CALIBRATION AND THE ROLE OF CALIBRATION SAMPLES IN METAL OPTICAL EMISSION SPECTROMETER.

THEORY OF CALIBRATION:

Concentration vs Intensity calibration curve

Calibration comprises measurement of calibration samples and determination of the functional relationship between the intensity ‘I’ of the line of an analyte and its concentration c in these samples. The functional relationship is the calibration function or calibration curve. It includes relationships between vaporisation, excitation, radiation offtake, dispersion and the measured value. Since spectrochemical analysis is a process of analysis is a process of analysis by comparison ( in contrast to absolute methods such as weighing ), it is necessary to carry out calibration with samples of accurately known concentration, the calibration samples.

The calibration function must not be confused with the function inverse to it-the read out or evaluation function. In the case of the calibration function I = f1 (c), the concentrations of the calibration samples are assumed to be free of error, and the errors (deviations from a best fit curve after correction of the intensities for systematic errors) are imputed entirely to the spectrometer method, so that the preconditions for regression calculations showing correlation coefficients as a quality index are useless. With the evaluation function c = f2 = ( I ) the concentration c of an analyte in an analytical sample is determined, which is accordingly subject to error, f2 = 1/f1.

For optical emission spectrometry there is no theory of calibration curves which can be used for practical purposes. There are formulae for which it is assumed that it is possible to represent the relationship between line intensity and concentration as a power function : I = I0 ck. The calibration function can be represented mathematically in various ways :

linear calibration function : I = f(c) = a0 + a1 c

non-linear calibration function : I =f(c) = a0 + a1 c +a2 c2+...+an cn

The extent to which the regression approaches the true course of the calibration

curve can be discerned from the residual scatter, namely at the point when the

addition of further terms to the approximation function does not produce any

further improvement in the residual scatter.

CALIBRATION SAMPLES

Fundamental role of the calibration samples is attested by international community and by International Standardisation Organization (ISO), which delivered the following definitions :

Reference Materials (RM) : they are Materials or substances whose properties are so well defined that they can be used to calibrate the instrument, verify the measure or assign values to the materials.

CRM sample with Spark analysis spots

Certified Reference Materials (CRM) : they are Materials whose values concerning one or more properties are certified by means of a valid technical procedure and equipped by a Certificate or other documents from a qualified technical Body ( public or private Organization or Society., which deliver a certificate for the Reference Material )

Calibration samples present three disadvantages :

1) They are expensive

2) Their dimensions and shapes are not always available for the sample-holder stand of the spectrometer.

3) They are available only for some elements and concentrations

In some cases calibration samples can be synthesised, for example by alloying or diluting part of a charge. Because of this manipulation, the calculated values are rarely reliable and their composition should be confirmed by chemical analysis.

RECALIBRATION SAMPLES

When calibrating spectrometers with calibration samples (reference samples)

Recalibration samples are measured a number of times in order to obtain a reliable nominal value suitable for calibration. The additive and/or multiplicative changes in the sensitivity of the spectrometer bring about displacements of the calibration curves in the linear scale of the co-ordinate system. In order to trace (calculate) the actual intensity values at any later time back to the nominal intensity values submitted at the time of calibration a low (LP) and a high (HP) intensity is required for each analyte channel. In metal analysis with spark discharge the low points of all the analyte channels are usually measured with the pure base (Fe, Al, Cu,...). The high points are usually measured from synthetic samples having as many elements as possible with good homogeneity and precision.

The synthetic composition is given as a guide analysis and the samples often do not lie on the calibration curves. Mathematical procedure of calibration is a automated process.

In emission spectrometry recalibration samples run out, because of the polishing of the surface before recalibration. When recalibration samples are replaced there is no guarantee that, even with the same sample number, the new sample concentrations will correspond exactly to the sample being replaced. For this reason when calibrating a spectrometer for metal analysis, a minimum supply of recalibration samples should be available, for example five recalibration samples for each type.

The frequency of recalibration depends on the instrument and its use.

Interdependence with the instrument means that devices of the same kind, specially because of different phototubes stability, must be recalibrated at different intervals. Interdependence with use means that, even if stability is the same, recalibration frequency depends on the kind of analysis (traces analysis, sorting analysis).

(Note: The above post is written in context to calibration of Spark Optical emission spectrometer for metal and alloy analysis.)

