Saturday, 24 August 2013



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

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

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

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

For all electromagnetic radiation:

E = h ν ;

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

For all wavelengths,
ν = c / λ ;
c = speed of light (2.99782 108 m/s);
λ= wavelength (Å).
E = hc / λ = 1.9863610−24 /λ ;

where E is in Joule and λ in meters.
The conversion to angstroms and electron volts (1 eV = 1.6021 10-19 Joule) yields the
Duane-Hunt equation:
E(eV) 12.396/ (A)
= λ . 

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


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


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

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


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

                                                                   hV = Em - En

Therefore the energy of these secondary X-rays is the difference between the binding energies of the corresponding shells in the figure below. The excited atom can also recombine by emission of Auger electrons, instead of characteristic X-rays, via the Auger effect.
The probability that characteristic X-rays will be emitted - and not an Auger electron- varies from one element to another and is described as the fluorescence yield. For elements of low atomic numbers, the Auger effect dominates, whereas emission of characteristic X-rays is more likely for heavy elements.
Each element has its unique characteristic energy spectrum (Fluorescence spectrum) composed by the allowed transitions of the specific atom in the result of X-ray excitation. XRF technique consists on the study of the produced characteristic spectrum. The XRF emission induced by photoelectron effect is shown in figure below for an atom of titanium (Z=22), whose K-shell electron acquires sufficient energy to escape from the atom.

Photoelectric effect on the K-shell
An electron in the K-shell absorbs a
photon of the primary x-ray beam and
becomes free, while the atom gains a
vacancy in the K-shell.

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

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

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

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

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

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

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

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

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


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