X-Ray Fluorescence Analytical Techniques

X-Ray Fluorescence Analytical

Techniques

Moussa Bounakhla

&

Mounia Tahri

CNESTEN

CONTENT

SECTION I: Basic in X-Ray Fluorescence

I. History of X-Ray Fluorescence II. Introduction

III. Physics of X-Rays

III.1 Electromagnetic Radiation, Quanta III.2 Properties of X-Rays

III.3 The Origin of X-Rays III.4 Bohr’s Atomic Model III.5 Nomenclature

III.6 X-Ray Emission III.6.1 Continuum

III.6.2 Characteristic Emission III.7 Interactions of X-Ray with Matter

III.7.1 Photoelectric Absorption III.7.2 Compton Effect

III.7.3 Rayleigh Scattering (Elastic Scattering) III.7.4 Competitive Interactions

III.8 Fluorescence Yield IV. X-Ray Production Sources

IV.1 X-Ray Tubes

IV.1.1 Side-window Tubes IV.1.2 End-window Tubes IV.2 Radioisotope Sources

SECTION II: Energy Dispersive X-Ray Fluorescence (ED-XRF)

I. Introduction II. Instrumentation

II.1 Excitation Mode

II.1.1 Direct Tube Excitation II.1.2 Secondary Target Excitation II.1.3 Radio-Isotopic Excitation II.2 Detectors

II.4 Energy Resolution III. Spectrum Evaluation IV. Detector Artefacts

IV.1 Escape Peaks IV.2 Compton Edge

IV.3 Resulting Spectral Background

V. The Approach to Quantification in EDXRF Analysis V.1 Thin Samples Technique

V.2 Intermediate Thickness Samples V.3 Infinitely Thick Samples

SECTION III: Total Reflexion X-Ray Fluorescence (TXRF)

I. Introduction

II. Advantages of TXRF

III. Principle of Total Reflection X-Ray Fluorescence Analysis IV. Instrumentation

IV.1 Excitation Sources for TXRF IV.2 Sample Reflectors

IV.3 Detectors V. Quantification

VI. Influence on Detection Limits VII. General Sample Preparation VIII. Application of TXRF

SECTION IV: Wavelength Dispersive X-Ray Fluorescence (WD-XRF)

I. Introduction

II. Principle of WD-XRF II.1 Collimator Masks II.2 Collimator

II.3 Analyzing Crystals II.3.1 Bragg’s Law

II.3.2 Reflections of Higher Orders II.3.3 Crystal Types

II.3.4 Dispersion, Line Separation II.3.5 Synthetic Multilayers II.4 Detectors

II.4.1 Gas Proportional Counter II.4.2 Scintillation Counters

II.4.3 Pulse Height Analysis (PHA), Pulse Height Distribution III. Points of Comparison between ED-XRF and WD-XRF

SECTION V: Sample Preparation

I. Solids

II. Powders and Briquets III. Fused Materials

IV. Filters and Ions-Exchange Resins V. Thin Films

VI. Liquids

SECTION VI: Quantitative Analysis

I. Detection Limits II. Disturbing Effects

II.1 Interelement Radiation II.2 Matrix Effects

II.2.1 Absorption Effect II.2.2 Enhancement Effect II.3 Particle-Size Effects

II.4 Mineralogical Effects II.5 Surface Effects III. Mathematical Models

III.1 Sherman Equation III.2 Empirical Alpha Models

III.3 Fundamental Parameters Method III.4 Fundamental Alphas

III.5 Semi-Quantitative Analysis

Module:

Title: X-Ray Fluorescence Analytical Techniques

Learning objective:

Make potential users proficient in the use of X-Ray Fluorescence Analytical Techniques

Target public:

Potential users including students in science and technology

Profile:

Senior technicians, Students, Teachers, Researchers and Analytical Specialists in Scientific Fields.

Qualifications:

University education related to application of sciences and technology English and French literacy

SECTION I

BASIC IN X-RAY FLUORESCENCE

I.

History of X-Ray Fluorescence

The history of X-ray fluorescence dates back to the accidental discovery of X-rays in 1895 by the German physicist Wilhelm Conrad Roentgen. While studying cathode rays in a high-voltage, gaseous-discharge tube, Roentgen observed that even though the experimental tube was encased in a black cardboard box the barium-platinocyanide screen, which was lying adjacent to the experiment, emitted fluorescent light whenever the tube was in operation. Roentgen's discovery of X-rays and their possible use in analytical chemistry went unnoticed until 1913. In 1913, H.G.J. Mosley showed the relationship between atomic number (Z) and the reciprocal of the wavelength (1/λ) for each spectral series of emission lines for each element. Today this relationship is expressed as:

2 ) s Z ( a / c λ= − ; (I.1) where: a is a proportionality constant,

s is a constant dependent on a periodic series.

Mosley was also responsible for the construction of the early X-ray spectrometer. His design centered around a cold cathode tube where the air within the tube provided the electrons and the analyte which served as the tube target. The major problem experienced laid in the inefficiency of using electrons to create x-rays; nearly 99% of the energy was lost as heat.

In the same year, the Bragg brothers built their first X-ray analytical device. Their device was based around a pinhole and slit collimator. Like Mosley's instrument, the Braggs ran into difficulty in maintaining efficiency. Progress in XRF spectroscopy continued in 1922 when Hadding investigated using XRF spectrometry to analyse mineral samples. Three years later, Coster and Nishina put forward the idea of replacing electrons with X-ray photons to excite secondary X-ray radiation resulting in the generation of an X-ray spectrum. This technique was attempted by Glocker and Schrieber, who in 1928 published Quantitative Roentgen Spectrum Analysis by Means of Cold Excitation of the Spectrum in Ann. Physics.

