Infrared Spectroscopy: Fundamentals and Applications


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Examination of the transmitted light reveals how much energy was absorbed at each frequency or wavelength. This measurement can be achieved by scanning the wavelength range using a monochromator.

IR Infrared Spectroscopy - Introduction and Principle

Alternatively, the entire wavelength range is measured using a Fourier transform instrument and then a transmittance or absorbance spectrum is generated using a dedicated procedure. This technique is commonly used for analyzing samples with covalent bonds. Simple spectra are obtained from samples with few IR active bonds and high levels of purity. More complex molecular structures lead to more absorption bands and more complex spectra.

Gaseous samples require a sample cell with a long pathlength to compensate for the diluteness. The pathlength of the sample cell depends on the concentration of the compound of interest. Sample gas concentrations well below ppm can be measured with a White's cell in which the infrared light is guided with mirrors to travel through the gas. White's cells are available with optical pathlength starting from 0. Liquid samples can be sandwiched between two plates of a salt commonly sodium chloride , or common salt, although a number of other salts such as potassium bromide or calcium fluoride are also used.

Solid samples can be prepared in a variety of ways. One common method is to crush the sample with an oily mulling agent usually mineral oil Nujol. A thin film of the mull is applied onto salt plates and measured. The second method is to grind a quantity of the sample with a specially purified salt usually potassium bromide finely to remove scattering effects from large crystals. This powder mixture is then pressed in a mechanical press to form a translucent pellet through which the beam of the spectrometer can pass.

The sample is first dissolved in a suitable, non hygroscopic solvent. A drop of this solution is deposited on surface of KBr or NaCl cell. The solution is then evaporated to dryness and the film formed on the cell is analysed directly. Care is important to ensure that the film is not too thick otherwise light cannot pass through. This technique is suitable for qualitative analysis.

This is one of the most important ways of analysing failed plastic products for example because the integrity of the solid is preserved. In photoacoustic spectroscopy the need for sample treatment is minimal. The sample, liquid or solid, is placed into the sample cup which is inserted into the photoacoustic cell which is then sealed for the measurement.

The sample may be one solid piece, powder or basically in any form for the measurement. For example, a piece of rock can be inserted into the sample cup and the spectrum measured from it. It is typical to record spectrum of both the sample and a "reference". This step controls for a number of variables, e. The reference measurement makes it possible to eliminate the instrument influence.

The appropriate "reference" depends on the measurement and its goal. The simplest reference measurement is to simply remove the sample replacing it by air. However, sometimes a different reference is more useful.


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For example, if the sample is a dilute solute dissolved in water in a beaker, then a good reference measurement might be to measure pure water in the same beaker. Then the reference measurement would cancel out not only all the instrumental properties like what light source is used , but also the light-absorbing and light-reflecting properties of the water and beaker, and the final result would just show the properties of the solute at least approximately.

A common way to compare to a reference is sequentially: first measure the reference, then replace the reference by the sample and measure the sample. This technique is not perfectly reliable; if the infrared lamp is a bit brighter during the reference measurement, then a bit dimmer during the sample measurement, the measurement will be distorted. More elaborate methods, such as a "two-beam" setup see figure , can correct for these types of effects to give very accurate results. The Standard addition method can be used to statistically cancel these errors. Nevertheless, among different absorption based techniques which are used for gaseous species detection, Cavity ring-down spectroscopy CRDS can be used as a calibration free method.

The fact that CRDS is based on the measurements of photon life-times and not the laser intensity makes it needless for any calibration and comparison with a reference [4]. Fourier transform infrared FTIR spectroscopy is a measurement technique that allows one to record infrared spectra. Infrared light is guided through an interferometer and then through the sample or vice versa. A moving mirror inside the apparatus alters the distribution of infrared light that passes through the interferometer. The signal directly recorded, called an "interferogram", represents light output as a function of mirror position.

A data-processing technique called Fourier transform turns this raw data into the desired result the sample's spectrum : Light output as a function of infrared wavelength or equivalently, wavenumber. As described above, the sample's spectrum is always compared to a reference. An alternate method for acquiring spectra is the "dispersive" or "scanning monochromator " method. In this approach, the sample is irradiated sequentially with various single wavelengths. One reason that FTIR is favored is called " Fellgett's advantage " or the "multiplex advantage": The information at all frequencies is collected simultaneously, improving both speed and signal-to-noise ratio.

