TOTAL REFLECTION X-RAY FLUORESCENCE ANALYSIS

INTRODUCTION

Total reflection x-ray fluorescence (TXRF) analysis is a powerful analytical tool with respect to detectable elemental range, simplicity of quantification and detection limits. This includes the capacity to detect almost all elements of the periodic system, namely from boron to uranium. Even the highest-Z elements of the actinides can be detected. Quantitatively, the dynamic range covers several orders of magnitude, so ultra-trace element levels to major elemental concentrations can be determined. In terms of detection limits, the levels of femtogram absolute detectable masses under optimized excitation–detection conditions can be reached. Some of these features can be topped with additional properties such as rapid analysis time of a few seconds and simultaneous detection of the elements present. In some applications, non-destructiveness is of importance, e.g. while dealing with precious substances of cultural values from fine arts or also in cases of forensic investigations if only small amounts of sample are available. TXRF is an energy-dispersive XRF (EDXRF) technique, and excitation geometry with angles below the critical angle of total reflection is perfectly suited for these investigations.

The above statements emphasize the analytical power, and in addition to these arguments one can add the large number of applications that has led to the revival of x-ray fluorescence analysis for ultra-trace element analysis. The applications range from the interesting fields of medicine, techniques and environment to forensic, fine arts, extra-terrestrial samples and fundamental research. With new physical and technical ideas leading to modifications of the physical properties of the primary radiation, e.g. monoenergetic, linearly polarized, highly intense, or on the detector side high resolution, high counting capacity, large area or even arrays of detectors, new perspectives are opening up for TXRF

In Fig. 1 the experimental set-up of conventional EDXRF and TXRF is schematically shown. As TXRF is basically an energy-dispersive analytical technique, the main difference to conventional EDXRF is neither the source nor the detector but the geometry of excitation at small incidence angles below the critical angle of total reflection.

     Figure 1 Comparison between conventional (left) and total reflection mode of excitation (right).

THEORY

The theory of x-ray total reflection is based on the phenomenon that at an incident angle below the critical angle the narrow collimated primary beam is totally reflected. A beam gets reflected from a flat polished surface of any material at the same angle as the incident one and has almost the same intensity as the primary beam (total intensity is reflected), except for a small portion that is refracted and penetrates the reflecting medium. This evanescent wave loses intensity exponentially as it penetrates deeper into the medium. In Fig. 2, the fundamental formalism of x-ray total reflection is shown, based on the Fresnel formalism and the complex index of refraction for x-rays, which is given below. The index of refraction for x-rays differs only slightly from 1, which is described theoretically by the value of υ which is in the range of 10-5 . For many materials the angles involved are small, typically a few milli radians or a tenth of a degree.

      Figure 2 Sketch of the theoretical conditions for x-ray total

Applications to chemical analysis:

The incident radiation in TXRF is a fine, collimated, almost parallel beam with typical dimensions of 8 mm width and only 50 μm height. This narrow beam impinges at an angle below the critical angle of total reflection (1.8 mrad or 0.1 degrees in the case of a monoenergetic Mo K˛ radiation and Si reflector) on the surface of a flat polished material. that serves as the sample carrier. In the case of chemical analysis of different samples, such as from the environment, medicine or technical products, different procedures apply. The sample has to be transferred into the liquid form by chemical digestion procedures. A small volume of 1–20 μl of the dissolved sample is taken using a pipette. The acidic or aqueous solution is dropped at the center of the reflector and dried by infrared heating, on a hot plate or in vacuum.

Possible applications of TXRF.

