XRF
X-ray fluorescence analysis
A
nondestructive physical method used for chemical elemental analysis of materials
in the solid or liquid state. The specimen is irradiated by photons or charged
particles of sufficient energy to cause its elements to emit (fluoresce) their
characteristic x-ray line spectra. The detection system allows the determination
of the energies of the emitted lines and their intensities. Elements in the
specimen are identified by their spectral line energies or wavelengths for
qualitative analysis, and the intensities are related to their concentrations
for quantitative analysis. Computers are widely used in this field, both for
automated data collection and for reducing the x-ray data to weight-percent and
atomic-percent chemical composition or area-related mass (of films). See also: Fluorescence
The materials to be analyzed may be solids,
powders, liquids, or thin foils and films. The crystalline state normally has no
effect on the analysis, nor has the state of chemical bonding, except for very
light elements. All elements above atomic number 12 can be routinely analyzed in
a concentration range from 0.1 to 100 wt %. Special techniques are required for
the analysis of elements with lower atomic numbers (4–11) or of lower
concentrations, and for trace analysis. The counting times required for analysis
range from a few seconds to several minutes per element, depending upon specimen
characteristics and required accuracy; but they may be much longer for trace
analysis and thin films. The results are in good agreement with wet chemical and
other methods of analysis. The method is generally nondestructive for most
inorganic materials in that a suitably prepared specimen is not altered by the
analytical process.
Basis of
method
The theory of the method has its origin in
the classic work by H. G. J. Moseley, who in 1913 measured x-ray wavelengths of
a series of elements. He found that each element had a simple x-ray spectrum and
characteristic wavelengths, and that there was a linear relationship between and
Z, where λ is the x-ray wavelength and Z is the atomic number of the element
emitting the x-ray. For example, a plot of Moseley's law can be used to show the
K and L x-ray lines (Fig. 1). Aside from the discovery of the element hafnium in
zirconium ores by G. von Hevesy, only a few practical uses of the relationship
were reported until about 1950, when the introduction of modern x-ray equipment
made it feasible to use x-rays for routine spectrochemical analysis of a large
variety of materials.
Fig.
1 Plot of Moseley's law, showing
dependence of characteristic x-ray-line wavelengths λ on atomic number Z. 1 A =
0.1 nm. (After Philips Tech. Rev., vol. 17, no. 10,
1956)
An
x-ray source is used to irradiate the specimen, and the emitted x-ray
fluorescence radiation is analyzed with a spectrometer. The fluorescence
radiation is diffracted by a crystal at different angles in order to separate
the wavelengths and identify the elements, and the concentrations are determined
from the relative intensities. Scintillation or gas proportional counters are
generally used as detectors. This procedure is widely used and is called the
wavelength dispersive method.
Around 1965, lithium-drifted silicon and
germanium [Si(Li) and Ge(Li)] solid-state detectors became available for x-ray
analysis. These detectors have better energy resolution, and the average pulse
amplitudes are directly proportional to the energies of the x-ray quanta, which
can be sorted electronically with a multichannel pulse-height analyzer. This
eliminates the need for the crystal and is called the energy dispersive method.
Recent developments include cryogenically cooled detectors based on
superconducting tunnel junctions. They combine a far better energy resolution
with the ability to detect the emission lines from very light elements.
X-ray
spectra
The origin of x-ray spectra may be
understood from the simple Bohr model of the atom in which the electrons are
arranged in orbits within the K, L, M, … shells. If a particle or photon with
sufficient energy is absorbed by the atom, an electron may be ejected from one
of the inner shells and is promptly replaced by an electron from one of the
outer shells. This results in the emission of a characteristic x-ray spectral
line whose energy is equal to the difference of the binding energies of the two
orbits involved in the electron transition. The new vacancy is filled by an
additional transition from the outer shells, and this is repeated until the
outermost vacancy is filled by a free electron. The sum of energies of all
photons emitted during the vacancy-refilling cascade is the ionization energy.
