Rayleigh scatter. If a beam of X-ray photons is directed towards a slab of material a fraction is transmitted through, a fraction is absorbed (producing fluorescent radiation), and a fraction is scattered back. Scattering can occur with a loss of energy and without a loss of energy. The first is known as Compton scatter and the second is called Rayleigh scatter. The fluorescence and the scatter depend on the thickness (t), density (d), and composition of the material, and on the energy of the X-rays as shown in Fig 3a.

Fig 3 X-ray radiation

The classical model of an atom is a nucleus with positively charged protons and non-charged neutrons, surrounded by electrons grouped in shells or orbitals. The innermost shell is called the K-shell, followed by L-shells, M-shells etc. as one moves outwards. The L-shell has 3 sub-shells called LI, LII, and LIII. The M-shell has 5 subshells MI, MII, MIII, MIV, and MV. The K-shell can contain 2 electrons, the L-shell, 8 and the M-shell 18. The energy of an electron depends on the shell it occupies, and on the element to which it belongs.

When irradiating an atom, particles such as X-ray photons and electrons with sufficient energy can expel an electron from the atom as shown in Fig 3b. This produces a ‘hole’ in a shell. In the example at Fig 3b, a hole is created in the K-shell, putting the atom in an unstable excited state with a higher energy. The ‘hole’ is also called the initial vacancy. The atom wants to restore the original configuration, and this is done by transferring an electron from an outer shell such as the L-shell to the hole in the K-shell. An L-shell electron has a higher energy than a K-shell electron, and when an L-shell electron is transferred to the K-shell, the energy surplus can be emitted as an X-ray photon. In a spectrum, this is seen as a line.

The energy of the emitted X-rays depends on the difference in energy between the shell with the initial hole and the energy of the electron which fills the hole (in the example in Fig 3b, the difference between the energy of the K and the L shell). Each atom has its specific energy levels, so the emitted radiation is characteristic of that atom. An atom emits more than a single energy (or line) since different holes can be produced and different electrons can fill these. The collection of emitted lines is characteristic of the element and can be considered a fingerprint of the element.

To expel an electron from an atom, the X-rays are to have a higher energy level than the binding energy of the electron. If an electron is expelled, the incoming radiation is absorbed, and the higher is the absorption, the higher is the fluorescence. If, on the other hand, the energy is too high, several photons ‘pass’ the atom and only a few electrons are removed.

High energies are hardly absorbed and they produce low fluorescence. If the energy of the incident photons is lower and comes closer to the binding energy of the K-shell electrons, more and more of the radiation is absorbed. The highest yield is reached when the energy of the photon is just above the binding energy of the electron to be expelled. If the energy becomes lower than the binding energy, a jump or edge can be seen i.e., the energy is too low to expel electrons from the corresponding shell, but is too high to expel electrons from the lower energetic shells.

Not all initial vacancies created by the incoming radiation produce fluorescent photons. Emission of an Auger electron is another process which can take place. The fluorescent yield is the ratio of the emitted fluorescent photons and the number of initial vacancies. The fluorescence yield for K- and L-lines is the function of the atomic number Z. The yield is low for the very light elements, explaining why it is so difficult to measure these elements.

There are several ways to indicate different lines. The Siegbahn and IUPAC notations are the two most frequently used. The Siegbahn notation indicates a line by the symbol of an element followed by the name of the shell where the initial hole is plus a Greek letter (alpha, beta, gamma, etc.) indicating the relative intensity of the line. For example, Fe K alpha is the strongest iron line because of an expelled K electron. The Siegbahn notation however does indicate which shell the electron comes from that fills the hole.

In the IUPAC notation, a line is indicated by the element and the shell where the initial hole was, followed by the shell where the electron comes from which fills this hole. For example, Cr KLIII is chromium radiation because of a hole produced in the K-shell filled by an electron in the LIII-shell. Normally, K-lines are more intense than L-lines, which are more intense than M-lines, and so on.

X-ray fluorescence (XRF) spectrometry is an analytical method to determine the chemical composition of all kinds of materials. The materials can be in solid, liquid, powder, filtered or other form. XRF can also sometimes be used to determine the thickness and composition of layers and coatings. The method is fast, accurate, and non-destructive, and normally needs only a minimum of sample preparation. Applications are very broad and include the metal, cement, oil, polymer, plastic and food industries, along with mining, mineralogy and geology, and environmental analysis of water and waste materials.

The precision and reproducibility of XRF analysis is very high. Very accurate results are possible when good standard samples are available, but also in applications where no specific standards can be found. The measurement time depends on the number of elements to be determined and the needed accuracy, and varies between seconds and 30 minutes. The analysis time after the measurement is only a few seconds. Fig 4 shows a typical spectrum of a soil sample measured with EDXRF – the peaks are clearly visible. The positions of the peaks determine the elements present in the sample, while the heights of the peaks determine the concentrations.

Fig 4 Typical spectrum of a soil sample measured with an EDXRF spectrometer

Theory of XRF spectrometry

In XRF, X-rays produced by a source, irradiate the sample. In the majority of the cases, the source is an X-ray tube but alternatively it could be a synchrotron or a radioactive material. The elements present in the sample emit fluorescent X-ray radiation with discrete energies (equivalent to the colours in optical light) which are characteristic for these elements. A different energy is equivalent to a different colour. By measuring the energies (determining the colours) of the radiation emitted by the sample, it is possible to determine which elements are present. This step is called qualitative analysis. By measuring the intensities of the emitted energies (colours), it is possible to determine how much of each element is present in the sample. This step is called quantitative analysis.