Environment	Water: sea, rain, pore water, river, mineral, spring water, drinking water, chemicals and deionized water
	Air: aerosols, vapour, air dust, airborne particles, fresh air
	Soil: sewage sludge, sediments
	Plant material: Algae, fine roots, cucumber plants, pollen.
	Foodstuff: fish, flour,  fruits, crab, mussel, mushrooms, nuts, vegetables, wine, tea, soft drinks, onion
	Drinks: Coffee,  spirits and beverages, honey.
Medicine/biology	Body fluids: blood, serum, urine, amniotic fluid,  cerebrospinal fluid
	Tissue: hair, kidney, lung, liver, stomach, nails, colon
	Various enzymes, polysaccharides, glucose, proteins, cosmetics, biofilms, human bones
Industrial/technical applications	Surface analysis: Si wafer surfaces, GaAs wafer surfaces
	Implanted ions: Depth and profile variations
	Thin films: single layers, multilayers
	Oil: Crude oil,  fuel oil, grease, pure fuel oil, waste oil, petroleum, oil-shale ash, diesel
	Chemicals: Acids,  bases,salts, solvents
	Fusion/fission research: trans mutational elements in Al C Cu, iodine in water
Mineralogy	Ores, rocks, minerals, rare earth elements, quartz, mineral sands, diamond, crystals
	Geological materials, bio-mineralisation
Fine arts/archaeological/forensic	Pigments, paintings, varnish21
	Bronzes, pottery, jewellery, manuscripts, Egyptian masks
	Textile fibres, glass, cognac, dollar bills, gunshot residue, drugs, tapes, sperm, finger prints.

Sample preparation

The samples can be from many scientific disciplines and thus the physical state will be different. The best-suited samples for TXRF are in the liquid state—either in the form of aqueous or acidic solutions—so if solids or powders are to be analysed, these samples must be transferred into the liquid state. The presented procedures are typical but can of course be adapted to the sample type, and the world of chemistry is fully open to new ideas, given in detail in the respective literature. Sample preparation has been discussed by several authors and many publications deal with special methods. Even so, the complex subject leaves a lot of ideas open to get the sample prepared in a way that the elements present can be detected even if they are at the lowest concentrations. Pre-concentration methods or selective enrichment techniques by chelation or electrochemical methods can be introduced to ensure that adequate masses are present on the sample reflector in the range of absolute picograms from very low-concentration samples, e.g. sea water in which the salt extraction also is an important preparation step. Recently, the collection of fine dust and also aerosols directly on the sample carrier in a short time of a few minutes to several hours by multi-stage samplers and the direct analysis of the minute masses collected by TXRF were successfully proven in large-scale experimental series in different parts of the world at locations of interest.

INSTRUMENTATION IN TXRF

Various combinations of x-ray sources, spectral modification elements, reflector materials and detectors can be used to optimize excitation and detection conditions. Measurements can be performed in air, in a He atmosphere or in a vacuum chamber. Vacuum conditions are mandatory for the detection of light elements to avoid absorption, but it is also advantageous because the scattering of primary x-rays from air is avoided. The components of a TXRF spectrometer are shown in the below figure

        Figure 3 Components of a TXRF spectrometer

 Sources of x-rays for TXRF are mainly x-ray tubes, ranging from low power (50–75W) to high-power standing anodes of up to 3000W and finally rotating anodes up to 18 kW. The appropriate focus is a line focus with dimensions 8 or 12mm long and 40 μm wide. Everything is done to get a high flux of photons onto the sample. There is radiation from the ultimate source with best properties of having a naturally collimated beam characteristic, an extremely high flux and a linearly polarized beam—the SR. Even though it is difficult to get access to SR, the results achievable show the importance of this effective combination of the source and TXRF, from which ultimate low detection limits of a few femtogram have been achieved.