Progress appeared to be at a standstill until 1948, when Friedman and Birks built the first XRF spectrometer. Their device was built around a diffractometer, with a Geiger counter for a detection device and proved comparatively sensitive for much of the atomic number range. It might be noted that XRF spectrometers have progressed to the point where elements ranging from Beryllium to Uranium can be analysed.

Although the earliest commercial XRF devices used simple air path conditions, machines were soon developed utilizing helium or vacuum paths, permitting the detection of lighter elements. In the 1960’s, XRF devices began to use lithium fluoride crystals for diffraction and chromium or rhodium target X-ray tubes to excite longer wavelengths. This development was quickly followed by that of multichannel spectrometers for the simultaneous measurement of many elements. By the mid 60’s computer controlled XRF devices were coming into use. In 1970, the lithium drifted silicon detector (Si(Li)) was created, providing

very high resolution and X-ray photon separation without the use of an analysing crystal. An XRF device was even included on the Apollo 15 and 16 missions.

Meanwhile, Schwenke and co-workers have fine tuned a procedure known as total reflection X-ray fluorescence (TXRF), which is now used extensively for trace analysis. In TXRF, a Si(Li) detector is positioned almost on top of a thin film of sample, many times positioned on a quarts plate. The primary radiation enters the sample at an angle that is only slightly smaller than the critical angle for reflection. This significantly lowers the background scattering and fluorescence, permitting the detection of concentrations of only a few tenths of a ppb.

II.

Introduction

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.

While the principles are the same, a variety of instrumentation is used for performing X-ray fluorescence spectroscopy. There are two basic classes of instruments: Wavelength Dispersive and Energy Dispersive. Wavelength Dispersive spectrometers measure X-ray intensity as a function of Wavelength while Energy Dispersive spectrometers measure X-ray intensity as a function of energy.

An extremely important aspect of X-ray fluorescence spectroscopy is the method by which the inner orbital vacancy is created. Bombarding the sample with high energy X-rays is one method. Bombarding with high-energy electrons and protons are other approaches. An incident photon beam experiences a photon absorption interaction with the specimen while electron and proton beams primarily experience a Coulomb interaction with the specimen.

X-ray tubes accelerate high-energy electrons at a target within the tube that is then caused to fluoresce X-rays. The resulting X-ray beam includes a continuum and characteristic lines of the tube target. Radioactive sources can also be used to generate X-ray, electron (beta

emitters), and proton (alpha emitters) beams. X-ray tubes can generate a high power X-ray beam, but the radiation is not monochromatic. Radioactive sources produce monochromatic beams, but of comparatively lower power. Proton-Induced X-ray Emission (PIXE) utilises a beam of protons. Wavelength Dispersive Spectrometry (WDS) generally utilises an X-ray tube as does Energy Dispersive X-ray Spectrometry (EDX). Instruments such as the electron microprobe and electron microscope directly bombard the sample with high-energy electrons to eject inner orbital electrons (EDS). Note that the charged particle beam approaches require the specimen to be electrically conductive.

III.

Physics of X-Rays

III.1 Electromagnetic Radiation, Quanta

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.

Table I.1: Energy and names of various wavelength range.

Energy range (eV) Wavelength range Name

< 10-7 cm to km Radio Waves (short, medium, long waves)

< 10-3 mm to cm Micro Wave < 10-3 mm to mm Infra Red 0.0017 – 0.0033 380 to 750 nm Visible Light 0.033 – 0.1 10 to 380 nm Ultra Violet 0.11 - 100 0.01 to 12 nm X-Rays 10 - 5000 0.0002 to 0.12 nm Gamma Radiation

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 microprobe 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:

ν =h

E ; (I.2)

where:

h is the Planck constant (6.62 10-24 J.s); ν is the frequency expressed in Hertz.

For all wavelengths, λ

=

where: c = speed of light (2.99782 108 _m/s); λ= wavelength (Å). Thus: λ = λ =hc/ 1.9863610− / E 24 ; (I.4) 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: ) A ( / 396 . 12 ) eV ( E = λ o . (I.5)

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 ray energies suggested to early workers that X-rays 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.

III.2 Properties of X-Rays

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

• Propagate with velocity of light (3.108 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 ionising gases;

• Capable of affecting electrical properties of solids and liquids; • Capable of blackening a photographic plate;

• Able to liberate photoelectron. 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.

III.3 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 I.1). 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.

Figure I.1: A pictorial representation of X-ray fluorescence using a generic atom and generic energy levels. This picture uses the Bohr model of atomic structure and is not to scale.

III.4 Bohr’s Atomic Model

Bohr’s atomic model describes the structure of an atom as an atomic nucleus surrounded by electron shells (Figure I.2). The positively charged nucleus is surrounded by electrons that move within defined areas (shell). The differences in the strength of the electron’s bonds to the atomic nucleus are very clear depending on the area or level they occupy, i.e., they vary in their energy. When we talk about this, we refer to energy levels or energy shells. This means that a clearly defined minimum amount of energy is required to release an electron of the innermost shell from the atom. To release an electron of the second innermost shell from the atom, a clearly defined minimum amount of energy is required that is lower that that needed to release an innermost electron. An electron’s bond to an atom is weaker the further away it is from the atom’s nucleus. The minimum amount of energy required .to release an electron from an atom, and thus the energy with which it is bound to the atom, is also referred to as the binding energy of the electron to the atom.

Figure I.2: Bohr’s atomic model, shell model.

The binding energy of an electron in an atom is established mainly by determining the incident. It is for this reason that the term absorption edge is very often found in literature.

Energy level = binding energy = absorption edge

The individual shells are labelled with the letters K, L; M; N, …, the innermost shell being the K-shell, the second innermost the L-shell etc. the K-shell is occupied by 2 electrons; the L-shell has three sub-levels and can contain up to a total of 8 electrons. The M-shell has five sub-levels and can contain up to 18 electrons.

