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.

BREATH ALCOHOL ANALYSER

INTRODUCTION

Many humans are addicted to the psychoactive effects of alcohol thus, it is the most common, legal drug of choice. However, the influence of alcohol or the over-consumption of alcoholic drinks by humans is often the cause of crimes and violence, including fatal traffic accidents. Traffic deaths rank highest among all causes of death & alcohol related traffic fatalities rank highest within this category. Safety Agencies are challenged to locate intoxicated drivers and to remove them from the public roadways.

The analysis of alcohol in breath was considered a very desired and objective test specimen for determination of a vehicle operator’s breath-alcohol concentration and impairment level for evidential purposes. In the early 1950s, first Breathalyzer set the basis for the scientific acceptance of analyzing alcohol in breath. Law-Enforcement personnel implemented and administered these noninvasive and efficient tests as part of their drunk-driving enforcement.

THE TECHNOLOGY OF BREATH-ALCOHOL TESTING

The technology of breath-alcohol testing has changed fundamentally over the years. This was partially driven by general technology advancements and in part due to defense challenges. The following techniques describing the most recognized technologies used for preliminary (“screening”) and evidentiary breath-alcohol analysis as well as its advantages and disadvantages:

1. Wet-chemical Oxidation technology: 

The analytical principle was based on chemical oxidation by alcohol within a mixture of dichromate and sulfuric acid in vials. It paved the way for scientific acceptance of evidential breath alcohol testing by the international forensic community and the courts.

Advantages:

• Compact table-top package.
• Relatively quick analysis.
• Accurate and specific to alcohol.

Disadvantage:

• Minimum required breath volume < 60mL.
• The handling of the vials is critical as they contain sulfuric acid.
• The Breathalyzer’s biggest short-coming however, was the fact that the system was operator dependent.
• Growing legal attacks in the eighties were vulnerable to manipulation by the operator thus; the equipment was rapidly replaced by newer and less operator dependent instruments.

 2. Solid-state sensor technology:

Commonly called “Taguchi” cells, a metal oxide semiconductor based sensor manufactured by Figaro located in Japan. The Taguchi cell operates by adsorption of gas molecules on the surface of a semi-conductor. This transfers electrons due to the differing energy levels of the gas molecules on the semi-conductor’s surface. These types of instruments are sold mainly to the consumer markets as opposed to law enforcement. None of these sensor-type instruments are approved by the National Highway Safety Administration as evidential breath testers.

Advantages:

• The sensors are small in size and rather inexpensive to manufacture. Lowest priced breath testers.
• These instruments are sold in convenience stores and mail-order-catalogues.

Disadvantages:

•  The sensor is very unstable, drifty and non-specific to alcohol.
•  It reads all hydrocarbons (organic vapors) and will habitually produce false positive alcohol readings caused by smoker’s and car exhaust CO as well as many other environmental vapors and gases.
• This senor is partial pressure sensitive and therefore changes sensitivity with change in altitude and elevation.
• This sensor is sensitive to changes in ambient temperature, humidity and breath flow patterns.
• For these and other reasons, solid-state sensor instruments can’t be employed in evidential and legal applications.

3. Electro-chemical cell technology (“EC”):

Most commonly called “fuel-cell”. Fuel-cell technology for alcohol analysis was first introduced in the early 1970s by an Austrian researcher. The EC sensor requires a sampling system consisting of a piston or bellow pump assembly, applying a very precise amount (~ 1 ccm) of breath to the sensor. The volume consistency is highly important because the current produced by the sensor is proportional to the total number of alcohol molecules converted in the sensor.

 The sensor is composed of an immobilized electrolyte, flanked by an active and a passive electrode. The electrolyte and the electrode material are selected such that the alcohol to be measured is electrochemically oxidized and converted at the active electrode. The change in the electronic conductivity causes a rise in current flowing from the active to the passive electrode. The total electrochemical reaction is evaluated by time integration of the sensor’s current. This sensor’s life expectancy is approximately 4-5 years.

Advantages:

• The sensor is highly specific to alcohol.
• The measurement cannot be biased or influenced by endogenous substances such as acetone (diabetics and starving people), CO or Toluene.
• The sensor is highly sensitive, down to 0.1 ppm.
• Accuracy meets specifications for evidential instruments (NHTSA) and remains stable ≥ 6 months before having to calibrate it again.
• Its expected life term is approximately 5 years.