The energy of the emitted line from the first transition in the cascade has a
slightly lower energy than the ionization energy. For example, the ionization
energy for the copper K shell is 8.98 keV, and the observed lines have energies
of 8.90 keV (CuKβ) and 8.04 keV (CuKα); the corresponding wavelengths are 0.138,
0.139, and 0.154 nanometer. Altogether the energies of x-ray K-lines extend over
three orders of magnitude from 0.111 keV (11.2XXX nm, BeKα) to 114.45 keV
(0.0108 nm, UKβ2).
Optical emission lines result from resonant
electron transitions in the outer (valence) shells, producing complex spectra
with a large number of lines. By contrast, the x-ray lines arise only from a
limited number of transitions between the high-energy levels of the inner
shells, so that the x-ray spectrum of an element consists of relatively few
lines. They are always initiated by a primary ionization event. Lines are named
after the shell where the corresponding electron transition ends (K, L, M, …
lines). The most probable transition yielding the highest line intensity in this
series is named alpha, followed by beta, gamma, and others, and the indices 1,
2, 3, … define a specific transition within the subseries. Depending on the
number of energy sublevels in each shell, there are usually only a few important
lines in the K spectrum (Kβ, Kα1, Kα2) and a dozen or more lines in the L
spectrum. The M lines are rarely used in x-ray analysis.
Auger
effect
Occasionally, instead of the emission of
the characteristic photon in the course of an electron transition, inner atomic
absorption occurs (internal conversion or the Auger effect) when the photon
appears to ionize the atom in an additional shell. The existence of an
intermediate fluorescent photon is, however, denied by the quantum-mechanical
explanation of the Auger effect and should serve only as an aid to illustrate
the energy transfer. The ejected Auger electron has a well-defined energy,
namely, the energy of the internally absorbed (virtual) photon minus its
ionization energy, and can be used for chemical analysis. The probability that
no Auger effect occurs, that is, that the photon is actually emitted from the
atom and can be used for analysis, is called fluorescence yield. It is thereby
the complementary probability to the Auger effect and is higher than 50% for
K-shell ionization of elements with atomic numbers above 31 (gallium). For
low-atomic-number elements, the Auger effect dominates and the fluorescence is
low. This is one of the main reasons for the difficulties in the analysis of
very light elements, such as berillium, boron, and carbon, where the fluorescent
yield is only 10−4 to 10−3. See
also: Auger effect; Electron spectroscopy
X-ray
absorption
The type of absorption of the photon or
particle leading to the original ionization of the atom is called
photoabsorption, to distinguish it from absorption by coherent scattering or
Fig.
2 Mass absorption coefficients of
molybdenum (Mo) and silver (Ag) in the 1–50-keV region. Roman numerals indicate
edges associated with subshells of the L
shell.
The absorption of x-rays is usually given
as a mass absorption coefficient μ/ρ (usually expressed in cm2 g−1) and is
independent of the physical state of the material. If more than one element is
present, the weighted average of the coefficients of the individual elements is
used. Tables of mass absorption coefficients have been compiled. The decrease of
intensity of x-rays as they traverse the material is given by the linear
absorption coefficient μ (usually expressed in cm−1), obtained by multiplying
the mass absorption coefficient by the density ρ of the material. The intensity
decreases to e−μx of its original value when the x-rays pass through a layer x
centimeters thick.
Radiation
sources
There are two general methods for producing
x-ray spectra for fluorescence analysis excitation by photons and excitation by
charged particles. The most common method is to expose the specimen to the
entire spectrum emitted from a standard x-ray tube. It is sometimes modified by
using a secondary target material (or monochromator) outside the x-ray tube to
excite fluorescence. This has the advantage of selecting the most efficient
energy close to the absorption edge of the element to be analyzed and reducing
or not exciting other interfering elements, but the intensity is reduced by two
or three orders of magnitude. Further alternatives are radioactive sources and
synchrotron radiation.
The other method, used in electron
microscopes and the electron microprobe, uses an electron beam directly on the
specimen, and each element generates its own x-ray spectrum, under electron
bombardment, as in an x-ray tube.
See also: Electron microscope
X-ray
tubes
The radiative spectrum from an x-ray tube
consists of continuous radiation (bremsstrahlung) and characteristic lines.
