Analysis by X-ray Fluorescence Spectrometry

Analysis by X-ray Fluorescence Spectrometry

X-ray fluorescence (XRF), is an emission spectroscopic technique which has found wide application in the area of elemental identification and determination. The technique depends on the emission of characteristic x-radiation, normally in the 1 keV to 60 keV energy range, following excitation of atomic electron energy levels by an external energy source, such as an electron beam, a charged particle beam, or an x-ray beam. In most sample matrices, x-ray spectrometry can detect elements at concentrations of less than 1 micro-gram /g of sample (1 ppm). In a thin film sample, it can detect total amounts of a few tenths of one microgram. Initially, x-ray spectrometry found wide acceptance in applications related to metallurgical and geochemical analyses. More recently, x-ray spectrometry has proved valuable in the analysis of environmental samples, in the determination of sulphur and wear-elements in petroleum products, in applications involving forensic samples, and in measurements of electronic and computer-related materials.

X-ray fluorescence (XRF) spectrometry is a versatile tool in many analytical problems. Major, minor and trace elements can be qualitatively and quantitatively determined in various kinds of samples such as  metals, alloys, glasses, cements, minerals, rocks, ores, polymers as well as environmental and biological materials. Elements from sodium (Na) to uranium (U) are routinely determined using energy-dispersive x-ray fluorescence (EDXRF) spectrometer whereas application of wavelength-dispersive x-ray fluorescence (WDXRF) spectrometer allows efficient determination of low-Z elements down to even beryllium (Be). Although the samples can be analyzed without treatment, high quality results can be ensured if appropriate sample preparation is applied. This can vary from simple cleaning and polishing of the sample (metals, alloys), powdering and pelletizing with or without binder (ceramics, minerals, ores, soils, etc.), fusing the sample with appropriate flux (ceramics, rocks, ores, etc.) to digestion with acids (metals, alloys). This way errors resulting from surface roughness, particle size effect or inhomogeneity of the material can be eliminated or minimized.

Roentgen discovered x-rays in 1895. H.G.J. Moseley developed the relationships between atomic structure and x-ray emission and in 1913 published the first x-ray spectra, which are the basis for modern x-ray spectrometry. Moseley recognized the potential for quantitative elemental determinations using x-ray techniques. The development of routine x-ray instrumentation, leading to the x-ray spectrometer known today, took place over the following decades. Coolidge designed an x-ray tube in 1913 which is similar to those presently used. Soller achieved collimation of x-rays in 1924. Improvements in the gas x-ray detector by Geiger and Mueller in 1928 eventually led to the design of the first commercial WDXRF by Friedman and Birks in 1948. More recently, other detectors, such as the germanium and the lithium-doped silicon semi-conductor detectors have resulted in modified x-ray spectrometer designs. Modern energy-dispersive instrumentation facilitates qualitative identification of elements in various samples. The information content of an energy dispersive x-ray spectrum is among the highest obtainable from inorganic materials in a single measurement. The position and intensity of the spectral peaks provide qualitative and quantitative information, and the intensity of the background yields information on bulk composition of the sample matrix.

X-ray spectrometry is one of the few techniques which can be applied to solid samples of different forms. Although the majority of the XRF spectrometers are used in laboratories, many are finding application in routine analyses for production and quality control and in specialized tasks. A structural diagram of EDXRF spectrometer is given in Fig 1.

Fig 1 Structural diagram of EDXRF spectrometer

Electromagnetic radiation

Electromagnetic radiation is an energy form which can be propagated through space and can interact with atoms and molecules to alter their energy state. Both properties are important to spectroscopy. Electromagnetic radiation shows behaviour which needs two theories to explain. The wave theory describes behaviour of electromagnetic radiation, such as refraction, reflection, diffraction, and scatter. Radiation is defined as an energy form consisting of two orthogonal waves, each having the same frequency and wavelength. One is an oscillating electric field, and the other an oscillating magnetic field, thus producing the term electromagnetic radiation.

In a vacuum, the velocity of propagation of the wave through space is the speed of light (c = 3 × 10 to the power 10 cm/s). This leads to an important fundamental relationship represented by the equation w.v = c. This expression states that the product of the wavelength (w) of electromagnetic radiation and its frequency (v) is equal to its velocity. The wavelength of electromagnetic radiation varies over many orders of magnitude. For example, radio waves in the normal AM broadcast band have wavelengths of several hundred meters and ultraviolet wave lengths are in the range of 10 nm to 100 nm (nanometer). By contrast, x-rays useful in spectroscopy range from 0.01 nm to 10 nm (Fig 2).

Fig 2 X-rays and other electromagnetic radiations

For wavelength-dispersive spectrometry, it is often more convenient to use wavelength units, but for energy-dispersive x-ray spectrometry (EDS), the energy description is more convenient. However, the inter conversion is simple.

Several normally used descriptions of the characteristics of x-rays are significant. The proper meaning of the intensity of electromagnetic radiation is the energy per unit area per unit time; however, the number of counts per unit time from the detector is frequently used as intensity. Because the area is the active area of the detector used, and time is an adjustable parameter, the use of counts is a practical description of x-ray intensity. The terms hard or soft x-rays are frequently used to differentiate x-rays of short (0.01 nm to 0.1 nm) and long (0.1 nm to 1 nm) wavelengths, respectively. X-radiation falls in the high-energy region of the electromagnetic spectrum.

X-ray emission

X-rays are generated from the disturbance of the electron orbitals of atoms. This can be done in several ways, the most common being bombardment of a target element with high-energy electrons, x-rays, or accelerated charged particles. The first two are frequently used in x-ray spectrometry directly or indirectly. Electron bombardment results in a continuum of x-ray energies as well as radiation characteristic of the target element. Both types of radiation are encountered in x-ray spectrometry.

Continuum – Emission of x-rays with a smooth, continuous function of intensity relative to energy is called continuum, or bremsstrahlung, radiation. An x-ray continuum can be generated in several ways. However, the most useful is the electron beam used to bombard a target in an x-ray tube. The continuum is generated as a result of the progressive deceleration of high-energy electrons impinging on a target, which is a distribution of orbital electrons of various energies. As the impinging electrons interact with the bound orbital electrons, some of their kinetic energy is converted to radiation. The amount converted depends on the binding energy of the electron involved. Hence, a somewhat statistical probability exists as to how much energy is converted with each interaction.