 Disadvantages:

• EC based instruments cannot observe the breath alcohol concentration throughout the subject’s exhalation . This doesn’t allow detection of alveolar breath (“deep lung air”), mouth alcohol, belching, burping, Gastro Esophageal Reflux Disease (GERD) and residual alcohol trapped under dentures or alcohol from bleeding gums.
• The EC sensor is cross sensitive to other alcohols such as methanol and isopropanol.The EC sensor’s output is temperature dependent and suffers short term fatigue if the sensor is exposed to a series of successive alcohol containing tests.
• EC based instruments are not accepted for evidential use in many countries, states and jurisdictions.

4. Infrared Spectroscopy (“IR”):

IR technology (IR Spectra-photometry) based breath-alcohol testers were first introduced in the mid-1970s. IR instruments have become the standard worldwide for legal, evidential breath analysis.

The analytical concept is based on the Beer-Lambert Law of physics, the “Law of absorption”. It addresses the linear relationship between absorbance and concentration of an absorber of  electromagnetic radiation. Alcohol vapor introduced into an absorption chamber will absorb some of that IR radiation transmitted through the chamber. The amount of IR absorption is in direct proportion to the quantity of alcohol present (breath-alcohol). However, only IR-radiation of a specific wavelength will absorb alcohol. The two predominantly utilized wavelengths are centered at 3.39 and 9.5 μm. The latest generation instrumentation monitors IR absorption at 9.5 μm because the measurements are far less prone to interference from any hydrocarbons and acetone which absorb IR energy at 3.4 μm.

The most significant benefits of “real-time” IR absorption analysis (continuous measurement) requires understanding the dynamics of alcohol in the human breath. Some of these dynamics relate to gas exchange in the mucus membranes, residual alcohol in the upper respiratory tracks, belching, burping, Gastro Esophageal Reflux Disease (GERD), exhaled air volume, breath flow rates and the subject’s breathing pattern.

Only IR technology is capable of addressing these dynamic, physiological factors to determine a legitimate, rightful and legally as well as forensically justifiable breath alcohol measurement.

Advantages:

• IR based equipment observes the breath-alcohol concentration throughout the subject’s exhalation. This allows the plot of the entire IR-absorption curve and the instrument’s intelligence to assure that.
• The breath sample was of alveolar nature.
• No residual or mouth alcohol was present.
• The recorded absorption curve can be presented in court if the case is challenged.
• The IR system does not have a limited life expectancy, will not fatigue with successive, high alcohol concentration test series and remains extremely stable for years.
• These instruments are equipped with many other important peripherals and functionalities (please observe “Other required performance features for evidential breath testers” below).
• IR instruments are today’s standard worldwide for legal, evidential breath-alcohol analysis and consequently face fewer legal challenges than all other breath testing devices and technologies. 

Disadvantages: 

• IR instruments are larger in size thus, not suitable for portable, handheld operation.
• These instruments are more expensive than handheld (screening) equipment employing solid-state or EC sensors.

Various human specimens can be considered for measuring a person’s alcohol concentration level. All body fluids as well as expired breath are legitimate specimens for alcohol concentration measurements. However, the two most popular methodologies for medico legal alcohol testing are blood analysis and breath analysis.

Roadside tests or so called screening tests are conducted with handheld, mainly EC based instruments. These instruments are portable, battery operated and provide quick test results.The main objective of these tests are for confirmation of probable cause for submission to an evidential test procedure.

COMPARISON BETWEEN ED-XRF AND WD-XRF

We have discussed about  ED-XRF & WD-XRF in the earlier posts . Now I would like to highlight the major differences between the two X-ray techniques . The most important point of comparison are listed below ::

1. RESOLUTION :

It describes the width of the spectra peaks. The lower the resolution number the more easily an elemental line is distinguished from the nearby X-ray line intensities.

a) The resolution of the WD-XRF system is dependent on the crystal and optics design,particularly collimation, spacing and positional reproducibility. The effective resolution of a WD-XRF system may vary from 20 eV in an inexpensive bench top to 5 eV or less in a laboratory instrument. The resolution is not detector dependant.