III.5 Nomenclature

The production of X-rays involves transitions of the orbital electrons at atoms in the target between allowed orbits or energy states, associated with ionization of the inner atomic shell. The permissible transitions that electrons can undergo from initial to final state are specified by three quantum selection rules:

1.The change in n must be ≥ 1 (∆n ≠ 1); 2.The change in l only can be ±1; 3.The change in j can only be ±1 or 0.

When an electron is ejected from the K-shell by electron bombardment or by the absorption of a photon, the atom becomes ionized. If this electron vacancy is filled by an electron coming from an L shell, the transition is accompanied by the emission of an X-ray line known as K line; this process leaves a vacancy in the L shell. On the other hand, the vacancy in the L shell might be filled by an electron coming from the M shell that is accompanied by the emission of an L line (Figure I.3). The terminology of energy levels and X-ray lines are showed in Figure I.4.

Figure I.3: Schematic illustration of production of K and L lines.

Figure I.4: X-ray line labelling.

III.6 X-Ray Emission

X-rays re generated from the disturbance of the electron orbitals of atoms. This may be accomplished in several ways, the most common of which is to bombard a target element with high energy electrons, X-rays or accelerated charged particles. The first two are frequently used in X-ray spectrometry, either directly or indirectly. Electron bombardment results in both a continuum of X-ray energies and radiation that is characteristic of the target elements. Because both types of radiation will be encountered in X-ray spectrometry, each will be discussed.

III.6.1 Continuum

Continuum X-rays are produced when electrons or high energy charged particles lose energy in passing through the Coulomb field of a nucleus. In this interaction, the radiant energy (photon) lost by the electron is called Bremsstrahlung (Figure I.5). The emission of

continuous X-rays finds a simple explanation in terms of classic electromagnetic theory, since according to this; the acceleration of charged particles should be accompanied by emission of radiation. In the case of high energy electrons striking a target, they must be rapidly

decelerated as they penetrate the material of target, and such a high negative acceleration should produce a pulse of radiation.

Figure I.5: On the left, the classical model showing the production of Bremsstrahlung. On the right, the Continuum X-ray emission spectrum.

The probability of radiative energy loss (Bremsstrahlung) is roughly proportional to q2z2T/M02, where q is the particle charge in units of the electron charge e, Z is the atomic number of the target material, T is the particle kinetic energy, and M0 is the rest mass of the particle. Because of the fact that protons and heavier particles have large masses, compared to the electron mass, they irradiate relatively little, e.g., the intensity of continuous X-rays generated by protons is about four orders of magnitude lower than the generated by electrons.

The ratio of energy lost by Bremsstrahlung to that lost by ionization can be approximated by: 2 0 2 0 0 c m 1600 T Z M m ⎟⎟ ⎠ ⎞ ⎜⎜ ⎝ ⎛ , (I.6) where m0 is the rest of the electron.

III.6.2 Characteristic Emission

The purpose of X-ray fluorescence is to determine chemical elements both qualitatively and quantitatively by measuring their characteristic radiation. To do this, the chemical elements in a sample must be caused emit X-rays. As characteristic X-rays only rise in the transition of atomic shell electron to lower, vacant energy levels of the atom, a method must be applied that is suitable for releasing electrons from the innermost shell of an atom. This involves adding to the inner electrons amounts of energy that are higher than the energy bonding them to the atom.

This can be done in a number ways:

• Irradiation using elementary particles of sufficient energy (electrons, protons, a-particles…) that transfer the energy necessary for release to the atomic shell electrons during collision processes.

• Irradiation using X- or gamma rays from radionuclides. • Irradiation using X-rays from an X-ray tube.

III.7 X-Ray Interactions with Matter

When X-rays are directed into an object, some of the photons interact with the particles of the matter and their energy can be absorbed or scattered. This absorption and scattering is called attenuation. Other photons travel completely through the object without interacting with any of the materials particles. The number of photons transmitted through a material depends on the thickness, density and atomic number of the material, and the energy of the individual photons.

Even when they have the same energy, photons travel different distances within a material simply based on the probability of their encounter with one or more of the particles of the matter and the type of encounter that occur. Since the probability of an encounter increases with the distances travelled, the umber of photons reaching a specific point within the matter decreases exponentially with distance travelled (Figure I.6).

Figure I.6: Exponential attenuation of photon energy with distance travelled in the material.

The formula that describes this curve is:

x 0e

I

I= −µ (Beer-Lambert law); (I.7) where:

I0 is the initial intensity of photons; µ is the linear absorption coefficient; X is the distance travelled.

The linear absorption coefficient has the dimension [1/cm] and is depend on the energy or the wavelength of the X-ray quants and the special density ρ (in [g/cm3]) of the material that was passed through.

It is not the linear absorption coefficient that is specific to the absorptive properties of the element, but the coefficient applicable to the density ρ of the material that was passed through:

The mass attenuation coefficient has the dimension [cm2/g] and only depends on the atomic number of the absorber element and the energy, or wavelength, of the X-ray quants.

The mass attenuation coefficient accounts for the various interactions and is therefore composed of here major components:

) E ( ) E ( ) E ( ) E ( =τ +σ_coh +σ_inc µ ; (I.8) τ(E) is the photoelectric mass absorption coefficient;

σcoh(E) is the coherent mass absorption coefficient; σinc(E) is the incoherent mass absorption coefficient.

III.7.1 Photoelectric Absorption

In the photoelectric interaction, a photon transfers all its energy to an electron located in one of the atomic shells (Figure I.7). The electron is ejected from the atom by this energy and begins to pass through the surrounding matter. The electron rapidly loses its energy and moves only a relatively short distance from its original location. The photon’s energy is, therefore, deposited in the matter close to the site of the photoelectric interaction. The energy transfer is a two-step process. The photoelectric interaction in which the photon transfers its energy to the electron is the first step. The depositing of the energy in the surrounding matter by the electron is the second step.