Continuous radiation is emitted in the course of scattering (that is,
deceleration) of electrons by the nuclei of the target atoms. Characteristic
radiation is excited by electrons similarly to excitement by photons, and comes
from the electronic shells. The primary x-ray-tube targets are usually tungsten,
copper, rhodium, molybdenum, silver, and chromium. It is usually necessary to
avoid the use of a tube whose target is identical to that of an element in the
specimen, because the line spectrum from the target is scattered through the
system, adding to the element signal. It is also desirable to select a target
whose characteristic line energies lie closely above the absorption edges of the
elements to be analyzed. For example, the WL lines and CuK lines are more
efficient in exciting fluorescence in the transition elements chromium to copper
than are the MoK lines; RhL lines are most useful to excite K lines of elements
below sulfur in the periodic table. Tubes for fluorescence analysis usually have
a single thin beryllium window placed at the side of the tube. See also: Bremsstrahlung
Equipment is normally operated at
x-ray-tube voltages of 20–60 kV in dc operation at up to 3 kW or more with water
cooling. These voltages generate the K spectra of all the elements up to the
rare earths and the L spectra of the higher-atomic-number elements. Since the
detector is moved from point to point, it is essential to have a constant
primary intensity and to stabilize the voltage and tube current. See also: X-ray tube
Radioactive
isotopes
Radioactive isotopes that produce x-rays,
such as iron-55 (MnK x-rays) and americium-241 (NpL x-rays), are used in place
of an x-ray tube to excite fluorescence in some applications. These sources are
much weaker than x-ray tubes and must be placed close to the specimen. They are
often used in field applications where portability and size may be
considerations. Alpha particles have been occasionally used. An example is the
excitation source in the α-proton x-ray spectrometer (APXS) built into the Mars
exploration vehicle Sojourner (Mars Pathfinder mission 1997/1998; Fig. 3). See also: Radioactivity
Fig.
3 Alpha-Proton X-ray Spectrometer
(APXS) used on Mars Pathfinder Mission of 1997/1998. (a) Mars rover Sojourner,
rear view showing spectrometer (copyright © 1997, Jet Propulsion Laboratory,
California Institute of Technology, and the National Aeronautics and Space
Administration). (b) Comparison of chemical composition of rocks on Earth, of
various meteorites found on Earth but presumably originating from Mars, and
materials analyzed by APXS near the landing site on
Mars.
Synchrotron
radiation
Synchrotron radiation has many potential
advantages. The continuous radiation is several orders of magnitude more intense
than that of x-ray tubes and can be used with a crystal spectrometer. In
addition, a tunable crystal monochromator can be placed in the incident beam to
select the optimum wavelength for fluorescing each element in the specimen.
Because of its high intensity and parallelism, a very narrow beam of synchrotron
radiation can be masked out in order to illuminate individual spots or grains of
inhomogeneous materials. Another application is ultra-trace analysis. See also: Synchrotron radiation
Crystal
spectrometer
A
single-crystal plate is used to separate the various wavelengths emitted by the
specimen. Diffraction from the crystal occurs according to Bragg's law, Eq. (1),
where n is a small integer giving the order
of reflection, λ the wavelength, d the spacing of the particular set of lattice
planes of the crystal that are properly oriented to reflect, and θ the angle
between those lattice planes and the incident ray. See also: X-ray crystallography
Reflection for a particular λ and d occurs
only at an angle 2θ with respect to the incident ray, and it is therefore
necessary to maintain the correct angular relationship of the crystal planes at
one-half the detector angle. This is done by the goniometer, which is geared to
rotate the crystal at one-half the angular speed of the counter tube, and
therefore both are always in the correct position to receive the various
wavelengths emitted by the specimen (Fig. 4). For a given d, there is only one
angle (for each order of reflection) at which each wavelength is reflected, the
angle increasing with increasing wavelength. The identification of elements by
the reflection angles for their emission lines is greatly simplified by modern
computer-controlled spectrometers. The angular separation of the lines, or the
dispersion, given by Eq. (2),
increases with decreasing d. It is thus
easy to increase the dispersion simply by selecting a crystal with a smaller d.
Reducing d also limits the maximum wavelength that can be measured since λ = 2d
at 2θ = 180°; the maximum 2θ angle that can be reached in practice with the
goniometer is about 150°.
Fig.