For reaching the atoms inside the sample, the X-rays have to pass through the layer above it, and this layer absorbs a part of the incoming radiation. The characteristic radiation produced also has to pass through this layer to leave the sample, and again part of the radiation is absorbed. The magnitude of the absorption of incoming and fluorescent X-rays depends on the energy of the radiation, the path length ‘l’ of the atoms which have to be passed, and the density of the sample (Fig 5a). The absorption increases as the path length, density and atomic number of the elements in the layer increase, and as the energy of the radiation decreases.

The absorption can be so high that elements deep in the sample are not reached by the incoming radiation or the characteristic radiation can no longer leave the sample. This means that only elements close to the surface are measured. The incoming radiation is made up of X-rays, and the characteristic radiation emitted by the atoms in the sample itself is also X-rays. These fluorescent X-rays are sometimes able to expel electrons from other elements in the sample. This, as with the X-rays coming from the source, results in fluorescent radiation. The characteristic radiation produced directly by the X-rays coming from the source is called primary fluorescence, while that produced in the sample by primary fluorescence of other atoms is called secondary fluorescence (Fig 5b).

Fig 5 Absorption of X-rays and primary and secondary X-rays

An XRF spectrometer measures the sum of the primary and secondary fluorescence, and it is impossible to distinguish between the two contributions. The contribution of secondary fluorescence to the characteristic radiation can be considerable (of the order of 20 %). Similarly, tertiary and even higher order radiation can occur. In almost all practical situations, these are negligible, but in very specific cases, these can reach values of 3 %. As the sample gets thicker and thicker, more radiation is absorbed. Eventually radiation produced in the deeper layers of the sample is no longer able to leave the sample. When this limit is reached depends on the material and on the energy of the radiation. When a sample is measured, only the atoms within the analysis depth are analyzed. If samples and standards with various thicknesses are analyzed, the thickness has to be taken into account.

A part of the incoming X-rays is scattered (reflected) by the sample instead of producing characteristic radiation. Scatter happens when a photon hits an electron and bounces away. The photon loses a fraction of its energy, which is taken in by the electron as shown in Fig 6a. It can be compared with one billiard ball colliding with another. After the collision, the first ball loses a part of its energy to the ball which has been hit. The fraction which is lost depends on the angle at which the electron (ball) has been hit. This type of scatter is called Compton or incoherent scatter (Fig 6a).

Fig 6 Compton and Rayleigh scatters

Another phenomenon is called Rayleigh scatter. This happens when photons collide with strongly bound electrons. The electrons stay in their shell but start oscillating at the frequency of the incoming radiation. Because of this oscillation, the electrons emit radiation at the same frequency (energy) as the incoming radiation. This gives the impression that the incoming radiation is reflected (scattered) by the atom. This type of scatter is known as Rayleigh or coherent scatter (Fig 6b).

Rayleigh scatter samples with light elements give rise to high Compton scatter and low Rayleigh scatter since they have several loosely bound electrons. When the elements get heavier the scatter reduces. For the heavy elements, the Compton scatter disappears completely, and only Rayleigh scatter remains. The spread of energy in the Compton scatter is larger than for Rayleigh scatter. In a spectrum this can be observed by the Compton peak being wider than the Rayleigh peak.

Polarization X-rays are electromagnetic waves with electric and magnetic components. The amplitude of the electromagnetic waves corresponds to the intensity of the X-rays. Electromagnetic waves are transversal waves, which means that the electrical component is perpendicular to the propagation direction. This is similar to waves in water. If a stone is thrown into water, the waves are vertical but the propagation direction is horizontal. X-rays are said to be linear polarized if the electrical components are all in one plane. If the electrical component has no preferred direction, then the waves are called non-polarized.

An electrical component pointing in any direction can always be resolved into two perpendicular directions. Electrical component resolved in horizontal and vertical components If non-polarized X-rays are reflected (scattered) by a sample through 90 degrees, the reflected X-rays are polarized in one direction. The vertical electrical component is not reflected since this points to the new propagation direction. What remains after one reflection is the horizontal component alone, and the scattered X-rays are polarized horizontally. If the X-rays are scattered again but perpendicular to the previous direction then in the second reflection the horizontal component is not reflected because it points in the new propagation direction. Nothing is left from the incoming radiation after two perpendicular reflections. This feature is used in EDXRF spectrometers to eliminate the background profile from a spectrum.

XRF spectrometer systems can be divided into two main groups namely (i) energy dispersive systems (EDXRF), and (ii) wavelength dispersive systems (WDXRF). The elements which can be analyzed and their detection levels mainly depend on the spectrometer system used. The elemental range for EDXRF goes from sodium to uranium (Na to U). For WDXRF it is even wider, from beryllium to uranium (Be to U). The concentration range goes from (sub) ppm levels to 100 %. Normally speaking, the elements with high atomic numbers have better detection limits than the lighter elements. Fig 7 shows the basic designs of EDXRF and WDXRF spectrometers.

Fig 7 shows the basic designs of EDXRF and WDXRF spectrometers

The basic concept for all spectrometers is a source, a sample, and a detection system. The source irradiates a sample, and a detector measures the radiation coming from the sample. In majority of the cases the source is an X-ray tube. The difference between the two EDXRF and WSDXRF systems is found in the detection system. EDXRF spectrometers have a detector which is able to measure the different energies of the characteristic radiation coming directly from the sample. The detector can separate the radiation from the sample into the radiation from the elements in the sample. This separation is called dispersion. WDXRF spectrometers use an analyzing crystal to disperse the different energies. All radiation coming from the sample falls on the crystal. The crystal diffracts the different energies in different directions, similar to a prism which disperses different colours in different directions.