IR spectroscopy is often used to identify structures because functional groups give rise to characteristic bands both in terms of intensity and position frequency. The positions of these bands are summarized in correlation tables as shown below. A spectrograph is often interpreted as having two regions. In the functional region there are one to a few troughs per functional group. In the fingerprint region there are many troughs which form an intricate pattern which can be used like a fingerprint to determine the compound.

For many kinds of samples, the assignments are known, i. In such cases further information can be gleaned about the strength on a bond, relying on the empirical guideline called Badger's Rule. Originally published by Richard Badger in , [7] this rule states that the strength of a bond correlates with the frequency of its vibrational mode.

That is, increase in bond strength leads to corresponding frequency increase and vice versa. Infrared spectroscopy is a simple and reliable technique widely used in both organic and inorganic chemistry, in research and industry. It is used in quality control, dynamic measurement, and monitoring applications such as the long-term unattended measurement of CO 2 concentrations in greenhouses and growth chambers by infrared gas analyzers. It is also used in forensic analysis in both criminal and civil cases, for example in identifying polymer degradation. It can be used in determining the blood alcohol content of a suspected drunk driver.

IR-spectroscopy has been successfully used in analysis and identification of pigments in paintings [8] and other art objects [9] such as illuminated manuscripts. A useful way of analyzing solid samples without the need for cutting samples uses ATR or attenuated total reflectance spectroscopy. Using this approach, samples are pressed against the face of a single crystal. The infrared radiation passes through the crystal and only interacts with the sample at the interface between the two materials. With increasing technology in computer filtering and manipulation of the results, samples in solution can now be measured accurately water produces a broad absorbance across the range of interest, and thus renders the spectra unreadable without this computer treatment.

Some instruments also automatically identify the substance being measured from a store of thousands of reference spectra held in storage. Infrared spectroscopy is also useful in measuring the degree of polymerization in polymer manufacture. Changes in the character or quantity of a particular bond are assessed by measuring at a specific frequency over time. Modern research instruments can take infrared measurements across the range of interest as frequently as 32 times a second.

This can be done whilst simultaneous measurements are made using other techniques.

INFRARED SPECTROSCOPY: FUNDAMENTALS AND APPLICATIONS

This makes the observations of chemical reactions and processes quicker and more accurate. Infrared spectroscopy has also been successfully utilized in the field of semiconductor microelectronics: [11] for example, infrared spectroscopy can be applied to semiconductors like silicon , gallium arsenide , gallium nitride , zinc selenide , amorphous silicon, silicon nitride , etc. Another important application of Infrared Spectroscopy is in the food industry to measure the concentration of various compounds in different food products [12] [13]. PAHs seem to have been formed shortly after the Big Bang , are widespread throughout the universe, and are associated with new stars and exoplanets.

Recent developments include a miniature IR-spectrometer that's linked to a cloud based database and suitable for personal everyday use, [16] and NIR-spectroscopic chips [17] that can be embedded in smartphones and various gadgets. The different isotopes in a particular species may exhibit different fine details in infrared spectroscopy.

The reduced masses for 16 O— 16 O and 18 O— 18 O can be approximated as 8 and 9 respectively. The effect of isotopes, both on the vibration and the decay dynamics, has been found to be stronger than previously thought. In some systems, such as silicon and germanium, the decay of the anti-symmetric stretch mode of interstitial oxygen involves the symmetric stretch mode with a strong isotope dependence. For example, it was shown that for a natural silicon sample, the lifetime of the anti-symmetric vibration is Processes of change, including those of vibration and rotation associated with infrared spectroscopy, can be represented in terms of quantized discrete energy levels E0, E1, E2, etc.

Each atom or molecule in a sys- tem must exist in one or other of these levels. In a large assembly of molecules, there will be a distribution of all atoms or molecules among these various energy levels. The latter are a function of an integer the quantum number and a param- eter associated with the particular atomic or molecular process associated with that state. Introduction 5 photon is either emitted or absorbed. Associated with the loss of energy by emission of a quantum of energy or photon is some prior excitation mechanism.

Both of these associated mechanisms are represented by the dotted lines in Figure 1. SAQ 1. Calculate the follow- ing: i wavelength of this radiation; ii frequency of this radiation; iii energy change associated with this absorption. This is the selection rule for infrared spectroscopy.