Photoelectric interactions usually occur with electrons that are firmly bound to the atom, that is, those with a relatively high binding energy. Photoelectric interactions are most probable when the electron binding energy is only slightly less than the energy of the photon. If the binding energy is more than the energy of the photon, a photoelectric interaction cannot occur. This interaction is possible only when the photon has sufficient energy to overcome the binding energy and remove the electron from the atom. The probability of photoelectric interactions occurring is also dependent on the atomic number of the material. An explanation for the increase, the binding energies move closer to the photon energy. The general relationship is that the probability of photoelectric interactions is proportional to Z3. In general, the conditions that increase the probability of photoelectric interactions are low photon energies and high atomic number materials.

This process is often the major contributor of the absorption X-rays, and is the mode of excitation of the X-rays 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. There are sharp discontinuities at which the photoelectric process is especially efficient. Energies at which these discontinuities occur are called absorption edges (Figure I.8).

Figure I.7: Schematic description of photoelectric principle.

Figure I.8: Absorption edges for different shells.

The Figure I.8 supplies the following:

•The overall progression of the coefficient decreases as energy increases, i.e. the higher the energy of the X-ray quants, the less they are absorbed.

•The rapid changes in the mass attenuation coefficient reveal the binding energies of the electrons in the appropriate shells. If an X-ray quant has a level of energy that is equivalent to the binding energy of an atomic shell electron in an appropriate shell, it is then able to transfer all its energy to this electron and displace it from the atom. In this case, absorption increases sharply. Quants whose energy is only slightly below the absorption edge are absorbed far less rapidly.

III.7.2 Compton Effect

Also known as incoherent scattering, Compton effect is the interaction of a photon with a free electron that is considered to be at the rest. The weak binding of electrons to atoms may

be neglected provided that momentum transferred to the electron greatly exceeds the momentum of the electron in the bound state. Figure I.9 shows the Compton effect schematically.

Relativistic energy and momentum are conserved in this process and the scattered X-ray photon has less energy and therefore a longer wavelength than the incident photon. Compton scattering is important for low atomic number specimens.

The change in wavelength of the scattered photon is given by: ) cos 1 ( c m h c c o o o θ − = λ − λ′ = ν − ν′ . (I.9) Theta is the scattering angle of the scattered photon.

Figure I.9: Compton effect.

III.7.3 Rayleigh Scattering (Elastic Scattering)

Elastic scattering is a process by which photons are scattered by bound atomic electrons and in which the atom is neither ionized nor excited. The incident photons are scattered with unchanged energy and with a definite phase relation between incoming and scattered waves (Figure I.10). The intensity of the radiation scattered by an atom is determined by summing the amplitudes of the radiation coherently scattered by each of the electrons bound in the atom. It should be emphasized that coherence extends only over the Z electrons of individual atoms. The interference is always constructive, provided the phase change over the diameter of the atom is less than one-half a wavelength. Rayleigh scattering occurs mostly at the low energies and for high Z materials.

Figure I.10: Coherent scattering of an X-ray by an atom.

III.7.4 Competitive Interactions

The energy at which interactions change from predominantly photoelectric to Compton is a function of the atomic number of the material. The Figure I.11 shows this crossover energy for several different materials. At the lower photons energies, photoelectric interactions are much more predominant than Compton. Over most of the energy range, the probability of both decreases with increased energy. However, the decrease in photoelectric interactions is much greater. This because the photoelectric rate changes in proportion to (1/E3), whereas Compton interactions are much less energy dependent.

Figure I.11: Comparison of Photoelectric and Compton interaction rates for different materials and photon energies.

In higher atomic number materials, photoelectric interactions are more probable, in general, and they predominate up to higher photon energy levels. The conditions that cause photoelectric interactions to predominate over Compton are the same conditions that enhance photoelectric interactions, hat is, low photon energies and materials with high atomic numbers.

III.8 Fluorescence Yield

When an electron is ejected from an atomic orbital by the photoelectric process, there two possible results: X-ray emission, or Auger electron ejection (Figure I.12). One of these two events occurs for each excited atom, but not both. Therefore, Auger electron production is a process which is competitive with X-ray photon emission from excited atoms in a sample. The faction of the excited atoms which emits X-rays is called the Fluorescent yield. This value is a property of the element and the X-ray line under consideration. Figure I.13 shows a plot of X-ray fluorescent yield versus atomic number of the elements for the K and L lines. It is an unfortunate fact that low atomic number elements also have low fluorescent yield.

Figure I.12: The excitation energy from the inner atom is transferred to one of the outer electrons causing it to be ejected from the atom (Auger electron).

IV.

X-Ray Production Sources

IV.1 X-Ray Tubes

A variety of radiation sources of sufficient energy, emitting ether particles, γ-rays, or X-rays, are potential candidates as sources for exciting the elements of interest in a sample to emit characteristic radiation. The use of sample excitation by electrons is used in electron probe micro-analysis (EPMA), and excitation by charged particles, like protons, is achieved in articles-induced X-ray emission (PIXE). Most XRF analyzers have an X-ray tube for sample excitation.

All modern X-ray tubes owe their existence to Coolidge’s hot-cathode X-ray tube (Coolidge 1913). It consists essentially of a vacuum sealed glass tube containing a tungsten filament for the production for electrons, an anode and a beryllium window. From variety of modifications, two geometries have emerged as the most suitable for all practical purposes: the end-window tube and the side-window tube, both having their own merits and limitations. The general requirements are as follows:

1. Sufficient photon flux over a wide spectral range, with increasing emphasis on the intensity of the low-energy continuum. The actual intense interest in low-Z element analysis certainly activated research in this direction.

2. Good stability of the photon flux (< 0.1 % at least). Short-term stability is an absolute requirement for obtaining acceptable precision.

3. Tunable tube potential allowing the creation of the most effective excitation conditions for each element, because the intensity of the analyte lines varies considerably with excitation conditions.