The probability of an impinging electron interacting with an orbital electron of the target element increases with the atomic number of the element, thus, the intensity of the continuum emission increases with the atomic number of the target element. Further, the probability of an interaction increases with the number of electrons per unit time in the beam, or flux. Hence, the intensity of the continuum increases with electron beam current, expressed in milli-amperes. Moreover, the ability of the impinging electrons to interact with tightly bound electrons of the target element increases with the kinetic energy of the bombarding electrons. Since the kinetic energy of the electrons in the beam increases with acceleration potential, the integrated intensity of the continuum increases with electron acceleration potential, expressed in kilovolts. Finally, the maximum energy manifested as x-ray photons equals the kinetic energy of the impinging electron, which in turn relates to acceleration potential. The energy of the maximum intensity in the continuum lies at around two thirds the maximum emitted energy. Further, there is the absorption of x-rays within the target material or absorption by materials used for windows in the x-ray tube and detectors. Therefore, some modification of the intensity distribution can occur, especially at low x-ray energies.

Characteristic emission – Most of the electrons impinging on a target interact with the orbital electrons of the target element in non specific interactions and result in little or no disturbance of the inner orbital electrons. However, some interactions result in the ejection of electrons from these orbitals. The resulting vacancies, or holes, represent high-energy unstable states. If the orbital vacancies are in the innermost shells, electrons from outer shells cascade to fill them and this result in a lower energy and more stable state. The energy released by the process may be manifested as x-rays. Each of the transitions which can occur, lead to the emission of sharp x-ray lines characteristic of the target element and the transition involved. These characteristic radiation lines are emitted with the continuum.

X-ray absorption

X-rays impinging on a sample undergo two important interactions with the elements of the sample: absorption and scatter. Absorption of the radiation can occur by specific interactions which are considerable in sample excitation in x-ray spectrometry or by more general interactions which influence the emitted x-ray intensity from the sample. Scatter of x-rays leads to background intensity in the observed spectra.

Mass absorption – When an x-ray beam passes through a material, the photons (electromagnetic fields) can interact in non specific ways with electrons in the orbitals of the target elements, reducing the intensity of the x-ray beam. The interactions can lead to photoelectric ejection of electrons or scatter of the x-ray beam. In either case, the overall result is frequently described in terms of an exponential decrease in intensity with the path length of the absorbing material. The mass absorption coefficient is characteristic of a given element at specified energies of x-radiation. Its value varies with the wavelength of the x-radiation and the atomic number of the target element.

The photoelectric effect is the most important of the processes leading to absorption of x-rays as they pass through matter. The photoelectric effect is the ejection of electrons from the orbitals of elements in the x-ray target. This process is frequently the major contributor to absorption of x-rays and is the mode of excitation of the x-ray spectra emitted by elements in samples. Primarily as a result of the photoelectric process, the mass absorption coefficient decreases steadily with increasing energy of the incident x-radiation. The absorption versus energy curve for a given element has sharp discontinuities. These result from characteristic energies at which the photoelectric process is especially efficient.

Scatter – When x-ray photons impinge on a collection of atoms, the photons can interact with electrons of the target elements to result in the scatter of the x-ray photons, as illustrated in Fig 3. Scatter of x-rays from the sample is the major source of background signal in the spectra obtained in x-ray spectrometry. The scatter of x-rays is caused mainly by outer, weakly held electrons of the elements. If the collisions are elastic, scatter occurs with no loss of energy and is known as Rayleigh scatter. If inelastic, the x-ray photon loses energy to cause the ejection of an electron, and the scatter is incoherent. The path of the x-ray photon is deflected, and the photon has an energy loss or a longer wavelength. This is Compton scatter.

Fig 3 X-ray tube and x-ray emission and absorption

Scatter affects x-ray spectrometry in two ways. First, the total amount of scattered radiation increases with atomic number because of the greater number of electrons. However, samples with low atomic number matrices show a larger observed scatter because of reduced self-absorption by the sample. Second, the ratio of ‘Compton-to-Rayleigh’ scatter intensity increases as the atomic number of the sample matrix decreases. The energy loss associated with Compton scatter results in a predictable change in the wavelength of the radiation.

Relationships between elements and x-rays

The different relationships between elements and x-rays are shown in Fig 4.

 Fig 4 Relationships between elements and x-rays

Absorption – X-ray photons can interact with orbital electrons of elements to be absorbed or scattered. The relationship between absorption and the atomic number of the element is important in selecting optimum operating conditions for x-ray spectrometry.

Mass absorption coefficients differ for a given element or substance for each element or substance at a given energy of x-ray and at each energy of x-ray. Because of the higher probability of interaction with orbital electrons, the mass absorption coefficient increases with the atomic number of the element of the target material. At a given atomic number, the mass absorption coefficient decreases with the wavelength of the x-ray radiation. These results from specific energies needed for the photoelectric ejection of electrons from the different orbitals of the atom and are characteristic of the element.

Absorption edges are discontinuities or critical points in the plot of mass absorption versus wavelength or energy of incident x-radiation. Absorption-edge energy is the exact amount which photo-eject an electron from an orbital of an element. The lower the principal quantum number, the higher is the energy heeded to eject an electron from that shell. The wavelength of an x-ray which can eject an L electron is longer (of less energy) than that needed to eject an electron from the K shell. That is, the K absorption edge energy is greater than the L-absorption edge energy for a given element.

Emission – The photoelectric effect is an x-ray absorption mechanism by which unstable states in the electron orbitals of atoms are created. Once the vacancies in the inner orbitals are formed, relaxation to the stable ground state can occur by the emission of x-rays characteristic of the excited element. The energy of the 1s electron is shielded from the state of the valence electrons such that the absorption-edge energy and the energy of the emitted x-rays are essentially independent of the oxidation state and bonding of the atom.

