Intensity ratios

Three principal approaches can be developed in order to extract quantitative information from Raman spectra. The first one is based on intensity ratio, which is a straightforward approach. The second relies on nonlinear least square fitting of the spectra by known functions. The third uses the arsenal of chemometric techniques, such as factor analysis. 

The most elementary data processing that can be implemented is based on intensity ratios. 7 intensity ratio rv,v2 can be defined as the relative intensities of two bands appearing at wavenumbers Vi and V2, so rv,v2 = ht/hz- Since the intensity of the Raman scattering is hnear with respect to concentrations, it is possible to compare respective intensities recorded at different wavenumbers. In the absence of bands overlapping, the intensity ratio r, v2 is proportional to the concentration ratio of the corresponding species and then rv,v2 oc C1/C2, where Q and C2 ocare the respective concentrations of the two species involved. When Raman bands are overlapped some additional precaution must be taken. 

it is possible to find a band featuring a specific molecular group whose concentration remains constant throughout the whole medium investigated. In this case, and without overlapping, it can be used as reference to compute intensity ratios. This reference band has to be strong enough in order to minimize the errors on the computed ratios. 

When a solution is investigated, an internal reference can be added as a new solute whose concentration is known exactly. Obviously, every interaction of the added solute with the other species previously present in the solution (in terms of chemical reaction, coupled transport or any other effect) has to be avoided. 

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Figure A3.9.4. The ratio of specular reflectivity to incident beam intensity ratio for D2 molecules scattering from a Cii(lOO) surface at 30 K [21],...

On metals in particular, the dependence of the radiation absorption by surface species on the orientation of the electrical vector can be fiilly exploited by using one of the several polarization techniques developed over the past few decades [27, 28, 29 and 30], The idea behind all those approaches is to acquire the p-to-s polarized light intensity ratio during each single IR interferometer scan since the adsorbate only absorbs the p-polarized component, that spectral ratio provides absorbance infonnation for the surface species exclusively. Polarization-modulation mediods provide the added advantage of being able to discriminate between the signals due to adsorbates and those from gas or liquid molecules. Thanks to this, RAIRS data on species chemisorbed on metals have been successfidly acquired in situ under catalytic conditions [31], and even in electrochemical cells [32]. 

Photoelectron peaks are labelled according to the quantum numbers of the level from which the electron originates. An electron coming from an orbital with main quantum number n, orbital momentum / (0, 1, 2, 3,. .. indicated as s, p, d, f,. ..) and spin momentum s (+1/2 or -1/2) is indicated as For every orbital momentum / > 0 there are two values of the total momentum j = l+Ml and j = l-Ml, each state filled with 2j + 1 electrons. Flence, most XPS peaks come in doublets and the intensity ratio of the components is (/ + 1)//. When the doublet splitting is too small to be observed, tire subscript / + s is omitted. 

In the case of metal particles distributed on a support material (e.g. supported catalysts), XPS yields infomiation on the dispersion. A higher metal/support intensity ratio (at the same metal content) indicates a better dispersion [3]. 

Figure Bl.25.9(a) shows the positive SIMS spectrum of a silica-supported zirconium oxide catalyst precursor, freshly prepared by a condensation reaction between zirconium ethoxide and the hydroxyl groups of the support [17]. Note the simultaneous occurrence of single ions (Ff, Si, Zr and molecular ions (SiO, SiOFf, ZrO, ZrOFf, ZrtK. Also, the isotope pattern of zirconium is clearly visible. Isotopes are important in the identification of peaks, because all peak intensity ratios must agree with the natural abundance. In addition to the peaks expected from zirconia on silica mounted on an indium foil, the spectrum in figure Bl. 25.9(a)...

Figure C2.3.18. Vibronic peak fluorescence intensity ratio (III/I) as a function of SDS concentration for 0.1 % PEO solutions o, —35 000 Daltons —600 000 Daltons). Open symbols are for aqueous solution without added salt, and filled symbols are for 100 mM aqueous NaCl. Reproduced with pennission from figure 2 of [111].