Advantage of WD-XRF: High resolution means fewer spectral overlaps and lower

background intensities

b)  The resolution of ED-XRF system is dependent on the resolution of the detector. This can vary from 150 V or less for a liquid nitrogen cooled Si(Li) detector, 150 – 220 eV for various solid state detectors, or 600 eV or more for gas filled proportional counter.

Advantage of ED-WRF: WD-XRF crystal and optics are expensive, and are one more failure mode.

2. SPECTRAL OVERLAPS:

Spectral deconvolutions are necessary for determining net intensities when two spectral lines overlap because the resolution is too high for them to be measured independently.

a) With a WD-XRF instrument with very high resolution (low number of eV) spectral

overlap corrections are not required for a vast majority of elements and applications.

The gross intensities for each element can be determined in a single acquisition.

Advantage WD-XRF: Spectral deconvolutions routines introduce error due to counting statistics for every overlap correction onto every other element being corrected for. This can double or triple the error

b) The ED-XRF analyzer is designed to detect a group of elements all at once. The some type of deconvolutions method must b used to correct for spectral overlaps. Overlaps are less of a problem with 150 eV resolution systems, but are significant when compared to WD-XRF. Spectral overlaps become more problematic at lower resolutions.

3. BACKGROUND: 

The background radiation is one limiting factor for determining detection limits, repeatability, and reproducibility.

a) Since a WD-XRF instrument usually uses direct radiation flux the background in the region of interest is directly related to the amount of continuum radiation within the region of interest the width is determined by the resolution.

b) The ED-XRF instrument uses filters and/or targets to reduce the amount of continuum radiation in the region of interest which is also resolution dependant, while producing a higher intensity X-ray peak to excite the element of interest.

Even, WD-XRF has the advantage due to the resolution. If a peak is one tenth as wide it has one tenth the background. ED-XRF counters with filters and targets that can reduce the background intensities by a factor of ten or more.

4. EXCITATION EFFICIENCY:

Usually expressed in PPM per count-per-second (cps) or similar units, this is the other main factor for determining detection limits, repeatability, and reproducibility. The relative excitation efficiency is improved by having more source x-rays closer to but above the absorption edge energy for the element of interest.

a. WDXRF generally uses direct unaltered x-ray excitation, which contains a continuum of energies with most of them not optimal for exciting the element of interest.

b. EDXRF analyzers may use filter to reduce the continuum energies at the elemental

lines, and effectively increasing the percentage of X-rays above the element absorption edge. Filters may also be used to give a filter fluorescence line immediately above the absorption edge, to further improve excitation efficiency. Secondary targets provide an almost monochromatic line source that can be optimized for the element of interest to achieve optimal excitation efficiency.

WAVELENGTH DISPERSIVE X-RAY FLUORESCENCE (WD-XRF)

INTRODUCTION

Wavelength Dispersive X-Ray Fluorescence Spectrometry (WD-XRF) is the oldest method of measurement of X-rays, introduced commercially in the 1950’s. This name is descriptive in that the radiation emitted from the sample is collimated with a Soller collimator, and then impinges upon an analyzing crystal. The crystal diffracts the radiation to different extents, according to Bragg’s law, depending upon the wavelength or energy of the X radiation. This angular dispersion of the radiation permits the sequential or simultaneous detection of X-rays emitted by elements in the sample. Simultaneous instruments normally contain several sets of analyzing crystals and detectors; one is adjusted for each desired analyte in the sample. These instruments tend to be very expensive, but efficient for the routine determination or preselected elements.

WD-XRF spectrometers are usually larger and more expensive than other spectrometers. Because the analyzing crystal d-spacing determines wavelength sensitivity, they are usually more sensitive than other spectrometers. To overcome losses in X-ray optics of the WD-XRF spectrometers and to maximize primary radiation intensity, X-ray tubes are usually employed. The sample is usually held under vacuum to reduce contamination and avoid absorption of light element characteristic radiation in air.

Typical uses of WD-XRF include the analysis of oils and fuel, plastics, rubber and textiles, pharmaceutical products, foodstuffs, cosmetics and body care products, fertilizers, minerals, ores, rocks, sands, slags, cements, heat-resistant materials glass, ceramics, semiconductor wafers; the determination of coatings on paper, film, polyester and metals; the sorting or compositional analysis of metal alloys, glass and polymeric materials; and the monitoring of soil contamination, solid waste, effluent, cleaning fluids, sediments and air filters.