K lines – Once the photoelectric effect creates a vacancy in the K shell, the excited state relaxes by filling the vacancy with an electron from an outer orbital. Only certain transitions are allowed because of quantum mechanical rules called selection rules. The transitions which follow the selection rules are termed allowed (diagram) lines, those that do not are called forbidden, and those that result in atoms with two or more vacancies in inner orbitals at the time of the emission are called satellite (non-diagram) lines. The number of K lines, and the exact one observed for an element, depends in part on the number of filled orbitals.

L Lines – Since the practical energy range for most WDXRF x-ray spectrometers is 0 keV to 100 keV, and 0 keV to 40 keV for EDXRF spectrometers, the use of emission lines other than the K lines are to be considered. For a given element, L lines are excited with lower x-ray energy than K lines. The use of L lines is particularly valuable for elements with atomic numbers higher than around 45.

M lines –M lines find limited application in routine x-ray spectrometry. The lines are not observed for elements with atomic numbers below around 57, and when observed, the transition energies are low. The only practical use for these lines is for such elements as thorium, protactinium, and uranium. They are to be used only in these cases to avoid interferences with L lines of other elements in the sample.

Fluorescent yield – An electron is ejected from an atomic orbital by the photoelectric process with two possible results either x-ray photon emission or secondary (Auger) electron ejection. One of these events occurs for each excited atom, but not both. Hence, secondary electron production competes with x-ray photon emission from excited atoms in a sample. The fraction of the excited atoms which emits x-rays is termed the fluorescent yield. This value is a property of the element and the x-ray line under consideration. Low atomic number elements also have low fluorescent yield. Coupled with the high mass absorption coefficients which low-energy x-rays show, the detection and determination of low atomic number elements by x-ray spectrometry is challenging.

Inter-element effects – For transitions in x-ray spectrometry, no emission line for a given series (K, L, M) of an element has energy equal to or greater than the absorption edge for that series. An important result is that the x-rays emitted from an element cannot photo-eject electrons from the same orbital of other atoms of that element. However, a sample composed of a mixture of elements can show interactions which are frequently called inter-element effects. Such interactions of elements within a sample frequently need special data analysis.

WDXRF spectrometers

 X-ray spectrometric instrumentation introduced commercially in the 1950s has been known as wavelength dispersive which denoted that the radiation emitted from the sample is collimated using a Soller collimator, then impinges upon an analyzing crystal. The crystal diffracts the radiation to different extents according to Bragg’s law and depending on the wavelength or energy of the x-radiation. This angular dispersion of the radiation permits sequential or simultaneous detection of x-rays emitted by elements in the sample.

Simultaneous instruments normally contain several sets of analyzing crystals and detectors; one is adjusted for each desired analyte in the sample. Although expensive, these instruments are efficient for routine determination of pre-selected elements, but are not easily converted to determine elements other than the ones selected at installation.

More common are sequential instruments which contain a mechanical system known as a goniometer which varies the angle among the sample, analyzing crystal, and detector. In this way, the desired wavelength of x-radiation can be selected by movement of the goniometer. Sequential WDXRF spectrometers can be computer controlled for automatic determination of many elements. Quantitative applications of automated WDXRF spectrometers are efficient, since the instrument can be programmed to go to the correct angles for desired determinations. However, qualitative applications are less efficient since the spectrum is to be scanned slowly.

X-ray tubes – Various energy sources can be used to create the excited electronic states in the atoms of elements which produce x-ray emission. Among these are electron beams, charged particle beams, and x-radiation. Electron beams are directed on the sample in such techniques as scanning electron microscopy (SEM) and electron microprobe analysis. However, use of an electron beam needs a high vacuum to avoid energy losses of the electron. X-ray spectrometry is best used as a versatile analytical tool rather than as a specialty tool. Many samples are not suited for a high vacuum or are non-conductors, which cause problems of electrical charging when under an electron beam. Hence, this energy source is not practical for x-ray spectrometry.

Radioactive isotopes which emit x-radiation are another possibility for excitation of atoms to emit x-rays. However, the x-ray flux from isotopic sources which can be safely handled in a laboratory is too weak for practical use. Because these sources normally emit only a few narrow x-ray lines, several are needed to excite many elements efficiently. The most practical energy source for x-ray spectrometry is an x-ray tube (Fig 3).

WDXRF spectrometer needs efficient high-power excitation to perform well. Hence, stability and reliability of the x-ray tube is important. All components are in a high vacuum. A filament is heated by a filament voltage of 6 V to 14 V. The heated filament thermally emits electrons. The flux of electrons which flows between the filament and the target anode is to be highly regulated and controlled. This electron flow is electrical current and is normally measured in milli-amperes. The tube current is often referred to as the mA.

A potential of several kilovolts is applied between the filament (cathode) and the target anode, which serves as the acceleration potential for the electrons. This voltage is normally measured in kilovolts. The anode is normally copper, and the target surface is plated with high-purity deposits of such elements as rhodium, silver, chromium, molybdenum, or tungsten. X-ray tubes used for WDXRF spectrometry operate at 2 kW to 3 kW. Much of this power dissipates as heat, and provisions for water cooling of the x-ray tube are necessary. The power supplies and associated electronics for these x-ray tubes are large. The electrons strike the target with a maximum kinetic energy equivalent to the applied tube potential. If the kinetic energy of the electron exceeds the absorption-edge energy corresponding to the ejection of an inner orbital electron from atoms of the target material, the tube emits x-ray lines characteristic of the target element. Interaction of the electrons in the beam with electrons of the target element also leads to emission of a continuum. The area of the continuum and the wavelength of maximum intensity  depends on the potential, current, and anode composition.

Analyzing crystals – X-rays emitted by the x-ray tube are directed onto the sample. In most x-ray spectrometers, the sample is placed above the x-ray tube in what is known as inverted optics. This facilitates positioning the surface of a liquid using the bottom surface rather than the top. The x-radiation emitted from the sample is collimated and impinges on the surface of an analyzing crystal, which disperses the radiation. The parallel beam of polychromatic x-radiation from the sample is diffracted from different lattice planes in the crystal. Reinforcement occurs if the additional distance the radiation is to travel by diffraction from different lattice planes equals an integer multiple of the wavelength. If this is not the case, destructive interference takes place. Bragg’s law permits calculation of the angle at which a wavelength is to be selected for the analyzing crystal.