Figure 1. The dipole moment of such a molecule changes as the bond expands and contracts. An understanding of molecular symmetry and group theory is important when initially assigning infrared bands.

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A detailed description of such theory is beyond the scope of this book, but symmetry and group theory are discussed in detail in other texts [1, 2]. For gases, the Doppler effect, in which radiation is shifted in frequency when the radiation source is moving towards or away from the observer, is a factor. There is also the broadening of bands due to the collisions between molecules. There is a relationship between the lifetime of an excited state and the bandwidth of the absorption band associated with the transition to the excited state, and this is a consequence of the Heisenberg Uncertainty Principle.

In order to begin with a basic model, a molecule can be looked upon as a system of masses joined by bonds with spring-like properties. The atoms in the molecules can also move relative to one other, that is, bond lengths can vary or one atom can move out of its present plane. This is a description of stretching and bending movements that are collectively referred to as vibrations. For a diatomic molecule, only one vibration that corresponds to the stretching and compression of the bond is possible.

This accounts for one degree of vibrational freedom. Polyatomic molecules containing many N atoms will have 3N degrees of freedom. Two simple examples of linear and non-linear triatomics are represented by CO2 Table 1. Both CO2 and H2O have three degrees of translational freedom. N in both examples is three, and so CO2 has four vibrational modes and water has three. The degrees of freedom for polyatomic molecules are summarized in Table 1.


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Whereas a diatomic molecule has only one mode of vibration which corre- sponds to a stretching motion, a non-linear B—A—B type triatomic molecule has three modes, two of which correspond to stretching motions, with the remainder corresponding to a bending motion. A linear type triatomic has four modes, two of which have the same frequency, and are said to be degenerate.

Two other concepts are also used to explain the frequency of vibrational modes. These are the stiffness of the bond and the masses of the atoms at each end of the bond. A molecule can only absorb radiation when the incoming infrared radiation is of the same frequency as one of the fundamental modes of vibration of the molecule.

This means that the vibrational motion of a small part of the molecule is increased while the rest of the molecule is left unaffected. Vibrations can involve either a change in bond length stretching or bond angle bending Figure 1. Some bonds can stretch in-phase symmetrical stretching or out-of-phase asymmetric stretching , as shown in Figure 1.

If a molecule has different terminal atoms such as HCN, ClCN or ONCl, then the two stretching modes are no longer symmetric and asymmetric vibrations of sim- ilar bonds, but will have varying proportions of the stretching motion of each group. In other words, the amount of coupling will vary. Bending vibrations also contribute to infrared spectra and these are summa- rized in Figure 1. It is best to consider the molecule being cut by a plane through the hydrogen atoms and the carbon atom.

The hydrogens can move in the same direction or in opposite directions in this plane, here the plane of the page. For more complex molecules, the analysis becomes simpler since hydrogen atoms may be considered in isolation because they are usually attached to more massive, and therefore, more rigid parts of the molecule. This results in in-plane and out-of-plane bending vibrations, as illustrated in Figure 1. As already mentioned, for a vibration to give rise to the absorption of infrared radiation, it must cause a change in the dipole moment of the molecule.

The larger this change, then the more intense will be the absorption band. Because of the difference in electronegativity between carbon and oxygen, the carbonyl group is permanently polarized, as shown in Figure 1. In CO2, two different stretching vibrations are possible: a symmetric and b asymmetric Figure 1. The change in dipole may be very small and, hence, lead to a very weak absorption. Answer A dipole moment is a vector sum. CO2 in the ground state, therefore, has no dipole moment. Therefore, the vibration shown in Figure 1.

O C O Figure 1. This leads to the conclusion that symmetric vibrations will generally be weaker than asymmetric vibrations, since the former will not lead to a change in dipole moment. It follows that the bending or stretching of bonds involving atoms in widely separated groups of the periodic table will lead to intense bands. This again is because of the small change in dipole moment associated with their vibrations. There will be many different vibrations for even fairly simple molecules.

The complexity of an infrared spectrum arises from the coupling of vibrations over a large part of or over the complete molecule. Such vibrations are called skeletal vibrations. Bands associated with skeletal vibrations are likely to conform to a These factors should be considered when studying spectra as they can result in important changes to the spectra and may result in the misinterpretation of bands.