The beam from an x-ray tube is unpolarised and has a continuous spectral distribution of the characteristic radiation. In many cases, a monoenergetic excitation is the preferred one because the background is optimally low as only scattered photons of single energy are present and will appear as two lines elastically and Compton-scattered in the spectrum. The first low-cost approach to modify the spectrum was an optical flat in the beam path and taking advantage of the energy dependence of the critical angle to suppress the high-energy part of the bremsstrahlung spectrum. This leads to reduced background, in particular in the low-energy region, as the Compton edge produced by the backscattered high-energy photons disappears. Versions with two reflectors attached togetherwith a spacing of 50 mm lead to a double-reflector monochromator. Efficient monochromators are nowadays available using multilayers with reflectivities in the range of up to 80% of the characteristic radiation of the anode material of choice. Typically in use are combinations of layered structures made of W–C, Ni–C andMo–Si with a d spacing of 2–3 nm. Thus, they are adjusted to fulfill the Bragg equation and the full spectrum is modified to be monoenergetic. Using modern technology to bend these structures, it is possible to design x-ray optical components that focus the beam with a small divergence, thereby increasing the flux of photons in the focal spot which is designed to be at the sample position. The result is an increase in intensity on the sample several times more than that with the non-focussing flat multilayer. These optical components are commercially available and can be inserted in the beam path of the TXRF spectrometer to improve further detection limits. 

Quantitative TXRF

The conversion of the measured intensities into concentrations is one of the most important steps in analytical XRF. In the special case of TXRF, the complications are rather completely removed, as the approach for the thin-film sample can be applied, which leads to a simple and linear relation between the intensity, I, and concentration, C, of the element considered. The addition of an internal standard with known concentration leads to a simple quantification procedure, as follows:

• Choose or add to the multi-element standard one element as internal standard, which is the reference for calibration of the spectrometer.
• Establish the intensity vs concentration curve as the regression curve with reference to the internal standard to determine the sensitivity, Sstd/Si, from multi-element standard.
• Add the internal standard of known concentration Cstd to the unknown sample.
• Measure the intensity of element Ii and intensity of internal standard Istd.
• Determine the concentration of unknown element Ci using the relation:

Advantages of TXRF

• Double excitation by direct and reflected beams
• Almost no penetration of the primary radiation into the substrate, resulting in low background Large solid angle, as the detector can be placed close to the reflector surface 
• Large solid angle, as the detector can be placed close to the reflector surface
• The consequent improved signal/background and improved detection limits
• Very low detection limits: femtogram levels, picograms per gram concentrations, 108 atoms/cm2 of metal contamination detectable on wafer surfaces

Environment

Water:

sea, rain, pore water, river, mineral, spring water, drinking water, chemicals and deionized water

Air:

aerosols, vapour, air dust, airborne particles, fresh air

Soil:

sewage sludge, sediments

Plant material:

Algae, fine roots, cucumber plants, pollen.

Foodstuff:

fish, flour,  fruits, crab, mussel, mushrooms, nuts,

vegetables, wine, tea, soft drinks, onion

Drinks:

Coffee,  spirits and beverages, honey.

Medicine/biology

Body fluids:

blood, serum, urine, amniotic fluid,  cerebrospinal fluid

Tissue: hair, kidney, lung, liver, stomach, nails, colon

Various enzymes, polysaccharides, glucose, proteins,

cosmetics, biofilms, human bones

Industrial/technical

applications

Surface analysis:

Si wafer surfaces, GaAs wafer surfaces

Implanted ions:

Depth and profile variations

Thin films:

single layers, multilayers

Oil:

Crude oil,  fuel oil, grease, pure fuel oil, waste oil, petroleum, oil-shale ash, diesel

Chemicals:

Acids,  bases,salts, solvents

Fusion/fission research:

trans mutational elements in Al C Cu, iodine in

water

Mineralogy

Ores, rocks, minerals, rare earth elements, quartz,

mineral sands, diamond, crystals

Geological materials, bio-mineralisation

Fine

arts/archaeological/forensic

Pigments, paintings, varnish21

Bronzes, pottery, jewellery, manuscripts, Egyptian masks

Textile fibres, glass, cognac, dollar bills, gunshot residue, drugs, tapes, sperm, finger prints.