EDXRF spectrometers can be divided into spectrometers with 2D and 3D optics. Both types have a source and an energy dispersive detector, but the difference is found in the X-ray optical path. For 2D spectrometers, the X-ray path is in one plane, so in 2 dimensions. For the 3D spectrometers, the path is not limited to one plane but involves 3 dimensions. Fig 8 shows working principle of EDXRF spectrometer.

Fig 8 Working principle of EDXRF spectrometer

In the majority pf the XRF applications, the size of the samples is around 10 mm giving the average composition of the samples. For some application the local composition at different spots on the sample is needed like spots on a chip-wafers or on magnetic disks. For other applications, only a very small sample is available like a sliver of paint. Typical needed spot diameters range is between 50 micrometres to a few millimetres (mm). An option is to use pinholes between tube and sample and / or between sample and detector but the sensitivity is very low. In majority of the cases, lenses are used for small spot analysis.

In the case of EDXRF spectrometers with 2D optics, in its the simplest configuration, the tube irradiates the sample directly, and the fluorescence coming from the sample is measured with an energy dispersive detector. An alternative is to place a secondary target between the tube and the sample. In this case, the tube irradiates the secondary target and this target emits its characteristic radiation. The advantage of a secondary target is that it emits (almost) monochromatic radiation but its disadvantage is that energy is lost.

Use of different secondary targets can achieve optimum excitation for all elements. The detector is able to measure the energies of the incoming radiation directly. Besides the fluorescence, scattered tube radiation reaches the detector, which results in a background profile and background noise. Due to this background, it is difficult to detect low peaks and as a result to determine low concentrations. The X-ray path is in one plane, so is 2-dimensional, and the X-ray optics are called 2D optics. When the same sample is measured with 3D optics, then the background with 3D optics is considerably lower.

In the EDXRF spectrometers with 3D optics, the X-ray path is not in one plane but in two perpendicular planes. The tube irradiates a secondary target which emits its characteristic X-rays and scatters a part of the incoming X-rays. The radiation coming from the target is used to irradiate the sample, so for the sample the target behaves like a source. The sample emits its characteristic radiation, which is measured by an energy dispersive detector.

The energy dispersive spectrometer with 3D optics and indirect excitation geometry has the advantage of that the scattered tube radiation cannot reach the detector because of polarization. To reach the detector, the tube radiation is required to scatter in two perpendicular directions, but the X-rays vanish after two perpendicular reflections. As a consequence, the radiation coming from the tube does not reach the detector. This results in a very low background to the spectrum and makes it possible to detect very weak peaks, and hence to determine very low concentrations. The characteristic radiation of the target is partly scattered by the sample and reaches the detector. This radiation is scattered in only one direction and so it does not vanish. Hence, the background to a spectrum measured with 3D optics is considerably lower than the same spectrum measured with 2D optics.

In case of WDXRF spectrometers, the first part of the WDXRF spectrometer is equivalent to an EDXRF spectrometer with 2D optics and without a secondary target. The tube irradiates a sample and the radiation coming from the sample is detected. The detection system is however different from EDXRF spectrometers. For WDXRF, the detection system is a set of collimators, a diffraction crystal, and a detector. The X-rays coming from the sample fall on the crystal, and the crystal diffracts (reflects) the X-rays with different wavelengths (energies) in different directions. (This is equivalent to a prism which separates white light into all the different colours). By placing the detector at a certain angle, the intensity of X-rays with a certain wavelength can be measured. It is also possible to mount the detector on a goniometer and move it through an angular range to measure the intensities of several different wavelengths.

Spectrometers which use a moving detector on a goniometer, are called sequential spectrometers since they measure the intensities of the different wavelengths one after another. Simultaneous spectrometers are equipped with a set of fixed detection systems. Each detection system has its crystal and detector, and each system measures the radiation of a specific element. The intensities are measured all at the same time, explaining why these are called simultaneous spectrometers. Combined systems having a moving detector and fixed detectors are also manufactured. Simultaneous WDXRF spectrometer are with crystals and detectors for different elements. EDXRF and WDXRF spectrometers have their advantages and disadvantages. The comparison is shown in Tab 1.

Tab 1 Comparison of EDXRF and WDXRF spectrometers
Elemental rangeSodium (Na) ———–Uranium (U)Beryllium (Be) ———– Uranium (U)
Detection limitLess optimal for light elementsGood for ‘Be’ and all heavier elements
Good for heavy elements
SensivityLess optimal for light elementsReasonable for light elements
Good for heavy elementsGood for heavy elements
ResolutionLess optimal for light elementsGood for light elements
Good for heavy elementsLess optimal for heavy elements
CostsRelatively inexpensiveRelatively expensive
Power consumption5 W to 1,000 W200 W to 4,000 W
MeasurementSimultaneousSequential /Simultaneous
Critical moving partsNilCrystal, Goniometer

The basic design of an X-ray tube is shown in Fig 1. It contains a filament (wire) and an anode (target) placed in a vacuum housing. An electrical current heat up the filament and electrons are emitted. A high voltage (20 kV to 100 kV) is applied across the filament and the anode, and this high voltage accelerates the electrons towards the anode. When the electrons hit the anode, they are decelerated, which causes the emission of X-rays. This radiation is called Bremsstrahlung radiation. The energy and intensity of the emitted X-rays is uniform, but a spectrum of energies each with its own intensity is emitted. This part of the spectrum is frequently called the continuum, since it is a continuous band of emitted energies.