LASER INDUCED BREAKDOWN SPECTROSCOPY

LIBS, is a spectroscopy technique in which a short laser pulse beam is focused on a target sample. Laser energy ionizes the sample material by heating it,  creating small area of plasma. Excited ions in the plasma state emits light waves which are collected and the spectrum is resolved by a spectrometer and analyzed by suitably calibrated  photon or light detector. Each chemical element has a unique wavelength or signature which can be optically resolved from the obtained spectrum. As  result, the composition of the elements which constitutes in the target sample can be determined. Below provided some of the general information about the technique : i Advantages ii Considerations Spectral coverage vs. resolution Light sensitivity iii. General Applications I. Advantages LIBS is considered one of the most  efficient and user friendly analytical techniques for trace elemental analysis in gases, solids, and liquids. Some of its major advantages include: Real-time measurements: online monitoring and quality control of industrial processes Noninvasive, nondestructive technique: valuable samples can be reused, sensitive materials can be analyzed, suitable for in-situ biological analysis Remote measurements can be done from up to 50 meters distance: can be used in hazardous environments and for space exploration missions on other planets Compact and inexpensive equipment: can be widely used in industrial environments, perfect for field measurements High-spatial resolution: can obtain 2D chemical and mechanical profiles of virtually any solid material with up to 1 µm precision Non or very little sample preparation is required: reduced measurement time, greater convenience, less opportunity for sample contamination Samples can be in virtually any form: gas, liquid, or solids Analysis can be performed with a very small amount of sample (nanograms): very useful in chemistry for characterization of new chemicals and in material science for characterization of new composite materials or nanostructures Virtually any chemical element can be analyzed, such as heavier elements unavailable for X-ray fluorescence Analysis can be done on extremely hard materials like ceramics and superconductors; these materials are difficult to dissolve or sample to perform other types of analysis In aerosols both particle size and chemical composition can be analyzed simultaneously II. Considerations  Spectral Coverage vs. Resolution Compact echelle spectrometers designed for LIBS applications are offered by several manufacturers. In the rare occasion that an application requires even higher resolution, the Acton Series of spectrometers with their long focal lengths are extremely useful. The latest models  use toroid mirrors with improved spectral quality. For a  detector with 1024 horizontal pixels, each of which is 26 m wide, the theoretical field of view is 26.6 mm. But since a standard 25 mm intensifier is used, the field of view is 25 mm. For example, if you decided to utilize a 2400 groove/mm grating in the Acton Series 2500 in order to enhance resolution, the linear dispersion will be 0.6 nm/mm while the spectral coverage will be 0.6*25 = 15 nm. To cover a spectral range between 300 and 600 nm (for example), you will need to perform at least 20 laser shots each time, moving the spectrometer grating to a new position and "gluing" all 20 spectra together. This is a very standard procedure which can be done painlessly and automatically. The only disadvantage to this is that acquisition of one spectrum could take up to a few dozen seconds or longer, which is why the echelle spectrometer has become extremely popular, especially in industrial and field applications where real-time measurements such as online quality control is a must.  Light sensitivity Typically, the laser pulse in LIBS applications lasts for femto- to nanoseconds (10-15 to 10-9 s). Especially in applications where non-invasive and non-destructive analysis is required, a relatively small amount of laser energy is transferred to the sample. Therefore, one laser pulse produces a weak emission signal which is hard or impossible to collect with conventional CCD detectors. That is why intensified CCDs (ICCDs) are widely used in LIBS. To improve the emitting signal on the order of 10-30 times, a scheme with two orthogonal lasers beams is often used. In this dual-scheme, the first and usually more powerful laser pulse ablates and atomizes sample material while the second one heats the ablated material even further, allowing it to improve the intensity of atomic or ionic lines. Factors such as the level of laser excitation energy for both pulses and the time delay between the pulses play a crucial role in achieving signal intensity enhancement. This technique increases the sensitivity of LIBS by  at least one order of magnitude and allows for a greater possible number of applications. If measurement time duration is not an issue, a regular CCD, (1024x1024 pixels, 13 µm pixel size), can be used together with the an spectrometer for LIBS applications. To obtain the reasonable light level required for a non-intensified CCD, long exposure time measurements should be performed. In this case, plasma emission signal is accumulated on the CCD from a multiple laser pulse. However, one should be careful about excessive accumulation of background noise and low signal-to-noise ratio. It is especially important when performing measurements in the open air without an enclosed sample chamber. Since the CCD stays open for a long period of time, all sources of stray light in the room should be eliminated and measurements should be conducted in darkness.  CCD usually proves a more sophisticated system than the  ICCD because intensified CCDs are prone to permanent damage by excessive light levels. Extra care should be taken so as not to expose ICCDs to the bright sources of light like laser reflections. In the case of a regular CCD, it is difficult to damage with excessive light. III. General Applications The fact that LIBS generally requires little-to-no sample preparation, simple instrumentation, and can easily be performed on-the-field in hazardous industrial environments in real-time, it is a very attractive analytical tool. The following are a few examples of real life applications, where LIBS is successfully used: Express-analysis of soils and minerals (geology, mining, construction) Exploration of planets (such as projects using LIBS for analyzing specific conditions on Mars and Venus to understand their elemental composition) Environmental monitoring (Real-time analysis of air and water quality, control of industrial sewage and exhaust gas emissions) Biological samples (non-invasive analysis of human hair and teeth for metal poisoning, cancer tissue diagnosis, bacteria type detection, detection of bio-aerosols and bio-hazards, anthrax, airborne infectious disease, viruses, sources of allergy, fungal spores, pollen). Replacing antibody, cultural, and DNA types of analysis Archeology (analysis of artifacts restoration quality) Architecture (quality control of stone buildings and glasses restoration) Army and Defense (detection of biological weapons, explosives, backpack-based detection systems for homeland security) Forensic (gun shooter detection) Combustion processes (analysis of intermediate combustion agents, combustion products, furnace gases control, control of unburned ashes) Metal industry (in-situ metal melting control, control of steel sheets quality, 2D mapping of Al alloys) Nuclear industry (detection of cerium in U-matrix, radioactive waste disposal)

X RAY FLUORESCENCE

INTRODUCTION

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 ;

where:

h is the Planck constant (6.62 10-24 J.s);

ν is the frequency expressed in Hertz.

For all wavelengths,

ν = c / λ ;

where:

c = speed of light (2.99782 108 m/s);

λ= wavelength (Å).

Thus:

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.

PROPERTIES OF X-RAYS

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.

THE ORIGIN OF X-RAYS

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

(photon) of sufficient energy. The energy of the photon (hν) must be greater than the energy with which the electron is bound to the nucleus of the atom. When an inner orbital electron is ejected from an atom, an electron from a higher energy level orbital will transfer into the vacant lower energy orbital (Figure). 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.

PRINCIPLE OF THE X-RAY FLUORESCENCE PROCESS

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.