ENERGY DISPERSIVE X-RAY FLUORESCENCE (ED-XRF)

INTRODUCTION

In Energy Dispersive X-Ray Fluorescence spectrometry (ED-XRF), the identification of characteristic lines is performed using detectors that directly measure the energy of the photons. In energy dispersive X-ray fluorescence analysis (EDXRF), a solid-state detector is used to count the photons, simultaneously sorting them according to energy and storing the result in a multichannel memory. The result is an X-ray energy vs. intensity spectrum. The range of detectable elements ranges from Be (Z = 4) for the light elements and goes up to U (Z = 92) on the high atomic number Z side. In principle, XRF analysis is a multielement analytical technique and in particular, the simultaneous determination of all the detectable elements present in the sample is inherently possible with EDXRF. In WDXRF both the sequential and the simultaneous detection modes are possible. Although energy dispersive detectors generally exhibit poorer energy resolution than wavelength dispersive analyzers, they are capable of detecting simultaneously a wide range of energies. The most frequently used detector in EDXRF is the silicon semiconductor detector, which nowadays can have excellent energy resolution.

INSTRUMNTATION

An ED-XRF system consists of several basic functional components, as shown in

Figure The major components are as follows :

1. X- Ray excitation source
2. Sample Chamber
3. Si (Li) detector
4. Preamplifier
5. Main Amplifier
6. Multichannel Pulse Height Analyzer

The properties and performances of an EDXRF system differ upon the electronics and the enhancements from the computer software.   

Typical ED-XRF detection arrangement.

We will discuss in detail for every component :

1. Excitation Mode

A) Direct Tube Excitation .

Because of the simplicity of the instrument and the availability of a high photon output flux by using direct tube excitation, the X-ray fluorescence spectrometer equipped with an Xray tube as direct excitation source is gaining more and more attention from manufactures. The spectrometer is more compact and cheaper compared to secondary target systems. Of course, the drawback is still the less flexible selection of excitation energy. However, by using an appropriate filter between tube and sample, one can obtain an optimal excitation.

The most popular X-ray tube used in direct excitation ED spectrometer is the side window tube for reasons of simplicity and safety. With direct tube excitation, low powered X-ray tubes (< 100 W) can be used. These air cooled tubes are very compact, less expensive, and only require compact, light, inexpensive, highly regulated solid state power supplies. In a WD spectrometer, on the other hand, high-power tubes (3-4 kW) are essential to compensate for the losses in the crystal and collimator. With the low-power tubes used in ED spectrometer, better excitation of light elements (i.e. low-Z element), analysis of smaller samples, small spot analysis, and compact systems can be obtained.

B) Secondary Target Excitation.

The principle of secondary target excitation was developed to avoid the intense

Bremsstrahlung continuum from the X-ray tube by using a target between tube and sample. 

Schematic illustration of secondary target excitation

The ratio of the intensity of the characteristic lines to that the continuum in secondary target excitation is much higher than that in direct tube excitation because the continuum part of the excitation spectrum of the secondary target is generated only by scattering. One can excite various elements efficiently by selecting a secondary target that has characteristic lines just above the absorption edges of the elements of interest in the sample. Therefore, secondary target excitation has some obvious advantages over direct tube excitation: its flexibility for getting an optimized and near monochromatic excitation providing a better selectivity and an improved sensitivity. However, to compensate for the intensity losses that occur at the secondary scatterer, a high-powered tube as used in WD spectrometers is required; making the whole system more sophisticated and expensive compared to direct tube excitation setups.

C) Radio Isotopic Excitation.

A variety of about 30 commercially available radio-isotopic materials can be chosen for an optimal excitation. The X-rays and/or γ-rays emitted from these radio-isotopic sources cover a wide range (10 – 60 keV) of excitation energies. With a high energy source like 241 Am, K lines instead L lines can be used for quantification in the case of analyzing high-Z rare earth elements, with considerably less matrix effects and spectrum overlaps. Sometimes the same idea as in the secondary target excitation is used to avoid non-photon radiation. A proper design of excitation-detection geometry can improve greatly the sensitivity and accuracy of the XRF analysis with such excitation source. The disadvantages of using radioisotopic sources however lie in their low photon output, intensity decay and storage problems.