PRINCIPLE OF  WD-XRF

WD-XRF spectrometers measure X-ray intensity as a function of wavelength. This is done by passing radiation emanating from the specimen through an analyzing diffraction crystal mounted on a 2θ goniometer. By Bragg’s Law, the angle between the sample and detector yields the wavelength of the radiation:

2d sin θ = nλ ;

where:

d    is the d-spacing of the analyzing crystal,

θ    is half the angle between the detector and the sample,

n    is the order of diffraction.

The analyzing crystal must be oriented so that the crystal diffraction plane is directed in the appropriate direction. Figure shows a simplified schematic of the WD-XRF spectrometer.  A scintillation or flow-proportional detector usually measures the fluoresced radiation. The heights of the resulting pulses are proportional to energy so using a pulse height analyzer (PHA), scattered or undesired diffraction-order X-rays can be ejected. The X-ray beam is usually collimated before and after the analyzing crystal. Each of the components showed in the below (Figure 1)  were be described in the following sections.

1. Schematic description of WD-XRF principle

1. COLLIMATOR MASKS

The collimator masks are situated between the sample and collimator and serve the

purpose of cutting out the radiation coming from the edge of the cup aperture (Figure 2).

The size of the mask is generally adapted to suit of the cup aperture being used.

The masks perform one of the two functions: background reduction and improved

fluorescence (Figure 3).

2.Use of Cu 200 μm filter for cutting off the radiation coming from Rh X-ray tube.

3. Use of Al 100 μm filter for improvement of the ratio peak/background.

2. COLLIMATOR

4. Collimators with different angles of resolution.

Collimators consist of a row of parallel slats (Figure 4) and select a parallel beam of X-rays coming from the sample and striking the crystal. The spaces between the slats determine the degree of parallelism and thus the angle resolution of the collimator.

A 0.077° collimator is adequate for high resolution measurement parameters. Collimators with low resolution (e.g. 1.5 -2.0°) are advantageous for light elements such as Be, B and C (Figure 5). Using a collimator with a low resolution increases then intensity significantly. This enables intensity to be increased without a loss in angle resolution when analyzing light elements.

5. Example of the influence of collimator resolution on the intensity of a light

element.

3. THE ANALYZING CRYSTALS

a. Bragg’s Law

Crystals consist of a periodic arrangement of atoms (molecules) that form the crystal lattice. In such an arrangement of particles you generally find numerous planes running in different directions through the lattice points (= atoms, molecules), and not only horizontally and vertically but also diagonally. These are called lattice planes. All of the planes parallel to a lattice plane are also lattice planes and are at a defined distance from each other. This distance is called the lattice plane distance “d”.

6. Bragg’s Law.

When parallel X-ray light strikes a lattice plane, every particle within it acts as a scattering center and emits a secondary wave. All of the secondary waves combine to form a reflected wave. The same occurs on the parallel lattice planes for only very little of the X-ray wave is absorbed within the lattice plane distance “d”. All these reflected waves interfere with each other. If the amplification condition “phase difference = a whole multiple of the wavelength” (Δλ = nλ) is not precisely met, the reflected wave will interfere such that cancellation occurs. All that remains is the wavelength for which the amplification condition is met precisely. For a defined wavelength and a defined lattice plane distance, this is only given with a specific angle, the Bragg angle (Figure 6).

Under amplification conditions, parallel, coherent X-ray light (1,2) falls on a crystal

with a lattice plane distanced ‘d’ and is scattered below the angle θ (1′,2′). The proportion of the beam that is scattered on the second plane has a difference of ‘ACB’ to the proportion of the beam that was scattered at the first plane. The amplification condition is fulfilled when the phase difference is a whole multiple of the wavelength λ. This results in Bragg’s Law:

2d sin θ = nλ ;

n = 1, 2, 3… Reflection order.

On the basis of Bragg’s Law, by measuring the angle θ, we can determine either the

wavelength λ, and thus chemical elements, if the lattice plane distance ‘d’ is known or, if the wavelength λ is known, the lattice plane –value distance ‘d’ and thus the crystalline structure.

This provides the basis for two measuring techniques for the quantitative and qualitative determination of chemical elements (XRF) and crystalline structures (molecules, XRD), depending on whether the wavelength λ or the 2d-value is identified by measuring the angle θ.