A fraction of the electrons which hit the atoms in the anode expels electrons from these atoms, causing emission of characteristic radiation. The energy of this radiation is determined by the element(s) in the anode. The X-rays emitted by the anode can leave the tube through a beryllium (Be) window. The energy of the X-rays emitted cannot be higher than the applied voltage, and the X-rays with very low energies are not capable of passing through the Be window.

The continuum of an X-ray tube depends on the applied kV, the mA, and on the material used for the anode. These tubes are called side window tubes since the Be window is on the side of the tube housing. It is also possible to rearrange the filament and the anode, and have a window at the end of the tube (an end window tube). An alternative design is also there. In alternative design, the electrons hit the anode on one side, the X-rays pass through the anode leaving it at the opposite side, and the radiation leaves the tube through the Be window. These tubes are called target transmission tubes.

A secondary target is that target which is irradiated by a source and emits its characteristic radiation in a similar way to the target (anode) in the tube. It also scatters a part of the incoming radiation. The target acts as a source, and the radiation coming from the target is used to irradiate the sample. There are three types of secondary targets namely (i) fluorescent targets, (ii) Barkla targets, and (iii) Bragg targets.

Fluorescent targets use the fluorescence of elements in the target to excite the sample. These targets also scatter the tube radiation, but the fluorescence dominates. Scatter is low since the targets predominantly contain heavy elements. The tube irradiates the target, and the element(s) in the target emit their characteristic fluorescent radiation. This radiation falls on the sample, causing fluorescent radiation. To achieve the highest fluorescence in the sample, the energy of the X-rays coming from the target is to be just above the binding energy of the electrons of the elements in the sample. Spectrometers can be equipped with a set of different targets, and optimum fluorescence is achieved by selecting the correct target.

Barkla targets use scattered tube radiation to excite the sample. These targets also fluorescence but the energy or intensity of these lines is too low to excite elements in the sample. Barkla targets are made of light elements like Al2O3 and B4C, since these give the highest scattered radiation. Barkla targets scatter a wide energy spectrum and can be used to measure a large range of elements. Normally Barkla targets measure the heavier elements.

Bragg targets are crystals which reflect only one specific energy in a certain direction. By mounting the crystal between the tube and the sample, it is possible to select a single tube line to irradiate the sample, with no other radiation diffracted towards the sample. This reduces the background level and improve the detection limit. If the spacing of the planes in the crystal is such that the tube line is diffracted at an angle of 90 degrees, it can be used in 3D optics as a perfect polarizer.

Different types of detectors are used in XRF. EDXRF mainly uses solid-state detectors whereas WDXRF uses gas-filled detectors and scintillation detectors. The EDXRF detector is a wide-range detector and measures all elements from Na up to U. Gas-filled detectors measure elements from Be up to Cu and the scintillation detector from Cu up to U. All these detectors produce an electrical pulse when an X-ray photon enters the detector, and the height of this pulse is proportional to the energy of the incoming photon. The pulses are amplified and then counted by a multi-channel analyzer (MCA).

There are three important properties of detection systems namely (i) resolution, (ii) sensitivity, and (iii) dispersion. Resolution is the ability of the detector to distinguish between different energy levels. A high resolution means that the detector can distinguish between several different energies. Sensitivity indicates how efficiently incoming photons are counted. If for instance a detector is very thin, incoming photons can pass it without producing a pulse. Sensitivity is high if the ratio of the number of pulses against the number of incoming photons is high. Dispersion indicates the ability of the detector to separate X-rays with different energies. A high dispersion means that different energies are separated well.

The multi-channel analyzer counts how several pulses are generated in each height interval. The number of pulses of a certain height gives the intensity of the corresponding energy. The ability of the detector and the multi-channel analyzer to distinguish between different energies is called the resolution. A multi-channel analyzer makes a histogram of the energy of the detected photons.

Strictly speaking, a WDXRF only has to count pulses and does not have to distinguish between their heights since the crystal has already selected X-rays with one specific energy. In practical situations the multi-channel analyzer for a WDXRF detector is able to distinguish 100 to 255 different energy levels. In EDXRF spectrometers, the detector and multi-channel analyzer are able to distinguish between 1,000 and 16,000 different energy levels. This is sufficient to analyze spectra and to separate the radiation from the various elements in a sample.

The solid-state detector is constructed with a body of silicon, germanium, or other semiconducting material. A beryllium window allows X-ray photons to enter the detector. On the front, there is a dead layer, and on the back, there is a collecting plate. Photons pass through the window and penetrate the body of the detector to produce electron-hole pairs in the body. The number of electrons depends on the energy of the incoming photons. The higher is the energy. the more are the electrons produced. A high voltage (1,500 V) across the dead layer and the back means that the electrons are attracted to the back. When the electrons reach the back, the potential drops and gives a negative pulse. The depth of the pulse is proportional to the number of electrons and hence proportional to the energy of the incoming radiation. After amplification, a multi-channel analyzer counts the pulses.