4 X-ray fluorescence spectrograph
(not to scale). Diffracted-beam Soller slit is
optional.
Soller
slits
The crystals are usually mosaic, and the
reflection is spread over a small angular range. To increase the resolution,
that is, decrease the line breadth, it is necessary to limit the angular range
over which a wavelength is recorded. Parallel or Soller slits are used for this
purpose (Fig. 4). These slits consist of thin (0.002-in. or 0.05-mm) equally
spaced flat foils of materials such as nickel and iron, and the angular aperture
is determined by the length and spacing. A typical set for fine collimation
would have 0.005-in. (0.13-mm) spacings and 4-in. (100-mm) length with angular
aperture 0.15° and cross section 0.28 in. (7.11 mm) square. Wider angular
apertures of up to a few degrees are used with multilayer mirrors for
light-element analysis. The absorption of the foils is sufficiently high to
prevent rays that are inclined by more than the angular aperture to extend
beyond the specimen area and enter the counter tube. Two sets of parallel slits
may be used, one set between the specimen and crystal and the other between
crystal and detector. This greatly increases the resolution and
peak-to-background ratio, and causes a relatively small loss of peak intensity.
Diffracting
crystals
Crystals commonly used in spectrometers are
lithium fluoride (LiF) with reflecting plane (200) or (220), silicon (111) and
(220), pentaerythritol (001), acid phthalates of potassium and thallium (001),
and ethylene diamine d-tartrate (020). It is essential that the crystal be of
good quality to obtain sharp, symmetrical reflections. Unless the crystal is
homogeneous, the reflection may be distorted, and portions of the reflections
may occur at slightly different angles. Such effects would decrease the peak
intensities of the wavelengths by varying amounts, causing errors in the
analysis.
Multilayer
mirrors
The longest wavelength that can be
routinely analyzed with a natural crystal is around 2.4 nm (OKα). Multilayer
structures are employed as dispersive devices for lighter elements. They consist
of a periodic stack of layer pairs alternating a heavy element (with high
scattering power for x-rays) and light elements (serving as a spacer). The
scattered partial waves from the heavy-element layers interfere constructively
at certain angles in a way similar to that in crystals, but can have much longer
wavelengths corresponding to the layer spacing.
Rapid analysis
systems
In
certain industrial applications such as the manufacture of cement, steels, and
glass, and in geological exploration, large numbers of specimens containing up
to a dozen or more elements must be rapidly analyzed. In some cases, the
analysis must be done in a few minutes to correct the composition of a furnace
that is standing by. Generally the same qualitative compositions have to be
routinely analyzed, and instead of sequentially scanning over the wavelength
regions, a number (up to 30) of fixed crystals and detectors are positioned
around the specimen in order to allow simultaneous measurements of several
elements at peak and background positions. Automated trays load the specimens
into the spectrometer.
Detectors
The detectors generally used in crystal
spectrometers are scintillation counters with thin beryllium windows and
thallium-activated sodium iodide [NaI(Tl)] crystals for higher energies (above 4
keV), and gas flow counters with very low absorbing windows and argon/methane
gas for the low-energy region (below 6 keV). A single-channel pulse-amplitude
analyzer limits photon counting to a selected energy interval to improve the
peak-to-background ratio and to eliminate higher-order reflections. However, no
sharp energy separation is possible due to the rather limited energy resolution
of these detectors. See also:
Gamma-ray detectors; Particle detector; Scintillation counter
Energy dispersive
systems
Solid-state detectors with good energy
resolution are used in conjunction with a multichannel pulse-amplitude analyzer.
No crystals are required, and the detector and specimen are stationary during
the measurement. The method is used with either electron-beam excitation in
electron microscopes or with x-ray-tube sources. The photons of various energies
are registered, and their energies are determined as soon as they enter the
detector. As this occurs statistically for the various fluorescence line
energies, the acquisition of the spectral data appears to be simultaneous for
all lines.