Detectors – Detectors and associated electronics in WDXRF spectrometer detect x-rays diffracted from the analyzing crystal and reject undesired signals such as higher or lower order diffraction by the analyzing crystal or detector noise. Two detectors are normally positioned in tandem. The first is a gas-filled or flowing-gas proportional detector. These detectors consist of a wire insulated from housing. Thin polymer windows in the front and back of the housing permit entry and possible exit of x-radiation. A bias potential of a few hundred volts is applied between the wire and housing.

Although many gases can be used, the typical gas is P-10, a mixture of 90 % argon (Ar) and 10 % methane. When x-rays enter the detector, the argon is ionized to produce many Ar+-e- pairs. The anodic wire collects the electrons, and the electrons at the cathodic walls of the housing neutralize the Ar+ ions. The result is a current pulse for each x-ray photon which enters the detector. The P-10 filled proportional detectors are most efficient for detecting x-ray photons of energies less than around 8 keV (wavelengths higher than around 0.15 nm). More energetic x-radiation tends to pass through the proportional detector.

A second detector frequently located behind the proportional counter is normally a scintillation detector. This detector consists of a thallium-doped sodium iodide crystal [NaI(Tl)], which emits a burst of blue (410 nm) light when struck by an x-ray photon. The crystal is mounted on a photomultiplier tube which detects the light pulses. The number of light photons produced is proportional to the energy of the incident x-ray photon. After electronic processing, the scintillation burst is converted into a voltage pulse proportional in amplitude to the x-ray photon energy. These two detectors can be operated independently or simultaneously. In simultaneous operation, the detector operating potential and output gain is to be adjusted so that an x-ray photon of a given energy produces the same pulse-height voltage from both detectors. Both detector types need around 1 micro-second to recover between pulses. Some counts can be lost at incident photon rates greater than around 30,000/s. Pulse-height discrimination of the x-ray pulses from the detector(s) rejects higher or lower order x-rays diffracted from the analyzing crystal.

Fundamentals of operation – When a sample is considered and the analyte element selected, the first decision is to select the emission line. In the absence of specific interferences, the most energetic line plausible is typically used. For elements with atomic numbers less than around 75, this normally is the K line, since many WDXRF spectrometers can operate to 100-kV potentials for the x-ray tubes. When possible, an x-ray tube is selected that emits characteristic lines at energies just above the absorption edge for the line to be used for the analyte element. When such a tube is not available, the excitation is to be accomplished by use of the continuum for an available x-ray tube.

The potential of the x-ray tube is to be set around 1.5 times the absorption-edge energy or higher. The detector is to be selected based on the wavelength region to be used. The proportional counter is to be used for x-rays longer than around 0.6 nm, the scintillation detector for wavelengths shorter than around 0.2 nm, and both for the overlapping region of 0.2 nm to 0.6 nm. An analyzing crystal is to be selected which allows the desired wavelength to be detected. Majority of the parameter selections are being performed through computer control.

Energy-dispersive x-ray spectrometers

Use of a goniometer in WDXRF x-ray spectrometers is based on the requirement to resolve into components the x-rays emitted by various elements in a sample. The use of a dispersion device is common in many types of spectroscopy to accomplish this task. Instruments without the mechanical components are desirable if adequate resolution can be achieved. The development of lithium-drifted silicon detectors and their application to x-ray detection in the mid-1960s led to a field of spectroscopic analysis which became known as EDXRF spectrometry.

X-ray tubes used in WDXRF spectrometers are rated at 2 kW to 3 kW and are to be water cooled. Those used in EDXRF spectrometers operate at much lower power and are usually air cooled. Typical tubes ranges from 9 W to 100 W. Different anode materials are available, and each manufacturer of x-ray spectrometers offers special x-ray tube features. However, after many trials of tube design, most remain with the traditional ‘side window’ design, although it is much smaller than those used in WDXRF spectrometers. A major factor in the design of the tube and associated power supply is the stability of the tube and voltage.

An alternative to the direct x-ray tube excitation is the use of secondary-target excitation. In this mode, an x-ray tube is used to irradiate a secondary target, whose characteristic x-ray fluorescence is in turn used to excite the x-ray emission of the sample. Because of substantial efficiency loss when using a secondary target, higher wattage x-ray tubes are needed than required for direct excitation.

Secondary-target excitation sometimes affords significant advantages. For example, to determine the low concentration levels of vanadium and chromium in an iron sample, these elements can be excited with an iron secondary target without excitation of the iron in the sample. With direct-tube excitation this is difficult. Several secondary targets are needed to cover a wide range of elements. Use of secondary-target excitation has been supported as a source of monochromatic radiation for excitation. The significance of this advantage is that many of the fundamental-parameter computer programs, used to compute intensities directly from the basic x-ray equations, need monochromatic excitation radiation.

In practice, secondary-target excitation only approaches the ideal monochromatic radiation. Direct-tube excitation with appropriate primary filters performs well when compared to secondary-target techniques. Hence, direct x-ray tube excitation remains the most practical for the largest number of applications of energy dispersive spectrometry (EDS). The main strength of the EDS technique lies in its simultaneous multi-element analysis capabilities. Although special cases occur in which selective excitation is desirable, this frequently can be accomplished with intelligent use of an appropriate x-ray tube and filter. Any fundamental design features which limit the simultaneous multi-element capability diminish the advantage of the EDXRF spectrometer.

Since direct x-ray tube excitation is the most common method used in EDS, there are factors which govern the selection of an x-ray tube. In wavelength-dispersive techniques, several x-ray tubes are normally available for the spectrometer. These can be changed for different applications. This is not normally the case with EDS-systems, since many WDXRF spectrometer has few if any choices of primary filters. In wavelength-dispersive techniques, it is customary to attempt to excite the desired element by the characteristic emission lines of the tube anode material, but the continuum is used more efficiently in EDXRF spectrometers. The use of EDXRF spectrometers has been enhanced by computer control of tube current and voltage and selection of the primary filter. Selection and efficient use of a single x-ray tube is important in the configuration of an EDXRF system.