Multivariate data analysis usually starts with generating a set of spectra and the corresponding chemical structures as a result of a spectrum similarity search in a spectrum database. The peak data are transformed into a set of spectral features and the chemical structures are encoded into molecular descriptors [80]. A spectral feature is a property that can be automatically computed from a mass spectrum. Typical spectral features are the peak intensity at a particular mass/charge value, or logarithmic intensity ratios. The goal of transformation of peak data into spectral features is to obtain descriptors of spectral properties that are more suitable than the original peak list data. 

For most purposes only the Stokes-shifted Raman spectmm, which results from molecules in the ground electronic and vibrational states being excited, is measured and reported. Anti-Stokes spectra arise from molecules in vibrational excited states returning to the ground state. The relative intensities of the Stokes and anti-Stokes bands are proportional to the relative populations of the ground and excited vibrational states. These proportions are temperature-dependent and foUow a Boltzmann distribution. At room temperature, the anti-Stokes Stokes intensity ratio decreases by a factor of 10 with each 480 cm from the exciting frequency. Because of the weakness of the anti-Stokes spectmm (except at low frequency shift), the most important use of this spectmm is for optical temperature measurement (qv) using the Boltzmann distribution function. 

Table 14. Selected Values of the K and Electron-Binding Energies, K- and L2-Shell Fluorescent Yields, and /K x-Ray Intensity Ratio ...

Atomic number, Z Binding energy keV Fluorescent yield X-ray intensity ratio, IN/Kb... 

The reaction of bis(benzene)vanadium [12129-72-5] with TCNE affords an insoluble amorphous black soHd that exhibits field-dependent magnetization and hysteresis at room temperature, an organic-based magnet (12). The anion radical is quite stable in the soHd state. It is paramagnetic, and its intense electron paramagnetic resonance (epr) spectmm has nine principal lines with the intensity ratios expected for four equivalent N nuclei (13) and may be used as an internal reference in epr work (see Magnetic spin resonance). 

The electron impact mass spectrometric fragmentations of (E)-3- and ( )-4-styryl-pyridazines show that the intensity ratio of the M and (M -1)" ions, the general degree of fragmentation and the elimination pathways of nitrogen are the most characteristic features distinguishing between the two isomeric compounds (81JHC255). 

INTERELEMENT INFLUENCE CORRECTION IN THE XRFA USING INTENSITIES RATIO... 

A particular strength of Equation (7) is that the intensity ratio is formed between mea-surements of the same X-ray energy in both the unknown and standard. This procedure has significant advant es First, there is no need to know the spectrometer s efficiency, a value that is very difficult to calibrate absolutely, since it appears as a multiplicative factor in both terms and therefore cancels. Second, an exact knowledge of the inner shell ionization cross section or fluorescence yields is not needed, since they also cancel in the ratio. 

Define Iq to be the intensity of the light incident upon the sample and I to be the intensity of the beam after it has interacted with the sample. The goal of the basic inftared experiment is to determine the intensity ratio I/Iq as a function of the frequency of the light (w). A plot of this ratio versus the frequency is the infrared spectrum. The inftared spectrum is commonly plotted in one of three formats as transmittance, reflectance, or absorbance. If one is measuring the fraction of light transmitted through the sample, this ratio is defined as... 

Practically it is more convenient to measure intensity ratios instead of absolute intensities. Thus, e.g., Cu may serve as a reference material, relative to which the ion intensities back-scattered from the atoms of the surface under consideration are measured ... 

Large Specific Surface Area Porous materials can have a large proportion of surface atoms - their surface area within a typical sampling volume of 10 pm can reach 10 pm, which is approximately 10 larger than for a smooth surface crossing the same volume. These effects lead to clearly increased Raman intensities of surface species and also to improved intensity ratios of surface and bulk Raman bands. 

In Raman spectroscopy the intensity of scattered radiation depends not only on the polarizability and concentration of the analyte molecules, but also on the optical properties of the sample and the adjustment of the instrument. Absolute Raman intensities are not, therefore, inherently a very accurate measure of concentration. These intensities are, of course, useful for quantification under well-defined experimental conditions and for well characterized samples otherwise relative intensities should be used instead. Raman bands of the major component, the solvent, or another component of known concentration can be used as internal standards. For isotropic phases, intensity ratios of Raman bands of the analyte and the reference compound depend linearly on the concentration ratio over a wide concentration range and are, therefore, very well-suited for quantification. Changes of temperature and the refractive index of the sample can, however, influence Raman intensities, and the band positions can be shifted by different solvation at higher concentrations or... 