4. Freedom from two many interfering lines from the characteristic spectrum of the anode (scatter peaks).

All X-ray tubes work on the same principle: accelerating electrons in an electrical field and decelerated them in a suitable anode material. The region of the electron beam in which this takes place must be evacuated in order to prevent collisions with gas molecules. Hence there is a vacuum within housing. The X-rays escape from the housing at a special point that is particularly transparent with a thin beryllium window.

An X-ray tube emits the characteristic radiation of the anode material, in addition to the Bremsstrahlung radiation; a typical spectrum obtained with an X-ray tube of Rh anode material is shown in Figure I.14.

The main differences between tube types are in the polarity of the anode and cathode and the arrangement of the exit window.

Figure I.14: A Bremsstrahlung (Continuum) with characteristic radiation of the anode material (Rh as example).

IV.1.1 Side-window Tubes

In side-window tubes, a negative high voltage is applied to the cathode. The electrons emanate from the heated cathode and are accelerated in the direction of the anode. The anode is set on zero voltage and thus has no difference in potential to the surrounding housing material and the laterally mounted beryllium exit window (Figure I.15).

Figure I.15: The principle of the side-window tube.

For physical reasons, a proportion of the electrons are always scattered on the surface of the anode. The extent to which these back-scattering electrons arise depends, amongst other factors, on the anode material and can be as much as 40 %. In the side-window tube, these back-scattering electrons contributes to the heating up of the surrounding material, especially the exit window, the exit window must withstand high levels of thermal stress any cannot be selected with just any thickness. The minimum usable thickness of a beryllium window for side-window tubes is 300 µm. this causes an excessively high absorption of the low-energy characteristic L radiation of the anode material in the exit window and thus a restriction of the excitation of lighter elements in a sample.

IV.1.2 End-window Tubes

The distinguishing feature of the end-window tubes is that the anode has a positive high voltage and the beryllium exit window is located on the front end of the housing (Figure I.16).

Figure I.16: The principle of the end-window tube.

The cathode is set around the anode in a ring (anular cathode) and is set at zero voltage. The electrons emanate from the heated cathode and are accelerated towards the electrical field lines on the anode. Due to the fact that there is a difference in potential between the positively charged anode the surrounding material, including the beryllium window, the back-scattering electrons are guided back to the anode and thus do not contribute to the rise in the exit window’s temperature. The beryllium window remains cold and can therefore be thinner than the side-window tube. Windows are used with a thickness of 125 mm and 75 mm. this provide a prerequisite for exciting light elements with the characteristic L radiation of the anode material (e.g. rhodium).

Due to the high voltage applied, non-conductive, de-ionised water must be used for cooling. Instruments with end-window tubes are therefore equipped with a closed, internal circulation system containing de-ionised water that cools the tube head as well.

End-window tubes have been implemented by all renowned manufacturers of wavelength dispersive X-ray fluorescence spectrometers since the early 80’s.

IV.2 Radioisotope Sources

Radioisotopes are commonly used because of their stability and small size when continuous and monochromatic sources are required. Safety regulations require that X-ray emission from these sources is limited to about 107 photons s-1 steradian-1 compared with 1012 or 1013 photons for X-ray tubes; the difference is only partly compensated for by the small size of the source, which allows very compact source-specimen-detector assemblies to be constructed that are very convenient due to their portability. On the other hand, the low intensities preclude crystal dispersion so that these sources are used almost exclusively in energy dispersion techniques. Separation of analytical lines is sometimes done with selective

filters but more often with pulse height analysers in combination with high resolution Si(Li) semiconductor detectors.

Radioisotope XRF systems are often tailored to a specific but limited range of applications. They are simpler and often considerably less expensive than analysis systems based on X-ray tubes, but these attributes are often gained at the expense and flexibility. Radioisotope excitation is preferred to X-ray tubes when simplicity, ruggedness, reliability and cost of equipment are important; when a minimum size, weight and power consumption are necessary; when a very constant and predictable X-ray output is required; and when the use of high energy X-rays is advantageous. Radioisotope systems, especially those involving scintillation or proportional detectors, must be carefully matched to the specific application.

The activity of radioisotopes is specified in terms of the rate of disintegration of the radioactive atoms, i.e. decays per second or Becquerels (Bq) (the Becquerel replaces the non-SI unit, the Curie (Ci), which equals 3.7 107 Becquerels). The activity decreases with the time from Ao to A(t) after an elapsed time t:

) T / t 693 . 0 ( exp A ) t ( A = _o − _1/2 ,

where T1/2 is the half-life of the radioisotope. The source decays to half of its original emission rate after the time equal to its half-life has passed. The radioisotope source has usually to be replaced after several half-lives. Several sources are listed in Table I.2.

Table I.2: Typical radioisotope sources used for XRF.

Isotope Fe-55 Cm-244 Cd-109 Am-241 Co-57

Energy (keV) 5.9 14.3 - 18.3 22.88 59.5 122

Elements (K-lines) Al - V Ti - Br Fe - Mo Ru - Er Ba - U Elements (L-lines) Br - I I - Pb Yb - Pu None None

An important property of a given radioisotope is the type of its decay and the spectrum of the electromagnetic radiation accompanying the nuclear disintegration. The basic radioactive decays are:

1.α decay: when a radioactive nucleus emits a helium nucleus (α particle) consisting of two protons and two neutrons. The energy spectrum of alpha particles is linear because of the quantization of the energy levels of nuclei.

2.β+ _{decay: when one of the protons is transformed into a neutron, emitting a positron (β}+ particle) and a neutrino. The energy spectrum of positrons is also continuous.

3.K capture: when a nucleus captures one of the K-shell electrons, the final result also being the proton-into-neutron transformations, as in the case of the β+ _decay.