2. Detectors

Energy dispersive X-ray spectrometry is based upon the ability of the detector to create signals proportional to the X-ray photon energy, therefore, mechanical devices, such as analyzing crystals, are not required as in wdxrf . Several types of detectors have been employed, including silicon, germanium and mercuric iodide .

Cross section of an Si(Li) detector crystal with p-i-n structure and the

production of electron-hole pair.

The solid state, lithium-drifted silicon detector, Si(Li), was developed and applied to Xray detection in the 1960’s. Early 1970’s, this detector was firmly established in the field of X-ray spectrometry, and was applied as an X-ray detection system for scanning Electron Microscopy (SEM) as well as X-ray spectrometry. The principal advantage of the Si(Li) detector is its excellent resolution.

Si(Li) detector can be considered as a layered structure in which a lithium-drifted active region separates a p-type entry side from an 

n-type side. Under reversed bias of approximately 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, photoionization occurs with an electron-hole pair created for each 3.8 eV of photon energy. Ideally, the detector should completely collect the charge created by each photon entry, and result in a response for only that energy. In reality, some background counts appear because of the energy loss in the detector. Although these are kept to a minimum by engineering, incomplete charge collection in the detector is a contributor to background counts. In the X-ray spectrometric, important region of 1 – 20 keV, silicon detectors have excellent efficiency for conversion of X-ray photon energy into charge. Some of the photon energy may be lost by photoelectric absorption of the incident X-ray, creating an excited Si atom which relaxes to yield an Si Kα X-ray. This X-ray may escape from the detector, resulting in an energy loss equivalent to the photon energy; in the case of Si Kα, this is 1.74 keV. Therefore, an escape peak 1.74 keV lower than the true photon energy of the detected X-ray may be observed for intense peaks. For Si(Li) detectors, these are usually a few tenths of one percent, and never more than 2%, of the intensity of the main peak.

 The Si(Li) detector schematic

Resolution of an energy dispersive X-ray spectrometer is normally expressed as the Full Width at Half Maximum amplitude (FWHM) of the Mn X-ray at 5.9 keV. The resolution will be somewhat count rate dependent. Commercial spectrometers are supplied routinely with detectors which display approximately 145 eV (FWHM @ 5.9 keV). The resolution of the system is a result of both electronic noise and statistical variations in conversion of the photon energy. Electronic noise is minimized by cooling the detector, and the associated preamplifier with liquid nitrogen (Figure). In many cases, half of the peak width is a result of electronic noise.

3. Pulse Height Analysis

The X-ray spectrum of the sample is obtained by processing the energy distribution of X-ray photons which enter the detector. A single event of one X-ray photon entering the detector causes photoionization and produces a charge proportional to the photon energy. Numerous electrical sequences must take place before this charge can be converted to a data point in the spectrum.

When an X-ray photons enters the Si(Li) detector, it is converted into an electrical charge which is coupled to a Field Effect Transistor (FET). The FET, and the rest of the associated electronics which make up 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. Because photons vary in both energy and number per unit time, the output signal, due to successive photons being emitted by a multielement sample, resembles a staircase with various step heights and time spacing. When the output reaches a predetermined level, the detector and the FET circuitry is reset to its starting level, and the process repeated.

The preamplifier stage integrates each detector charge signal to generate a voltage step proportional to the charge. This is then amplified and shaped in a series of integrating and differentiating stages. Owing to the finite pulse-shaping time, in the range of microseconds, the system will not accept any other incoming signals in the meanwhile (dead time), but extend its measuring time instead. In a further step the height of these signals is digitized as a channel number (analog-to-digital converter, ADC), stored to a memory (multichannel analyzed, MCA) and finally displayed as a spectrum, where the number of counts reflects the respective intensity. In a more modern approach, the output signals of the preamplifier are digitized directly, which can increase the throughput of the system significantly.