Characteristic lines emitted by an x-ray tube have much larger intensity at their maxima than the continuous radiation emitted. These lines are to be used for excitation whenever possible. In addition, use of a primary filter between the x-ray tube and the sample can effectively approximate monochromatic radiation impinging on the sample from these characteristic lines. EDXRF spectrometers normally offer various x-ray tube anode materials. For selecting the x-ray tube anode material, the applications most likely to be encountered are to be considered.

The principal concern is to select an anode which has characteristic lines close to, but always higher, in energy than the absorption-edge energies to be encountered. None of the characteristic lines are to create spectral interference with elements to be determined. This includes consideration of such details as the Compton scatter peak for the characteristic lines. In addition, it is difficult to perform determinations of the element of the anode material. This is especially true with samples having low concentrations of that element.

Rhodium is a favourable tube anode material for general-purpose use. The characteristic lines of this element are efficient for the excitation of elements with absorption edges to around 15 keV. The excitation efficiency for the K lines of the transition elements is low. However, the continuum can be used efficiently in this region. Rhodium also has characteristic L lines at around 2.7 keV to 3.0 keV. These are efficient for the excitation of the K lines of low atomic number elements, such as aluminum, silicon, phosphorus, and sulphur. However, in these cases, a silver anode is preferable because of the Compton scatter radiation from the rhodium lines. The characteristic lines and the continuum from the x-ray tube can be used for excitation.

Although the elements of many samples can be excited effectively using a combination of the characteristic x-ray lines from the tube anode element and the continuum, more monochromatic radiation is sometimes desired. One such situation involves enhancing the use of fundamental-parameter computations which permit quantitative determination of elements without the need for several concentration standards. A more frequent situation is the need to reduce the background in the spectrum energy range to be used in the analysis. Use of primary filters placed between the x-ray tube and the sample can be effective in these cases and are normally incorporated under computer control in commercial spectrometers.

The object is to filter the primary radiation from the x-ray tube and selectively pass the characteristic lines of the anode element. This is accomplished using a filter made of the same element as the tube anode. Since x-rays of a given line (K, L, and so on) of an element are lower in energy than the absorption edge for that element, the photoelectric component of the mass absorption coefficient is small. Such a filter does not efficiently absorb the characteristic line emitted by the x-ray tube. The higher energy x-rays from the continuum are efficient for the photoelectric process in the filter and are highly attenuated by absorption. X-rays of lower energy than the filter material absorption edge are absorbed more efficiently as the energy decreases.

The result is x-radiation striking the sample with an intensity which is largely determined by the characteristic lines of the tube anode and that approximates monochromatic radiation. Increasing the thickness of the filter decreases the total intensity, with further gain in the monochromatic   approximation.

Detectors – The selective determination of elements in a mixture using x-ray spectrometry depends upon resolving into separate components the spectral lines emitted by the different elements. This process needs an energy-sorting or wavelength-dispersing device. For the WDXRF spectrometer, this is accomplished by the analyzing crystal, which needs mechanical movement to select each desired wavelength according to Bragg’s law. Optionally, several fixed-crystal channels can be used for simultaneous measurement. In contrast, EDS is based on the ability of the detector to create signals proportional to the x-ray photon energy. Hence, mechanical devices, such as analyzing crystals, are not needed.

Several types of detectors have been used, including silicon, germanium, and mercuric iodide. The solid-state, lithium-drifted silicon detector [Si(Li)] was developed and applied to x-ray detection in the 1960s. By the early 1970s, this detector was firmly established in the field of x-ray spectrometry and was applied as an x-ray detection system for SEM and x-ray spectrometry. The Si(Li) detector provides excellent resolution. It can be considered as a layered structure. Under reversed bias of around 600 V, the active region acts as an insulator with an electric-field gradient throughout its volume.

When an x-ray photon enters the active region of the detector, photo ionization occurs with an electron-hole pair created for each 3.8 eV of photon energy. Ideally, the detector is to completely collect the charge created by each photon entry and result in a response for only that energy. Some background counts appear because of energy loss in the detector. Although these are kept to a minimum by engineering, incomplete charge collection in the detector contributes to background counts. From 1 keV to 20 keV, an important region in x-ray spectrometry, silicon detectors are efficient for conversion of x-ray photon energy into charge.

Analyzer systems – The x-ray spectrum of the sample is obtained by processing the energy distribution of x-ray photons which enter the detector. One x-ray photon entering the detector causes photo-ionization and produces a charge proportional to the photon energy. Several electrical sequences are to take place before this charge can be converted to a data point in the spectrum. A detailed knowledge of the electronics is not necessary, although an understanding of their functions is important. Upon entering the Si(Li) detector, an x-ray photon is converted into an electrical charge which is coupled to a field effect transistor (FET). The FET and the electronics comprising the preamplifier produce an output proportional to the energy of the x-ray photon. Using a pulsed optical preamplifier, this output is in the form of a step signal. Since photons vary in energy and number per unit time, the output signal, due to successive photons being emitted by a multi-element sample, resembles a staircase with various step heights and time spacing. When the output reaches a determined level, the detector and the FET circuitry reset to their starting level, and the process is repeated.

The preamplifier output is coupled to a pulse processor which amplifies and shapes the signal into a form acceptable for conversion to a digital form by an analog-to-digital converter (ADC). Amplification is necessary to match the analog signal to the full-scale range of the ADC. This process involves the energy calibration of the spectrometer. Drift in the gain and/or offset (zero) of the amplification results in errors in the energy assigned to the x-ray photons producing the signal. Hence, these calibrations are to be as stable as possible, and calibration is to be routinely checked.

The energy calibration is important for qualitative identification of the elements and for precise quantitative results when using spectrum-fitting programs. The amplifier provides gain and zero controls for calibrations. Normal operation in x-ray spectrometry is to set the time on the system clock to be used to acquire the spectrum. The processing of the pulses is not instantaneous. At high count rates, the time needed can become significant. When a pulse is detected and processing initiated, the clock is ‘stopped’ until the system is ready to process a new photon. The length of time the clock is off is called dead time; the time the clock is on is called live time. Their total is real time. The system monitors live time. If the spectrometer is operated with a 50 % dead time, the real time is twice the live time.