In addition to the above nuclear transformations (decays), resulting in transformations of original nuclei into nuclei of other elements, the following accompanying processes may also occur:

1.Emission of gamma radiation: occurring when the resulting nucleus is not in its ground state. The existing energy surplus can be either emitted in the form of electromagnetic radiation or transferred to the atomic shell electrons (internal conversion). Sometimes a nucleus reaches its ground state through subsequent intermediate (compound) states. In such cases, every decay may be accompanied by several photons and/or internal conversion electrons, with energies being equal to the energy differences between the individual

compound states of the nucleus. An example for such a cascade transition to the ground state is given in Figure I.17.

Figure I.17: Decay scheme showing the principal transitions in Am-241, Fe-55 and Cd-109.

2.Internal conversion: when the excitation energy of the nucleus is given up to one of the atomic electrons, which is then ejected from the atom with the kinetic energy: Ee = En – Eb

; where En is the excitation energy of the nucleus and Eb is the binding energy of the electron in a given atomic shell. The quantitative description of this phenomenon uses the concept of the internal conversion coefficient, defined as the ration of the number on internal conversion electrons to the number of gamma photons emitted during the same time interval. The internal conversion coefficient increases strongly as the atomic number increases and conversion is a competitive process with respect to the emission of gamma radiation, just as the Auger effect is competitive with respect to the emission of X-rays. 3.Emission of X-rays: resulting from filling the holes in the atomic shells with electrons from

higher levels. The holes in the atomic shells are due both to K-capture and to internal conversion.

SECTION II

ENERGY DISPERSIVE X-RAY FLUORESCENCE

(ED-XRF)

I. 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 the simplest case an electron is ejected from an atom of the detector material by photoabsorption. The loss of energy of this just created primary electron results in a shower of electron-ion pairs in the case of a proportional counter, optical excitations in the case of scintillation counter, or showers of electron-hole pairs in a semiconductor detector. The resulting detector signal is proportional to the energy of the incident photon, in contrast to wavelength dispersion in which the Bragg reflecting properties of a crystal are used to disperse X-rays at different reflection angles according to their wavelengths. 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. The two other types of detectors, mentioned above, with their poorer energy resolution are limited to special cases where certain features of semiconductors are not acceptable. Also the germanium semiconductor detector with its comparable characteristics has a major drawback for conventional XRF: inherently the escape peaks of intense lines can obscure other lines of interest.

II. Instrumentation

An ED-XRF system consists of several basic functional components, as shown in Figure II.1: an –ray excitation source, sample chamber, Si(Li) detector, preamplifier, main amplifier and mutlichannel pulse height analyzer. The properties and performances of an ED-XRF system differ upon the electronics and the enhancements from the computer.

II.1 Excitation Mode

II.1.1 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 ray fluorescence spectrometer equipped with an X-ray tube as direct excitation source is gaining more and more attention from manufactures as well as from analytical chemists. 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 understanding of the process of continuum excitation and the possibility to obtain a good estimate of the continuum excitation spectrum originating from the tube has minimized the problems associated with quantization, so that very satisfactory quantitative analysis can be carried out. 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. The use of X-ray tubes with a multi-element anode having a thin layer of low-Z element (e.g. Cr) sputtered onto a heavy element target (e.g. Mo) has been reported. Optimized excitation can be obtained by operating the multi-element anode tube at different voltages to switch between the excitation by the light element and the heavy element targets.

II.1.2 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 (Figure II.2).

Figure II.2: 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.

II.1.3 Radio-Isotopic Excitation

Radio-isotopic sources are simple, cheap and quasi-monochromatic excitation sources. They are very suitable sources when combined with a solid state detector for in situ analysis (Figure II.3).

Figure II.3: Geometry of an EDXRF spectrometer with annular source 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 radio-isotopic sources however lie in their low photon output, intensity decay and storage problems.

II.2 Detectors

The selective determination of elements in a mixture, using X-ray spectrometry, depends upon resolving the spectral lines emitted by the various elements into separate components. This process requires some form of energy sorting or wavelength dispersing device. In the case of wavelength dispersive X-ray spectrometers, this is accomplished by the analyzing crystal, which requires mechanical movement to select each desired wavelength according to Bragg’s Law. Optionally, several fixed-crystal channels may be used for simultaneous measurements. In contrast, 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. Several types of detectors have been employed, 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 1960’s. By the 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. Figure II.4 shows a diagram of a Si(Li) detector.

Figure II.4: Cross section of an Si(Li) detector crystal with p-i-n structure and the production of electron-hole pair.

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 escape peak intensity relative to the main peak is energy dependent, but not count rate dependent. For precise quantitative determinations, the spectroscopist must be aware of the possibility of interference by escape peaks.

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 II.5). In many cases, half of the peak width is a result of electronic noise.

Figure II.5: The Si(Li) detector schematic.

II.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. It is not necessary for the spectroscopist to have a detailed knowledge of the electronics; however, it is important to have an understanding of their functional use.

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.

For high count rates there is an increasing probability that two photons of, for example, a very intense line, are absorbed in the detector crystal within such a short time interval that their charges are not collected as two individual signals with a certain energy, but rather as a single signal with twice the energy (sum peak).

II.4 Energy Resolution

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.

Figure II.6: Mn-Kα spectrum and calibrated pulser.

The instrumental energy resolution of a semiconductor detector spectrometer is a function of 2 independent factors:

(

) (

) (

)

total elec

E E E

∆ = ∆ + ∆ . (II.1)

The FWHM of the X-ray line (∆Etotal) is described as the convolution of a contribution due to the detector processes (∆Edet), which is determined by the statistics of the free charge production processes together with a component associated with limitations in the electronic pulse processing (∆Eelec).