Solid-state
detectors
Lithium-drifted silicon [Si(Li)] detectors
are generally used for the lower energies of fluorescence analysis, while
lithium-drifted germanium [Ge(Li)] detectors are more often used for nuclear
high-energy gamma-ray detection. The energy resolution of good Si(Li) detectors
is below 130 eV (full width at one-half maximum) for MnKa radiation. The
lithium-drifted detectors require cooling during operation, for which liquid
nitrogen is often used. See also:
Junction detector
The resolution of the detector is closely
linked to its temperature. Some types allow operation at room temperature with
degraded resolution, or with Peltier cooling stages. The most recent development
are superconducting tunneling junction devices, which are operated at liquid
helium temperature. Their energy resolution is comparable to wavelength
dispersive spectrometers or is even much better, particularly for light elements
(Fig. 5).
Fig.
5 Spectrum of boron nitride
partially covered with titanium powder obtained with a cryogenically cooled
superconducting tunnel junction detector. The energy resolution of all lines up
to several hundred electronvolts is around 10–12 eV. A crystal spectrometer with
a multilayer mirror would have a resolution of about 16 eV at BKα. (After M.
Frank et al., Cryogenic high-resolution x-ray spectrometers for SR-XRF and
microanalysis, J. Synchrotron Rad., 5:515–517,
1998)
Analyzer
The output signals from the detector are
fed into the analyzer, where the photon counts are stored in memory locations
(1024–8192 channels are generally used) that are related to the energies of
these photons. This also allows visual observation on a cathode-ray-tube screen
of the accumulated spectrum and of the simultaneous counting process. Analyzers
are usually provided with cursor markers to easily identify the peaks in the
spectrum. Computer memories can be used for storage of the spectral counts, thus
providing efficient access to computer routines for further data evaluation.
Use
Energy dispersive x-ray spectrometers are
useful to accumulate spectra in short time intervals (for example, 1 min) that
often allow a preliminary interpretation of the qualitative and quantitative
composition of the specimen. The instruments are comparatively small, because
they are designed to accept a large aperture of radiation. They require only
low-power x-ray tubes that sometimes can be air-cooled.
Limitations
An
important limitation of energy dispersive systems with Si(Li) detectors is the
energy resolution, which is about an order of magnitude poorer in the lower
energy region than that of crystal spectrometers. For example, the Kα lines of
the transition elements overlap with the Kβ lines of the element preceding it in
atomic number, causing severe analytical difficulties in an important region of
the spectrum. The peak-to-background ratio is significantly lower than in
crystal spectrometers because of the lower resolution. Another limitation is
that the maximum number of photons that can be processed by the electronic
circuits is limited to about 15,000–50,000 counts per second. This is the total
photon count from the entire detected spectral region. Trace elements with low
count rates in a matrix of high-count elements are therefore difficult to detect
with sufficient statistical accuracy. Various attempts have been made to
overcome this drawback by selectively exciting the elements of interest by using
selective filters or secondary targets, which also greatly reduces the amount of
x-ray-tube radiation that is scattered into the detector.
Microanalysis
The electron microprobe is widely used for
elemental analysis of small areas. An electron beam of 1 micrometer (or smaller)
is used, and the x-ray spectrum is analyzed with a focusing (curved) crystal
spectrometer or with an energy dispersive solid-state detector. Usually two or
three spectrometers are used to cover different spectral regions. Light elements
down to beryllium, boron, and carbon can be detected. An important use of the
method is in point-to-point analysis with a few cubic micrometers of spatial
resolution. X-Y plots of any element can be made by moving the specimen to
determine the elemental distribution.
Figure 6 illustrates the spectra obtained
with three of the most frequently used methods of analysis. The specimen, a
high-temperature alloy of the type used in aerospace and other industries, was
prepared by the National Institute of Standards and Technology with stated
composition in weight percent: molybdenum (Mo) 3.13, niobium (Nb) 4.98, nickel
(Ni) 51.5, cobalt (Co) 0.76, iron (Fe) 19.8, chromium (Cr) 17.4, titanium (Ti)
0.85, and aluminum (Al) 0.085, total 99.27%.
Fig.
6 Fluorescence spectra of
high-temperature alloy obtained with (a) crystal spectrometer, (b) energy
dispersive method with x-ray-tube excitation, and (c) energy dispersive method
with electron-beam excitation. Spectral lines: 1, Mo + NbLα + Lβ. 2, TiKα. 3,
TiKβ. 4, CrKα. 5, NbKα1,2III. 6, MoKα1,2III. 7, CrKβ. 8, NbKβ1,3III. 9, FeKα.