Processing of the pulse created by a photon is to be complete before another pulse occurs. A pulse pile-up rejector circuit blocks a pulse if it is received too soon. Once activated, the pulse pile-up rejector prevents the new signal from being processed if a second x-ray enters the detector before a prior pulse is fully processed. If analysis of the prior pulse had not yet been complete, it is also to be blocked from further processing. If this blockage is not performed, pulse pile-up occurs, resulting in an artifact which appears at energies equal to the sum of the photon energy of the first and second photons to enter the detector. These are frequently called sum peaks.

Despite pulse pile-up rejection circuitry, sum peaks are observed for intense peaks in the spectrum. This is the result of two photons entering the detector simultaneously or within a time difference faster than the fast discriminator can act. Sum peaks can be observed at twice the energy of an intense peak and / or at the sum of the energies of two intense peaks in the spectrum. Sum peaks decrease rapidly in intensity with count rate. The importance of electronic pulse-processing components to system performance is easily overlooked in EDS. However, stability, linearity, and proper calibration of these components are important for the use of the spectrometer.

EDXRF spectrometers require a dedicated computer system for data acquisition. Early spectrometers were heavy, unwieldy units which used hard-wired multichannel analyzers which could acquire data, but could do little to process it. Current spectrometer and data systems based on microprocessor technology are available as table-top units.

Fundamentals of operation – The simultaneous multi-element capability of EDS complicates the selection of optimum conditions because of the factors to be considered for each element. The compromises in spectroscopy are to be made, but the initial selection of instrument operating conditions can follow a logical sequence of decisions.

Qualitative analysis needs similar procedures, normally with less stringent requirements. Once a sample is received for analysis and the elements to be determined by x-ray spectrometry are identified, the next decision is to ascertain which x-ray lines are to be used for the determinations. As a general rule, K lines are used upto a K absorption-edge energy a few keV below the characteristic line of the x-ray tube anode element. The continuum can be used for excitation if the voltage to the x-ray tube is set sufficiently high to place the continuum maximum at energy higher than the absorption edge and if a back-ground filter is used. In these cases, K absorption-edge energies can be used upto around 66 % of the maximum operating kV of the x-ray tube. However, the observed peaks lie on a continuum background and reduce the signal-to-noise ratio.

For a 50-kV x-ray tube, absorption edges as high as 30 keV can be used if the element is present in sufficient concentration. For a 30-kV rhodium or silver tube, one is restricted essentially to excitation by the characteristic tube lines. This is of no great concern unless there is a special interest in the elements between atomic numbers 41 and 50 (niobium to tin). Elements above atomic number 50 (40 for a 30-kV system) are normally to be determined using the L lines of their x-ray spectra.

To excite all L lines, the incident x-ray photon energy is to exceed the LI absorption edge. For practical use, the energy of the L lines is to be higher than around l keV. For the L line spectra, this needs atomic numbers higher than 30. At such low x-ray energies, absorption of the x-rays and low fluorescent yield in the L emission in this region needs high concentration of the element to be determined and excellent sample preparation. Overlap of the K lines of the low atomic number elements in this region also causes difficulty. For example, the K lines of phosphorus overlap with the L lines of zirconium and the M lines of iridium at around 2 keV. These problems are to be considered, but are to a large degree solved by careful use of processing software.

Once the x-ray spectral lines are selected for determination of the elements, the next step is to decide whether all analyte elements in the sample can be determined with one instrumental setting. Although the multi-element capability of EDS is useful, all elements in every sample cannot be determined with a single set of instrument parameters. Some applications need more than one condition, such as a mixture of low atomic number elements and transition elements. The transition elements are best determined by excitation using the K lines of rhodium or silver and the low atomic number elements with the L lines or a properly adjusted continuum using a background filter. Computer control of instrument parameters facilitates changing the conditions. Whether automatic or manual control is used, all samples are to be analyzed under one set of conditions, then analyzed again using the alternate set. This is preferred over changing conditions between samples.

X-ray tube operating voltage affects the efficiency of excitation of each element in the spectrum and the integrated x-ray photon flux from the tube. The tube current affects the flux only. Hence, once the operating kV has been set, the tube current typically is adjusted until the system is processing counts efficiently. System dead time is to be maintained below, but near, 50 %. The voltage and current settings for the x-ray tube have a sensitive effect on the rate of information acquisition and count distribution among the respective spectral peaks for a given type of sample.

Selection of primary tube filter thickness is important. If the filter is changed, the tube current, and sometimes the voltage, frequently needs resetting since the filter alters the intensity distribution of the x-rays striking the sample. When characteristic tube lines are used for excitation, the filter is normally made from the tube anode element. The intensity of the transmitted x-rays decrease exponentially with increasing filter thickness. It is common to have two or three primary filters made from the tube anode element in the filter holder. The selection is to reflect optimum count rate corresponding with reasonable current and voltage settings. Thicker filters attenuate lower energy radiation more effectively and reduce the excitation efficiency for the element with low absorption coefficients.

The remaining decision is the choice of atmosphere in the sample chamber. If x-rays below around 5 keV are to be implemented, use of a vacuum can be advantageous. Intensity can increase sufficiently to reduce significantly the counting time needed to achieve an adequate number of counts. If the concentration of elements yielding these x-rays is sufficiently high, the vacuum may not be needed. Because of the extra precautions needed in sample criteria and handling, a vacuum path is not to be used unless significant benefit is realized. Similar reasoning applies to the helium atmosphere.

These guidelines are useful for initial selection of operating conditions. The instrumental parameters are interactive, and a change in one parameter needs adjustment of another. For example, selection of a thicker primary filter or a decrease in the tube voltage needs an increase in the tube current.

Sample preparation

The care taken to determine the best method of sample preparation for a given material and careful adherence to that method frequently determine the quality of results obtained. Sample preparation is the single most important step in an analysis, yet it is frequently given the least attention. In most cases, the stability and overall reproducibility of x-ray instrumentation are the least significant factor affecting the precision of analytical measurements. Frequently, the precision of analytical results expected from x-ray spectrometric determinations is expressed in terms of the theoretical statistics of measurement of x-ray intensities.