The average number of electron hole pairs produced by an incident photon can be calculated as the photon energy divided by the mean energy required for the production of a single electron-hole pair. If the fluctuation in this average were governed by Poisson statistics, the variance would be n. In semiconductor devices the details of the energy loss process are

such that the individual events are not strictly independent and a departure from Poisson behaviour is observed. This is considered by the addition of the FANO-Factor in the expression for the detector contribution to the FWHM:

(

) (

)

E E F

E is the photon energy, ε is the average energy required to produce a free electron-hole pair, F is the FANO factor and 2.35 converts the root means square deviation to FWHM. For an equivalent energy, the detector contribution to the resolution is 28 % less for the case of Ge compared to Si.

The contribution to resolution associated with electronic noise (∆Eelec) is the result of random fluctuations in thermally generated leakage currents within the detector and in the early stages of the amplifier components.

III. Spectrum Evaluation

Spectrum evaluation in energy dispersive XRF is certainly more critical than in WD-XRF, because of the relatively low resolution of the solid-state detectors employed. The aim is the extraction of the analytically relevant information (net number of counts under a peak) from experimental spectra.

In EDXRF, the characteristic radiation of a particular line can be described in an adequate first-order approximation by a Gaussian function (detector response function). The spectral background results a variety of processes: for photon excitation, the main contribution is the incoherently scattered primary radiation and therefore depends on the shape of the excitation spectrum and on the sample composition. For particle-induced X-ray emission and electron excitation, the background observed is mainly due to Bremsstrahlung.

The most straightforward method to obtain the net data area under a line of interest consists of interpolating the background under the peak and summing the background-corrected channel contents in a window over the peak. In practice, this approach is limited by the curvature of the background and by the presence of other peaks and can therefore not be used as a general tool for spectrum processing in EDXRF. An example of overlapping peaks is the analysis of lead and arsenic simultaneously present in a sample (Figure II.7).

Figure II.7: A spectrum of As K, overlapped with a Pb L line spectrum, both excited by a Mo X-ray tube, under identical conditions. The energy of AsKα1,2 (10.53

A widely used method is non-linear least squares fitting of the spectral data with an analytical function. This algebraic function, including all important parameters, such as the net areas of the fluorescent lines, their energy, resolution, etc., is used as a model for the measured spectrum. It will consist of the contribution from all peaks (modified Gaussian peaks, with corrections for low-energy tailing, escape peaks, etc.) within a certain region of interest and the background (described by, for example, linear or exponential polynomials). The optimum values of the parameters are those for which the difference between the model and the measured spectrum is minimal. Unfortunately some of these parameters are non-linear, which places some importance on the minimization procedure (usually the Marquardt algorithm is used).

In another frequently used approach the discrete deconvolutions of a spectrum with a so-called top-hat filter suppresses the low-frequency component, i.e. the slowly varying background. A severe distortion of the peaks is introduced. But applying this filter to both the unknown spectrum and well defined, experimentally obtained, reference spectra, a multiple linear least-squares fitting to the filtered spectra will result in the net peak areas of interest. A disadvantage of this method is that reference and unknown spectra should be acquired under preferably identical conditions; especially,

energy calibration changes of

more than only few e can generate large systematic errors.

IV. Detector Artefacts

IV.1 Escape Peaks

A photon is detected in the Si(Li) diode primarily by ionizing the K-shell of a Si atom besides the interaction of elastic and inelastic scattering. Subsequently a Si-Kα photon is produced. If the Si-Kα is absorbed within the active volume of the detector, the resulting amplitude pulse will have the amplitude which is proportional to the original photon energy. If the Si-Kα photon escapes the active volume of the detector, the event will be recorded at an energy which is too low by an amount equal to the energy of the escaping photon. Thus, a peak with an energy E-E(Si-Kα) will occur in the spectrum. Figure II.8 shows this schematically.

Figure II.8: Escape effect.

IV.2 Compton Edge

At low energy of the spectrum lies the Compton shoulder. This rise in the background is caused by high-energy photons incoherently scattered from the front side of the detector crystal, leaving only a small fraction of their energy with the recoiled Compton electron in the detector (Figure II.9). The energy at which the Compton edge occurs is given by the formular beneath. Both the detector resolution and multiple scattering tend to smear out this sharp edge.

Figure II.9: Compton edge.

IV.3 Resulting Spectral Background

Figure II.10 shows the spectrum obtained by monochromatic excitation of 17.5 keV and a Si(Li) detector. The width of the coherent scatter peak reflects the detector resolution at 7.4 keV. The incoherent peak is much broader due to the range of scattering angles included about the nominal 90° scattering angle. The low energy tail on the incoherent peak extending down to about 10 keV is primarily due to multiple Compton scattering in the specimen.

The major background represented by the cross-hatched area, is due to incomplete charge collection in the Si(Li) detector. This occurs when a portion of the positive and negative charges produced in the detector by the 16.8 and 17.4 keV photons recombine before they are collected. The result is a pulse of abnormally low amplitude recorded at a lower than normal energy. The intensity of background due to incomplete charge collection is a function of detector quality and X-ray energy.

Figure II.10: Background contribution in an EDX spectrometer with monochromatic 17.5 keV excitation.

V. The Approach to Quantification in EDXRF Analysis

The approach to quantification in EDXRF analysis is usually different for thin, intermediate thickness and infinitely thick samples.

V.1 Thin Samples Technique

If a homogeneous sample to be analysed has a very small mass per unit area (or thickness), the detected intensity of characteristic X-rays, Ithin, of the ith element is simply given by: thin i i I =S m, (II.3) with

( ) ( )

Where G is the geometry factor; φ is the effective incidence angle for primary radiation; Io(Eo) is the intensity of primary photons of energy Eo (monochromatic excitation), ε(Ei) is the detector efficiency for recording the photons of energy Ei; τi(Eo) is the photoelectric mass absorption coefficient for the ith element at the energy o, in cm2.g-1; ji is the jump ratio; mi and µi are the mass per unit area and the weight fraction of the ith element, respectively; and m is the total mass per unit area of a given sample.