Quantification at surfaces is more difficult, because the Raman intensities depend not only on the surface concentration but also on the orientation of the Raman scat-terers and the, usually unknown, refractive index of the surface layer. If noticeable changes of orientation and refractive index can be excluded, the Raman intensities are roughly proportional to the surface concentration, and intensity ratios with a reference substance at the surface give quite accurate concentration data. 

When the alcohol 1 is dissolved in fluorosulfonic acid at — 136°C and then allowed to warm to — 110°C, it gives rise to a cation having a C-NMR spectmm consisting of five lines in the intensity ratio 2 1 2 2 2. Suggest possible stmctures for this cation, and discuss any stabilizing features which might favor a particular stmcture. 

Theory predicts and experiment establishes 2/1 as the intensity ratio of Kal/Ka2 for sulfur. Where 3 lines appear in a spectrum, in Figure 1-19, the presumption is that more than one kind of sulfur atom is present, and that an intensity ratio exceeding 2 results because certain lines coincide. The observed intensities in Figure 1-19 are those to be expected on the basis of this presumption, 2 being the known value of K l/K 2 for every kind of sulfur atom. 

Moxnes24 used the characteristic lines of one element to bracket the absorption edge of another. He showed, for example, that the addition of 2% ZnO to AI2O3 shifted the intensity ratio of tungsten L(3S to L/34 from 3 2 to about 1 1. 

In Equation 6-1, Io/I, usually an intensity ratio, is the quotient of the corrected average counting rate for the exposed substrate by that for the substrate covered with d cm of iron foil. The mass absorption coefficients of iron are m, a mean value for the incident (polychromatic) beam and g2, for the characteristic line being counted. The angles d and 02 are those made with the sample by the incident beam (30°) and by the emergent beam (60°), the beams being regarded as rays and... 

The data in Figure 6-4 are intensity ratios according to Equation 6-8 plotted against thickness alongside curves calculated for five values of a. The experimental points fit the curve for a = 4410 except in two cases... 

Fig. 6-4. Calculated curves showing relationship between intensity ratio and thickness for various values of exponent a. The abscissa scale is logarithmic. Circles = plated coatings squares = evaporated coatings. (Liebhafsky and Zemany, Anal. Chem., 28, 455.)...

The modification improves performance and is interesting in connection with x-ray emission spectrography (Chapters 7, 8, and 9). It consists in measuring the intensity of tin Ka relative to that of scattered x-rays entering the detector from an analyzing crystal set for the reflection of x-rays 2.2 A in wavelength. As the tin coating becomes thicker, increased attenuation of the x-rays scattered by the iron cause s the intensity ratio to increase more rapidly than does the intensity of tin Ka. Table 6-3 contains performance data for the Quantrol on Method II (modified). The instrument can also be set up to use industrially a modification of Method III. 

No calibration was required and the percentage of only one element needed to be established, for the alloy was binary. The atomic numbers of copper and zinc being adjacent, the intensity ratio of their K lines could, after an appropriate adjustment of experimental conditions, be assumed equal to the ratio of the number of atoms present of each metal. Under these simple conditions, compositions could be calculated satisfactorily from intensity ratios, as is shown by the following results for a series of 16 x-ray determinations on such an alloy found by chemical methods (details not given) to contain 73.00% copper average copper content, 73.16% standard deviation for a single determination, 0.27%... 

The question arises whether an internal standard can be relied upon to eliminate physical differences among samples, the Class II deviations of Section 7.8. No clear answer is possible. Variations in intensity ratios with particle size and with length of grinding time have been observed, especially in the analysis of minerals, but these effects seem due primarily to a nonuniform distribution of the internal standard, and not to particle size as such. These two possible causes of nonuniformity are difficult to separate. 

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