4. Energy Resolution

Mn-Kα spectrum and calibrated pulser

The energy resolution of the EDXRF spectrometer determines the ability of a given system to resolve characteristic X-rays from multiple-element samples and is normally defined as the full width at half maximum (FWHM) of the pulse-height distribution measured for a monoenergetic X-ray. A conventional choise of X-ray energy is 5.9 keV, corresponding to the Kα energy of Mn. Figure II.6 shows a typical pulse-height spectrum of Mn-Kα X-rays simultaneously with a calibrated pulser. The purpose of the pulser measurement is to monitor the resolution of the electronic system independent of any peak broadening due to the detector itself. Typical state-of the art detectors Si(Li) and Ge(HP) achieve 130 to 170 eV, but depends strongly on the size of the crystal. The smaller the crystal, the better is the resolution.

X RAY FLUORESCENCE

INTRODUCTION

X-ray fluorescence (XRF) analysis is one of the most common non-destructive methods for  qualitative as well as quantitative determination of elemental composition of materials. It is suitable for solids, liquids as well as powders. There are two main methodological techniques that are wavelength dispersive analysis (WD-XRF) and energy dispersive analysis (ED-XRF) (In the next post we will briefly discuss about WDXRF & EDXRF ,this post will only explain the basics of x-ray fluorescence which is required to understand the upcoming posts about WDXRF & EDXRF ). The spectra are collected simultaneously in a wide energy range. The range of detectable materials covers all elements from Sodium (Na) to Uranium (U) and the concentration can range from 100% down to ppm. Detection limit depends upon the specific element and the sample matrix but in general heavier elements have higher detection limit.

X-ray Fluorescence (XRF) Spectroscopy involves measuring the intensity of X-rays emitted from a specimen as a function of energy or wavelength. The energies of large intensity lines are characteristic of atoms of the specimen. The intensities of observed lines for a given atom vary as the amount of that atom present in the specimen. Qualitative analysis involves identifying atoms present in a specimen by associating observed characteristic lines with their atoms. Quantitative analysis involves determining the amount of each atom present in the specimen from the intensity of measured characteristic X-ray lines. The emission of characteristic atomic X-ray photons occurs when a vacancy in an inner electron state is formed, and an outer orbit electron makes a transition to that vacant state. The  energy of the emitted photon is equal to the difference in electron energy levels of the transition. As the electron energy levels are characteristic of the atom, the energy of the emitted photon is characteristic of the atom. Molecular bonds generally occur between outer electrons of a molecule leaving inner electron states unperturbed. As X-ray fluorescence involves transitions to inner electron states, the energy of characteristic X-ray radiation is usually unaffected by molecular chemistry. This makes XRF a powerful tool of chemical analysis in all kinds of materials. In a liquid, fluoresced X-rays are usually little affected by other atoms in the liquid and line intensities are usually directly proportional to the amount of that atom present in the liquid. In a solid, atoms of the specimen both absorb and enhance characteristic X-ray radiation. These interactions are termed 'matrix effects' and much of quantitative analysis with XRF spectroscopy is concerned with correcting for these effects.

X rays are electromagnetic radiation. All X-rays represent a very energetic portion of

the electromagnetic spectrum (Table 1) and have short wavelengths of about 0.1 to 100 angstroms (Å). They are bounded by ultraviolet light at long wavelengths and gamma rays at short wavelengths X-rays in the range from 50 to 100 Å are termed soft X-rays because they have lower energies and are easily absorbed.The range of interest for X-ray is approximately from 0.1 to 100 Å. Although,angstroms are used throughout these notes, they are not accepted as SI unit. Wavelengths should be expressed in nanometers (nm), which are 10-9 meters (1 Å = 10-10 m), but most texts and articles on micro probe analysis retain the use of the angstroms. Another commonly used unit is the micron, which more correctly should be termed  micrometer  (μm), a micrometer is 104 Å. The relationship between the wavelength of electromagnetic radiation and its corpuscular energy (E) is derived as follows. 