• In X-ray diffraction (XRD) the sample is excited with monochromatic radiation of a known wavelength (λ) in order to evaluate the lattice plane distance as per Bragg’s equation.
• In XRF, the ‘d’-value of the analyzer crystal is known and we can solve Bragg’s equation for the element characteristic wavelength (λ).

b.  Reflections of Higher Orders

Figures 7a and 7b illustrate the reflections of the first and second order of one wavelength below the different angles θ1 and θ2. Here, the total reflection is made up of the various reflection orders (1, 2 …, n). The higher the reflection order, the lower the intensity of the reflected proportion of radiation generally is. How great the maximum detectable order is depends on the wavelength, the type of crystal used and the angular range of the spectrometer.

7 a.  First order reflection: λ = 2 d sin θ1.

7 b.  Second order reflection: 2λ = 2 d sin θ2.

It can be seen from Bragg’s equation that the product of reflection orders ‘n = 1; 2; ..’

and wavelength ‘λ’ for greater orders, and shorter wavelengths ‘λ* < λ’ that satisfy the

condition ‘λ* = λ/n’, give the same result.

Accordingly, radiation with one half, one third, one quarter etc. of the appropriate

wavelength (using the same type of the crystal) is reflected below the identical angle θ:

1λ = 2(λ / 2) = 3(λ / 3) = 4(λ / 4) = ……......

As the radiation with one half of the wavelength has twice the energy, the radiation with one third of the wavelength three times the energy etc., peaks of twice, three times the energy etc. can occur in the pulse height spectrum (= energy spectrum) as long as appropriate radiation sources.

c.  Crystal Types

The wavelength dispersive X-ray fluorescence technique can detect every element

above the atomic number 4 (Be). The wavelengths cover the range of values of four

magnitudes: 0.01 – 11.3 nm. As the angle θ can theoretically only be between 0° and 90° (in practice 2° to 75°), sinθ an only accept values between 0 and +1. When Bragg’s equation is applied:

  0 < nλ/2d = Sinθ < 1

 This means that the detectable element range is limited for a crystal with a lattice plane difference ‘d’. Therefore a variety of crystal type with different ‘2d’ values is necessary to detect the whole element range (from atomic number 4).

Besides the ‘2d’ values, the following selection criteria must be considered when a

particular type of crystal is to be used for a specific application:

• Resolution
• Reflectivity (→ intensity)

Further criteria can be:

• Temperature stability
• Suppression of higher orders
•       Crystal fluorescence.

d.  Dispersion, Line Separation

The extent of the change in angle Δθ upon changing the wavelength by the amount Δλ (thus: Δθ/Δλ) is called “dispersion”. The greater the dispersion, the better is the separation of two adjacent or overlapping peaks. Resolution is determined by the dispersion as well as by surface quality and the purity of the crystal.

Mathematically, the dispersion can be obtained from the differentiation of the Bragg

equation. 

Δθ /Δλ =  n/2dsinθ

It can be seen from this equation that the dispersion (or peak separation) increases as the lattice plane distance ‘d’ declines.

e. Synthetic Multilayers

8.  Diffraction in the layers (here: Si/W) of a multilayer.

Multilayers are not natural crystals but artificially produced ‘layer analyzers’. The lattice plane distances ‘d’ are produced by applying thin layers of two materials in alternation on to a substrate (Figure 8). Multilayers are characterized by high reflectivity and a somewhat reduced resolution. For the analysis of light elements the multilayer technique presents an almost revolutionary improvement for numerous applications in comparison to natural crystals with large lattice plane distances.

4.    DETECTORS

When measuring X-ray, use is made of their ability to ionize atoms and molecules, i.e. to displace electrons from their bonds by energy transference. In suitable detector materials, pulses whose strengths are proportional to the energy of the respective X-ray quants are produced by the effect of X-ray. The information about the X-ray quarts energy is contained in the registration of the pulse height. The number of X-ray quants per unit of time, e.g. pulses per second (cps = counts per second, KCps = kilocounts per second), is called their intensity and contains in a first approximation the information about the concentration of the emitting in the sample. Two main types of detectors are used in wavelength dispersive X-ray fluorescence spectrometers: the gas proportional counter and the scintillation counter.

a. Gas Proportional Counter

9: A gas proportional counter.