When replicate samples are prepared and actual standard deviations measured, deviations are found to be larger than those predicted by counting statistics. If precision is poor, any one analytical result can also be poor, since it can differ substantially from the ‘true’ value. The variety of sample types which can be analyzed using x-ray spectrometry necessitates different sample preparation techniques.

Samples are frequently classified as infinitely thick or infinitely thin based on measurement of the attenuation of x-rays. Samples are considered to be infinitely thick if further increase in the thickness yields no increase in observed x-ray intensity. The critical value for infinite thickness depends on the energy of the emitted x-radiation and the mass absorption coefficient of the sample matrix for those x-rays. For pure iron, the critical thickness is around 40 m for iron x-rays.

Although infinitely thin samples afford several advantages, it is rarely feasible to prepare them from routine samples. Many samples fall between these two cases and need extreme care in preparation. In addition to preparation of the sample, precise positioning of the sample in the spectrometer is critical for quantitative determinations.

Solid samples – These are defined as single bulk materials, as opposed to powders, filings, or turnings. Solid samples can frequently be machined to the shape and dimensions of the sample holder. The processing is not to contaminate the sample surface to be used for analysis. In other cases, small parts and pieces are to be analyzed as received. The reproducible positioning of these samples in the spectrometer is critical. It is frequently useful to fashion a wax mould of the part which fits into the sample holder. Using the mould as a positioning aid, other identical samples can be reproducibly placed in the spectrometer.

Samples taken from unfinished bulk material frequently needs surface preparation prior to quantitative analysis. Surface finishing can be done using a polishing wheel, steel wool, or belt grinder, with subsequent polishing using increasingly fine abrasives. Surface roughness less than 100 micrometers is normally sufficient for x-ray energies above around 5 keV, but surface roughness of less than 20 micrometers to 40 micrometers is needed for energies down to around 2 keV. Several precautions are necessary. Alloys of soft metals can smear on the surface as the sample is polished, resulting in a surface coating of the soft metal which yields high x-ray intensities for that element and subsequently high analytical results.

Polishing grooves on the surface of the sample can seriously affect the measured intensity of low-energy x-rays. This can be examined by repetitive measurement of the intensity of a sample after 45 degrees or 90 degrees rotation. Use of a sample spinner reduces this effect. If a sample spinner is not available, the sample is to be placed in the spectrometer such that the incident x-radiation is parallel to the polishing direction.

Powders and briquettes – Powder samples can be received as powders or prepared from pulverized bulk material too inhomogeneous for direct analysis. Typical bulk samples pulverized before analysis are ores, and refractory materials. Powders can be analyzed using the spectrometer, pressed into pellets or briquettes, or fused with a flux, such as lithium tetra borate. The fused product can be reground and pressed or cast as a disk. For precise quantitative determinations, loose powders are rarely acceptable, especially when low-energy x-rays are used. Pressed briquettes are more reliable. However, experience indicates that the best compromise is reground and pressed fusion products. This technique eliminates several problems associated with particle-size effects.

Particle-size effects result from the absorption of the incident and emitted x-rays within an individual particle. If the mass absorption coefficient of the sample matrix is high for the x-radiation used, particles even a few microns in diameter can considerably affect attenuation of the radiation within each particle. If the sample consists of particles of various sizes, or the particle size varies between samples, the resulting x-ray intensities can be difficult to interpret. This problem is compounded by the tendency of a material composed of a mixture of particle sizes to segregate when packed.

Determination of elements using low-energy x-radiation can lead to errors from particle-size effects of as much as 50 %. If the needed speed of analysis prohibits use of fusion techniques, direct determination from packed powders can be considered. The sample is to be ground, if possible, to a particle size below the critical value. The grinding time needed frequently can be ascertained by measuring the intensity from a reference sample at increasing grinding times until no further increase is observed. The lowest energy x-ray to be used in analysis is to be selected for this test.

Briquettes or pressed powders yield better precision than packed powder samples and are relatively simple and economical to prepare. In several cases, only a hydraulic press and a suitable die are needed. In the simplest case, the die diameter is to be the same as the sample holder so that the pressed briquettes fit directly into the holder. The amount of pressure needed to press a briquette which yields maximum intensity depends on the sample matrix, the energy of the x-ray to be used, and the initial particle size of the sample. Hence, prior grinding of the sample to a particle size which is less than 100 micrometers is advisable.

A series of briquettes are to be prepared from a homogeneous powder using increasing pressure. The measured intensity of the x-ray lines to be used in the analysis is plotted versus the briquetting pressure. The measured intensity is to approach a fixed value, perhaps asymptotically. Pressures of 138 MPa to 276 MPa may be needed. For materials which do not cohere to form stable briquettes, a binding agent is needed. Acceptable binding agents include powdered cellulose, detergent powders, starch, stearic acid, boric acid, lithium carbonate, polyvinyl alcohol, and commercial binders.

Briquettes which are not mechanically stable can be improved by pressing them into backing of pre-pressed binder, such as boric acid, or by the use of a die which presses a cup from a binding agent. The sample powder can then be pressed into a briquette supported by the cup. Improved results are frequently achieved if around 0.1 mm to 0.5 mm is removed from the surface of the briquette prior to the measurement.

Fusion of materials – Fusion of materials with a flux can be performed for several reasons. Some refractory materials cannot be dissolved, ground into fine powders, or converted into a suitable homogeneous form for x-ray spectrometric analysis. Other samples can have compositions which lead to severe inter-element effects, and dilution in the flux reduces these. The fused product, cast into a glass button, provides a stable, homogeneous sample well suited for x-ray measurements. The disadvantages of fusion techniques are the time and material costs involved as well as the dilution of the elements which can result in a reduction in x-ray intensity. However, when other methods of sample preparation fail, fusion frequently provides the needed results.