Gas-filled detector is constructed from a metal (frequently aluminium) cylinder at earth potential with a co-axial 50 mm tungsten anode wire running down its length. The anode wire is raised to a high voltage (1,300 V to 2,000 V). A beryllium entrance window allows X-ray photons to enter the detector, which is filled with an inert counting gas (Ne, Ar, Kr or Xe, and occasionally He). When an X-ray photon enters the detector, it creates a small cloud of electrons, which are attracted by the wire. When the electrons reach the wire, they cause a drop in voltage. This is registered as a negative pulse in the amplifier. The number of electrons is proportional to the energy of the incoming radiation, and hence the height of the pulse. A multi-channel analyzer counts the pulses produced by the detector. The Be window is to be thin to allow photons to enter the detector. If it is too thin, however, gas can penetrate the window. The detector is hence sometimes connected to an Ar gas bottle to replace the lost Ar. Such detectors are called flow detectors, and those with thicker windows to prevent gas from escaping are called sealed detectors.

Scintillation detector consists of four main parts namely (i) a beryllium window, (ii) sodium iodide (NaI) scintillator crystal, (iii) a photo multiplier tube with (iv) Sb/Cs photo cathode. X-ray photons pass through the beryllium window and hit the scintillator crystal, which produces a blue light flash. The light photons travel into the photomultiplier tube and impact on the photo cathode producing a burst of electrons, which are accelerated through a series of dynodes to the anode. When the resulting electrons reach the anode, they cause a drop in voltage. This is registered as a negative voltage pulse in the amplifier. The number of electrons is proportional to the energy of the incoming radiation, and hence the height of the pulse. A multi-channel analyzer counts the pulses produced by the detector.

Detectors suffer from two artefacts namely (i) escape peaks, and (ii) pile-up peaks. The atoms in the detector (Ar, Si, Ge) also emits their own characteristic radiation when hit by the incoming X-rays. Because of this, the incoming X-rays loses a part of their energy, which is equivalent to the energy of the line of the detector element. For Si this is around 1.7 keV, for Ge 10 keV, and for Ar about 3 keV. Besides counting photons with the initial energy, the detector also hence counts a fraction with a lower energy. In the spectrum, this results in two peaks namely (i) a main peak, and (ii) an escape peak. Pile-up or sum peaks are the result of two photons entering the detector simultaneously. Both photons produce a cloud of electrons, but they are detected as one large cloud. The energy detected is equivalent to the sum of the two initial energies. Pile-up peaks and escape peaks appearing in a spectrum can interfere with other peaks, or lead to wrong conclusions about the elements present in the sample.

The resolution of gas-filled and scintillation detectors is very poor, and they are not suited for energy dispersive spectrometers. They can however be used in wavelength dispersive spectrometers since, in these instruments, the resolution is achieved by the diffraction crystal. The sensitivity depends on the type of detector and on the energy of the incoming X-rays. Gas-filled detectors have a high sensitivity for low energies and a low sensitivity to high energies and are best suited for detecting lower energies. The opposite applies for scintillation detectors, which are better suited to high energies than to low energies. Solid-state detectors in general have a very low sensitivity to low energies and high resolution for the higher energies. EDXRF spectrometers normally use solid-state detectors, while WDXRF spectrometers use a combination of gas-filled and scintillation detectors.

Filters are placed between the source and the sample. They reduce the intensity of interfering lines and background, and hence improve the signal-to-noise ratio. In 2D optics, a fraction of the scattered tube spectrum reaches the detector and is present in the measured spectrum. In some cases, the tube lines of the spectrum interfere with lines coming from the sample (for example, the Rh K lines coming from the tube can interfere with the Ag and Cd K lines coming from the sample). By mounting a filter between tube and sample, the tube lines are absorbed and the lines coming from the sample are not.

When the background radiation can be reduced more than the analytical lines, then, the analytical lines can be determined with higher precision, and with better detection limits. Commonly used filter materials are aluminium and brass with a thickness between 100 micrometres and 1,000 micrometres, depending on the tube lines which have to be filtered out. Filter is used to reduce background and improve detection limit If the intensity is too high for the detector and it becomes saturated, a filter can absorb part of the radiation to prevent saturation.

A crystal can be seen as a stack of thin layers all having the same thickness. If a parallel beam of X-rays falls on the crystal, the first layer reflects a fraction of the X-rays. The remaining radiation penetrates the crystal and is reflected by the subsequent layers. If the difference in path length between reflections from layers is a multiple of half the wavelength of the radiation, the two reflected beams vanish. If the difference is exactly an integer times the wavelength, the two reflected beams reinforce. The difference in path length is an integer times the wavelength if the relation n x L = 2d x SinA, called Bragg’s law, holds.

At an angle ‘A’, all reflected radiation with a wavelength ‘L’ and obeying Bragg’s law are ‘in phase’ and add up. All other wavelengths at the same angle vanishes. A detector placed at angle ‘A’ can hence measure the intensity of the corresponding wavelength. Reflected wavelengths obeying Bragg’s law for n=1, are called first-order reflections, and for n=2 second-order etc. It is to be noted that, at a specific angle, radiation is visible with wavelength ‘L’, ‘L/2′, and ‘L/3’, but the detector is able to distinguish between them.

Crystals are used to separate the characteristic radiation coming from a sample. Crystals can be naturally grown like LiF and Ge crystals but also a stack of deposited layers of W, Si, Mo, Sc or other elements. To cover all elements more than one crystal with different 2-d values are needed. At any specific angle, only radiation with a wavelength obeying Bragg’s law is reflected. Radiation with slightly different wavelengths is reflected at slightly different angles, but still reaches the detector and interferes with the energy to be measured.

A collimator, which is a set of parallel plates, is used to obtain a parallel X-ray beam which falls exactly at the needed angle on the crystal. The primary collimator is placed between the sample and the crystal, and a secondary collimator can be placed between the crystal and the detector.