The gas proportional counter comprises a cylindrical metallic tube in the middle of which a thin wire (counting wire) is mounted. This tube is filled with a suitable gas (e.g. Ar+ 10% CH4). A positive high voltage (+U) is applied the wire. The tube has a lateral aperture or window that is sealed with a material permeable to X-ray quants (Figure 9).

An X-ray quant penetrates the window into the counter’s gas chamber where it is absorbed by ionizing the gas atoms and molecules. The resultant positive ions move to the cathode (tube), the free electrons to the anode, the wire. The number of electron-ion pairs created is proportional to the energy of the X-ray quant. To produce an electron-ion pair,approx. 0.03 keV are necessary, i.e. the radiation of the element boron (0.185 keV) produces approx. 6 pairs and the K-alpha radiation of molybdenum (17.5 keV) produces approx. 583 pairs. Due to the cylinder geometric arrangement, the primary electrons created in this way see an increasing electrical field on route to the wire.

The high voltage in the counting tube is now set so high that the electrons can obtain enough energy from the electrical field in the vicinity of the wire to ionize additional gas particles. An individual electron can thus create up to 10.000 secondary electron-ion pairs. The secondary ions moving towards the cathode produce measurable signal. Without this process of gas amplification, signals from boron, for example, with 6 or molybdenum with 583 pairs of charges would not be able to be measured as they would not be sufficiently discernible from the electronic noise. As amplification is adjustable via high voltage in the counting tube and is set higher for measuring boron than for measuring molybdenum. The subsequent pulse electronics supply pulses of voltage whose height depends, amongst other factors, on the energy of the X-ray quants.

b.  Scintillation Counters

10.   Scintillation counter including photomultiplier.

The scintillation counter, “SC”, used in XRF comprises a sodium iodide crystal in which thallium atoms are homogeneously distributed ‘NaI(Tl)’. The density of the crystal is sufficiently high to absorb all the XRF high energy quants. The energy of the pervading X-ray quants is transferred step by step to the crystal atoms that then radiate light and cumulatively produce a flash. The amount of light in this cintillation flash is proportional to the energy that the X-ray quant has passed to the crystal. The resulting light strikes a photocathode from which electrons can be detached very easily. These electrons are accelerated in a photomultiplier and, within an arrangement of dynodes, produce so-called secondary electrons giving a measurable signal once they have become a veritable avalanche (Figure 10). The height of the pulse of voltage produced is, as in the case of the gas proportional counter, proportional to the energy of the detected X-ray quant.

c.  Pulse Height Analysis (PHA), Pulse Height Distribution

If the number of the measured pulses (intensity) dependent on the pulse height is displayed in a graph, we have the ‘pulse height spectrum’. Synonymous terms are: ‘pulse height analysis’ or ‘pulse height distribution’. As the height of the pulses of voltage is proportional to the X-ray quants energy, it is also referred to as the energy spectrum of the counter (Figure 11a and 11b). The pulse height is given in volts, scale divisions or in ‘%’ (and could be started in keV after appropriate calibration). The “%”-scale is defined in such a way that the peak to be to be analyzed appears at 100 %.

11.a.    Pulse height distribution (S) Gas proportional counter

11.b .   Pulse height distribution (Fe) Scintillation counter.

12.    Pulse height distribution (Fe) with escape peak.

If argon is used as the counting gas component in gas proportional counters, an

additional peak, the escape peak (Figure 12), appears when X-ray energies are irradiated that are higher than the absorption edge of argon.

The escape peak arises as follows:

The incident X-ray quant passes its energy to the counting gas thereby displaying a K electron from an argon atom. The Ar atom can now emit an Ar Kα1,2 X-ray quant with an energy of 3 keV. If this Ar-fluorescence escapes from the counter then only the incident energy minus 3 keV remains for the measured signal. A second peak, the escape peak that is always 3 keV below the incident energy, appears in the pulse height distribution.

When using other counting gases (Ne, Kr, Xe) instead of argon, the escape peaks appear with an energy difference below the incident energy that is equivalent to the appropriate emitted fluorescence radiation (Kr, Xe). Using neon as the counting gas component produces no recognizable escape peak as the Ne K-radiation, with energy of 0.85 keV, is almost completely absorbed in the counter. Also, the energy difference to the incident of 0.85 keV and the fluorescence yield are very small.