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.
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Figure 2 Sketch of the theoretical conditions for x-ray total
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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
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sea,
rain, pore water, river, mineral, spring water, drinking water, chemicals and
deionized water
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aerosols,
vapour, air dust, airborne particles, fresh air
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Algae, fine roots, cucumber plants, pollen.
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fish, flour,
fruits, crab, mussel, mushrooms, nuts,
vegetables,
wine, tea, soft drinks, onion
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Coffee,
spirits and beverages, honey.
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blood,
serum, urine, amniotic fluid, cerebrospinal
fluid
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Tissue:
hair, kidney, lung, liver, stomach, nails, colon
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Various
enzymes, polysaccharides, glucose, proteins,
cosmetics,
biofilms, human bones
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Si
wafer surfaces, GaAs wafer surfaces
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Depth
and profile variations
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single
layers, multilayers
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Crude
oil, fuel oil, grease, pure fuel oil, waste
oil, petroleum, oil-shale ash, diesel
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Acids,
bases,salts, solvents
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trans
mutational elements in Al C Cu,
iodine in
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Ores,
rocks, minerals, rare earth elements, quartz,
mineral
sands, diamond, crystals
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Geological
materials, bio-mineralisation
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arts/archaeological/forensic
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Pigments,
paintings, varnish21
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Bronzes,
pottery, jewellery, manuscripts, Egyptian masks
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Textile
fibres, glass, cognac, dollar bills, gunshot residue, drugs, tapes, sperm, finger
prints.
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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
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Figure 3 Components of a TXRF spectrometer
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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
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