10, MoKβIII. 11, CoKα. 12, FeKβ. 13, NiKα. 14, CoKβ. 15, NiKβ. 16, MoKα1,2II.
17, NbKβ1,3II. 18, MoKβ1,3. 19, NbKα. 20, MoKα. 21, NbKβ1,3. 22,
MoKβ1,3.
Figure 6a shows the high-resolution
spectrum obtained in about an hour with a lithium fluoride (LiF; 200) crystal
spectrometer using 50-kV, 12-milliampere x-ray-tube excitation and scintillation
counter. This spectrum also contains the second-order (II) and third-order (III)
crystal reflections of molybdenum and niobium whose Kβ1 and Kβ3 components are
resolved. The lower resolution of the energy dispersive method is shown in Fig.
6b, recorded in about 10 min using 50-kV, 2-microampere x-ray-tube excitation,
Si(Li) detector, and 40 eV per channel (about 400 channels are shown). The
spectral range includes the unresolved molybdenum and niobium L lines and
titanium. Figure 6c is an energy dispersive spectrum excited by a 25-keV
electron beam. The molybdenum and niobium spectra are weakly excited at this low
voltage and are not visible on the scale used in the plot. The differences in
the relative intensities of the lines in the spectra arise from differences in
the conditions of excitation and detection, and they illustrate the necessity of
using the proper correction factors for each method of analysis to derive the
correct weight percent composition.
Specimen
preparation
The specimens may be in the form of
powders, briquettes, solids, thin films, or liquids. The surface exposed to the
primary x-ray beam must be flat, smooth, and representative of the sample as a
whole, because usually only a thin surface layer contributes to the fluorescent
beam in a highly absorbing specimen. The thickness of this layer is called
information depth and may be only a micrometer or less for electron-beam
excitation and 10–100 μm or more for x-rays. The degree of surface roughness,
which is difficult to measure quantitatively, causes losses in intensity and
results in errors in the analysis. Consequently, solid samples are generally
polished; and then, if necessary, they are lightly etched or specially cleaned
to remove contaminants. This is particularly important when light elements are
measured. Special care must be taken when a measured element is a constituent of
such surface contamination.
Powders
Powders are processed in one of two ways.
The first is to press the ground material into briquettes. The pressure should
be several tons per square centimeter (1 ton/cm2 equals approximately 15,000
lb/in.2 or 100 megapascals), and in most cases organic binders have to be used
to improve the mechanical stability. The second way is to use fusion techniques,
where the powders (mostly mineralogical or metal oxides) are dissolved at high
temperatures in borax or similar chemicals, and glassy pellets are obtained
after cooling. The advantage of the second method is a high homogeneity of the
specimen and a reduction of interelement effects; but the intensities are
reduced.
Liquids
Liquids can be analyzed by using small
containers with a thin window cover. Examples are sulfur determination in oils
during the refining process, lubrication oil additives, the composition of
slurries, and the determination of lead, zinc, and other elements in ore
processing. Low concentrations of elements in solution can be concentrated with
specific ion-exchange resins and collected on filter papers for analysis. Gases
containing solid particles can be filtered and the composition of the particles
determined as for atmospheric aerosol filters for environmental studies. In
certain industrial applications, liquids are continuously analyzed while flowing
through a pipe system with a thin window in the x-ray apparatus.
Quantitative
analysis
The observed fluorescent intensities must
be corrected by various factors to determine the concentrations. These include
the spectral distribution of the exciting radiation, absorption, fluorescence
yield, and others. Two general methods have been developed to make these
corrections: the fundamental parameter method and the empirical parameter
method.
Fundamental parameter
method
In
the fundamental parameter method, a physical model of the excitation is
developed and described mathematically. The method derives its name from the
fact that the physical constants, like absorption coefficients and atomic
transition probabilities, are also called fundamental parameters. Primary and
secondary excitation are taken into account; the first is the amount of
fluorescent radiation directly excited by the x-ray tube. Secondary excitation
is caused by other elements in the same specimen, whose fluorescent radiation
has sufficient energy to excite the characteristic radiation of the analyzed
element. In practical applications, the count rate must be calibrated for each
element by comparing it to the count rate from a standard of accurately
predetermined composition. A standard may contain several elements or can be a
pure element.