Lenses are used in XRF to focus X-rays on a small spot or to receive only fluorescence from a small spot. Visible light has a refractive index higher than 1, so a convex glass can be used to focus light. X-rays have a refractive index just below 1, so to achieve the same effect the lens is to be concave. Since the refractive index is very close to 1, the focal distance is long (around 1 m), making it unsuitable for practical use. Another way to focus X-rays is to use capillaries made of carefully bent hollow glass fibres. (Because of the difference in refractive index, visible light needs solid glass fibres). A mono-capillary has one fibre and a poly-capillary has a group of fibres. The X-rays are scattered in the fibres and all focused on one spot. The focal distance and the transmission of the lens is not the same for all energies. Very low energies are absorbed by the lens and very high energies are not focused but just pass through the lens.

A mask is a plate with a hole in it. A tube irradiates the sample, but also the cup in which the sample is placed. This cup also emits its characteristic radiation, but this is not to reach the detector or it interferes with the radiation coming from the sample. A mask is placed between the sample and the detection system so that the detector ‘sees’ only the sample.

Samples are not always perfectly homogeneous, and scratches on the surface cab also influence measurements. A spinner rotates the sample during the measurement to even out effects of non-homogeneity and scratches.

The source, sample, and detection system are mounted in a vacuum chamber. Air absorbs tube radiation, especially low-energy radiation. This makes analysis of light elements impossible since all X-rays are absorbed by the air and do not reach the detector. Liquids and wet powders cannot be measured in a vacuum since they evaporate. These types of samples are normally measured in a helium-filled spectrometer. Helium absorbs the radiation of the light elements, up to about fluorine, so it is not possible to measure these elements in liquids. Helium does not, however, affect the radiation from heavier elements.

A good XRF analysis starts with a well-prepared sample and a good measurement. Samples are to be prepared for accurate measurement. After a sample is measured, it is analyzed. This is done in two steps i.e., qualitative analysis followed by quantitative analysis. Qualitative analysis determines which elements are present and their net intensities from the measured spectra. In several routine situations, the elements in the sample are known and only the net intensities need to be determined. The net intensities are used in the quantitative analysis to calculate the concentrations of the elements present. EDXRF and WDXRF frequently use slightly different methods for qualitative analysis. In EDXRF the area of a peak gives the intensity while in WDXRF the height of the peak gives the intensity. Both methods work for EDXRF and WDXRF, but both have their specific advantages and disadvantages.

Frequently, only a small sample of material is analyzed, for example in a steel plant a small disk represents the full furnace contents. The sample is to be representative of the entire material, and hence is to be taken very carefully. Once taken, it is also be handled carefully. The sensitivity of modern spectrometers is so high that they even detect fingerprints, which can disturb the analysis. Another basic requirement is that a sample is to be homogeneous. Spectrometers only analyze the sample’s surface layer, so it is to be representative of the whole sample. Majority of the spectrometers are designed to measure samples which are circular disks with a radius between 5 mm and 50 mm. The sample is placed in a cup, and the cup is placed in the spectrometer. Special supporting films allow the measurement of loose powders and liquids.

Solids need only a minimum of sample preparation. In several cases, cleaning and polishing are sufficient. Metals can oxidize when exposed to air, so they are frequently ground or polished before they are measured to remove the rust. Powders can be placed on a supporting film and measured directly. Another technique is to press them under very high pressures (20,000 kg) into a tablet. A binding material is sometimes added to improve the quality of the tablet. The tablet is then measured and analyzed. If a binding material is used, this has to be taken into account in the analysis since it does not belong to the initial sample. Care is to be taken that the sample is homogeneous.

Powder together with a binding additive called flux can also be melted (1,000 deg C to 1,200 deg C) into a glass sample called a bead. This sample is homogenous and can be measured directly. Because of the melting process, a part of the sample can evaporate as H2O or CO2 so the sample loses part of its contents. Elements like S, Hg and Cd are also candidates for leaving the sample when heated. This loss is called loss on ignition (LOI). Weighing the sample before and after fusion helps to determine the total LOI. The analysis is to take into account the flux used and the LOI. Flux materials mostly contain light elements like Li2B4O7, so they cannot be measured. To correct this, the analyst is to take into account which, and how many, flux materials are being used.

Liquids are poured into special cups with supporting films. Diluents are sometimes added to obtain sufficient liquid. Liquids cannot be measured in vacuum since they evaporate. Measuring in air is possible, but the air absorbs much of the radiation and makes it impossible to measure light elements. The spectrometer chamber is hence filled with He gas so liquids do not evaporate and hardly any radiation is absorbed. Filters used to filter air or liquid can be analyzed using XRF. The filter contains only a very small quantity of the material to be analyzed. Filters do not need specific sample preparation and can be analyzed directly.

XRF spectrometry is a very sensitive technique and samples are to be clean. Even fingerprints on a sample can affect the result of the analysis. For accurate results, the spectrometer (for example, the kV settings of the tube or the detector settings) is tuned to the elements to be analyzed. Bad settings can lead to poor results. In EDXRF a whole spectrum is measured simultaneously and the area of a peak profile determines the concentration of an element. Measuring the height of the peak profile is an alternative, but a lot of information is lost since the area of a peak profile is less sensitive to noise than the height of the same peak. In WDXRF it is common practice to measure only at the top of the peak profile. The positions of the peaks are known and measuring only at the top position gives the best accuracy and the lowest measuring time.