Overtone bands in an infrared spectrum are analogous and are multiples of the fundamental absorption frequency. The energy levels for overtones of infrared modes are illustrated in Figure 1. Fundamental 1st overtone 2nd overtone Figure 1. When an overtone or a combination band has the same frequency as, or a similar frequency to, a fundamental, two bands appear, split either side of the expected value and are of about equal intensity.

The effect is greatest when the frequencies match, but it is also present when there is a mismatch of a few tens of wavenumbers. The two bands are referred to as a Fermi doublet. Such vibrations are not restricted to one or two bonds, but may involve a large part of the carbon backbone and oxygen or nitrogen atoms if present. The energy levels mix, hence resulting in the same number of vibrational modes, but at different frequencies, and bands can no longer be assigned to one bond.

This is very common and occurs when adjacent bonds have similar frequencies. A further requirement is that to be strongly coupled, the motions must be in the same part of the molecule. This type of structure is due to the excitation of rotational motion during a vibrational tran- sition and is referred to as an vibration—rotation spectrum [1].

The absorptions fall into groups called branches and are labelled P, Q and R according to the change in the rotational quantum number associated with the transition. The sep- aration of the lines appearing in a vibration—rotation spectrum may be exploited to determine the bond length of the molecule being examined.

Summary The ideas fundamental to an understanding of infrared spectroscopy were intro- duced in this chapter. The electromagnetic spectrum was considered in terms of various atomic and molecular processes and classical and quantum ideas were introduced. The vibrations of molecules and how they produce infrared spectra were then examined. The various factors that are responsible for the position and intensity of infrared modes were described.

Factors such as combination and overtone bands, Fermi resonance, coupling and vibration—rotation bands can lead to changes in infrared spectra. An appreciation of these issues is important when Introduction 13 examining spectra and these factors were outlined in this chapter. For further reference, there is a range of books and book chapters available which provide an overview of the theory behind infrared spectroscopy [3—7]. References 1. Atkins, P. Vincent, A. Hollas, J. Steele, D.

Eds , Wiley, Chichester, UK, , pp. Barrow, G. This Page Intentionally Left Blank In recent decades, a very different method of obtaining an infrared spectrum has superceded the dispersive instrument. Fourier-transform infrared spectrometers are now predominantly used and have improved the acqui- sition of infrared spectra dramatically. In this present chapter, the instrumentation required to obtain an infrared spectrum will be described. Infrared spectroscopy is a versatile experimental technique and it is relatively easy to obtain spectra from samples in solution or in the liquid, solid or gaseous Infrared Spectroscopy: Fundamentals and Applications B.

In this chapter, how samples can be introduced into the instrument, the equipment required to obtain spectra and the pre-treatment of samples are exam- ined. First, the various ways of investigating samples using the traditional trans- mission methods of infrared spectroscopy will be discussed. Infrared spectroscopy has also been combined with other well-established analyt- ical techniques such as chromatography and thermal analysis.

Such combination techniques are introduced here. The popularity of prism instruments fell away in the s when the improved technology of grating construction enabled cheap, good- quality gratings to be manufactured. The dispersive element in dispersive instruments is contained within a monochromator.

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Figure 2. The dispersed spectrum is scanned across the exit slit by rotating a suitable component within the monochromator. The widths of the entrance and exit slits may be varied and programmed to compensate for any variation of the source energy with wavenumber. In the absence of a sample, the detector then receives radiation of approximately constant energy as the spectrum is scanned. Atmospheric absorption by CO2 and H2O in the instrument beam has to be considered in the design of infrared instruments.

These contributions can be taken into account by using a double-beam arrangement in which radiation from a source is divided into two beams. These beams pass through a sample and a reference path of the sample compartment, respectively. The information from these beams is rationed to obtain the required sample spectrum. A detector must have adequate sensitivity to the radiation arriving from the sample and monochromator over the entire spectral region required.

Sources of infrared emission have included the Globar, which is constructed of silicon carbide. Most detectors have consisted of thermocouples of varying characteristics. CO2 and H2O. This contains narrow slits at the entrance and exit which limit the wavenumber range of the radiation reaching the detector to one resolution width. Samples for which a very quick measurement is needed, for example, in the eluant from a chromatography column, cannot be studied with instruments of low sensitivity because they cannot scan at speed. However, these limitations may be overcome through the use of a Fourier-transform infrared spectrometer.