The fundamental parameter method is capable
of accuracies around 1% (absolute weight percentage) for higher concentrations,
and between 2 and 10% (relative) for low concentrations. The method has the
advantage of allowing the use of pure-element standards. Significantly higher
accuracies can be obtained with standard specimens of similar composition to the
unknown.
The fundamental parameter method can also
be used to determine thickness and chemical composition of thin films.
Empirical parameter
method
The empirical parameter method is based
upon simple mathematical approximation functions, whose coefficients (empirical
parameters) are determined from the count rates and concentrations of standards.
A widely used set of approximation functions is given by Eq. (3),
where ci is the concentration of the
analyzed element i in the unknown specimen, r is the corresponding count rate,
Ri is the count rate from a pure-element specimen i, Ci are the concentrations
of the other elements in the unknown specimen, n is the number of elements, and
αi are the empirical parameters (also called alpha coefficients).
A
minimum of n − 1 standard specimens, each of which contains the full set of n
elements (or a correspondingly higher number, if they contain fewer elements),
is required to calculate the empirical parameters, αij, before actual analysis
of an unknown is possible. In practical applications, however, at least twice as
many standards should be used to obtain good accuracy, thus requiring
considerable effort in standard preparations. The empirical parameter method is
therefore mainly used in routine applications, where large numbers of similar
specimens must be analyzed. The accuracy of the method depends upon the
concentration range covered by the standards; around ±0.1% or better can be
obtained if a set of well-analyzed standards with similar compositions to the
unknowns are used. If pure-element standards are not available, the pure-element
counts rates, Ri in Eq. (3), can also be determined by computation from
additional multielement standards.
Trace
analysis
There are two distinct analytical tasks
that are called trace analysis: the detection or quantification of small amounts
of a material (possibly a pure element), and the determination of very low
concentrations in an abundantly available sample. In both cases, the
relationship between concentration and count rates is practically linear. The
minimum detection limit is defined by that amount or concentration for which the
peak is just statistically significant above background level B, usually 3B1/2.
The background arising from scattered continuous radiation from the x-ray tube
is a limiting factor in determining the peak-to-background ratio. Since
intensity measurements can theoretically be made arbitrarily accurate by using
long counting times, the minimum detection limits could be indefinitely low.
However, in practice, the limiting factors are the background level and
long-term instrument drift. Depending upon excitation conditions, matrix, and
counting times, traces in the parts-per-million region may be detected with
conventional instruments, and in the parts per trillion region by total
reflection x-ray fluorescence.
Total reflection XRF
(TRXFA)
Ultra-trace analysis by x-ray fluorescence
is possible by a special technique and instrumentation which is based upon
background suppression by total reflection of the primary x-ray beam. The
physical explanation is that the index of refraction of x-rays is very slightly
smaller than 1, and a beam impinging at a flat surface at angles of a few tenths
of a degree is totally reflected without noticeably penetrating the material. In
practice, a substrate of a silicon-single crystal (such as a wafer) is used and
a small droplet of dissolved analyte material applied and dried. The x-ray beam
penetrates only the sample material, not the substrate. A Si(Li) energy
dispersive detector is placed at close distance to the specimen. With
conventional x-ray tubes, detection limits in the picogram range have been
reported, and in the femtogram range by using synchrotron radiation. Total
reflection x-ray fluorescence analysis instrumentation is commercially available
(Fig. 7).
Fig.
7 Example of trace analysis by
total reflection x-ray fluorescent analysis (TXRF). A droplet containing 3 ng
dissolved nickel (Ni) was applied to a substrate (silicon-wafer), dried, and
measured. The sensitivity S in this particular setup was 20 counts per second
and per nanogram Ni, and the theoretical detection limit for 100 s counting time
was 4 picograms corresponding to 4 × 1010 atoms/cm2. The elements sulfur (S),
potassium (K), and iron (Fe) are contaminants of the solvent, and the silicon
(Si) and oxygen lines originate mainly from a thin silicon dioxide (SiO2) layer
on top of the wafer. (Data provided by P. Wobrauschek, Atominstitut der
Österreichischen Universitäten, Vienna).