Optimum measurement conditions can be defined in several different ways, and the definition depends on the criteria used. The criteria can be highest intensity, lowest background, minimum line overlap, and several others. A high intensity and low background have the advantage that lines can be detected and measured accurately and quickly. Minimum line overlap has the advantage that the intensity of the lines can be determined directly, without sophisticated mathematical techniques. Weak lines can also be difficult to detect on the tails of strong lines. The maximum intensity of a line is achieved if the energy of the incoming radiation is just above the absorption edge of that line.

In WDXRF systems and EDXRF systems with direct excitation, this can be done by applying a voltage to the tube so that the largest part of the tube spectrum (continuum or tube line) has an energy just above the absorption edge of the analytical line. In EDXRF systems using secondary targets, it is done by using a target which has a fluorescent line with an energy just above the absorption edge of the analytical line. The voltage applied to the tube is such that the spectrum of the tube excites the element(s) in the target optimally, according to the same principles described for WDXRF systems. If no such target is available, a Barkla target is used to scatter the total tube spectrum. The tube voltage is selected so that the largest part of the tube spectrum has an energy just above the absorption edge of the analytical line.

Line overlap occurs when the line of one element overlaps the line of another element. The interfering line can come from an element in the sample, but also from an element in the tube, crystal, secondary target, or any other component in the optical path. High resolution and / or dispersion achieve minimum line overlap. In WDXRF spectrometers, the crystal and collimator have a large effect on the line overlap, which can be minimized by selecting the proper crystal and collimator. In EDXRF spectrometers, the detector and the multi-channel analyzer settings have a large effect on the resolution and are to be selected carefully. In some cases, it is also worth measuring a weaker line of an element if a strong line is overlapped and the weaker line is not.

For spectrometers using secondary targets, the selection of the proper target is necessary. Scattered target lines can interfere with the lines of the sample so selecting the target which gives the lowest interference is advisable. Using a target which only excites the elements of interest and not elements which give interfering lines helps to reduce the line overlap.

The first step in the qualitative analysis in EDXRF is to determine the top positions and the areas of the line profiles. The positions of the tops represent the presence of elements and the areas represent the intensities of the lines. Where the elements in a sample are known a priori, only the intensities need to be determined. The quantitative analyses need net intensities, meaning that the background is to be subtracted from the spectrum.

Peak search and peak match are used to find which elements are present in the sample. XRF analysis uses a mathematical technique to find the peaks in a spectrum. Peak match determines the elements to which the peak profiles belong. This is done by comparing the positions of the peaks to a database holding the positions of all possible lines.

For deconvolution and background fitting, if an example of a spectrum is taken with two peak profiles and a background, then a spectrometer measures the sum of the background and the profiles. In this example, the profiles do not overlap and the area of both can be determined without problems. In other cases, peak profiles can overlap. In such cases, deconvolution is used to determine the area of the individual profiles. The measured spectrum is fitted to theoretical profiles. The area of these profiles is changed, but keeping the shape fixed, until the sum of all the profiles gives the best fit with the measured spectrum. One way is to try all possible combinations of profiles, but this takes a long time to find the best fit. Instead, a mathematical method called least squares fitting finds the best fitting peak profiles, but this can still be time-consuming. Theoretical calculations are also used to find the best fit. From theory, it is possible to calculate the ratios between groups of line intensities. This reduces the number of free parameters, finding the best fit more quickly. The background has to be taken into account when fitting the peak profiles. First stripping the background, and fitting the profiles to the resulting net spectrum can do this. It is also possible to fit background and peak profiles to the measured spectrum in one process.

For the qualitative analysis in WDXRF, as with EDXRF, peak search and peak match are used to discover which elements are present in the sample. Once again, peak search finds the peaks, and peak match determines the associated elements by referring to a database. Peak height is measured and background subtraction is done. In WDXRF, it is common practice to measure the intensity at the peak of a line and at a few background positions close to the peak. The positions are to be chosen carefully and other peaks are avoided. The background under the peak is determined by interpolating the intensities measured at the background positions.

For line overlap correction taking an example of two overlapping lines and their sum, where, the height of the peak cannot be determined as the raw intensity minus the background, the intensity is measured at position 1 is the sum of the net height of peak 1 and a fraction of peak 2, and vice versa. Mathematically this can be written as a set of two linear equations, and the net intensities of both peaks can be calculated if the factors f12 and f21 are known. These two factors can be determined using a reference sample contains only element 1, and another containing only element 2.

The detector counts incoming photons, which is similar to counting raindrops. When it rains, the number of drops falling into a bucket in a second is not always exactly the same. Measuring for a longer time and calculating the average per second gives a more accurate result. If it is raining heavily, only a short time is needed to give an accurate number of drops per second, but a longer time is needed if it is only raining lightly. Raindrops have different sizes and counting all the drops with a specific size is equivalent to measuring the intensity of the radiation of one particular element in the complete spectrum. To tell whether there are more drops of one size than of another, sufficient drops have to be counted. A histogram of the counted raindrops is prepared. The height of a bar corresponds to the number of drops counted having a specific size. The longer the count, the clearer it becomes that the number of drops is not the same for each size.

In X-rays, to detect a peak of an element, it is to be significantly above the noise (variation) in the background. The noise depends on the number of X-ray photons counted. The lower is the number of photons counted, the higher is the noise. The analysis is normally based on the number of photons counted per second, but the noise depends on the total number of photons counted. By measuring for a longer period, it is possible to collect more photons and hence reduce the noise.