The latter is a signal produced as a function of the change of pathlength between the two beams. The two domains of distance and frequency are interconvertible by the mathematical method of Fourier-transformation. The radiation emerging from the source is passed through an interfer- ometer to the sample before reaching a detector. The beamsplitter material has to be chosen according to the region to be examined. The moving mirror produces an optical path difference between the two arms of the interferometer. The resultant interference pattern is shown in Figure 2.

The former is a simple cosine function, but the latter is of a more complicated form because it contains all of the spectral information of the radi- ation falling on the detector. If the far-infrared region is to be examined, then a high-pressure mercury lamp can be used.

For the near-infrared, tungsten—halogen lamps are used as sources. There are two commonly used detectors employed for the mid-infrared region. The normal detector for routine use is a pyroelectric device incorporating deu- terium tryglycine sulfate DTGS in a temperature-resistant alkali halide window. Reproduced with permission from Barnes, A. For more sensitive work, mercury cadmium telluride MCT can be used, but this has to be cooled to liquid nitrogen temperatures. In the far-infrared region, ger- manium or indium—antimony detectors are employed, operating at liquid helium temperatures.

Experimental Methods 21 These two equations are interconvertible and are known as a Fourier-transform pair. The second shows the variation in intensity as a function of wavenumber. Each can be converted into the other by the mathematical method of Fourier-transformation. The essential experiment to obtain an FTIR spectrum is to produce an interfer- ogram with and without a sample in the beam and transforming the interferograms into spectra of a the source with sample absorptions and b the source with- out sample absorptions. The ratio of the former and the latter corresponds to a double-beam dispersive spectrum.

The major advance toward routine use in the mid-infrared region came with a new mathematical method or algorithm devised for fast Fourier-transformation FFT. This was combined with advances in computers which enabled these calculations to be carried out rapidly. It has to be accurately aligned and must be capable of scanning two distances so that the path difference corresponds to a known value. A number of factors associated with the moving mirror need to be considered when evaluating an infrared spectrum.

The interferogram is an analogue signal at the detector that has to be digi- tized in order that the Fourier-transformation into a conventional spectrum can be carried out. There are two particular sources of error in transforming the dig- itized information on the interferogram into a spectrum. The consequence of this necessary approximation is that the apparent lineshape of a spectral line may be as shown in Figure 2. The process of apodization is the removal of the side lobes or pods by multi- plying the interferogram by a suitable function before the Fourier-transformation is carried out.

A suitable function must cause the intensity of the interferogram to fall smoothly to zero at its ends. This cosine function provides a good compromise between reduction in oscillations and deterioration in spectral reso- lution. When accurate band shapes are required, more sophisticated mathematical functions may be needed.


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Another source of error arises if the sample intervals are not exactly the same on each side of the maxima corresponding to zero path differences. The resolution for an FTIR instrument is limited by the maximum path dif- ference between the two beams. For example, a pathlength difference of 10 cm is required to achieve a limiting resolution of 0. This simple calculation appears to show that it is easy to achieve high resolution. SAQ 2. The accumulation of a large number of repeat scans makes greater demands on the instrument if it is to exactly reproduce the conditions.

It is normal to incorporate a laser monochromatic source in the beam of the continuous source. Two of these are the Fellgett or multiplex advantage and the Jacquinot or throughput advantage. The Fellgett advantage is due to an improvement in the SNR per unit time, proportional to the square root of the number of resolution elements being monitored.

This results from the large number of resolution ele- ments being monitored simultaneously. In addition, because FTIR spectrometry does not require the use of a slit or other restricting device, the total source output can be passed through the sample continuously. This results in a substantial gain in energy at the detector, hence translating to higher signals and improved SNRs.

Another strength of FTIR spectrometry is its speed advantage. The mirror has the ability to move short distances quite rapidly, and this, together with the SNR improvements due to the Fellgett and Jacquinot advantages, make it possible to obtain spectra on a millisecond timescale. In interferometry, the factor which determines the precision of the position of an infrared band is the precision with which the scanning mirror position is known.

By using a helium—neon laser as a reference, the mirror position is known with high precision. The computer controls the instrument, for example, it sets scan speeds and scanning limits, and starts and stops scanning. It reads spectra into the computer memory from the instrument as the spectrum is scanned; this means that the spectrum is digitized.