Thin-film
analysis
As
a rule of thumb, materials with a thickness exceeding a few hundred micrometers
can be considered “infinitely thick” from the viewpoint of x-ray fluorescence.
This limit decreases by a factor 5–20 for light elements. The intensities of
thinner specimens are correspondingly lower, depending upon element, matrix, and
experimental setup. In the analysis of very thin films (a few tens of
nanometers), the count rates are a linear function of element concentration and
of film thickness. Absorption and interelement effects must be taken into
account in the analysis of thicker films and foils. This can be done with
special fundamental parameter methods, but it requires adequate computing power
for efficient evaluation of data.
Fundamental parameter methods allow the
determination of thickness and element concentrations of thin films as well as
individual layers in multilayer structures. Limitations apply to common elements
of two or more layers and with respect to very light elements.
Limitations on
accuracy
In
both the fundamental parameter and empirical parameter methods, limitations of
the accuracy are due mainly to uncertainties in the composition of the standards
and variations in the specimen preparation; intensity fluctuations due to
counting statistics and instrument instabilities may also contribute.
Supplemental
methods
As
in all analytical methods, it is sometimes necessary to supplement the chemical
data from fluorescence analysis with data by other methods to properly
characterize the material. The first three elements in the periodic table
(hydrogen, helium, lithium) cannot be measured by x-ray fluorescence, because
none of their emission lines are in the x-ray regime. The light elements
beryllium through magnesium (including such important elements as carbon,
oxygen, and nitrogen) can be measured, but frequently with difficulties. Often
they are crucial in the characterization of a specimen, such as carbon in
steels, and oxygen in rocks and oxide samples, which may require optical
emission, atomic absorption, Auger and electron spectroscopy, or other
analytical methods. See also:
Analytical chemistry; Atomic spectrometry; Surface physics
An
important supplementary method is x-ray polycrystalline diffraction, in which
the crystalline chemical phases are identified by comparing the pattern of the
unknown with standard patterns. Computer methods are widely used to search the
40,000 phases currently contained in the Powder Diffraction File published by
the
Applications
X-ray fluorescence analysis is widely used
for compositional control in large-scale industrial processing of metals and
alloys, cements, the petroleum industry, and inorganic chemicals. Among the many
other major applications are geological exploration and mineralogical analysis,
soils and plants, glasses, corrosion products, the analysis of raw materials,
and the measurement of plating coating thickness. It is an important method in
materials characterization for research and technology, providing chemical
information without destroying the sample. It is the only feasible method for
many complex analyses that would require extremely long times by conventional
wet chemical methods on materials such as the refractory metals, high-speed
cutting steels, and complex alloys.
Besides the large-scale industrial
applications, the method has been used in a variety of analyses in the medical
field, for environment protection and pollution control, and for many research
applications. Examples are trace analysis of heavy metals in blood; analysis of
airborne particles, historic coins, potteries, lead and barium in Roman
skeletons, and various elements in archeological specimens; analysis of pigments
to establish authenticity of a painting (Fig. 8); quality control of noble
metals in alumina-based exhaust catalysts for cars; and analysis of ash and
sulfur in coals, slags from furnace products, and surface deposits on bulk
metals. The method is also widely used in forensic problems, where it is often
combined with x-ray powder diffraction. Remote analysis of rocks using x-ray
spectrometers carried by spacecraft and stellar landers has proven to be a
valuable source of information in search of the origin of the solar system and
its planets.
Fig.
8 Analysis of pigments in an Indian
miniature, Mughal period, seventeenth century, Schloss Schönbrunn,
این وبلاگ تمامی موضوعات و مقالات و اطالاعات تخصصی زمین شناسی را که از سایتهای علمی جهان برگرفته شده در اختیار بازدیدکنندگان محترم قرار می دهد.گفتنی است که مطالب موجود در این وبلاگ در نوع خود بی نظیر بوده و از هیچ وبلاگ ایرانی ای کپی برداری نشده است و اگر هم شده منبع آن به طور کامل ذکر شده است.