The relative error resulting from applying equation (II.3) instead of the exact equation does not exceed 5% when the total mass per unit area is lower than:

( )

( )

µ φ + µ ψ ; (II.6)

where µ(Eo) and µ(Ei) are the total mass attenuation coefficients for the whole specimen at the energy of primary radiation (Eo) and the energy of characteristic X-rays of the ith element (Ei), respectively; φ is the effective angle of incidence of the primary exciting beam; and ψ is the effective take-off angle of characteristic X-rays. The total mass attenuation coefficient µ(E) for the whole specimen at the energy E is given by the mixture rule:

( )

( )

where Wj and µj(E) are the weight fraction and the mass attenuation coefficient of the jth element present in the sample, respectively, and n is the total number of the elements in the sample. A major feature of the thin sample technique is that the intensity of characteristic X-rays, Ithin, depends linearly on the concentration of the ith element; it is equivalent to the fact that the so-called matrix effects can safely be neglected.

The values of the constant Si (called the sensitivity factors), which are necessary to

convert the measured intensity of the characteristic X-rays into mass concentrations, can be determined either experimentally as the slope of the straight calibration line for the ith element obtained on the basis of thin homogeneous standard samples or semi-empirically based on both the experimentally determined (G/sin φ)IoEo value and the relevant fundamental

parameters (τi(Eo), ωi, ρi and ji). Also the detector efficiency ε(Ei) can b determined either

experimentally or theoretically based on the parameters of a given detector. In multi-element XRF analysis, the calibration process can be greatly simplified because the elemental sensitivities Si vary as a smooth function with atomic number.

Various homogeneous standard samples are now commercially available from several manufactures. In many cases, one can also produce synthetic laboratory standard according to the actual needs and possibilities; for example, by precipitating known quantities of elements in solution, and filtering off as a thin layer or on a filter membrane.

V.2 Intermediate Thickness Samples

Intermediate thickness samples are defined as those samples whose masses per unit area fulfil following inequality:

thin thick

m < <m m , (II.8)

where mthick is the mass of the so-called infinitely thick or saturated sample, above which practically no further increase in the intensity of the characteristic radiation will be observed as the sample thickness is increased, given by:

( )

( )

Intermediate thickness samples can be preferable to thick specimens because less material is required, remaining uncertainties in the knowledge of the mass attenuation coefficients have a smaller effect on the analysis results, the sensitivity is more favourable for low-Z elements, and secondary enhancement effects are less important. In practice, samples of intermediate thickness are used when the investigated material is scarce and does not allow

preparation of a thick sample, and when preparation of a thin sample is difficult or even impossible. Such cases might occur in the analysis of biological and environmental specimens.

In recent years a number of approaches have been developed for quantitation in XRF analysis of intermediate thickness samples. Some of them are based on the emission-transmission (E-T) method. The original version of the E-T method requires the measurements of the specific X-ray intensities from the sample alone and from the sample and a certain target positioned behind it in a fixed geometry. Alternative correction procedures are based on the use of scattered primary radiation which suffers similar matrix absorption as fluorescent peaks and behaves similarly with instrumental variations. The scattered radiation peaks also provide the only direct spectral measure of the total or average matrix of the analysed materials when these contain large quantities of light elements such as carbon, nitrogen and oxygen, usually observed by their characteristic X-ray peaks.

For homogeneous, intermediate thickness samples, the mass per unit area of the element i, mi can be calculated from the following equation:

i i i I m t S = , (II.10)

where Ii is the measured intensity of the characteristic X-rays of the ith element and t is the absorption factor, given by:

( )

( )

{

}

( )

( )

1 exp [ cos cos ]

cos cos o i o i E ec E ec m t E ec E ec m − − µ φ + µ ψ = ⎡µ φ + µ ψ⎤ ⎣ ⎦ . (II.11)

In the E-T method, the t-factor, representing the combined attenuation of both the primary and fluorescent radiations in the whole specimen, is determined individually for each sample. This is done by measuring the X-ray intensities with and without the specimen from a thick multi-element target located at a position adjacent to the back of the specimen, as shown in Figure II.11. If (Ii)S, (Ii)T and (Ii)o are the intensities, after background correction, from the sample alone, from the sample plus target and from the target alone, respectively, then the combined fraction of the exciting and fluorescent radiations transmitted through the total sample thickness is expressed by:

( )

( )

{

}

( ) ( )

_{( )}

exp cos cos i T i S

o i i o I I E ec E ec m T I − ⎡ ⎤ − µ_⎣ φ + µ ψ_⎦ = = . (II.12)

Since the parameter T is determined experimentally, the following equation for the t-factor is obtained: 1 ln T t T − = − . (II.13)

It is necessary to emphasize that the E-T method can only be applied in quantitative XRF analysis of homogeneous samples of masses per unit area smaller than the critical value mcrit, defined as:

( )

( )

where Tcrit is the critical transmission factor, Equation (II.12) is equal, in practice, to 0.1 or 0.05. A number of more complex and more versatile versions of the E-T method have been developed.

Figure II.11: Schematic diagram of experimental procedure used in the emission-transmission method.

V.3 Infinitely Thick Samples

Samples exceeding the thickness mthick given in Equation (II.9) can be considered ‘infinitely thick’ or ‘saturated’ with respect to X-ray absorption. In this case, the exponential term in the nominator of the X-ray absorption factor given by Equation (II.11) can be neglected, giving:

( )

( )

and Equation (II.10) can be written as:

( )

( )

( )

( )

i i i i i o o o o S m S C m E ec E ec E ec E ec m = = µ φ + µ ψ ⎡µ φ + µ ψ⎤ ⎣ ⎦ . (II.16)

Hence, the characteristic X-ray intensity is directly proportional to the elemental concentration and not dependent on the sample thickness. Thus, knowledge of the sample thickness is no longer relevant. Various ways have been developed to cope with matrix effects in infinitely thick samples.