Spectra may be manip- ulated using the computer, for example, by adding and subtracting spectra or expanding areas of the spectrum of interest. The computer is also used to scan the spectra continuously and average or add the result in the computer mem- ory. Complex analyses may be automatically carried out by following a set of pre-programmed commands described later in Chapter 3. The computer is also used to plot the spectra. It is now unusual to use wavelength for routine samples and the wavenumber scale is commonly used. The output from the instrument is referred to as a spectrum. Most commercial instruments present a spectrum with the wavenumber decreasing from left to right.

These regions will be described later in more detail in Chapter 3. Many infrared applications employ the mid-infrared region, but the near- and far-infrared regions also provide important information about certain materials. It is commonplace to have a choice of absorbance or transmittance as a measure of band intensity. The relationship between these two quantities will be described in Chapter 3. Figures 2.

It almost comes down to personal preference which of the two modes to use, but the transmittance is traditionally used for spectral interpretation, while absorbance is used for quantitative work. It is possible to analyse samples in the liquid, solid or gaseous forms when using this approach.

Fixed- pathlength sealed cells are useful for volatile liquids, but cannot be taken apart for cleaning. Semi-permanent cells are demountable so that the windows can be cleaned. A semi-permanent cell is illustrated in Figure 2. Variable pathlength cells incorporate a mechanism for continuously adjusting the pathlength, while a vernier scale allows accurate adjustment. All of these cell Answer The demountable is by far the easiest to maintain as it can be readily dismantled and cleaned.

The windows can be repolished, a new spacer supplied and the cell reassembled. The pathlengths need to cali- brated regularly if quantitative work is to be undertaken. The calibration therefore suffers and the cells have to be calibrated regularly. An important consideration in the choice of infrared cells is the type of window material.

Infrared Spectroscopy: Fundamentals and Applications

The latter must be transparent to the incident infrared radiation and alkali halides are normally used in transmission methods. The cheapest material is sodium chloride NaCl , but other commonly used materials are listed in Table 2. The infrared modes of water are very intense and may overlap with the sample modes of interest. This problem may be overcome by substituting water with deuterium oxide D2O.

The infrared modes of D2O occur at different wavenumbers to those observed for water because of the mass dependence of Experimental Methods 27 Table 2. Table 2. Where water is used as a solvent, NaCl cannot be employed as a infrared window material as it is soluble in water. The small path- length also produces a small sample cavity, hence allowing samples in milligram quantities to be examined. A drop of liquid may be sandwiched between two infrared plates, which are then mounted in a cell holder. Why would this be necessary? When the spectrum of a volatile sam- ple is recorded, it progressively becomes weaker because evaporation takes place during the recording period.

Before producing an infrared sample in solution, a suitable solvent must be chosen. In selecting a solvent for a sample, the following factors need to be considered: it has to dissolve the compound, it should be as non-polar as pos- sible to minimize solute—solvent interactions, and it should not strongly absorb infrared radiation.

If quantitative analysis of a sample is required, it is necessary to use a cell of known pathlength. A guide to pathlength selection for different solution concen- trations is shown in Table 2. The choice of method depends very much on the nature of the sample to be examined. The use of alkali halide discs involves mixing a solid sample with a dry alkali halide powder.

The mixture is usually ground with an agate mortar and pestle and Experimental Methods 29 Table 2. This sinters the mixture and produces a clear transparent disc. The most commonly used alkali halide is potassium bromide KBr , which is completely transparent in the mid-infrared region. Certain factors need to be considered when preparing alkali halide discs. A disc of about 1 cm diameter made from about mg of material usually results in a good thickness of about 1 mm. If the crystal size of the sample is too large, excessive scattering of radiation results, particularly so at high wavenumbers this is known as the Christiansen effect.

The crystal size must be reduced, normally by grinding the solid using a mortar and pestle. If the alkali halide is not perfectly dry, bands due to water appear in the spectrum. The mull method for solid samples involves grinding the sample and then suspending this about 50 mg in one to two drops of a mulling agent. This is followed by further grinding until a smooth paste is obtained.

Infrared Spectroscopy: Fundamentals and Applications Infrared Spectroscopy: Fundamentals and Applications
Infrared Spectroscopy: Fundamentals and Applications Infrared Spectroscopy: Fundamentals and Applications
Infrared Spectroscopy: Fundamentals and Applications Infrared Spectroscopy: Fundamentals and Applications
Infrared Spectroscopy: Fundamentals and Applications Infrared Spectroscopy: Fundamentals and Applications
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