For all electromagnetic radiation:

E = h ν ;

where:

h is the Planck constant (6.62 10-24 J.s);

ν is the frequency expressed in Hertz.

For all wavelengths,

ν = c / λ ;

where:

c = speed of light (2.99782 108 m/s);

λ= wavelength (Å).

Thus:

E = hc / λ = 1.9863610−24 /λ ;

where E is in Joule and λ in meters.

The conversion to angstroms and electron volts (1 eV = 1.6021 10-19 Joule) yields the

Duane-Hunt equation:

E(eV) 12.396/ (A)

= λ . 

Note the inversion relationship. Short wavelengths correspond to high energies and long wavelengths to low energies. Energies for the range of X-ray wavelengths are 124 keV (0.1 Å) to 124 eV (100 Å). The magnitudes of X-ray energies suggested to early workers that Xrays are produced from within an atom. Those produced from a material consist of two distinct superimposed components: continuum (or white) radiation, which has a continuous distribution of intensities over all wavelengths, and characteristic radiation, which occurs as a peak of variable intensity at discrete wavelengths.

PROPERTIES OF X-RAYS

A general summary of the properties of X-rays is presented below:

• Invisible.
• Propagate with velocity of light (3.10^8 m/s).
• Unaffected by electrical and magnetic fields.
• Differentially absorbed in passing through matter of varying composition, density and thickness.
• Reflected, diffracted, refracted and polarized.
• Capable of ionizing gases.
• Capable of affecting electrical properties of solids and liquids.
• Capable of blackening a photographic plate.
• Able to liberate photo electron. And recoils electrons.
• Emitted in a continuous spectrum.
• Emitted also with a line spectrum characteristic of the chemical element.
• Found to have absorption spectra characteristic of the chemical element.

THE ORIGIN OF X-RAYS

An electron can be ejected from its atomic orbital by the absorption of a light wave

(photon) of sufficient energy. The energy of the photon (hν) must be greater than the energy with which the electron is bound to the nucleus of the atom. When an inner orbital electron is ejected from an atom, an electron from a higher energy level orbital will transfer into the vacant lower energy orbital (Figure). During this transition a photon may be emitted from the atom. To understand the processes in the atomic shell, we must take a look at the Bohr’s atomic model. The energy of the emitted photon will be equal to the difference in energies between the two orbitals occupied by the electron making the transition. Due to the fact that the energy difference between two specific orbital shells, in a given element, is always the same (i.e., characteristic of a particular element), the photon emitted when an electron moves between these two levels will always have the same energy. Therefore, by determining the energy (wavelength) of the X-ray light (photons) emitted by a particular element, it is possible to determine the identity of that element.

PRINCIPLE OF THE X-RAY FLUORESCENCE PROCESS

If the primary energy of X-rays is equal to or is larger than the binding energy of an inner shell electron it is likely that electrons will be ejected and consequently vacancies are created. The hole state has certain life time and becomes refilled again. The transition of the excited atom into a state with lower energy occurs via two competitive processes, the above mentioned photoelectric and Auger effects. In the photoelectric effect, the recombination is accompanied by a transfer of electrons from the outer shells with energy Em into the inner shells with energy En filling the vacancies. This process induces the emission of a characteristic X-ray (fluorescence) photon with energy

                                                                   hV = Em - En

Therefore the energy of these secondary X-rays is the difference between the binding energies of the corresponding shells in the figure below. The excited atom can also recombine by emission of Auger electrons, instead of characteristic X-rays, via the Auger effect.

The probability that characteristic X-rays will be emitted - and not an Auger electron- varies from one element to another and is described as the fluorescence yield. For elements of low atomic numbers, the Auger effect dominates, whereas emission of characteristic X-rays is more likely for heavy elements.

Each element has its unique characteristic energy spectrum (Fluorescence spectrum) composed by the allowed transitions of the specific atom in the result of X-ray excitation. XRF technique consists on the study of the produced characteristic spectrum. The XRF emission induced by photoelectron effect is shown in figure below for an atom of titanium (Z=22), whose K-shell electron acquires sufficient energy to escape from the atom.