Low-temperature fusions can be carried out using potassium pyro-sulphate. More common are the glass-forming fusions with lithium borate, lithium tetra-borate, or sodium tetra-borate. Flux-to-sample ratios range from 1:1 to 10:1. The lithium fluxes have lower mass absorption coefficients and hence less effect on the intensity of the low-energy x-rays. An immense variety of flux-additive recipes are reported for various sample types. Lithium carbonate can be added to render acidic samples more soluble in the flux. Lithium fluoride has the same effect on basic samples. Lithium carbonate also reduces the fusion temperature. Oxidants, such as sodium nitrate and potassium chlorate, can be added to sulphides and other mixtures to prevent loss of these elements.

Filters and ion-exchange resins – Various filters, ion-exchange resin beads, and ion-exchange resin-impregnated filter papers have become important sampling substrates for samples for x-ray spectrometric analysis. Filter materials can be composed of filter paper, membrane filters, glass fiber filters, and so on. Filters are used in a variety of applications. One widely used application is in the collection of aerosol samples from the atmosphere. Loadings of several milligrams of sample on the filter can correspond to sampling several hundred cubic meters of atmosphere. Such sampling can be performed in any environment. Many elements can be determined directly on these filters by x-ray spectrometric analysis. Particulate samples collected in this way present problems, stemming primarily from particle-size effects, which are reduced in part by the need to collect two particle-size regions using dichotomous samplers. With these units, particles are separated into those smaller and those larger than around 2 micrometers in diameter.

The smaller particles tend to represent man-made materials; the larger ones are of natural origin. The smaller particles show fewer particle-size effects, and an x-ray spectrometric determination of even low atomic number elements, such as sulphur, is possible. Glass fiber filters are frequently used for this purpose. Filters can also be used for non-aerosol atmospheric components, such as reactive gases. Filter materials can be impregnated with a reagent reactive to the gas which traps it chemically. Sampling is accomplished by conveying atmospheric gases through a treated filter under carefully controlled conditions. An example is a damp filter treated with ferric ion solution used to trap hydrogen sulphide. The excess iron can be rinsed from the filter, but the precipitated ferrous sulphide remains. The sulphur can be determined directly or indirectly by measuring the iron x-radiation. The key to determining atmospheric components is the development of suitable standards.

Filters can be used to determine solution components in ways parallel to those described for atmospheric components. Particulate materials can be filtered directly from solution. For example, particulate materials in environmental water samples are defined as that which is filtered using a 0.45 micrometer pore diameter membrane filter. Hence, filtration of particles from water can be accomplished using such filters, and direct x-ray spectrometric analysis performed. Application of filter sampling to dissolved elements in water is becoming more common. The principle is similar to the reactive reagent-impregnated filter application to atmospheric gases. In some cases, the filter can be impregnated with ion-exchange resins which trap ions as the solution passes through the filter.

Procedures using ion-exchange resin-impregnated filters are to be carefully checked, since several passes of the solution can be needed, and distribution of the ions across the paper thickness is seldom uniform. However, for solutions, a reaction can be performed prior to filtration. For example, many ions can be precipitated quantitatively from aqueous solution, even at parts per billion concentration levels. The precipitates can be collected using 0.45 micrometers pore diameter membrane filters, which are then mounted between two Mylar sheets retained by ring clips on a standard plastic sample cup. Simultaneous multi-element determinations are then performed using XRF spectrometer.

Detection limits on the filters of as low as a few tenths of a microgram are common. If 100 g of sample solution is used, this corresponds to the detection limits of a few parts per billion in the sample. Standards are easily prepared as aqueous solutions. ‘Standard reference materials’ (SRM) for environmental waters and industrial effluent water are available.

Thin-film samples – Thin-film samples are ideal for x-ray spectrometric analysis. The x-ray intensity of an infinitely thin sample is proportional to the mass of the element on the film, and the spectral intensities are free of inter-element and mass absorption coefficient effects. However, in practice, perfect thin-film samples are rarely encountered. Powder samples of sufficiently small and homogeneous particle size can be distributed on an adhesive surface, such as cellophane tape, or placed between two drum-tight layers of Mylar film mounted on a sample cup.

More important thin-film types are platings and coatings on various substrates. Analysis of these sample types is increasingly important for the electronics industry. Of particular concern are measurements of film thickness and composition. Several techniques can be used, including the substrate intensity attenuation method, the coating intensity method, various intensity ratio methods, and the variable takeoff angle method. The last method is not practical in most commercial spectrometers. To be infinitely thin to most x-rays used in x-ray spectrometric analyses, the samples are to be 10 micrometers to 200 micrometers thick.

Liquids – Liquids can also be analyzed using x-ray spectrometry. The design of x-ray spectrometric instrumentation using inverted optics, in which the sample is above the x-ray source and detector, facilitates the use of liquid samples. This convenient geometry demands caution in the preparation of liquid samples to avoid damaging the source or detector by such accidents as spills and leaking sample cups.

Quantitative standards are easily prepared for liquid samples. However, since solvents are normally composed of low atomic number elements, the Rayleigh and Compton scatter intensity is high, which increases background and leads to high limits of detection. These problems can be minimized by use of suitable primary tube filters, which reduce the scattered x-radiation in the analytically useful region.

Care is to be taken with liquids containing suspended solids. If the suspension settles during the measurement time, the x-ray intensity of the contents of the sediment is enhanced. The x-ray intensity from solution components or homogeneous suspension can decrease as a result of sediment absorption, which leads to erroneous results. This possibility is tested by brief, repetitive measurements, beginning immediately after a sample is prepared. Any observed increase or decrease in intensity with time indicates segregation in the sample. In these cases, an additive which stabilizes the suspension can be used, or the suspended content can be collected on a filter for analysis.

Special sample types – Applications of x-ray spectrometric analysis do not always provide convenient samples which can fit one of the above categories. Non-destructive analyses are occasionally needed on production products which are not 32 mm diameter circles of infinite thickness. Examples include computer disks, machined parts, and long, coated strips or wire. In these cases, a sample compartment which accommodates the samples can frequently be designed. With the development of the mercuric iodide detector, which can provide adequate resolution for many analyses without a liquid nitrogen dewar, special analytical systems for on-line and non-destructive analysis of large samples can become increasingly feasible.

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