A normally accepted definition for the detection limit is that the net intensity of a peak is to be three times higher than the standard deviation of the background noise. If the standard deviation of the background noise equals the square root of the intensity (in counts), then the elements are said to be detectable. With low backgrounds, low line intensities are sufficient to fulfil the requirement, so a low background gives low detection limits. 3D optics is used to reduce the background.

Quantitative analysis is basically the same for EDXRF and WDXRF. The only difference is that in EDXRF the area of a peak gives the intensity, while in WDXRF the height of a peak gives the intensity. The same mathematical methods can used to calculate the composition of samples. In quantitative analysis, the net intensities are converted into concentrations. The normal procedure is to calibrate the spectrometer by measuring one or more reference materials. The calibration determines the relationship between the concentrations of elements and the intensity of the fluorescent lines of those elements. Unknown concentrations can be determined once the relationship is known. The intensities of the elements with unknown concentration are measured, with the corresponding concentration being determined from the calibration.

Ideally, the intensity of an analytical line is linearly proportional to the concentration of the analyte and, across a limited range, this is the case. However, the intensity of an analytical line does not only depend on the concentration of the originating element. It also depends on the presence and concentrations of other elements. These other elements can lead to attenuation or to enhancement. To reach atoms inside a sample, the X-rays from the source is first to pass the atoms which are above them, and the fluorescence from the atoms also similarly is to pass these atoms. These overlying atoms absorb a part of the incoming radiation and a part of the fluorescent radiation. The absorption depends on which elements are present and on their concentrations. In general, heavy elements absorb more than light elements.

An element is excited by the incoming radiation and in some cases also by the fluorescence of other elements. Whether or not this occurs and how large the effect is depends on the elements and their concentrations. Across a limited range, the curve describing the relation between intensity and concentration can be approximated to a straight line given by C=D+E*R, where D and E are determined by linear regression. This line can only be used for samples which are similar to the standards used, and across a limited range. Normally, it cannot be used for other types of samples. A better fit and a wider range is possible by adding more terms such as C=D+E*R+F*R*R, but the range is still to be limited and only applicable to samples similar to the standards.

For the calibration with linear and parabolic fit, matrix correction models use terms to correct for the absorption and enhancement effects of the other elements. This is done in different ways, but they all, in one way or another, use a matrix correction factor ‘M’, and the difference between the models lies in the way they define and calculate ‘M’. Influence of coefficient matrix correction models have the shape. The corrections are numeric values depending on the concentrations and / or intensities of the matrix elements. Several people have suggested ways to define and model the corrections, and models are normally named after the person(s) who proposed them.

Fundamental parameter models are based on the physics of X-rays. In the 1950s, Sherman derived the mathematical equations which describe the relationship between the intensity of an element and the composition of a sample. This equation contains several physical constants and parameters which are called fundamental parameters.

Analysis uses the same equations as used for the calibration. In the calibration, the correction factors are the parameters which are to be determined. The concentrations are known since the standards with known composition were used. In the analysis, the opposite is true. The correction factors are known, and the concentrations are the unknowns which are to be determined. Frequently, this is done by iterative methods. The process starts with an initial guess at the concentrations, and these concentrations are substituted in the right-hand side of the equations. This gives new values for the concentrations which are substituted in the right-hand sides, again giving new values for the concentrations. This process is repeated until the concentrations converge to limiting values. The result of the final iterations is assumed to be the composition of the sample.

It is sometimes not needed or impossible to measure all compounds. For example, in steel, Fe is not measured, and compounds like H2O can also not be measured effectively (H cannot be measured, and O occurs in many other compounds). If all the other compounds are measured or known, the remaining compound can be determined, since the sum of all concentrations are to add up to 100 %. The compound which is determined by the difference calculation is frequently called the balance (compound).

Because of the inaccuracies in the calibration, the sample preparation or in the measurement, the sum is not be exactly 100 %. Some concentrations are overestimated and others are underestimated. If all compounds are analyzed, the concentrations can be normalized to 100 % and the average deviations, in several cases, be less than without normalization.

The quantitative analysis needs standard samples for the calibration. If the coefficient models are used, the calibration is only valid over a limited range and only for unknown samples which are similar to the standards. By using fundamental parameters instead of coefficient models, this can be extended to the full range. In both cases, however, the calibration determines the relation between the concentration of a compound and the intensity of an element. Compounds can be pure elements like Fe, Cu but also FeO or Fe2O3. If the calibration is done with FeO then the analysis also determines the FeO concentration, but if a sample with Fe2O3 is measured it is not possible to determine the concentration of this compound.

One way to make the calibration independent of the compounds is (i) the standards are entered as elements and / or compounds, but all concentrations are converted to element concentrations using the chemical formula of the compound and atomic weights of the elements, (ii) the calibration is done per element, so the concentrations of the elements are calibrated against their intensities, (iii) the concentration of the elements is determined for an unknown sample, and (iv) the element concentrations are converted to compound concentrations using the chemical sample, together with its chemical formula and the atomic weights of the elements. In this way, the calibration is independent of the samples to be analyzed. All types of materials can now be used as standards as long as they contain the elements of interest.

Since the standards can be chosen independently from the sample to be analyzed, they are no longer called standards but reference samples, and the method is called standardless. For the qualitative analysis, the composition of the sample is not important since it determines the intensities of radiation from elements and not from compounds. The qualitative and quantitative analysis can be fully automated, making it possible to analyze all kinds of materials with a single calibration.

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