Photoelectric effect on the K-shell

An electron in the K-shell absorbs a

photon of the primary x-ray beam and

becomes free, while the atom gains a

vacancy in the K-shell.

The K lines production

An electron from the L or M shell “jumps in” to fill the vacancy and in  turn, produces a vacancy in the L or M shell. In the process, the atom emits a characteristic photon from the x-ray  range of electromagnetic spectrum, unique to this chemical element

The L lines production

After a vacancy is created in the L shell by either the primary beam photon or by the previous event, an electron from the M or N shell “jumps in” to occupy the vacancy. In this process, the atom emits a characteristic photon, unique to this chemical element, and a vacancy in the M or N shell is produced

•  Ionization of the K-shell electron in the atom of Ti by photoelectric effect and emission of characteristic photons of different spectral series as a result of electron transitions in the atom.

              Electron transitions and emitted spectral lines in the atom after the K-shell ionization

X-ray fluorescence provides a rapid non-destructive means for both qualitative and quantitative analysis. A wide range of materials varying in size and shape can be studied with minimal requirements for sample preparation. Detection sensitivities as low as one part in a million can be obtained with this technique.The two types of X-ray fluorescence i.e EDXRF and WDXRF will be discussed and explained in the next post .

Some basic terms and definitions related to X- ray fluorescence, which can be useful in the upcoming post .

• Attenuation coefficient – a natural logarithm of the ratio of the emergent and incident radiation intensities I / I0 divided by either the depth of the radiation penetration (linear attenuation coefficient) or the surface density (mass absorption coefficient).
• Bremsstrahlung – a continuous spectrum produced by a charged particle moving with deceleration.
• Continuous spectrum – a spectrum formed by photons with non-quantized energies in a wide range.
• Detection limit – a lowest amount of chemical element that can be found with probability of 99%.
• Detector resolution – possibility to distinguish two overlapping peaks in the spectrum; depends on the ratio of the distance between the two peaks and FWHM; usually accepted as a value of FWHM.
• Efficiency of a detector – the ratio of the number of photons participated in creation of a useful signal in the detector to the total number of photons incident on the detector surface.
• Energy-dispersive technique – the technique used to simultaneously detect the photons of the line spectrum in a wide range of energies.
• Fluorescence – emission of photons by a substance that has absorbed photons with higher energy.
• FWHM – full width at half maximum of the peak usually measured in electronvolts.
• Ionizing radiation – the particles or electromagnetic waves whose energy is sufficient to ionize a neutral atom or a molecule.
• Line spectrum – a spectrum formed by photons with specific quantized energies only.
• Matrix effects – The combined effect of all components of the sample other than the analyte on the measurement of the quantity of the analyte. The two main matrix effects are::

                           -(a) The attenuation of characteristic peak intensity due to inelastic scattering of photons, emitted by atoms of one chemical element, on atoms and electrons of other components

                            -(b)The enhancement of characteristic peak intensity due to additional excitation of atoms of one element by photons, emitted by other components.

• Peak intensity – the value proportional to the total number of photons with same energy registered by a spectrometer and exposed as a bell-shaped curve called the peak.
• Quantitative analysis – determination of amount of each component (chemical element) of a sample.
• Spectral series – series of spectral peaks produced by electron transitions from different energy levels to one specific energy level; K-series corresponds to all transitions to the lowest possible energy level.
• Spectrum – a function of a number of photons versus their energy, or versus their wavelength.
• Spectrum background – A component of a spectrum which does not belong to the peak of interest, may be formed by bremsstrahlung radiation or by the tails of adjacent peaks.
• X-ray tube – A kind of a vacuum tube with a filament as a cathode, emitting electrons, and a pure metal plate as an anode, producing radiation in the x-ray range of electromagnetic spectrum.